Intrinsic interfacial phenomena in manganite heterostructures.

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Intrinsic interfacial phenomena in manganite heterostructures

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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 123001 (23pp)

doi:10.1088/0953-8984/27/12/123001

Topical Review

Intrinsic interfacial phenomena in manganite heterostructures C A F Vaz1 , F J Walker2,3 , C H Ahn3,4 and S Ismail-Beigi3,4 1

Swiss Light Source, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland Department of Applied Physics, Department of Electrical Engineering, Yale University, New Haven, CT 06520, US 3 Center for Research on Interface Structures and Phenomena (CRISP), Yale University, New Haven, CT 06520, US 4 Department of Applied Physics, Department of Physics, and Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT 06520, US 2

E-mail: [email protected], [email protected], [email protected] and [email protected] Received 31 October 2014 Accepted for publication 5 January 2015 Published 27 February 2015 Abstract

We review recent advances in our understanding of interfacial phenomena that emerge when dissimilar materials are brought together at atomically sharp and coherent interfaces. In particular, we focus on phenomena that are intrinsic to the interface and review recent work carried out on perovskite manganites interfaces, a class of complex oxides whose rich electronic properties have proven to be a useful playground for the discovery and prediction of novel phenomena. Keywords: manganite interfaces, perovskite interfaces, interfacial phenomena (Some figures may appear in colour only in the online journal)

where the interface manifests itself more actively, for example through the presence of band-gap interface states (traps), their presence was deemed nefarious, and indeed a major breakthrough in silicon technology was the healing of such interface states through hydrogen passivation [1]. Only more recently, with the advent of growth and characterisation tools that enable the controlled fabrication and characterisation of high quality interfaces, has a significant shift in focus taken place and attention been drawn to the study and investigation of intrinsic interfacial phenomena, i.e. processes that occur as a consequence of the break in symmetry at the interface and that are confined to atoms that mediate such a transition. In this light, the interface is regarded as a new artificial material in its own right: the atoms and electrons at the interface are not in a bulk-like configuration due to the asymmetric environment, and therefore the physical properties can differ from bulklike conditions. In addition to the basic scientific interest in understanding the physics associated with such systems,

1. Introduction

The concept of an interface is fundamental in physics, defined as the boundary separating two different media. The break in the translational symmetry of the crystal potential, the reduced site coordination of the lattice atoms at the interface, and the interaction with the atoms across the boundary make the interface a special region where the material properties may deviate considerably from the bulk. This transition region, which may or may not be atomically sharp, plays a fundamental role in many technological applications, and understanding the physical mechanisms that occur at the interface between different materials has been a longstanding problem in solid state physics, one textbook example of which is the charge distribution and the rectification properties of a semiconductor diode junction. However, until recently, the interface has played a relatively passive role, in the sense that it set boundary conditions for the manifestation of the function expected from the bulk properties. In some cases 0953-8984/15/123001+23$33.00

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© 2015 IOP Publishing Ltd Printed in the UK

J. Phys.: Condens. Matter 27 (2015) 123001

Topical Review

boost to our understanding of the physics of surfaces and interfaces has been provided by the dramatic increase in computing power, which has permitted the application of first principles calculations to increasingly complex systems. Tackling the reduced symmetry, the electronic behaviors, and correlations that characterise many complex materials have been instrumental to the understanding, at the atomic level, of the mechanisms giving rise to properties that can deviate strongly from those of the bulk. The concept of intrinsic interfacial phenomena has gained currency among many branches of condensed matter physics, and our goal here is to survey the range of physical phenomena that emerge at the interfaces of a particular class of materials, the doped perovskite manganites. These materials can be interfaced with a large number of other materials, and a panoply of new properties emerge as a result. By themselves, the bulk properties of the doped manganites are multifaceted as a consequence of the strong electron correlations that characterise these compounds and are manifested in the form of strong interactions between spin, lattice and charge degrees of freedom, giving rise to phenomena such as magnetic order, different charge transport states, colossal magnetoresistive effects, etc [26–33]. At manganite interfaces, the reduced symmetry and interaction with the adjacent medium lead to additional new properties that are absent in the bulk. In this Topical Review, we provide selected examples from the recent literature of phenomena that arise at the interface between the doped manganites and materials with which they form sharp and stable interfaces. Our aim is to illustrate how the emergence of novel properties can be understood only by considering the new electronic processes that are intrinsic to that interface.

there is a strong technological incentive to discover new physical properties with the potential for device applications, in particular, at a reduced physical scale [2–10]. Indeed, the range of interfacial phenomena is striking. One example is the onset of a metallic state at the interface between two band insulators, SrTiO3 and LaAlO3 , which is observed to set in when a layer of LaAlO3 deposited epitaxially on a suitably prepared SrTiO3 (0 0 1) surface exceeds a critical thickness of 4 unit cells [11, 12]. While still under debate, one possible origin of the effect is believed to come from the polar discontinuity that is present between the neutral SrTiO3 (0 0 1) surface termination and the polar LaAlO3 (0 0 1): the electrostatic potential that builds up with increasing LaAlO3 thickness collapses at about 3–4 unit cells through the transfer of charge to the interface region, leading to the onset of an electron gas-like metallic state [2–4, 13–18]. In addition, this metallic state has been found to be superconducting at low temperatures [19, 20], and has been found to be magnetically polarised [21–23]. The unusual properties found in this system, some of which are still not fully understood, continue to attract much interest, and indeed the LaAlO3 /SrTiO3 system has since become a well cited example of the novel functionalities that can emerge at the interface between different materials. Another example of novel phenomena that can emerge at the interface between dissimilar materials is that between a ferromagnet and a ferroelectric, where general symmetry arguments ensure that the broken inversion and timereversal symmetries permit the presence of a magnetoelectric coupling, i.e. for multiferroic behaviour coupling, in this case, magnetic and ferroelectric order parameters [24]. Indeed, the presence of a magnetoelectric coupling in such types of interfaces has been demonstrated and we will consider in closer detail this particular phenomenon in section 3.2. Despite their conceptual simplicity, real interfaces are challenging systems to study because the reduced symmetry increases the complexity of the system and also because the conditions necessary for the presence of a sharp and well defined interface can be difficult to meet. Chemically reactive materials will give rise to atomically or chemically diffuse interfaces, with chemical gradients allowing for the development of secondary phases [25], while systems with non-matching lattices will grow in polycrystalline fashion, exposing many different crystal facets, each with different interfacial properties. Defects can reduce the total free energy of the system by increasing the entropy at high temperatures and thus add an additional complexity extraneous to the interface, which can be difficult to control in the laboratory. Such complications, unavoidable in practice, tend to dull the properties that are intrinsic to the interface, and techniques for the growth and fabrication of abrupt and sharp interfaces have been central to the flourishing of this field of research. Equally critical has been the development of characterisation techniques that are capable of probing the very limited region that constitutes the physical interface, since in most cases the bulk of the system is made of a physical support in the form of a substrate. Hence, such techniques need to be sensitive down to monolayer thicknesses and/or capable of atomic-scale spatial resolution. Finally, a tremendous

2. Methodology 2.1. Interfacial growth

As already alluded to in the introduction, the recent surge of discoveries in interfacial and nanoscale phenomena has been made possible only by the development of advanced thin film growth techniques capable of synthesising materials systems with a high degree of crystalline perfection and with atomic control of the crystal structure and material parameters, such as stoichiometry, thickness, and strain [34–41]. Indeed, an important requirement for the presence of large interfacial effects in hybrid heterostructures is that the interface be sharp and atomically smooth, and that the constituent materials have the correct atomic composition, since incorrect stoichiometries, dull interfaces, and defects can lead to a rapid degradation of the electronic interfacial properties [21, 42–44]. For example, control of the electronic properties of materials can be achieved by modifying the lattice structure through misfit strain in epitaxial heterostructures [45–52]. At a more refined level, the control of the atomic bond angles, in particular in the oxygen octahedra across perovskite interfaces which includes their cooperative tiltings and rotations, can lead to important electronic modifications that are intrinsic to the interface [53–58]. 2


Topical Review

Figure 1. Transmission electron micrographs of (a) SMO/LMO multilayer grown by MBE. (Reprinted with permission from [78]. Copyright 2007 by the American Physical Society). (b) LMO/STO multilayer grown by sputtering. (Reprinted with permission from [79]. Copyright 2010 Wiley). (c) LSMO/STO multilayer grown by PLD. (Reprinted with permission from [43].)

Hence, growth techniques that can provide control over the crystal structure down to the atomic level are critical to enabling the tuning of electronic and materials properties in artificial heterostructures. Among the techniques that have been developed, molecular beam epitaxy (MBE), radio frequency magnetron sputtering, and pulsed-laser deposition (PLD) are routinely used for the growth of metal oxides in far from equilibrium conditions [38, 59–63], enabling the synthesis of novel functional artificial materials, for example super-tetragonal multiferroic BiFeO3 characterised by a very high spontaneous ferroelectric polarisation [64–75], conducting and superconducting LaAlO3 /SrTiO3 interfaces [11, 20], PZT/La0.8 Sr0.2 MnO3 heterostructures with multiferroic properties [76, 77], and complex oxide multilayers, as illustrated in figure 1 for (a) SrMnO3 /LaMnO3 (SMO/LMO), (b) LaMnO3 /SrTiO3 (LMO/STO), and (c) La0.7 Sr0.3 MnO3 /SrTiO3 (LSMO/STO) superlattices grown by MBE, sputtering, and PLD, respectively [43, 78, 79]. Among these techniques, molecular beam epitaxy is unrivaled in terms of control over the growth process and yields very high quality films. Its basic physical principle is simple and transparent: the condensation from the vapour phase of a focused beam of a molecule or element onto the substrate, in conditions that may be far from equilibrium. Through a proper preparation of the substrate surface, the growth of crystalline films in registry with the substrate crystal lattice (epitaxy) is often possible [59, 60]. The growth environment in MBE, which typically operates with base pressures in the ultrahigh vacuum (UHV) range (∼10−10 mbar), is well controlled, and compatible with a variety of electron-based characterisation tools, such as low energy electron diffraction (LEED), reflection high energy electron diffraction (RHEED), x-ray and ultra-violet photoemission spectroscopy (XPS, UPS), and Auger electron spectroscopy (AES), which make possible the in situ characterisation of the film during or immediately after growth without exposing the surface to air. Because of the grazing-incidence angle of measurement, RHEED is commonly used to monitor the surface during

the growth process in real time, namely film crystallinity and film thickness (possible when the growth proceeds layerby-layer and manifest in oscillations of the intensity of the diffracted electron beam with time). Further characteristics of MBE include the low kinetic energy of the arriving atoms or molecules (thermal energies), the ability to grow multi-element compounds from the elemental species, precise control of the film stoichiometry, good uniformity over large areas, and unique control over the growth environment. On this point, one can grow films under UHV or one can use molecular (O2 , ozone) or atomic oxygen in oxide-MBE. One can also introduce minute exposures of surfactants to the substrate to further control the growth process in order to achieve atomically flat film surfaces [80]. One striking example of the use of oxide-MBE is the demonstration of epitaxial growth of crystalline SrTiO3 on Si (0 0 1), without the formation of amorphous SiOx at the Si interface [81–83]. This achievement was made possible by a judicious control of the growth process, by first depositing a Sr passivation layer, which is also responsible for starting the growth of the crystalline SrTiO3 film upon oxygen exposure. Originally motivated by the search for high-κ dielectric materials for complementary metal-oxide semiconductor (CMOS) gates, the growth of a crystalline complex oxide on Si is particularly interesting from a device physics perspective, since it enables the integration of complex oxides on CMOS platforms, opening the possibility of utilising the unique multifunctional properties of strongly correlated oxide compounds in novel electronic devices. Magnetron sputtering is another growth technique widely used for the growth of thin films, including metal oxides. It operates through the ejection of atoms from a target surface by the transfer of kinetic energy of incoming energetic atoms, usually Ar+ ions generated in a plasma [61, 84, 85]. The kinetic energy of the impinging atoms ranges from 50–1000 eV with an energy distribution peaking at around 10–40 eV [36]. This growth technique allows for a stoichiometric transfer of the target material to the substrate and is therefore particularly suited to the growth of multi-element compounds, 3


Topical Review

including cuprates, manganites, ferroelectrics, and various magnetic oxides [61]. The deposition of atomic clusters and back-sputtering damage, which can be a concern in this technique, can be minimised by setting the sample off-axis, i.e. perpendicular to the target, a variant known as offaxis magnetron sputtering [61, 86, 87]. The presence of the highly reactive gas plasma and the high deposition pressures generally precludes the use of RHEED in sputtering, and film characterisation tends to be carried out ex situ after deposition. In PLD, the energy of a pulsed laser beam (above the ablation threshold of the material, typically at energy densities in the J/cm2 range) is transferred to the deposition target, whose elements are consequently vaporised and deposited stoichiometrically on the substrate [88, 89]. The direct transfer of the material from the target to the substrate is one key strength of PLD, enabling the deposition of complex multielement compounds, which in MBE requires the control of the evaporation flux of each individual element. However, the kinetic energies of the ablated species tend to be large, typically from a few eV up to 100 eV, and leave the target as a strongly directional plume. As a consequence, the area of uniform film thickness tends to be limited to lateral distances of a few mm; the plume itself may also lead to re-sputtering of the deposited film, which leads to film non-uniformity and off-stoichiometry. However, under optimal conditions, atomic control over the film thickness can be achieved by controlling the number of laser pulses. For the growth of metal oxides, PLD operates under relatively large oxygen partial pressures, whose control is critical for achieving the correct oxygen stoichiometry in the sample [21]. Despite the high deposition pressures, typically in the mbar range, the use of differential pumping stages allows for RHEED measurements in real time and a full control over the growth process, as in MBE (hence the term laser-MBE that is sometimes used for RHEED-assisted PLD growth) [88].

Figure 2. (c) Z-contrast image of an [LMO17/STO12]8 superlattice. The green box marks the approximate region for EELS imaging. Atomic elemental maps obtained from the (d) Ti L2,3 , (e) Mn L2,3 , (f ) La M4,5 , and (g) Sr L2,3 edges. Reprinted with permission from [79]. Copyright 2010 Wiley.

ferroelectric, and electronic (spectroscopic) characterisation. The latter is based on the ability to locally excite core level and valence electrons using sub-nm focused electron beams in STEM to measure electron energy loss spectra across a row of atoms, typically up to 100 nm in depth [100–102]. Such capabilities enable a direct access to the atomic and electronic structure of the interface with unprecedented detail. For example, by mapping energy loss features corresponding to core level electron transitions to empty states in the valence band, elemental composition maps can be obtained, which can reveal the electronic sharpness of the interface as opposed to structural sharpness. That the latter can be different has been shown in LaMnO3 /SrTiO3 superlattices, where a charge ‘leakage’ effect at specific LaMnO3 /SrTiO3 thickness ratios is observed, corresponding to a transfer of electrons with mainly Mn character to the Ti cations at the interface, which is otherwise structurally sharp, figure 2 [79]. A similar effect has been measured at the LSMO/BiFeO3 interface using x-ray scattering: while hard x-rays give structurally sharp interfaces, resonant x-ray reflectometry at the L edges of Mn and Fe show more diffuse interfaces, which is interpreted as due to electron delocalisation across the interface [103]. Reciprocal space techniques can also provide invaluable information about the interface atomic structure. In particular, surface x-ray diffraction, which relies on the measurement of the diffraction from the interface truncation rods as a function of energy and momentum transfer, can be used with the aid of computation methods to determine exact positions of the different atomic species at the interface [104–108].

2.2. Interfacial characterisation

If the creation of sharp interfaces through advanced growth techniques is critical for the onset of interfacial phenomena, another equally important aspect is the ability to probe and measure the electronic properties at the level of the interfacial atoms. The last few decades have seen tremendous progress in the development of experimental techniques that increasingly enable one to probe at shorter length and time scales. In particular, imaging and x-ray spectroscopy techniques have made large strides with the development of aberration-corrected scanning electron transmission electron microscopes and with the recent advances of synchrotron x-ray based spectro-microscopy and scattering techniques [90–93], including the recent development of free-electron laser sources that enable one to probe lateral length scales down to the pm and time scales down to the fs [94–99]. Transmission electron microscopy (TEM), in its highresolution (HRTEM) and scanning (STEM) modes of operation, has been proven to be a uniquely powerful tool to directly probe the atomic structure of interfaces with subatomic spatial resolution by combining a number of operation modes capable of atomic elemental, structural, magnetic, 4


Topical Review

Another related x-ray characterisation technique is that of x-ray resonant scattering [103]. In this technique, x-ray diffraction or reflectivity measurements as a function of light polarisation are carried out with the x-ray energy set to the resonant edge of the element of interest, enabling one to directly probe spin-dependent electron density distributions or charge order, including charge density waves and orbital ordering. In addition, electron-based diffraction techniques including reflection high energy electron diffraction (RHEED) and low energy electron diffraction (LEED), have been used extensively for the structural characterisation of thin film surfaces in ultrahigh vacuum conditions (during or immediately after growth). Their extreme surface sensitivity is a consequence of the small mean free path of electrons in solids [109, 110]. Electronic spectroscopy techniques, both electron and photon based, have also been instrumental to the characterisation of ultrathin films and interfaces. Photon-based spectroscopies vary in scope with the energy of the exciting light. At the lower end, Raman spectroscopy excites the system with infrared light to probe lattice degrees of freedom (phonon modes), while with optical light one probes optical transitions and band gap excitations. In magnetic materials, the magneto-optic Kerr effect (MOKE) [111–115] associated with optical transitions to spin-split conduction states is often used to probe the magnetic properties of the system, while non-linear optical effects associated with the simultaneous breaking of space inversion and time reversal symmetry, such as occur at a ferromagnetic interface with a non-magnetic material, can be used to probe genuinely interfacial magnetic phenomena using second harmonic signal generation (SHSG) [116]. At higher photon energies, in the ultraviolet and x-ray range, one probes directly the electronic structure of the materials through direct atomic excitations from occupied to empty states (x-ray absorption spectroscopy, XAS) [117]. At these photon excitation energies, on can access Fermi surfaces using angle-resolved photoemisson spectroscopy (ARPES) [118–120], magnetism through the magnetic circular and linear dichroism effect (XMCD, XMLD) [121–125], orbital occupancy and charge asymmetry distribution using the natural linear dichroism effect (NLD), valence states in the hard x-ray range using x-ray absorption near edge spectroscopy (XANES), and bond lengths and bond angles through interference effects in extended x-ray absorption fine-structure spectroscopy (EXAFS). The unique capabilities of x-ray absorption spectroscopy (elemental, chemical, and site specificity; magnetic and charge distribution sensitivity) to probe the electronic structure have been widely employed to determine the electronic structure at interfaces. Combined with spatial resolution, either in full field (in x-ray photoemission electron microscopy, XPEEM, and x-ray holography) or in scanning modes (in scanning x-ray transmission microscopy, STXM), synchrotron x-ray based spectroscopic techniques can provide spatial maps of electronic and magnetic properties of thin films and interfaces with a few tens of nm spatial resolution [126–133]. Dynamical responses to fast external stimuli can be studied with time resolution down to the sub-100 ps [90, 92, 93]. In photoemission spectroscopies, such as ultraviolet and x-ray photoemission spectroscopy (UPS, XPS), one

excites electrons from valence or core levels into the vacuum [134–136]. Therefore, such techniques are sensitive to the density of occupied states and can be used to determine the electronic structure just below the Fermi level, and/or to determine the valence and composition of the system by measuring binding energies of core electrons or the spectral weights at those energies, respectively. Since the detection relies on a measurement of electrons emitted from the sample, they are characterised by small probing depths, on the order of a few nm [109]. Electron-based spectroscopies include electron energy loss spectroscopy (EELS), where inelastic scattering processes (related to direct atomic transitions, and phonon, magnetic, or plasmon excitations, for example) are probed upon excitation of the system with an electron beam [100, 101]. In combination with scanning transmission electron microscopy, as discussed above, this a technique capable of unprecedented spectroscopic characterisation of materials at the sub-atomic level. Scanning probe techniques [137], such as atomic force microscopy (AFM), particularly in the non-contact mode (NCAFM), which is capable of atomic scale resolution [138, 139]; scanning tunneling microscopy (STM); piezoelectric force microscopy (PFM); magnetic force microscopy (MFM), among others, have enabled detailed local characterisation of thin films and surfaces in its multifaceted aspects (morphological, magnetic, spectroscopic, electric, dielectric, etc). The characterisation of interfaces is also possible by scanning a cross-section of the interface, an approach that has been employed to investigate the extent of the conduction region at the LaAlO3 /SrTiO3 (0 0 1) interface using AFM and STM [140, 141]. Techniques that are not inherently surface or interface specific can be made interface sensitive. One approach to extending bulk techniques to probe interface phenomena is that of discriminating between changes that occur at the interface. For example, in field effect devices, the physical effect is due to electrostatic screening and affects mostly the interface with the dielectric gate, which is confined to within the Thomas– Fermi length. Hence, by measuring relative changes in the properties of the material as a function of the gate voltage, bulksensitive techniques, such as commercial superconducting quantum interferometer device (SQUID) magnetometers or xray absorption near edge spectroscopy (XANES) measured in the fluorescence channel (which can probe 100 s of nm), and MOKE (which probe a few 10 s of nm), can be made extremely surface sensitive. Such an approach has been applied to measuring the magnetic and electronic changes that occur at the interface of PZT/LSMO heterostructures as a function of the ferroelectric polarisation direction to find directly changes in the valency with XANES [77] and in magnetism with MOKE [76] and SQUID [142, 143]. Another approach is to insert a probe right at the interface, for example in Mössbauer spectroscopy [144], in δ-doping, or in isotope doping, where atoms at the interface are substituted by isotopes which, although chemically similar, can be used to probe local electronic properties (although the modified mass can lead to modifications in the electronic properties per se, such as induction of ferroelectricity in SrTiO3 at low temperatures when the 16 O is replaced by 18 O [145]). 5


Topical Review

because a mean-field single-particle computation can never correctly capture the strong and physically relevant fluctuations of electronic occupancy and fluctuations between different electronic configurations for localized sites. The clearest examples occur for Hubbard-type model Hamiltonians which undergo metal to insulator Mott transitions driven strictly by electronic repulsion (correlation). Therefore, for systems where it is believed that strong correlations are present, failure of DFT-derived approaches for the electronic structure are often blamed on ‘strong correlations’. However, the actual situation is often more nuanced and is highly materials dependent: in many real materials it is often hard to pin down what is truly correlated behavior as distinct from strong Fock exchange and resulting symmetry breaking (e.g. magnetism or orbital ordering) at the mean field level. For example, for some transition metal oxides, the use of hybrid methods—which better describe Fock exchange—can deliver qualitative and quantitative agreement with experiment, a level of agreement that is not possible with simpler exchangecorrelation approximations. In such cases, it is fair to say that ‘strong correlations’, understood in the strict sense of many-body electronic localization and fluctuation between multiple configurations, may not have been the real problem; the culprit is the poor description of exchange in simpler approximations [159]. On the other hand, a better description of exchange and correlation at the DFT-level is not a panacea: for example, if we consider the ‘simple’ bulk metallic and paramagnetic perovskite LaNiO3 , the best overall DFT description compared to experiment is achieved for the simplest LDA approximation, while more advanced GGA, DFT+U, or hybrid approaches all fail in various ways [160]. Unfortunately, the state of ab initio theory for complex oxides is not yet mature enough to permit one-shot, ‘turn-the-crank’ calculations and predictions. Focusing specifically on the manganites, we conclude this section by describing when state-of-the-art ab initio methods do well and are reliable and when one may be pushing the limits in terms of quantitative prediction. As is standard for DFT methods, the stable atomic-scale structure is correctly predicted, and lattice constants, atomic positions, and bond lengths are accurate to within 1–2%, which is typical of most DFT structural predictions (see, e.g. [161, 162]). However, despite this impressive accuracy for a first principles approach that assumes nothing other than the stoichiometry and atomic numbers of the elements comprising the material, it is still not sufficient to predict systematically the correct electronic and/or magnetic ground state of bulk manganites due to the extreme sensitivity of these materials to strain and other perturbations. For example, the parent material LaMnO3 is an A-type antiferromagnetic (AFM) insulator in practice, but predicting such a ground state based on ab initio theory is neither straightforward nor guaranteed, as different exchangecorrelation approximations yield variable results depending on details (e.g. a metal instead of an insulator, or ferromagnetism (FM) instead of AFM) [163, 164]. Even if one fixes the theoretical approximation, one predicts different ground states based on whether one uses the experimentally observed or theoretically predicted lattice structure for LaMnO3 [163, 164].

2.3. Theoretical modeling

Theoretical models for the complex and unusual behavior of bulk manganites have played an important role in understanding their fascinating structural, electronic, magnetic, orbital, and magnetoresistive behaviors. Standard reviews, e.g. [146], attest to the breadth and depth of work, the majority of which is semi-empirical and phenomenological in nature in that model Hamiltonians with a number of parameters are used in order to describe macroscopic properties, such as electronic and polaronic transport, magnetic transitions due to inhomogeneities and electronic phase separation, dynamical behavior, etc. In this review we focus almost exclusively on first principles theoretical predictions for manganite interfaces. The main reason is that intrinsically interfacial behavior is almost by definition non bulk-like, so that models that are designed to capture the essence of bulk behavior (along with parameters often fit to experiment) may not be relevant to the interfacial behavior. The canonical approach would be to base the choice of model and parameters on experimental insights and observations, but with the widespread adoption of first principles methods based on density functional theory (DFT) and the simultaneous availability of high performance computers that enable the use of theory to perform detailed modeling of relatively large and complex segments of a material, one now has the option to directly and explicitly simulate a new interface at the scale of the constituent nuclei and electrons. Namely, one can perform detailed numerical experiments in order to see what an appropriate model should be, to understand observations by direct comparison of computations to experiment, and simultaneously to predict novel interfacial behavior to guide experiments. First principles or ab initio methods are computationally expensive, but do not contain adjustable parameters or a priori restrictions to particular types of model Hamiltonians and therefore should provide unbiased predictions for materials properties with uniform accuracy across a class of materials. With such theoretical methods, one does more calculation but less guessing in order to describe a novel interfacial system. Briefly, DFT [147, 148] is an approach that permits, in principle, the calculation of the exact ground-state energy and electron density for any interacting electron system with a complexity that involves only the self-consistent solution of single-particle, mean-field, Schrödinger-type equations. In practice, the complex electronic correlations must be approximated in some way, and this gives rise to a variety of approaches to approximating electronic exchange and correlation. This includes the simplest and canonical local (spin) density approximation (L(S)DA) [149–153], the improved generalized gradient approximations (GGA) [154], the widely used DFT+U method [155] for localized electronic states, and a variety of ‘hybrid’ methods that entail even greater computational costs but explicitly include key and important aspects of the physics of Fock exchange [156–158]. Due to the single-particle nature of the DFT description of the electronic states, it has long been realized that there are classes of ‘strongly correlated’ electronic behavior that can never be properly described by such an approach 6


Topical Review

Figure 3. DFT-predicted energy difference between A-type AFM (A-AFM) state and the FM state for bulk LaMnO3 in meV per formula unit for a variety of published calculations. Negative values of the vertical axis mean that the experimentally observed A-AFM magnetic state is the theoretical ground state. The horizontal axis represents various theoretical calculations using a variety of exchange-correlation models and other theoretical approximations. ‘EXP’ means the structure is frozen at the experimental one; ‘P-OPT’ means the lattice vectors are fixed at their experimental values, but the internal atomic positions are relaxed to the theoretical minimum energy state; ‘F-OPT’ means lattice and internal coordinates are both fully relaxed. The main observation is the relatively wide scatter in the data between nominally identical calculations, as well as the potentially strong differences between EXP and OPT results. Interestingly, most EXP predictions agree with experiment, while relaxation in various ways tends to spoil this accuracy in many calculations. More sophisticated treatment of exchange and correlation (+U methods or B3LYP/B3PW) generally improves agreement with experiment for relaxed structures. Reprinted with permission from [163]. Copyright 2010 by the American Physical Society.

Figure 3 shows an example of the theoretical scatter in the prediction of the magnetic ground state of LaMnO3 . Another example involves the doping of LaMnO3 , such as via Sr substitution to get La1−x Srx MnO3 , and the resulting phase diagram. Theoretically, the insulating and canted-AFM structure at low doping (x < 0.1) is not easy to obtain, as DFT will essentially always yield a metal in this region, but the metallic FM behavior starting at x 0.2 is well reproduced, as is the fact that a transition to AFM metallic behavior happens at larger x. The actual critical doping for the FM-AFM transition, which is x ≈ 0.5 experimentally, is hard to reproduce in a systematic manner: LSDA underestimates it, but LSDA+U can get it right. GGA+U at U = 0 gives an answer very close to x = 0.5 but overestimates it for U > 0 [162, 164, 165], etc. Given these examples of the present state of theory, the main take-home message is that any single choice of approximation will typically not provide a quantitative prediction for multiple physical properties. However, the trends of materials behavior versus various perturbations (strain, value of U , magnitude of structural distortions, magnetic state, doping level, etc) can be understood in detail using ab initio methods [161] and this forms the basis for a physical understanding of the behavior and, if desired, an appropriate simplified model capturing the essential physics. This is because first principles methods are unrivaled in providing detailed and precise information about materials at the scale of individual atoms or atomic layers. For example, figures 5 and 8 show the calculated atomic-scale distortions, screening behavior, and doping state of individual atomic sites taking place at a manganite-ferroelectric interface, showing the large modifications in the electron charge density and in

the ionic displacement that occur right at the interface as a consequence of the screening of the ferroelectric polarisation. 3. Multiferroic interfaces

Multifunctional compounds are characterised by the presence of multiple electronic responses, such as magnetic, optical, electric, and mechanic ones, a feature which makes them particularly interesting from both technological and basic science perspectives. While their rich functional behaviour is of potential use for device applications, their complexity offers a broad playground for a deeper understanding of electron correlation effects in the solid state. In this domain, the synthesis of novel materials that do not occur spontaneously in nature, such as type II superconductor cuprates, the doped manganites, and bismuth ferrite, have been particularly rewarding and their discovery has led to exciting new insights into the physics of electron correlations and to novel concepts in solid state physics. A particularly interesting sub-class is that of the so-called multiferroic materials, which are characterised by the simultaneous presence of magnetic and ferroelectric order, and a coupling between these two order parameters (magnetoelectric coupling) [166, 167]. A sizable number of single phase multiferroic compounds are known, and much interest has been devoted recently to discovering materials with high critical temperatures and large magnetoelectric couplings, as required for practical applications. However, the number of available single phase materials capable of room temperature operation, large susceptibilities, chemical stability, and good crystalline and structural properties is very limited. To date, BiFeO3 and the orthoferrites are the rare exceptions, with relatively large 7


Topical Review

magnetoelectric couplings and critical temperatures above room temperature [168–171]. One alternative to fashioning new single phase materials with the required electronic properties from the top-down (as is currently possible with the aid of first principles calculations), is to explore interfacial phenomena to couple the electronic properties of dissimilar materials. Of particular interest in this context is the possibility of inducing a magnetoelectric coupling between ferromagnetic and ferroelectric systems across the interface to achieve artificial multiferroic heterostructures [172–175]. By suitably engineering a strong magnetoelectric coupling, the electrostatic control of magnetism or magnetic field control of the ferroelectric polarisation may be attained, with potential for applications in novel electronic devices and ultrasensitive sensors and actuators. One advantage of this approach to achieving multiferroic behavior is that the individual magnetic and ferroelectric properties can be chosen from the larger class of magnetic and ferroelectric systems. Several mechanisms have been explored to achieving interfacial magnetoelectric couplings in artificial multiferroic heterostructures and composites: strain, spin-exchange, and charge couplings [172–175]. The doped manganites are particularly interesting in this context since their strong susceptibility to strain, charge, and magnetic and electric fields suggests that a fine control of their electronic properties can be achieved by coupling to a ferroelectric material. We describe next the various coupling mechanisms that have been explored to date to achieve a magnetoelectric coupling in artificial multiferroic heterostructures.

from one subsystem to the other, the resulting effect is, strictu sensu, not intrinsic to the interface. In fact, an evolution from an interface charge-dominant magnetoelectric coupling to a bulk strain-mediated coupling in artificial multiferroic heterostructures with increasing thickness has been identified in some systems [198–201]. Detailed discussions of strain-mediated magnetoelectric effects can be found in [10, 172, 173, 179, 182, 202]. 3.2. Charge-mediated magnetoelectric coupling

Changes in the charge carrier density can lead to profound modifications in the magnetic interactions by directly perturbing the relative weight of the kinetic and Coulomb energy terms of the system. In this context, the sensitivity of the electronic and magnetic properties of complex oxide materials to the charge density [203] offers a promising venue for the electrostatic control of the magnetic and electronic responses [204–207]. One materials system of particular interest involves the doped manganites, such as La1−x Ax MnO3 (A = Ca, Sr, Ba), which are characterized by rich magnetic and electronic phase diagrams as a function of chemical doping, including FM and AFM phases, charge ordered states, and the coexistence of competing ground states (phase separation) [208, 209]. As an example of the complex behaviour that is characteristic of these compounds, figure 4 displays the bulk phase diagram of La1−x Srx MnO3 as a function of chemical hole doping x and temperature, showing the existence of different ground states with increasing hole doping (obtained by substitution of trivalent La for divalent Sr): A-type antiferromagnetism for insulating LaMnO3 , a ferromagnetic insulating behaviour at low dopings, a ferromagnetic metallic regime with a peak in the critical temperature of about 370 K at around 0.3 doping, A-type AFM metallic behaviour at around half doping, and C- and G-type antiferromagnetic insulator ground states at larger dopings. The sensitivity to charge density suggests that large susceptibilities to external electric fields can be attained by driving the system across a boundary separating two different ground states by using field effects to modulate the charge density (electrostatic charge doping) [7, 173, 210]. In this context, a promising route to achieving large susceptibilities is to employ a ferroelectric gate in a field effect multiferroic heterostructure to achieve non-volatile and reversible large modulations in the charge carrier density (ferroelectric field effect approach) [204, 205, 210]. Since field effects are limited to within the screening length of the metal, and this length is of a few unit cells in the metallic manganites where typical charge carrier densities are of the order of 1021 cm−3 [211, 212], the resulting effects are necessarily interfacial in nature [24, 165, 213]. Figure 5 shows a theoretical demonstration of how the polarisation at the interface is screened in the manganite over such a length scale, where we note that the screened process is not purely electronic, but involves a significant ionic component with cation–anion separations of ∼0.1–0.2 Å [164, 165, 214] (see also section 3.5).

3.1. Strain-mediated magnetoelectric coupling

In strain-mediated magnetoelectric coupling, one uses the strain generated through the piezoelectric effect of a ferroelectric material or through the magnetostriction effect of magnetic materials to induce strain in the ferromagnetic or ferroelectric counterpart, respectively, in order to generate changes in the magnetic anisotropy or in the ferroelectric polarisation. Examples of this approach include ferroelectric-ferromagnetic bulk nanocomposites [176–178], laminar structures [172, 178–183], thin films [184–188], and nanostructured systems [172, 189–194], where large magnetoelectric susceptibilities have been achieved. In the case of the manganites, the control via strain of the magnetic state can have two distinct origins: (i) through magnetoelastic coupling, strain can couple into the orbital degree of freedom and modify the magnetic anisotropy of the system; (ii) by modifying the oxygen-manganese bond angle and/or length, a change in the electron hopping rates and orbital occupation can be effected, which directly modifies the electronic properties, such as the spin exchange interaction and charge transport [9, 188, 195–197]. Modulating the magnetic or ferroelectric properties of artificial multiferroic heterostrutures through strain has been shown to be a fruitful approach to multiferroic behaviour. However, although the interface plays the crucial role of setting and transmitting elastic strain 8


Topical Review

using such tuning of the magnetic spin state to devise gated spin-valve devices [224]. Experimentally, it was found that in PZT/4 nm La0.8 Sr0.2 MnO3 /SrTiO3 (0 0 1) heterostructures grown by off-axis r.f. magnetron sputtering, a large change in the saturation magnetic moment was observed as a function of the direction of the ferroelectric polarisation, with the larger moment observed for the depletion state (figure 6) [76]. The latter corresponds to the state where the ferroelectric polarisation points towards the La0.8 Sr0.2 MnO3 , which leads to the accumulation of electrons (depletion of holes) in the interfacial manganite in order to compensate and screen the ferroelectric surface polarisation (accumulation then refers to the opposite polarisation direction and accumulation of holes at the LSMO interface). This effect was coincident with a large decrease in the magnetic Curie temperature of about 20 K when switching from the accumulation to the depletion state. The latter effect demonstrates that hole accumulation increases the strength of the magnetic interactions, but reduces the overall magnetic moment, a trend which agrees qualitatively with the bulk phase diagram of LSMO [27, 225]. Importantly, by directly measuring the magnetic response as a function of the applied electric field, a direct demonstration of a large magnetoelectric coupling could be made (figure 6). More quantitative results were subsequently carried out on similar PZT/LSMO heterostructures with the LSMO layer grown by molecular beam epitaxy [77]. This experiment enabled more accurate control over the LSMO film thickness and also a better quality template for the subsequent growth of the ferroelectric layer resulting in higher ferroelectric polarisations and larger magnetoelectric responses [77, 226, 227]. By using x-ray absorption near edge spectroscopy, a direct observation of the modulation in the valence state of the Mn cations with the ferroelectric polarisation direction clarified the electronic origin of the magnetoelectric coupling in this system. It also permitted a quantitative estimate of the modulation in the charge carrier density (in fact, very similar to that expected based on the change in the ferroelectric surface polarisation, demonstrating the low density of charge traps at the manganite/ferroelectric interface [224]) revealing that the observed changes in the magnetic moment implied a change in the spin configuration at the interface from FM in the depletion state to AFM in the accumulation state [77]. This behaviour is understood by glancing at the bulk phase diagram (figure 4) and is explained by the change in the relative weights of the superexchange and double exchange energy terms as a function of doping in the interfacial region [164, 217]. Other studies corroborate these findings, including the measurement of similar modifications in the magnetic moment and critical temperature of La1−x Srx MnO3 films at x = 0.13 [142] and at x = 0.175 [143] with SQUID magnetometry. More recently, a striking demonstration of such a change in the interfacial spin configuration was carried out by magneto-optic Kerr effect (MOKE) second harmonic signal generation from a PZT/100 nm LSMO (x = 0.33)/LaAlO3 (0 0 1) structure [216]. Since the presence of a second harmonic component in the MOKE signal is directly associated to both time and space symmetry breaking, it arises

Figure 4. Experimental phase diagram of bulk La1−x Srx MnO3 : ‘FM’ is ferromagnetic metallic; ‘A-AF’, ‘C-AF’, and ‘C-AF’ is A-, C-, and G-type antiferromagnetic, respectively; O’, O* represent orthorhombic phases, R, rhombohedral, T, tetragonal, and C, cubic. Reprinted with permission from [32]. Copyright 2003 by the American Physical Society.

Figure 5. First principles theoretical predictions for the structure of the La0.5 Ba0.5 MnO3 /BaTiO3 interface. Cation-oxygen (M–O) polar displacements near the interface are shown for two polarisation states of the ferroelectric (red squares away from interface, blue triangles towards interface). The polarisation is screened in the metallic manganite over a length scale of a few unit cells. Reprinted with permission from [165]. Copyright 2009 by the American Physical Society.

In fact, charge-induced interfacial magnetic reconstructions driven by screening effects have been demonstrated experimentally [77, 142, 215, 216] and confirmed theoretically [164, 165, 214, 217] for a number of systems consisting of doped manganite layers in contact with a ferroelectric. Such a change in the interfacial magnetic configuration is found to yield large changes in the magnetic moment and very large magnetoelectric susceptibilities. This fascinating effect is described in more detail below. Since the doped manganites are characterised by high spin polarisations at the Fermi level [218, 219], and given the strong dependence of electron hopping rates with the relative spin alignment of adjacent Mn cations, a consequence of the double exchange interaction operative in these compounds [220–223], one may anticipate 9


Topical Review

The second and subsequent layers have hole doping x < 0.5 so one expects them to remain ferromagnetic based on the bulk phase diagram [77]. However, the precise nature of the predicted interfacial state depends on theoretical details. Figure 9 schematically illustrates three basic configurations among the large number of possibilities [217]. The first set of first principles calculations used the GGA approximation (a theory that successfully predicts the FM to AFM transition in bulk at close to the experimental chemical doping of x = 0.5) for La0.5 Ba0.5 MnO3 /BaTiO3 and found a reversal of the magnetisation in the second Mn layer from the interface despite the fact that the hole doping is highest in the first layer [165] (possibility A2 in figure 9). A thorough study of ferroelectric/La0.8 Sr0.2 MnO3 interfaces from first principles based on LSDA+U theory found that the predicted magnetic state can be any of F, A1, or A2, depending on the value of U chosen in the simulation [164]. However, if one requires the method to correctly reproduce the experimental FM to AFM transition at x = 0.5 for bulk La1−x Srx MnO3 , then the A1 magnetic structure is predicted at the interface for the accumulation state, in agreement with what one would intuitively expect from the bulk phase diagram and the hole doping profile. Furthermore, as a function of the chemical doping x of the film, one can stabilize either A1 or A2 in the accumulation state (with smaller x values favoring A1) [164]. Theoretical results using a self-consistent, tight-binding, two orbital double exchange model Hamiltonian approach [217] permitted the simulation of much larger interfacial unit cells with more complex magnetic orderings. In particular, the FM to AFM transition is reproduced for the accumulation state, but the predicted magnetic structures are more complex than the simple layered structures shown in figure 9. The large number of possibilities considered in that work are shown in figure 10. Further first principles computations on larger interfacial cells are needed to confirm these interesting model Hamiltonian predictions of complex AFM phases at the interface. We note that the results of Ma et al [216] on PZT/LSMO shown in figure 7 indicate that an AFM state is induced for the LSMO interfacial layer in the accumulation state. A final theoretical idea would be to push the bulk analogy to its limit: namely, armed only with the hole density profile at the interface and the bulk phase diagram, one would like to predict the interfacial magnetic state with a simple model. This is in fact possible with an effective Ising-like model of Mn–Mn spin interactions with some interesting qualifications [164]: while bulk La1−x Srx MnO3 information together with the doping profile can be used to predict whether each interface layer is FM or AFM, the energy difference between the two magnetic states is exaggerated when compared to the actual energy differences computed for the interfacial systems. Only by including the cation–anion displacements (i.e. details of the actual atomic-scale structure) in the bulk computations of energy differences can one begin to quantitatively reproduce the interfacial energetics [164]. The meaning of this result is what was discussed in the earlier parts of the text: while model approaches based on the bulk can give qualitative insight and perhaps correctly predict the qualitative behavior, genuinely interfacial effects (such as propagation of

Figure 6. Magnetoelectric hysteresis curve at 100 K showing the magnetic response of PZT/LSMO as a function of the applied electric field. The two magnetisation values correspond to modulation of the magnetisation of the LSMO layer. Insets represent the magnetic and electric states of the LSMO and PZT layers for the accumulation (left) and depletion state (right). The size of the arrows indicates qualitatively the magnetisation amplitude. Reprinted with permission from [76]. Copyright 2009 Wiley.

at a ferromagnetic interface but will be absent if the interfacial layer is non-magnetic or antiferromagnetic (layers deeper into the magnetic material preserve space symmetry and do not contribute to the second harmonic signal). The work by Ma et al [216] shows that the second harmonic signal is absent in the accumulation state (no net magnetisation corresponding to an interfacial antiferromagnetic state) and present in the depletion state (corresponding to a uniform ferromagnetic state across the interface), see figure 7. A similar effect to that observed in LSMO has been reported on 5 nm LCMO (x = 0.5)/BiFeO3 heterostructures, where the switching of the ferroelectric polarisation of the BiFeO3 controls the magnetism of the LCMO layer from antiferromagnetic in the accumulation state to ferromagnetic at the interface in the depletion state (accompanied also by the onset of a net moment in the BiFeO3 interfacial layer) [215]. Available theory generally agrees with the above findings and interpretations, whereby a FM to AFM phase transition is found upon reversal of the ferroelectric polarisation [164, 165, 217, 228]. We now describe some additional facts and complexities, related to the theory. Due to the special halfmetallic nature of ferromagnetic La0.8 Sr0.2 MnO3 , it is possible to count the electrons in each unit cell of the La0.8 Sr0.2 MnO3 directly from the microscopic electron density [164], without resorting to electron counting on atomic orbitals or other approximate methods. The resulting hole densities per Mn are shown in figure 8 for the case of PbTiO3 /La0.8 Sr0.2 MnO3 , where we can directly observe the screening behavior away from the interface and also see that the ferroelectric field effect is powerful enough to change the hole density of the interfacial Mn from its nominal value of x = 0.2 to close to x = 0.7 in the accumulation state, a value well into the AFM region of the phase diagram for bulk La1−x Srx MnO3 , as per figure 4. 10


Topical Review

Figure 7. (a) Interface (b) and bulk magnetic hysteresis loops from PZT/LSMO (x = 0.3) heterostructure for different external gate voltages Ug measured with magnetisation-induced second harmonic generation (MSHG) and MOKE techniques, respectively, at 78 K. (c) MSHG hysteresis loop at a gate voltage of +10 V and (d) MSHG magnetic contrast as a function of gate voltage. The direction of positive Ug is defined in the inset. Reprinted with permission from [216]. Copyright 2014, AIP Publishing LLC.

One possible explanation for this difference may be related to the different substrates used and the resulting different misfit strains in the LSMO films. For example, we have recently shown that slight changes in the strain of LSMO films at near half doping can have more drastic effects on the preferred magnetic state than changes in the chemical doping [232]. In general, it also known that compressive strains favour ferromagnetic states, while tensile strain favours antiferromagnetic states [161, 233, 234]. This is an aspect that merits further study, since it offers one further control parameter that can be used to achieve full electrostatic control of magnetism in these types of multiferroic heterostructures [201].

polarisation into a metallic material) can change the behavior of the system, necessitating first principles approaches prior to model building with any confidence. We note that the experimental and theoretical results described above are consistent and fit well together. However, there are other available results which are at odds with them. Other studies reported for La1−x Srx MnO3 at x = 0.3 find smaller and opposite changes in the saturation magnetisation [142, 229–231]. For example, in LSMO (x = 0.3)/BaTiO3 heterostructures grown by PLD [231], it was found that the magnetisation increases when going from the depletion to the accumulation state, while only a small modulation in the critical temperature of the system is observed. In addition, the same study found that the magnetic moment changes mostly for the depletion state, with a depletion layer that extends well beyond the interface. The results are explained in terms of a phase separation picture, whereby magnetism is suppressed over a layer thickness up to 2.9 nm due to charge depletion (which favours an antiferromagnetic insulating state).

3.3. Exchange-mediated magnetoelectric coupling

Most of the known single phase multiferroic materials order antiferromagnetically, a consequence of the strong superexchange magnetic interactions that tend to be dominant in the magnetic oxides. For example, BiFeO3 is 11


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Figure 8. Holes per Mn on each MnO2 layer starting at the interface (layer 1) for accumulation, depletion, and paraelectric states of the PbTiO3 /La0.8 Sr0.2 MnO3 interface. The horizontal dashed green line at 0.2 is the bulk doping density, and layer 8 is the last simulated layer of the La0.8 Sr0.2 MnO3 film. Reprinted with permission from [164]. Copyright 2012 by the American Physical Society.

Figure 9. A few possible magnetic structures on Mn sites at a manganite/ferroelectric interface; the manganite film only has four Mn layers for illustrative purposes: (a) FM configuration, F; (b) the spin flips in the first unit cell, A1, and (c) the spin flips in the second unit cell, A2. Reprinted with permission from [164]. Copyright 2012 by the American Physical Society.

ferroelectric and antiferromagnetic, with a complex spin structure [168, 235, 236]: the local ordering is G-type antiferromagnetic, with each Fe3+ ion surrounded by six antiparallel spins. However, the magnetoelectric coupling present in this system, in the form of a Dzyaloshinskii– Moriya exchange interaction [237, 238], results in a slight canting of the spins and in a small net local magnetic moment, which in turn winds in a long range incommensurate spin cycloid with a wavelength λ ≈ 62 nm, leading to an overall net zero magnetisation [168, 235, 239]. This spin spiral is expected to be suppressed in thin epitaxial BiFeO3 films, resulting in a small net magnetic moment [240, 241]. Hence, while the local magnetoelectric coupling in BiFeO3 is very strong [242, 243], the electric field induced changes in the magnetisation are relatively weak. In fact, larger overall magnetic moments and stronger effective magnetoelectric couplings have been achieved in multiferroic heterostructures by exchange-coupling the antiferromagnetic spins of BiFeO3 with the ferromagnetic spins of a ferromagnetic layer grown adjacent to it, through the so-called exchange-bias effect [244, 245]. The latter is manifest by a horizontal shift of the M–H hysteresis loop upon cooling the system from above the Néel temperature of the antiferromagnet under an applied magnetic field, where the magnitude of this shift is called the exchange-bias field [246, 247]. A broader discussion of this general approach to multiferroic behaviour has been presented in recent reviews [172, 173]. Here, we consider the particular case of BiFeO3 /LSMO as emblematic of the functionalities that can be attained using this approach to controlling magnetism with electric fields based on interfacial spin-exchange coupling [75, 248]. In an exchange-biased system, the exchange-bias is normally set by cooling down the system under a magnetic field from above the antiferromagnetic critical temperature but below the ferromagnetic critical temperature. In the simplest model for the exchange-bias effect, the interfacial ferromagnetic layer then couples to spins in the interfacial layer of the antiferromagnet, setting an overall preferred orientation that is frozen in place by the magnetic anisotropy of the antiferromagnet. This picture would seem to render the BiFeO3 /LSMO inauspicious for observing exchange-bias effects, given the high Néel critical temperature of BiFeO3

of 643 K, which is much higher than the ferromagnetic Curie temperature of LSMO at its optimal doping (x = 0.3) of about 370 K. However, not only are exchange-bias effects found to be present [249], but also a reversible electric field control of the exchange-bias effect has been demonstrated in this system [250]. Starting from a given remanent state, the sign of the exchange-bias field can be switched by switching the ferroelectric polarisation. The exchange-bias is seen to be largely independent of the ferroelectric domain wall structure and density, indicating that the coupling does not arise at the ferroelectric domain walls, where uncompensated spins may be expected to be present [75]. Rather, the origin of the effect has been attributed to exchange coupling to the magnetic moment that arises at the BiFeO3 interface with LSMO [249, 250]. Indeed, the observation of an induced net magnetisation at the BiFeO3 interface layer, coupled ferromagnetically to the spins in the LSMO layer, has been confirmed by magnetic resonant x-ray reflectometry [103], polarised neutron reflectivity [251], and has also been measured in BiFeO3 /LCMO using the x-ray magnetic circular dichroism effect [215]. Model Hamiltonian calculations suggest that the onset of a magnetic moment in BiFeO3 at the LSMO interface is an intrinsic interfacial effect that originates from a competition between the double exchange and superexchange interactions due to the modified interface charge carrier density resulting from charge screening [252]. More recently, full electric control of the exchange-bias without the need for temperature cycling has been demonstrated in La0.7 Sr0.3 MnO3 /BiFeO3 for the particular case when the magnetic field is applied along the [1 1 0] direction with respect to the SrTiO3 (0 0 1) substrate [253]. These results are summarised in figure 11, showing that the sign and amplitude of the exchange-bias is reversibly controlled by the gate voltage, and also that the direction of the exchange-bias can be reversed, depending on whether the electric field pulse is applied at negative or positive magnetic remanence. These findings are interpreted in terms of a model that takes into account the relative ionic displacements in BiFeO3 upon ferroelectric switching and the consequent change in the interatomic distance between the Fe and Mn cations at the interface that lead to a modification 12


Topical Review

Figure 10. Various candidate spin structures at a manganite/ferroelectric interface inspired by bulk magnetic phases. The indices 1 and 2 refer to the Mn layer at the interface and second from the interface, respectively. The remaining layers (3 and beyond) are fixed to be FM and ‘up’ (black). The model Hamiltonian approach predicts that in the accumulation state Cx1, CE1, and CE2 are the most likely possibilities. Reprinted with permission from [217]. Copyright 2011 by the American Physical Society.

in the exchange interaction and modulates the strength of the exchange-bias effect [253, 254]. In this context, a recent detailed investigation by Kim et al [255] of the LSMO/BFO interface using STEM-EELS over a region which include both directions of the ferroelectric polarisation, show an anomalous lattice expansion of BiFeO3 of about 5% for regions with a negative charge polarisation with an equally anomalous decrease in the Mn valency and a lower oxygen K-edge intensity, results that are interpreted in terms of screening by oxygen vacancies; for the other polarisation state, where such effects are absent, the screening is found to be purely electronic. Such results attest to the vast and complex behaviour that may be present at multifunctional oxide interfaces and to the need for a detailed characterisation down to the atomic scale. 3.4. Electronic reconstructions at manganite interfaces Figure 11. Exchange bias as a function of temperature for both remanent magnetization states of LSMO for a device oriented along [1 1 0] and with the magnetic field applied along [1 0 0]. Reprinted with permission from [253]. Copyright 2013 by the American Physical Society.

In this section we consider other examples of phenomena associated with ordered electronic states at the interface of manganite systems that arise as a consequence of a modified preference in the orbital occupancy with respect to the bulk, a process described in the literature as electronic orbital reconstruction. Such modifications in the orbital character of the interface atoms lead to distinct properties that are intrinsic to the interface. We consider the important interface between LSMO and SrTiO3 . SrTiO3 is a cubic perovskite at room temperature, with a lattice constant of 3.905 Å, but tetragonal at temperatures below about 108 K [256]. Because its lattice constant is close to that of several other important complex oxides, including the manganites and the cuprates, SrTiO3 is widely used as a substrate for the epitaxial growth of perovskite metal oxide films, and its surface properties and surface preparation are well documented, including procedures that yield singly TiO2 -terminated, atomically flat surfaces

[257–259]. SrTiO3 has a large tolerance for oxygen vacancies and a large oxygen and strontium mobility [260–264], and modifications to the surface and interface chemistry may arise during surface preparation or during subsequent film growth [265, 266]. In the case of the manganites, and of LSMO in particular, such modifications at the interface, including stoichiometry, the presence of interfacial strain, and point defects such as oxygen vacancies, have been held responsible for the degraded magnetic and electric properties that are found in ultrathin films, as manifested in the presence of a magnetic and electrical ‘dead’ layer (the layer thickness 13


(a) →

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Circularly polarized x ray

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Figure 12. Magnetic behaviour of LSMO/SrTiO3 (0 0 1) thin films as a function of thickness probed by x-ray magnetic circular dichroism in two configurations: with holding field (left panels) and at remanence, after application of a field pulse (right panels). Reprinted with permission from [271]. Copyright 2010 by the American Physical Society.

below which the system shows no magnetic or metallic charge transport response, respectively) [267–269]. For example, LSMO (x = 0.3) films grown on SrTiO3 (0 0 1) have a magnetic and electrical dead layer thickness of about 8 unit cells [268], while at 0.2 doping the electric dead layer is about 10 unit cells [226]. Other intrinsic phenomena, such as charge compensation at the polar LSMO/STO interface, may play a strong role on the modified electronic properties, as indicated by the STEM-EELS study by Mundy et al [270] that find the presence of an excess electron charge at this interface (or hole deficiency) for Sr dopings below about 0.3, which pushes the interface towards insulating and antiferromagnetic states according to the bulk phase diagram. A detailed study of the magnetic and electronic configuration of LSMO (x = 0.3)/SrTiO3 (0 0 1) investigated by x-ray spectroscopy has been reported by Lee et al [271], where it is found that the LSMO has an enriched Mn3+ region near the SrTiO3 interface, irrespective of the growth technique (PLD or MBE) [272]. This stoichiometrically modified interface region causes the onset of an intriguing magnetic behaviour, manifested by the observation of a reversal of the magnetisation orientation at remanence after the application of a pulsed magnetic field for film thicknesses above ∼10 unit cells, as shown in figure 12. This behaviour is attributed

to the onset of antiferromagnetic regions within the interface region induced by the lattice compression of LSMO at lower Sr doping, which results in a stronger magnetic anisotropy and in the onset of an exchange bias effect above a critical thickness [271, 273]. Also at the LSMO (x = 0, 0.3)/SrTiO3 interface, atomically resolved electron energy loss spectroscopy reveals that electrons from the 3d Mn orbitals extend to the Ti cations across the interface (figure 2), leading to the emergence of a magnetic moment in the latter, as detected by x-ray magnetic circular dichroism measurements, see figure 13(a) [79, 274, 275]. These measurements also show that the magnetisation from the Ti cations has the same temperature dependence as that of the LSMO magnetisation, indicating that the Ti cations are exchange-coupled to the Mn (figure 13(b)). In addition, the nature of the coupling is found to depend sensitively on the strain state in the LSMO, which determines the preferential orbital occupancy and consequently the sign of the superexchange coupling through the oxygen atoms [274, 275]. In these studies, the strain of the LSMO layer is controlled by changing the thickness of the SrTiO3 layers, such that the LSMO layers are constrained to adopt the SrTiO3 lattice constant (for thicker SrTiO3 layers), or instead adopt a more bulk-like lattice 14


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x 10

Ti Mn

Ti XMCD (466 eV) Mn XMCD (642 eV) VSM measurement

Figure 14. The MBE-grown La0.8 Sr0.2 MnO3 /BaTiO3 interface visualized with high resolution STEM for the case of an interface in the accumulation state (ferroelectric polarisation in BaTiO3 away from the interface). (a) STEM image displaying the BaTiO3 (left) and La0.8 Sr0.2 MnO3 (right), with the interfacial BaO layer indicated by the dashed vertical line. The measured Mn–O displacement in the interfacial MnO2 layer is 0.18 Å. (b) Intensity line scans from STEM along Mn–O (blue) and La0.8 Sr0.2 O atomic columns in the La0.8 Sr0.2 MnO3 , showing the polar displacement of MnO2 layers in the interfacial region as an offset in the peaks of Mn and O locations. Adapted with permission from [212]. Copyright 2014 American Chemical Society.

Figure 13. (a) X-ray magnetic circular dichroism measurements across the Ti and Mn absorption L edges for a 6 uc LSMO(x = 0.3)/2 uc STO superlattice showing that both Mn and Ti are magnetically polarised (measurements at 6 K, 1 T). (b) Temperature dependence of the magnetisation determined from XMCD and vibrating sample magnetometry. Reprinted with permission from [275]. Copyright 2011 by the American Physical Society.

Explicit experimental measurement of such an interfacial distortion is challenging as it requires a high quality interface and a method able to resolve atomic positions with subångstrom resolution. State-of-the-art STEM is a method of choice as it works in real space: observations from a recent work [212] in fact display the predicted polar displacement at the La0.8 Sr0.2 MnO3 /BaTiO3 (0 0 1) interface. Figure 14 shows STEM data for such interfacial region, showing a highly ordered and abrupt interface with the predicted polar displacement in the interfacial layers of the La0.8 Sr0.2 MnO3 . The next question is whether and how the presence of polar distortions in the LSMO modifies its physical properties. If differences exist that depend on the polarisation state of the ferroelectric, this opens the possibility of further multiferroic couplings. As described above, the interface is already magneto-electric. A separate, non-magnetic order parameter that can exist in transition metal oxides is differentiation of occupancies in the d shell: differences in orbital population of different orbitals in the same shell on the same atom are termed orbital polarisation. In the case of La0.8 Sr0.2 MnO3 /BaTiO3 , a significant difference in occupancy is found between the two eg orbitals (3z2 − r 2 and x 2 − y 2 ) of the interfacial Mn ions. Furthermore, the difference is reversed when the polarisation is reversed [212]. Specifically, for the accumulation state, the in-plane x 2 − y 2 Mn d orbital is more populated, while for depletion it is the 3z2 − r 2 orbital that is more populated. Figure 15 shows first principles results

parameter (for ultrathin SrTiO3 ). One finds that in the case of thin SrTiO3 strained to LaMnO3 or LSMO, the coupling is antiferromagnetic, while for relaxed SrTiO3 layers, the coupling is ferromagnetic [274, 275]. In the first case, a preferential occupation of the Mn 3z2 − r 2 orbitals and the Ti xz, yz orbitals leads to antiferromagnetic coupling, while in the latter case, preferential occupied Mn 3x 2 − y 2 orbitals couple ferromagnetically with the occupied Ti xz, yz states. 3.5. Orbital polarization

A further example of a genuinely interfacial effect that does not exist in bulk LSMO is polar displacement of the ionic lattice. As we have seen above, when LSMO has an atomically abrupt interface with a ferroelectric, a number of interesting properties arise at the interface. Since ferroelectric polarisation at the atomic scale involves polar ionic displacements, i.e. nonzero cation–anion separation along the polarisation direction, one cannot expect this type of displacement to drop suddenly to zero at the interface. Instead, the polar displacements are imprinted on the LSMO, decaying in magnitude with increasing distance from the interface. Thus the interfacial LSMO layers display polar displacements, and we gave some examples of theoretical predictions of this fact above (as exemplified by figure 5). 15


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Figure 15. First principles electronic structure of the La0.8 Sr0.2 MnO3 /BaTiO3 (0 0 1) interface based on local densities of states at the Fermi level. The [0 0 1] direction is vertical, and (a) shows the case of accumulation and (b) shows the case of depletion. Oxygen ions are in red, Ti in gold, Mn in bluish grey, Ba in grey, and La0 .8Sr0 .2 in light green. Atomic layers along [0 0 1] are labeled on the right. The background shows a planar slice in the x–z plane going through the transition metals (Ti and Mn) colored by the intensity of the local density of states (black is low, red and gold are high). We see a clear two-dimensional nature to the density in (a) where the x 2 − y 2 orbital is more occupied, while in (b) we see a vertical density stemming from the more occupied 3z2 − r 2 , which is out-of-plane and is also evidenced by the visible amplitude on the next MnO2 plane.

non-magnetic metallic layer, respectively (varying as the dot product of the layers’ magnetisation). In particular, LSMO at 0.3 doping, an electrical conductor with high spin polarisation and a relatively high critical temperature, has a lattice constant that allows epitaxy with many other oxides and has been widely employed as a magnetic layer in TMR and GMR spin-valve structures [289]. For such device structures, it is important that the spin polarisation be as high as possible, both in the bulk of the layer and at the interface with the non-magnetic layer [8]. However, despite the high spin polarisation expected for these materials (and measured at low temperatures), spin-valve devices based on the optimally doped manganites display moderate magnetoresistance effects, which decay strongly with increasing temperature [219]. Such degraded properties are thought to be related to modified interfacial properties and the loss of spin polarisation at the interface, either due to spin-scattering defects that randomise the electron spin or to the loss of magnetism and conductivity at the interface (magnetic and electrical dead layers). In tunneling magnetoresistance structures, additional functionality can be attained by using multiferroic tunnel barriers, permitting the use of both magnetic and ferroelectric order parameters to control the spin transport and to store information [290–294]. Ferroelectric tunnel junctions, where the tunnel barrier is composed of a ferroelectric sandwiched between non-magnetic metal electrodes, are found to exhibit a tunneling conductance that depends on the direction of the ferroelectric polarisation (tunnel electroresistance, or TER) [295–305]. The tunnel electroresistance effect can arise from three distinct mechanisms that can act in tandem: (i) changes in band alignment due to charge screening, (ii) changes in atomic bonding at the interface, and (iii) strain [306]. Here as well, the use of ferromagnetic electrodes [291, 305, 307–312] enables ferroelectric and ferromagnetic degrees of freedom to be explored to achieve non-volatile multi-state logic devices.

for the electronic structure of the interface as a function of ferroelectric polarisation displaying the difference in orbital polarisation. Numerically, the difference is computed to be ∼10% and, most critically, it is dynamically reversible by changing the ferroelectric polarisation. 4. Transport and tunneling phenomena

The complex and rich charge transport properties of the doped manganites have been a subject of enduring interest since the discovery of these compounds in the early 1950s [225, 276], of which the colossal magnetoresistive effect associated with a magnetic field-driven insulator to metal transition is perhaps the best known and striking example [277–281]. The close link between the magnetic and electrical properties dictated by the double exchange interaction [220–223] implies that manipulating the magnetic state of the system leads also to a control of the charge transport, an effect which can be exploited for device applications. Hence, it is natural to expect that the modified electronic and magnetic properties at manganite interfaces will result in new transport characteristics, as confirmed by results of both experimental and theoretical investigations carried out in these systems. One aspect that has attracted much interest in the doped manganites is that several have been theoretically predicted to be fully spin polarised at the Fermi energy [219]. Experimental results for LSMO at 0.3 doping indicate in fact a spin polarisation of ∼100%, as determined by Andreev reflection [218]. Such a property is highly beneficial for devices based on spin transport, for instance, in spin-valve structures using the tunneling (TMR) [282–284] and giant magnetoresistance (GMR) [285–288] effects, which relate to differences in the spin scattering rates of electrons traveling between two magnetic layers, either through an insulating barrier or a 16


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In the context of multiferroic heterostructures, a large effort has been devoted to the investigation of the interfacial transport properties of systems composed of ferroelectric and magnetic components [313, 314]. For example, the electrostatic control of the metal-insulator transition has been proposed as a logic switch device (Mott transistor) [28, 315]. Electric field induced metal-insulator transitions have been demonstrated in PZT/LSMO heterostructures, where the control of the charge carrier density in the manganite channel layer drives it from a metallic state in the accumulation state to an insulating state in the depletion state [211]. PZT/La0.65 Sr0.35 MnO3 , PZT/La0.70 Ca0.30 CoO3 , and PZT/La0.52 Ca0.48 MnO3 field effect device structures are found to exhibit large retention times and switching times that are limited by the RC time constant of the device [316]. Also, in 50 nm La1−x Cax MnO3 (x = 0.2, 0.3)/PZT ferroelectric field effect devices, large modulations in the electrical resistivity of the manganite channel layer are observed as a function of the ferroelectric polarisation [317, 318], an effect that is attributed to electronic phase separation in the Ca-doped lanthanum manganites [30, 319–321] and to the role of electrostatic doping in driving the system into an insulating state when holes are depleted from insulating-metallic interfaces within the phase-separated LCMO channel, or into a metallic state in the opposite case when the ferroelectric polarisation is reversed. Control of the interfacial spin configuration in PZT/LSMO heterostructures suggests that electrostatic control of the spin polarisation of the charge carriers can be achieved in this artificial multiferroic system [77, 224]. In particular, ab initio calculations predict that large modifications in the transport properties occur for charge flowing across a La0.7 Sr0.3 MnO3 /BaTiO3 /La0.6 Sr0.4 MnO3 multiferroic tunnel junction, a consequence of the different conductivities for the antiferromagnetic and ferromagnetic interfacial configurations of the La0.6 Sr0.4 MnO3 layer [322]. Such differences in conductivity at the LSMO interface reflect the different conductivities of ferromagnetic and A-type antiferromagnetic equilibrium states of bulk LSMO. In the FM state, the transport is three dimensional (i.e. an electron of fixed spin has the same energy on all neighboring sites), but for the A-type AFM phase transport is largely confined within the (0 0 1) planes (inside of which the Mn spins are ferromagnetically aligned) since electron motion along the [0 0 1] direction is strongly hindered by the large exchange splitting of the Mn sites (e.g. when a low energy up spin electron on a Mn site with up polarisation tries to move to its [0 0 1] Mn neighboring site with down polarisation, it would have to occupy the high energy up state due to the large exchange splitting). Hence, the A-type AFM state essentially blocks transport along the [0 0 1] direction. An experimental demonstration of such an effect has been reported in the work of Yin et al [323] for LSMO/BaTiO3 /LCMO/LSMO, where a TER enhancement of ∼104 % was observed and attributed to a metal-insulator phase transition in the LCMO layer driven by the modulation of the charge carrier density induced by the ferroelectric polarisation switching. This difference in conductivity at the BaTiO3 /LSMO interface is observed in the conductance maps

in reciprocal space for the different magnetoelectric states, as shown in figure 16. In the same spirit, Jiang et al [324, 325] have studied the tunneling electroresistance across PZT/LSMO heterostructures for various LSMO dopings (0.2, 0.3, 0.5) and thicknesses, to find the largest effect to be present at 0.2 doping, of up to ∼3 × 104 %, attributed to the role of the interfacial spin reconstruction induced by charge doping. Another striking example of modified interfacial transport properties of a manganite is provided by the demonstration of a strong resonant coupling between the soft phonon modes of SrTiO3 to LSMO at half doping in SrTiO3 /LSMO interfaces, which leads to strong modulations in the electric and magnetic properties of the manganite film [326]. In this study, it is observed that the resistivity of LSMO thin films at near half doping is strongly enhanced at near 108 K, which is the temperature corresponding to the cubic to tetragonal phase transition of SrTiO3 , the substrate on which the LSMO films are deposited (figure 17). At near half doping, LSMO films grown on SrTiO3 are found to be metallic and antiferromagnetic, although a small ferromagnetic component is also present [232, 326]. The cusp in resistivity is found to decrease with increasing film thickness and can be enhanced further by confining the charge carriers to a region closer to the SrTiO3 interface by using a ferroelectric gate to modulate the carrier density, as shown in figure 17(b), demonstrating the interfacial nature of this phenomenon. Concomitant with the changes in the resistivity, the temperature response of the saturation magnetisation shows a marked depression over the same temperature region over which the resistivity is enhanced. Although the effect is observed over a wider range of doping levels, it is particularly strong at x = 0.47 [232]. These experimental findings are explained by an interfacial coupling between the rotations of the oxygen octahedra that accompany the phase transition in SrTiO3 to the oxygen octahedra of the LSMO layer. Such coupling can originate from either static or dynamic mechanisms. In the former case, the coupling would issue from a static coupling, whereby the static rotations that occur in SrTiO3 below the phase transition would induce similar static rotations in the LSMO oxygen octahedra. The second possibility is associated with a resonant interfacial dynamic coupling between the SrTiO3 soft modes and phonon modes in the LSMO. The results of ab initio calculations and computation of lattice mode frequencies as a function of temperature demonstrate that only the latter scenario leads to a strong electron-phonon coupling in the LSMO, consistent with the amplitude of the resistivity enhancement [326]. Separately, in the static coupling scenario, one may expect the enhancement in resistivity to show a sudden jump below the critical temperature, rather than the cusp that is observed experimentally. Theoretical results show that the SrTiO3 soft phonons evanescently decay into the LSMO over a length scale of 1–2 unit cells [326], again underlining the purely interfacial nature of these phenomena. Such results point to the prospect and largely unexplored possibilities of coupling resonantly to phonon modes in the doped manganites in order to modulate its electronic, magnetic and transport properties. 17


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Figure 16. First principles predictions for the LSMO/BaTiO3 /LCMO/LSMO multiferroic tunnel junction. (a)–(c) Schematic side view of the layer-by-layer atomic positions and magnetoelectric state of the system. The ferroelectric polarisation in the BaTiO3 is indicated by large arrows, the magnetic moment on the Mn sites is indicated by the small arrows, and the magnetoelectrically active region is indicated by the dashed rectangle on the right-hand interface. (d) Profile of the relative metal-oxygen (MO) displacements in each atomic layer for two polarisation states. The filled symbols are BO2 displacements (B = Mn or Ti,) and the open symbols are AO displacements (A = La0.7 Sr0.3 , La0.5 Ca0.5 , or Ba). Red, blue and green symbols correspond to the magnetoelectric states depicted in (a)–(c), respectively. (e)–(g) The k -resolved distribution of the tunneling transmission in the two-dimensional Brillouin zone for the different magnetoelectric states depicted in (a)–(c), respectively. The integrated total conductance G per in-plane cell is given in the lower-left corner of each plot (in units of 10−6 e2 / h). The colour scale is logarithmic while the gray areas correspond to zero transmission. Reprinted by permission from Macmillan Publishers Ltd: Nature Materials [323], copyright 2013.

The microscopic origin of the interfacial effects lies in the break in symmetry and the reduced atomic coordination that in turn leads to electronic modifications in orbital character and orbital occupancy at the interface, and thus to novel electronic properties. In addition to being stimulating scientifically, such new properties are also of potential technological interest, in particular in the context of next generation electronic devices with good scaling properties and high energy efficiency, and also for applications as ultrasensitive detectors and actuators. Given the unrelenting progress in the ability to grow and characterize materials down to the atomic level, the coming years are likely to bring to light further improvements in the amplitude and temperature response of the effects already unraveled, and more importantly, new discoveries of interfacial phenomena with the potential for enabling

5. Conclusions and outlook

In this short review, we aimed at giving a flavour of the novel phenomena that emerge and are intrinsic to the interface between different materials. We focused on a prototypical class of complex materials, the doped manganite perovskites, to show how novel functionalities arise when interfaced with ferroelectrics, with dielectric materials used as tunnel barriers, and with other complex oxides, to induce multiferroic behaviour, new transport phenomena, and new electronic and magnetic interfacial states. Intrinsic interface phenomena have the characteristic that the effects originate in the few atomic layers closest to the boundary separating the different materials, typically within five unit cells, while the effect itself may propagate to the bulk of the system. 18

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(a)

11

0.4

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m [µB/Mn]

ρ [mΩ cm]


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12

100 Deplet.

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10 Accum.

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T[K] Figure 17. (a) Magnetotransport response of a PZT/11 u.c. La0.53 Sr0.47 MnO3 film demonstrating enhanced carrier-phonon scattering from the SrTiO3 (0 0 1) substrate. (a) Left axis: resistivity showing a strong cusp at 108 K, with the PZT overlayer in the depletion state. Right axis: magnetic moment of a 15 u.c. La0.53 Sr0.47 MnO3 film (measured at 1 kOe) showing a dip in the moment, overlapping the temperature range of the resistivity cusp (emphasized by the gray box). The dashed line is a linear interpolation between the edges of the dip region. (b) Resistivity of the 11 u.c. film for the two polarisation states of the PZT layer. (c) Energy of the 25 phonon mode in SrTiO3 , showing the softening around the SrTiO3 transition temperature (after [327]). Lines are a guide to the eye. Below the structural phase transition temperature the mode splits due to the breaking of cubic symmetry. Reprinted with permission from [326]. Copyright 2011 by the American Physical Society.

disruptive technologies. These effects also will shed further light onto the role of electron correlations at the atomic scale and in confined dimensions. Acknowledgments

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