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Polarized neutron reflectivity from monolayers of self-assembled magnetic nanoparticles
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 136001 (9pp)
doi:10.1088/0953-8984/27/13/136001
Polarized neutron reflectivity from monolayers of self-assembled magnetic nanoparticles ¨ 4, D Mishra1 , O Petracic1,2 , A Devishvili1,3 , K Theis-Brohl B P Toperverg1,5 and H Zabel1,6 1
Institute for Experimental Condensed Matter Physics, Ruhr-University Bochum, D-44780 Bochum, Germany 2 J¨ulich Centre for Neutron Science JCNS and Peter Gr¨unberg Institut PGI, JARA-FIT, Forschungszentrum J¨ulich GmbH, 52425 J¨ulich, Germany 3 Institut LaueLangevin, BP 156, F-38042 Grenoble, France 4 University of Applied Sciences Bremerhaven, D-27568 Bremerhaven, Germany 5 Petersburg Nuclear Physics Institute, Gatchina 188300, St Petersburg, Russia 6 Johannes Gutenberg-Universit¨at Mainz, D 55099 Mainz, Germany E-mail: [email protected] Received 26 November 2014, revised 7 February 2015 Accepted for publication 11 February 2015 Published 13 March 2015 Abstract
We prepared monolayers of iron oxide nanoparticles via self-assembly on a bare silicon wafer and on a vanadium film sputter deposited onto a plane sapphire substrate. The magnetic configuration of nanoparticles in such a dense assembly was investigated by polarized neutron reflectivity. A theoretical model fit shows that the magnetic moments of nanoparticles form quasi domain-like configurations at remanence. This is attributed to the dipolar coupling amongst the nanoparticles. Keywords: magnetic nanoparticles, iron oxide, self assembly, polarized neutron reflectivity (Some figures may appear in colour only in the online journal)
spin freezing, superspin glass (SSG) and superferromagnetic (SFM) states [2, 4, 32]. The detailed nature of the SFM state is still not well understood. Various explanations have been proposed. The SFM state was observed in a number of systems for e.g. microcrystal goethite [28], discontinuous metal insulator multilayers of CoFe and Al2 O3 [3], and dense packing of Co NPs [35]. In most of these cases the ferromagnetic state develops due to exchange interaction, rather than dipolar interaction. Although some theoretical and experimental evidence suggests that dipolar coupling can lead to a SFM state [10, 17, 18, 20, 34, 38, 41], certain other theoretical considerations [22, 37], on the contrary, suggest that point-like dipoles in two and three dimensions lead to antiferromagnetic ordering. The magnetic ground state and hence the magnetic ordering can be affected by various other factors, namely, the crystal symmetry, the nature of close packing or the spatial ordering of NPs and higher multipole (quadrupole, octopole) interactions [12, 13, 16, 36]. These
1. Introduction
Magnetic nanoparticles (NPs) are promising for application in numerous fields e.g. spintronics [1, 14, 23], photonics [24], plasmonics [31] and bio-medicine [21]. Self-assembly of NPs into ordered structures is particularly interesting, as they exhibit novel physical properties. These properties are unique and are completely different from individual NP properties. In most cases the physical attributes are manifested by the unique structure that can be achieved in self-assembly. For example, individual magnetic NPs can be superparamagnetic (SPM) in nature. Each NP is in a single domain state known as superspin and exhibits thermal fluctuations. However, closely packed NPs show collective behavior due to interaction amongst these superspins. The most dominant interaction in the case of SPM NPs is the dipolar coupling. Depending on the type and strength of the interaction, new collective states can be observed, in particular a modified SPM state, glass like 0953-8984/15/136001+09$33.00
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© 2015 IOP Publishing Ltd Printed in the UK
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factors are determined by the non-spherical nature and the irregular structure of the NPs. We report here the observation of an SFM domain-like structure arising in a hexagonally close-packed iron oxide NP monolayer via polarized neutron reflectivity (PNR). We would like to emphasize two points: one is the magnetic dipolar coupling which leads to enhanced magnetic correlations by suppressing thermal fluctuations; the second is the sensitivity of polarized neutron reflectivity (PNR) to specific details of the structural and magnetic arrangement over the NP monolayer. There are various other techniques to scrutinize the magnetic state in interacting NPs like M¨ossbauer spectroscopy [28], a.c. magnetic susceptibility measurement [33], magnetic force microscopy [35], x-ray photoemission electron microscopy [3], electron holography, and Lorentz microscopy [41]. However, due to specific coherence properties of the neutron beam impinging onto the layered systems at grazing incidence, the scope of information delivered by PNR experiment is unique [5, 39, 42, 43]. In particular, in our recent studies [25] carried out on a set of multilayers formed by magnetite NPs spin coated onto a silicon wafer it was demonstrated that magnetization in remanence is decomposed into a set of lateral ‘quasi-domains’ hence supporting the assumption of a super-ferromagnetic state of the system. Here we show the capability of PNR extended to single NP layers, also revealing magnetic domainlike correlations among the NPs. These results confirm a true 2D character of the super-ferromagnetic ordering in a close packed 2D structure of super-spins coupled via dipole–dipole interaction. The paper is organized as follows. In section 2 we describe the sample preparation, in section 3 we present PNR measurements and in section 4 we discuss results, followed by a summary and conclusion in the last section 5.
evacuated to the desired pressure and then inserted into a tubular furnace pre-heated to 230 ◦ C. The annealing was done for 30 min and then the quartz tube was removed from the furnace. The sample was kept under vacuum all the time till cooling down to room temperature. After this procedure we obtained magnetite as the prevailing phase [6]. Since the unannealed NPs consist of antiferromagnetic wustite as the major phase, this actually helps in obtaining a better selfassembly in the spin-coating process. For as-prepared NPs with smaller diameters, maghemite or magnetite are the major phases and lead to an agglomeration due to strong dipolar interaction. Even for cobalt NPs this is also valid. Hence the best close-packed hexagonal structure obtained was for the 18 nm diameter antiferromagnetic iron oxide, which was converted to magnetite afterwards by annealing. Amongst all the iron oxides, magnetite has the highest magnetization and is ferrimagnetic in nature [15]. It should be mentioned here that the Van der Waals interaction between NP–NP and NP-substrate mediated via toluene solvent is quite small compared to the magnetic dipolar interaction for iron oxide NPs (magnetite or maghemite). The Van der Waals force is of the order of 100 K compared to the magnetic dipole–dipole interaction, which is of order 3000 K for the same size of NPs and similar distances. Therefore the Van der Waals force plays an insignificant role in the selfassembly process and agglomeration [27]. Figure 1 shows scanning electron microscope (SEM) images of the NP film spin-coated on the vanadium film taken from two different regions ((a) and (b)) of the sample and from NP spin-coated onto a bare Si substrate with two different magnifications ((c) and (d)). The NPs are arranged in hexagonal close-packed structure over the entire surface, which was achieved by the spin-coating method. Some parts show two complete layers (figure 1(b)) and some parts show 1– 1.3 layers (figure 1(a)) of NPs. Similar features are observed in the SEM images of NPs deposited directly onto Si substrate, as can be seen in figure 1(c).
2. Sample preparation and characterization 2.1. Sample preparation
We used chemically synthesized iron oxide NPs of 18 nm diameter with 6.5% size distribution purchased from Ocean Nanotech. The NPs are coated with an oleic acid shell and are dispersed in toluene solvent. The preparation and characterization of the samples are reported elsewhere [6]. For comparison we used two different substrates in order to probe the influence of the substrate on the NP ordering [26]. In the standard procedure we used a silicon (Si) substrate covered by its natural oxide. In addition, we prepared a sample with a 50 nm thick vanadium (V) film rf sputtered onto a sapphire (Al2 O3 ) wafer and the NP dispersion was spin-coated on top of the V film. The NP dispersion was diluted in toluene with a 1:1 volume ratio and then spin-coated on the substrates at 2000 revolutions per minute for 30 s. Then the samples were heat treated on a hot plate at 80 ◦ C in air for 20 min to evaporate the solvent. In the next step the antiferromagnetic iron oxide (wustite) NPs were annealed in an evacuated quartz tube at a pressure of 3 × 10−3 mbar. The quartz tube was first
2.2. X-ray reflectivity
X-ray reflectivity (XRR) measurements were performed to verify the quality of the samples. The XRR measurements were performed in-house using a rotating anode machine, with Cu Kα radiation. Figure 2 shows the XRR measurements of the sapphire (Al2 O3 ) substrate coated with a vanadium film before and after spin-coating with NPs and annealing in vacuum. The sputtered vanadium film on sapphire substrate shows Kiessig oscillations [19] corresponding to a thickness of 51 nm. The well resolved Kiessig fringes are observed up to a qz value of 3.5 nm−1 . On the contrary, after spin-coating the NPs and annealing, the surface becomes less reflective. The thickness of the vanadium layer does not change, but the Kiessig fringes die out rapidly. Two critical angles corresponding to the NPs and to the vanadium film are also clearly visible. XRR data obtained for the NP monolayer deposited directly onto the silicon substrate are reported elsewhere [25]. 2
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Figure 1. SEM images of spin-coated NPs on vanadium and silicon substrates. (a) and (b) Images of NPs spin-coated on vanadium from two different regions. (c) and (d) Images of NPs spin-coated on Si at different magnification. The digitally zoomed-in image (d) shows a clear hexagonal arrangement of NPs as indicated by the hexagon drawn on it.
magnetometer. The sample measured by SQUID is a monolayer spin-coated onto the silicon substrate. However, the magnetic behavior is found to be similar, irrespective of the substrate used. The magnetization versus temperature plot (figure 3(a)) under zero field cooling (ZFC) and field cooling (FC) procedure shows that the monolayer is not in a blocked state at room temperature. The blocking temperature is 260 K. The step at 110 K in both the FC and ZFC magnetization curves is due to the Verwey transition [40], and is another strong indication for the presence of magnetite in our sample after annealing. The hysteresis plot in figure 3(b) measured at room temperature shows a typical SPM-like behavior with close to zero remanence and very low coercivity. The inset shows an enlargement of the low field region. 3. Polarized neutron reflectivity Figure 2. XRR measurements of vanadium film sputtered on
3.1. Scattering geometry
sapphire substrate (triangles) and after spin-coating NPs and annealing them in vacuum (circles). The reflectivities are offset with respect to each other by two orders of magnitude for clarity.
The PNR measurements were performed at the Super ADAM reflectometer stationed at the Institut Laue–Langevin (ILL), Grenoble, France [11]. The wavelength of neutrons selected by a HOPG monochromator was 0.441 nm, which corresponds to an energy of 4.22 meV or an equivalent temperature of 48.83 K. The incident polarization efficiency was about 98%.
2.3. Magnetization measurements
The magnetic characterization was performed with a superconducting quantum interference device (SQUID) 3
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Figure 4. Geometry of the PNR measurement. The incident and exit wave vectors are ki and kf , respectively, determined by incident and reflected angles of αi and αf with qz as the scattering vector. In the Cartesian axes the magnetic field H is directed along the Y -axis is the magnetization collinear with the neutron polarization axis. M vector, which may be tilted by an angle γ with respect to the Y -axis.
make an angle γ with the Y -axis. Then the Y -component, My = M cos γ , contributes to the NSF scattering (R ++ , R −− ), and the X-component, Mx = M sin γ , of the magnetization vector contributes to the SF scattering (R +− , R −+ ), even though the net magnetization of the sample, which is averaged over the whole surface, may be directed along the Y -axis [43]. The model reflectivities are captured in the following set of equations [43, 44]: 1 R ++ = (1) |R+ (1 + cos γ ) + R− (1 − cos γ )|2 4
Figure 3. (a) Magnetization versus temperature measurement under ZFC (solid circles) and FC (open circles) for monolayer of NPs annealed at 230 ◦ C in vacuum. The kink at 110 K is due to the Verwey transition and marks the presence of magnetite in the nanoparticles. (b) Hysteresis loop measured at room temperature. The inset shows a magnified plot at remanence.
R −− =
1 |R+ (1 − cos γ ) + R− (1 + cos γ )|2 4
(2)
1 (3) |R+ − R− |2 sin2 γ , 4 valid for ideal polarization Pi = Pf = 1, and where R+ and R− are the reflection amplitudes for two neutron spin states. The reflection amplitude appears due to scattering from the coherence ellipsoid and represents the average nuclear and magnetic scattering length density (nSLD and mSLD) over the ellipsoid. The coherence ellipsoid originates from the three dimensional resolution function defined by the beam divergence and uncertainty in angles of neutron detection [43]. The resolution function is convoluted to the reflectivity and the resultant intensity is fitted. The coherence ellipsoid is highly anisotropic in nature due to the slit configuration and grazing incidence. As shown in figure 4 it extends over a few dozens of micrometers along the X-axis and a few nanometers along the Y - and Z-axes. We used a slit of width 1 mm (X-direction) and several mm in height (Y -direction). That gives relaxed resolution in the Y -direction and about 10–50 µm resolution along the X-axis. Correspondingly, the coherence area illuminated in our case is a few nm along the Y and Z direction and about 10–50 µm along the X direction, which corresponds to a Qx resolution of R +− = R −+ =
The polarization of the reflected beam was analyzed with an efficiency of about 99%. Four reflectivities were recorded with a position sensitive 3 He detector (PSD): two non spin flip, R ++ , R −− (NSF) and two spin flip, R +− , R −+ (SF). All the measurements were carried out at room temperature. First, the reflectivities were recorded at an applied field of 2 kOe or 5 kOe. In remanence a guiding field of 6 Oe was applied to maintain the neutron polarization along the same direction as in the high field case. The geometry of the experiment is shown in figure 4. Incident neutrons with wave vector ki impinge at a glancing angle αi onto the sample surface. The reflected neutrons have a wave vector kf , scattered at an angle αf . For specular scans αi = αf and qz is the scattering vector. The coherence ellipsoid subtended by the neutron waves are also shown in this figure. The dotted lines represent the three different axes, ly , lz lx , of the coherence ellipsoid along three different cartesian axes. The neutron polarization is directed along with, or opposite to, the Y -axis which is set collinearly with averaged over the external field H . The magnetization M one of the coherence ellipsoids indicated in the figure may 4
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(a)
Figure 5. PNR measurements at high field of 5 kOe from a NP monolayer deposited directly onto a silicon wafer. All four reflectivities: two NSF (R++ , R−− ) and two SF (R+− , R−+ ) are displayed, together with the fits shown by solid lines.
(b)
about ∼10−3 –10−4 nm−1 . The component along the Z-axis gives rise to thickness oscillations. This provides the lateral resolution and the average mSLD value over the ellipse. The coherence ellipsoid spans a very small part of the total illuminated area and hence the reflectivity can be calculated by taking an incoherent average over the total illuminated area. In case of homogeneous samples the situation is trivial as the neutrons are scattered homogenously from all coherence ellipsoids, and the final intensity is an incoherent sum of intensities from all coherence ellipsoids.
Figure 6. PNR measurements from a NP/V/Al2 O3 heterostructure: (a) at high field of 2 kOe and (b) at remanence, respectively. All four reflectiviies: two NSF (R++ , R−− ) and two SF (R+− , R−+ ) are displayed, together with the fits shown by solid lines.
3.2. PNR measurements
Figure 5 shows PNR data collected from the NP monolayer deposited directly onto a silicon wafer and subjected to 5 kOe magnetic field, while figures 6(a) and (b) present PNR results obtained from the NP/V/Al2 O3 heterostructure at high fields of 2 kOe and at remanence, respectively, along with fits to the data points (solid lines). All scans were performed at room temperature. The NP covered layers are intrinsically rough due to the spherical shape of the NPs. Nevertheless, the small size distribution of our NPs and their uniform coating results in only a small roughness variation over the entire surface and gives rise to specular reflection from the sample. It shows that a simple spin-coating process may produce rather well defined monolayers, albeit containing islands and defects as seen in the SEM images. The effects of the latter are seen in figures 5 and 6 as smearing of the critical edges for total reflection, as well as by the fast damping of the Kiessig fringes at high wave vector transfer qz = (4π/λ) sin α. In fact, only two NP layer thickness oscillations are visible in figure 5, while faster oscillations in figure 6 are mostly due to the 500 Å vanadium film on the Si substrate. Surprisingly, no SF scattering was observed other than that due to imperfect spin polarizing and analyzing efficiencies. From this we infer that the mean magnetization averaged over the coherence volume is either well collinear with the Y -axis in figure 4, or equal to zero. On the other hand, at high fields one
can clearly recognize in figure 5 a small spin splitting between the critical edges of the total reflection for two NSF curves. Such splitting is harder to recognize in figure 6(a), but it still can be observed in the amplitudes of the thickness oscillations. Both effects unambiguously indicate a finite magnetization in both samples. At remanence the splitting in figure 6(b) almost vanishes, showing that the sample at low fields approaches a demagnetized state. 3.3. PNR fitting results Fitting scheme. More details on the microscopic arrangement of magnetic states become available via fitting of the data to theoretical models. But before delving into that we will first explain the fitting routine in some more detail. Fitting of the data in figure 5 was performed by use of a three layer model, while the best fit of data in figure 6 assumes a five layer model excluding the substrate. All four reflectivities, SF and NSF, in each case were fitted simultaneously by varying the nuclear scattering length density (nSLD or N b) and the magnetic scattering length density (mSLD or Np), the layer thicknesses and the interfacial roughnesses. Here PNR exposes another advantage compared to other experimental techniques, since one can retrieve the structural, as well as
3.3.1.
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(a)
Figure 7. Model for the reflectivity fit. The right panel shows the parabolic nuclear SLD profile.
(b)
(a)
Figure 9. Same as in figure 8, but for the sample with the vanadium sublayer on sapphire.
(b)
and oleic acid averaged over the lateral coordinates at a fixed coordinate z, respectively. The area fraction of iron oxide max can be expressed as XIO (z) = XIO (1 − z2 /r 2 ), which is max parabolic in nature. XIO , the area fraction at the center of the sphere z = 0 is the maximum value of area fraction of iron oxide, which contributes to the total nSLD value in the middle layer. Consequently the area fraction XIO vanishes at z = ±r, where r is the radius of the spherical iron oxide NP and d = 2r is the thickness of the iron oxide layer. This ideal nSLD profile is smeared out because of NP size distribution, uncertainties in NP positioning and packing defects, giving rise to an effective roughness at the interfaces. The roughness can be approximated by a Debye–Waller like factor. We used the Parratt [30] super-recursion scheme [43] for fitting the data, taking into account the neutron spin states. The reflectance at each interface is modified due to the roughness, which was incorporated in the fitting model according to the N´evot–Croce ansatz [29].
Figure 8. Nuclear (top) and magnetic (bottom) profiles obtained from the fitting of data in figure 5. z = 0 corresponds to the top layer and positive z-direction represents the SLD towards the silicon substrate.
the magnetic depth profiles from the same scans. Here the model discussed is similar to the one reported by Mishra et al [25]. Each NP layer is subdivided into three layers consisting of top oleic acid layer (OLA1), middle NP core layer and bottom oleic acid layer (OLA2) as sketched in figure 7. The z dependence of the nSLD for an ideal spherical NP in the trilayer model is shown in figure 7 right hand panel. The NP nSLD follows a parabolic shape, which is represented by the following equation. NbIO/OLA (z) = N bIO × XIO (z) + N bOLA × XOLA (z),
3.3.2. Nuclear SLD. Figures 8 and 9 show the nuclear and magnetic SLD profiles as obtained from fitting of the data in figures 5 and 6, respectively. In both cases the data are well described by a model taking into account one complete NP layer at the substrate and an additional incomplete layer with reduced SLDs on top. Such reduction is due to the fact that the top layer forms islands as seen in the SEM images of figure 1, and that the lateral dimension of the islands is smaller than the coherence length of the neutrons. One can also recognize an additional surfactant layer with low SLD between the NP core layer and either silicon, or vanadium.
(4)
where NbIO is the nominal nSLD of iron oxide, N bOLA is the nominal nSLD of oleic acid, XIO (z) = XIO (x, y)lateral and XOLA (z) = 1 − XIO (z) are the area fractions of iron oxide 6
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However, the SLD profile for NPs deposited onto silicon does not reveal an intermediate layer with low SLD between the complete NP core layer and the incomplete top NP layer. Such intermediate layer is clearly seen in figure 9. Also, previously no intermediate layer could be discerned via XRR [25] from the same sample. This fact, as well as smaller overall thickness of the NP bi-layer on Si substrate, indicates that NPs on Si are more closely packed than NPs deposited onto metallic vanadium. In the latter case the top incomplete layer is less ordered, while in the former case top NPs occupy positions between NPs of the base core layer. Note that the vanadium layer in figure 9 has a negative nSLD, a thickness of 50.8 nm and a roughness of 2.1 nm as obtained from the fitting. This is followed by the Al2 O3 substrate with the highest nSLD and roughness of 1.5 nm. The volume fraction of NPs in a layer can be calculated by using the equation: XIO =
N bIO/OLA − N bOLA N bIO − N bOLA
competing dipole interaction between different pairs of NPs in a 2D lattice. Interestingly, the magnetic induction of NP layer on the vanadium film is B ≈ 0.2 T, which is close to what is estimated from the NP concentration and the magnetite saturation induction. This supports the hypothesis of the role of frustration which should be less pronounced when the interparticle distance increases. The profiles of mSLD are identical at high fields and at remanence and therefore we show here only one of them. The non-zero mSLD in remanence is surprising because the hysteresis curve at room temperature (figure 3(b)) does not show remanent magnetization at zero field. In fact, there is no splitting of reflectivities for up and down polarizations in remanence, clearly showing a demagnetized state over the macroscopic area. But the positions of the critical edges of the total reflection and hence mSLD values at high field and at remanence are almost identical. This contradicting feature can be understood if the parameter cγ = cos γ lateral and the concept of coherence ellipsoid are considered [43] in the fitting routine. The projection onto parameter cγ provides the magnetization M the Y -axis, while an additional parameter sγ2 = sin2 γ lateral accounts for the magnetization projection onto the X-axis and gives rise to SF scattering.
(5)
which immediately follows from equation (4), and the nominal values of nSLD NbIO = 6.91 × 10−6 Å−2 for iron oxide, NbOLA = 0.078 × 10−6 Å−2 for oleic acid, and the effective SLDs values determined by the fit. For the NP layer deposited onto the bare silicon substrate the core layer SLD N bIO/OLA = 4.6 × 10−6 Å−2 is found to be in excellent agreement with the value earlier determined [25] for a multilayer consisting of 5 NP layers deposited onto a silicon wafer. In accordance with equation (5) this gives the volume fraction of magnetite in the core layer of 65%. In case of deposition onto the vanadium layer N bIO/OLA = 2.2 × 10−6 Å−2 , and the volume fraction of iron oxide is of only 32%, showing that NPs are less densely packed in the layer, which is appreciably smeared out due to blurred interfaces between the NP layers. The nature of some swelling of the NP monolayer deposited onto a metallic sub-layer is not clear, but one may speculate on the role of diamagnetic currents induced by thermal fluctuations of the NP magnetic moments. Then the interaction between those currents and moments may lead to a repulsion in an analogy with the Casimir effect [9].
4. Discussions
The magnetic configuration of magnetic NPs is quite unique. When high fields are applied, the NPs are expected to be aligned along the field direction and the mean SLD over different coherence ellipsoids are nearly identical. That means an incoherent averaging over all coherence ellipsoids is trivial and leads to the model intensity: see equation (3). But at remanence the situation becomes more complex. Two distinct cases have to be distinguished. First, the average mSLD over each ellipsoid may be zero due to complete randomness in directions of the NP magnetic moments. In the second scenario the superspins are collinear within each coherence ellipsoid, but are random over the total illuminated area. In both cases the net magnetization will be zero and the NSF reflectivities will be unsplit, i.e. R ++ R −− . The second scenario may lead to SF reflectivity and can be measured by analyzing the polarization of the reflected beam. This has indeed been performed for our case, but no significant SF intensity was observed within the finite accuracy of the polarization analysis. This means that the mean value sγ2 = sin2 γ lateral ≈ 0, i.e. the magnetization vector within each of the coherence ellipsoids is almost collinear with the polarization axis, and hence γ ≈ 0, or γ ≈ π . Such a situation corresponds to the case of domains separated by 180◦ domain walls recently observed [41] by Lorentz microscopy and electron holography in dipolar ferromagnetic phase of Fe3 O4 nanoparticle arrays. These domain walls separate domains in which the magnetization is directed along with, or opposite to, the direction of external field formerly applied to the sample. If both types of domains are equally populated, then cγ = 0. Alternatively, cγ determines the population of one or the other type of domains and hence the net magnetization is finite.
Next we consider the variation of the mSLD, which provides detailed insight into the magnetic correlation in a monolayer system at the microscopic level. The mSLD profiles for high fields and for remanence are shown in figures 8 (b) and 9(b). For the NP monolayer on the Si substrate the magnetic induction of the core iron oxide layer is B ≈ 0.28 T, i.e. it is more than a factor of two smaller bulk ≈ 0.6 T of bulk magnetite. than the saturation induction Bsat The magnetic induction can be calculated from the following equation: B = µ0 M, where µ0 is the permeability of free space, M = CNp is the magnetization, the conversion factor C ≈ 344 according to [39], and Np is the magnetic SLD obtained from the fitting. The layer induction is still 25% lower than the value B ≈ 0.4 T which one can expect due to the volume fraction of iron oxide in the NP core layer. Similar reduction observed earlier [25] was ascribed to the frustration effect caused by 3.3.3. Magnetic SLD.
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From fitting we obtain that the value of cγ is 0.7 at 2 kOe, whereas it is 0.3 at remanence. From this we infer that at high fields some of the NPs are oriented along the field direction, although full saturation is not achieved, as already noted [25]. The sample is only 70% saturated. So even at relatively high fields there exist microscopic areas, where the NP magnetic moments deviate from the applied field direction. The smaller value of 30% magnetization at remanence indicates that the sample probably is divided into microscopic regions, or quasidomains, where magnetic moments are antiparallel to those in the adjacent region. The non-zero mSLD at remanence also implies that a finite magnetization persists over the coherence ellipsoid. The area of these correlated regions are of the order of dozens of micrometers and greater than the coherence ellipsoid. Therefore, we do not observe any offspecular scattering from quasi-domains. On the other hand, individual NPs are too small and therefore scatter at high angles inaccessible in reflectivity measurements, but can be seen in small angle scattering at grazing incidence [25, 26]. The physical origin of enhanced correlations between NPs, forming quasi-domains, comes from pure dipolar coupling. The dipolar coupling amongst the NPs is relatively strong and can be estimated from the following relationship [7]: Udd ≈
m2 , 4πµ0 r 3
high magnetic field is applied, the superspins in single domain NPs act as magnetic dipoles, which align along the field axis according to the classical Langevin function [8], overcoming the thermal energy. Once the field is removed, dipolar coupling among the NPs becomes dominant, suppressing thermal fluctuations and supporting long range ferromagnetic correlations. The net magnetization resulting from such correlations, however, vanishes when averaged over the entire surface, and the sample enters a partially demagnetized state with magnetic flux closed via large quasi-domains. The nanoparticle monolayer, as well as the multilayer studied earlier [25], resembles a soft superferromagnet, which is formed due to dipolar coupling only. The distinction between a superspin glass and superferromagnet behavior from PNR measurement is not trivial. In conclusion, we prepared hexagonal close-packed iron oxide NP monolayer films on silicon substrates and on vanadium films via spin-coating. The vanadium films are sputtered on sapphire substrate. Both types of NP monolayers can be measured with polarized neutron reflectivity with reasonable statistics, which allows for further quantitative analysis. Complete fits to all four NSF and SF reflectivities reveal the microscopic magnetic states in the NP monolayers at high fields and at remanence. After exposing the magnetic nanoparticles to high magnetic field, the dipolar coupling starts to dominate over the thermal energy and gives rise to long range magnetic order resembling a soft superferromagnetic state even at remanence. The NP self-assembly after spin coating on Si and Al2 O3 /V substrates shows remarkable differences. On the latter substrate the NPs are less densely packed in the layer than on the former substrate.
(6)
where, m = µ0 V Ms is the magnetic moment of the N P , V = 4/3π a 3 is the volume of the NP of radius a, Ms is the saturation magnetization of the material, µ0 is the permeability of vacuum, and r is the distance between the dipoles. For magnetite NPs Ms is 4.8 × 105 Am−2 (the value taken from [15]) and for a radius of 9 nm and a dipole to dipole distance of 20 nm the dipolar energy corresponds to a thermal energy of 1942 K, which is the ordering temperature for purely dipolar interacting NPs. Such a high dipolar ordering temperature can lead to enhanced magnetic order spanning several NPs and hence gives rise to finite mSLD even at remanence and at room temperature. We can neglect the possibility of any exchange interaction as the NPs are separated by an oleic acid shell. At remanence the dipolar coupling dictates the spin arrangement in the monolayer, within which the superspins of the NPs are correlated. Quasi-domains formed in remanence differ from normal domains in ferromagnets in many aspects. First, they form due to dipolar or higher pole interactions unlike exchange interaction and anisotropy. Second, the origin of domain walls [41] is very different. In ferromagnets domain walls develop in order to reduce the magnetic field energy and the magnetic domain wall width is determined by the competition between exchange interaction and crystal anisotropy. But for dipolarly coupled systems the driving mechanism for domain wall formation is mainly entropy. The assumption that the magnetization stays in-plane and the magnetic flux line closes only in the same layer probably holds good.
Acknowledgments
We would like to acknowledge Mrs S Erdt-B¨ohm for preparing the vanadium films. DM would like to acknowledge a scholarship from NRW Research School on Bio- and Nanosciences. Financial support from BMBF project 05K10PC1 (SuperADAM) is also gratefully acknowledged. References [1] Bader S D 2006 Colloquium: opportunities in nanomagnetism Rev. Mod. Phys. 78 1 [2] Bedanta S, Barman A, Kleemann W, Petracic O and Seki T 2013 Magnetic nanoparticles: a subject for both fundamental research and applications J. Nanomater. 2013 952540 [3] Bedanta S, Eim¨uller T, Kleemann W, Rehnsius J, Stromberg F, Amaladass E, Cardoso S and Freitas P P 2007 Overcoming the dipolar disorder in dense CoFe nanoparticle ensembles: superferromagnetism Phys. Rev. Lett. 98 176601 [4] Bedanta S and Kleemann W 2009 Supermagnetism J. Phys. D: Appl. Phys. 42 013001 [5] Bedanta S et al 2010 Single-particle blocking and collective magnetic states in discontinuous CoFe/Al2 O3 multilayers J. Phys. D: Appl. Phys. 43 474002 [6] Benitez M J, Mishra D, Szary P, Badini G A, Feyen M, Lu A H, Agudo L, Eggeler G, Petracic O and Zabel H 2011 Structural and magnetic characterization of self-assembled iron oxide nanoparticle arrays J. Phys.: Condens. Matter 23 126003
5. Summary and conclusion
In a nutshell, individual magnetic NPs in absence of a magnetic field follow a N´eel–Brown like thermal fluctuation. When a 8
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[26] Mishra D, Greving D, Badini G A, Perlich J, Toperverg B P, Zabel H and Petracic O 2014 Growth modes of nanoparticle superlattice thin films Nanotechnology 25 205602 [27] Mishra D 2012 Structural and magnetic characterization of self-assembled magnetic nanoparticles PhD Thesis Ruhr-University Bochum [28] Mørup S, Madsen M B, Franck J, Villadsen J and Koch C J W 1983 A new interpretation of M¨ossbauer spectra of microcrystalline goethite: super-ferromagnetism or supe-spin-glass behaviour? J. Magn. Magn. Mater. 40 163 [29] N´evot L and Croce P 1980 Caract´erisation des surfaces par r´eflexion rasante de rayons x. application a` l´etude du polissage de quelques verres silicates Rev. Phys. Appl. 15 761 [30] Parratt L G 1954 Surface studies of solids by total reflection of x-rays Phys. Rev. 95 359 [31] Peng S, Lei C, Ren Y, Cook R E and Sun Y 2011 Plasmonic/magnetic bifunctional nanoparticles Angew. Chem. Int. Edn 50 3158 [32] Petracic O 2010 Superparamagnetic nanoparticle ensembles Superlatt. Microstruct. 47 569 [33] Petracic O, Chen X, Bedanta S, Kleemann W, Sahoo S, Cardoso S and Freitas P P 2006 Collective states of interacting ferromagnetic nanoparticles J. Magn. Magn. Mater. 300 192 [34] Politi P and Pini M G 2002 Dipolar interaction between two-dimensional magnetic particles Phys. Rev. B 66 214414 [35] Puntes V F, Gorostiza P, Aruguete D M, Bastus N G and Alivisatos A P 2004 Collective behaviour in two-dimensional cobalt nanoparticle assemblies observed by magnetic force microscopy Nat. Mater. 3 263 [36] Russier V 2001 Calculated magnetic properties of two-dimensional arrays of nanoparticles at vanishing temperature J. App. Phys. 89 1287 [37] Russier V, Petit C, Legrand J and Pileni M P 2000 Collective magnetic properties of cobalt nanocrystals self-assembled in a hexagonal network: theoretical model supported by experiments Phys. Rev. B 62 3910 [38] Scheinfein M R, Schmidt K E, Heim K R and Hembree G G 1996 Magnetic order in two-dimensional arrays of nanometer-sized superparamagnets Phys. Rev. Lett. 76 1541 [39] Theis-Br¨ohl K, Wolff M, Ennen I, Dewhurst C D, H¨utten A and Toperverg B P 2008 Self-ordering of nanoparticles in magneto-organic composite films Phys. Rev. B 78 134426 [40] Walz F 2002 The verwey transition: a topical review J. Phys.: Condens. Matter 14 R285–R340 [41] Yamamoto K, Hogg C R, Yamamuro S, Hirayama T and Majetich S A 2011 Dipolar ferromagnetic phase transition in Fe3 O4 nanoparticle arrays observed by Lorentz microscopy and electron holography Appl. Phys. Lett. 98 072509 [42] Zabel H 1994 X-ray and neutron reflectivity analysis of thin films and superlattices Appl. Phys. A 58 159 [43] Zabel H, Theis-Br¨ohl K and Toperverg B P 2007 Polarized Neutron Reflectivity and Scattering from Magnetic Nanostructures and Spintronic Materials (Handbook of Magnetism and Advanced Magnetic Materials vol 3) ed H Kronm¨uller and S Parkin (New York: Wiely) [44] Zhernenkov K, Gorkov D, Toperverg B P and Zabel H 2013 Frequency dependence of magnetization reversal in thin Fe(1 0 0) films Phys. Rev. B 88 020401
[7] Bishop K J M, Wilmer C E, Soh S and Grzybowski B A 2009 Nanoscale forces and their uses in self-assembly Small 5 1600 [8] Blundell S 2007 Magnetism in Condensed Matter (Oxford: Oxford University Press) [9] Bordag M, Mohideen U and Mostepanenko V M 2001 Advances in the casimir effect Phys. Rep. 353 1 [10] Cowburn R P, Adeyeye A O and Welland M E 1999 Controlling magnetic ordering in coupled nanomagnet arrays New J. Phys. 1 16.1 [11] Devishvili A, Zhernenkov K, Dennison A J C, Toperverg B P, Wolff M, Hj¨orvarsson B and Zabel H 2013 Super Adam: upgraded polarized neutron reflectometer at the Institut Laue-Langevin Rev. Sci. Instrum. 84 025112 [12] Disch S, Wetterskog E, Hermann R P, Salazar-Alvarez G, Busch P, Br¨uckel T, Bergstr¨om L and Kamali S 2011 Shape induced symmetry in self-assembled mesocrystals of iron oxide nanocubes Nano Lett. 11 1651 [13] Disch S, Wetterskog E, Hermann R P, Wiedenmann A, Vainio U, Salazar-Alvarez G, Bergstr¨om L and Br¨uckel Th 2012 Quantitative spatial magnetization distribution in iron oxide nanocubes and nanospheres by polarized small-angle neutron scattering New J. Phys. 14 013025 [14] Dong A, Ye X, Chen J and Murray C B 2011 Two-dimensional binary and ternary nanocrystal superlattices: the case of monolayers and bilayers Nano Lett. 11 1804 ¨ ¨ 1997 Rock Magnetism [15] Dunlop D J and Ozdemir O (Cambridge: Cambridge University Press) chapter 3 ¨ [16] Ewerlin M, Demirbas D, Br¨ussing F, Petracic O, Unal A A, Valencia S, Kronast F and Zabel H 2013 Magnetic dipole and higher pole interaction on a square lattice Phys. Rev. Lett. 110 177209 [17] Hauschild J, Elmers H J and Gradmann U 1998 Dipolar superferromagnetism in monolayer nanostripes of Fe(1 1 0) on vicinal W(1 1 0) surfaces Phys. Rev. B 57 R667 [18] Kechrakos D and Trohidou K N 1998 Magnetic properties of dipolar interacting single-domain particles Phys. Rev. B 58 12169 [19] Kiessig H 1931 Interferenz von R¨ontgenstrahlen an d¨unnen Schichten Ann. Phys. 10 769 [20] Kleemann W, Petracic O, Binek Ch, Kakazei G N, Pogorelov Yu G, Sousa J B, Cardoso S and Freitas P P 2001 Interacting ferromagnetic nanoparticles in discontinuous Co80 Fe20 /Al2 O3 multilayers: from superspinglass to reentrant superferromagnetism Phys. Rev. B 63 134423 [21] Laurent S, Forge D, Port M, Roch A, Robic C, Vander Elst L and Muller R N 2008 Magnetic iron oxide nanoparticles: synthesis, stabilization, vectorization, physicochemical characterizations, and biological applications Chem. Rev. 108 2064 [22] Luttinger J M and Tisza L 1946 Theory of dipole interaction in crystals Phys. Rev. 70 954 [23] Majetich S A, Wen T and Booth R A 2011 Functional magnetic nanoparticle assemblies: formation, collective behavior, and future directions ACS Nano 5 6081 [24] Marlow F, Muldarisnur, Sharifi P, Brinkmann R and Mendive C 2009 Opals: status and prospects Angew. Chem. Int. Edn 48 6212 [25] Mishra D et al 2012 Self-assembled iron oxide nanoparticle multilayer: x-ray and polarized neutron reflectivity Nanotechnology 23 055707
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Polarized neutron reflectivity from monolayers of self-assembled magnetic nanoparticles
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 136001 (9pp)
doi:10.1088/0953-8984/27/13/136001
Polarized neutron reflectivity from monolayers of self-assembled magnetic nanoparticles ¨ 4, D Mishra1 , O Petracic1,2 , A Devishvili1,3 , K Theis-Brohl B P Toperverg1,5 and H Zabel1,6 1
Institute for Experimental Condensed Matter Physics, Ruhr-University Bochum, D-44780 Bochum, Germany 2 J¨ulich Centre for Neutron Science JCNS and Peter Gr¨unberg Institut PGI, JARA-FIT, Forschungszentrum J¨ulich GmbH, 52425 J¨ulich, Germany 3 Institut LaueLangevin, BP 156, F-38042 Grenoble, France 4 University of Applied Sciences Bremerhaven, D-27568 Bremerhaven, Germany 5 Petersburg Nuclear Physics Institute, Gatchina 188300, St Petersburg, Russia 6 Johannes Gutenberg-Universit¨at Mainz, D 55099 Mainz, Germany E-mail: [email protected] Received 26 November 2014, revised 7 February 2015 Accepted for publication 11 February 2015 Published 13 March 2015 Abstract
We prepared monolayers of iron oxide nanoparticles via self-assembly on a bare silicon wafer and on a vanadium film sputter deposited onto a plane sapphire substrate. The magnetic configuration of nanoparticles in such a dense assembly was investigated by polarized neutron reflectivity. A theoretical model fit shows that the magnetic moments of nanoparticles form quasi domain-like configurations at remanence. This is attributed to the dipolar coupling amongst the nanoparticles. Keywords: magnetic nanoparticles, iron oxide, self assembly, polarized neutron reflectivity (Some figures may appear in colour only in the online journal)
spin freezing, superspin glass (SSG) and superferromagnetic (SFM) states [2, 4, 32]. The detailed nature of the SFM state is still not well understood. Various explanations have been proposed. The SFM state was observed in a number of systems for e.g. microcrystal goethite [28], discontinuous metal insulator multilayers of CoFe and Al2 O3 [3], and dense packing of Co NPs [35]. In most of these cases the ferromagnetic state develops due to exchange interaction, rather than dipolar interaction. Although some theoretical and experimental evidence suggests that dipolar coupling can lead to a SFM state [10, 17, 18, 20, 34, 38, 41], certain other theoretical considerations [22, 37], on the contrary, suggest that point-like dipoles in two and three dimensions lead to antiferromagnetic ordering. The magnetic ground state and hence the magnetic ordering can be affected by various other factors, namely, the crystal symmetry, the nature of close packing or the spatial ordering of NPs and higher multipole (quadrupole, octopole) interactions [12, 13, 16, 36]. These
1. Introduction
Magnetic nanoparticles (NPs) are promising for application in numerous fields e.g. spintronics [1, 14, 23], photonics [24], plasmonics [31] and bio-medicine [21]. Self-assembly of NPs into ordered structures is particularly interesting, as they exhibit novel physical properties. These properties are unique and are completely different from individual NP properties. In most cases the physical attributes are manifested by the unique structure that can be achieved in self-assembly. For example, individual magnetic NPs can be superparamagnetic (SPM) in nature. Each NP is in a single domain state known as superspin and exhibits thermal fluctuations. However, closely packed NPs show collective behavior due to interaction amongst these superspins. The most dominant interaction in the case of SPM NPs is the dipolar coupling. Depending on the type and strength of the interaction, new collective states can be observed, in particular a modified SPM state, glass like 0953-8984/15/136001+09$33.00
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factors are determined by the non-spherical nature and the irregular structure of the NPs. We report here the observation of an SFM domain-like structure arising in a hexagonally close-packed iron oxide NP monolayer via polarized neutron reflectivity (PNR). We would like to emphasize two points: one is the magnetic dipolar coupling which leads to enhanced magnetic correlations by suppressing thermal fluctuations; the second is the sensitivity of polarized neutron reflectivity (PNR) to specific details of the structural and magnetic arrangement over the NP monolayer. There are various other techniques to scrutinize the magnetic state in interacting NPs like M¨ossbauer spectroscopy [28], a.c. magnetic susceptibility measurement [33], magnetic force microscopy [35], x-ray photoemission electron microscopy [3], electron holography, and Lorentz microscopy [41]. However, due to specific coherence properties of the neutron beam impinging onto the layered systems at grazing incidence, the scope of information delivered by PNR experiment is unique [5, 39, 42, 43]. In particular, in our recent studies [25] carried out on a set of multilayers formed by magnetite NPs spin coated onto a silicon wafer it was demonstrated that magnetization in remanence is decomposed into a set of lateral ‘quasi-domains’ hence supporting the assumption of a super-ferromagnetic state of the system. Here we show the capability of PNR extended to single NP layers, also revealing magnetic domainlike correlations among the NPs. These results confirm a true 2D character of the super-ferromagnetic ordering in a close packed 2D structure of super-spins coupled via dipole–dipole interaction. The paper is organized as follows. In section 2 we describe the sample preparation, in section 3 we present PNR measurements and in section 4 we discuss results, followed by a summary and conclusion in the last section 5.
evacuated to the desired pressure and then inserted into a tubular furnace pre-heated to 230 ◦ C. The annealing was done for 30 min and then the quartz tube was removed from the furnace. The sample was kept under vacuum all the time till cooling down to room temperature. After this procedure we obtained magnetite as the prevailing phase [6]. Since the unannealed NPs consist of antiferromagnetic wustite as the major phase, this actually helps in obtaining a better selfassembly in the spin-coating process. For as-prepared NPs with smaller diameters, maghemite or magnetite are the major phases and lead to an agglomeration due to strong dipolar interaction. Even for cobalt NPs this is also valid. Hence the best close-packed hexagonal structure obtained was for the 18 nm diameter antiferromagnetic iron oxide, which was converted to magnetite afterwards by annealing. Amongst all the iron oxides, magnetite has the highest magnetization and is ferrimagnetic in nature [15]. It should be mentioned here that the Van der Waals interaction between NP–NP and NP-substrate mediated via toluene solvent is quite small compared to the magnetic dipolar interaction for iron oxide NPs (magnetite or maghemite). The Van der Waals force is of the order of 100 K compared to the magnetic dipole–dipole interaction, which is of order 3000 K for the same size of NPs and similar distances. Therefore the Van der Waals force plays an insignificant role in the selfassembly process and agglomeration [27]. Figure 1 shows scanning electron microscope (SEM) images of the NP film spin-coated on the vanadium film taken from two different regions ((a) and (b)) of the sample and from NP spin-coated onto a bare Si substrate with two different magnifications ((c) and (d)). The NPs are arranged in hexagonal close-packed structure over the entire surface, which was achieved by the spin-coating method. Some parts show two complete layers (figure 1(b)) and some parts show 1– 1.3 layers (figure 1(a)) of NPs. Similar features are observed in the SEM images of NPs deposited directly onto Si substrate, as can be seen in figure 1(c).
2. Sample preparation and characterization 2.1. Sample preparation
We used chemically synthesized iron oxide NPs of 18 nm diameter with 6.5% size distribution purchased from Ocean Nanotech. The NPs are coated with an oleic acid shell and are dispersed in toluene solvent. The preparation and characterization of the samples are reported elsewhere [6]. For comparison we used two different substrates in order to probe the influence of the substrate on the NP ordering [26]. In the standard procedure we used a silicon (Si) substrate covered by its natural oxide. In addition, we prepared a sample with a 50 nm thick vanadium (V) film rf sputtered onto a sapphire (Al2 O3 ) wafer and the NP dispersion was spin-coated on top of the V film. The NP dispersion was diluted in toluene with a 1:1 volume ratio and then spin-coated on the substrates at 2000 revolutions per minute for 30 s. Then the samples were heat treated on a hot plate at 80 ◦ C in air for 20 min to evaporate the solvent. In the next step the antiferromagnetic iron oxide (wustite) NPs were annealed in an evacuated quartz tube at a pressure of 3 × 10−3 mbar. The quartz tube was first
2.2. X-ray reflectivity
X-ray reflectivity (XRR) measurements were performed to verify the quality of the samples. The XRR measurements were performed in-house using a rotating anode machine, with Cu Kα radiation. Figure 2 shows the XRR measurements of the sapphire (Al2 O3 ) substrate coated with a vanadium film before and after spin-coating with NPs and annealing in vacuum. The sputtered vanadium film on sapphire substrate shows Kiessig oscillations [19] corresponding to a thickness of 51 nm. The well resolved Kiessig fringes are observed up to a qz value of 3.5 nm−1 . On the contrary, after spin-coating the NPs and annealing, the surface becomes less reflective. The thickness of the vanadium layer does not change, but the Kiessig fringes die out rapidly. Two critical angles corresponding to the NPs and to the vanadium film are also clearly visible. XRR data obtained for the NP monolayer deposited directly onto the silicon substrate are reported elsewhere [25]. 2
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Figure 1. SEM images of spin-coated NPs on vanadium and silicon substrates. (a) and (b) Images of NPs spin-coated on vanadium from two different regions. (c) and (d) Images of NPs spin-coated on Si at different magnification. The digitally zoomed-in image (d) shows a clear hexagonal arrangement of NPs as indicated by the hexagon drawn on it.
magnetometer. The sample measured by SQUID is a monolayer spin-coated onto the silicon substrate. However, the magnetic behavior is found to be similar, irrespective of the substrate used. The magnetization versus temperature plot (figure 3(a)) under zero field cooling (ZFC) and field cooling (FC) procedure shows that the monolayer is not in a blocked state at room temperature. The blocking temperature is 260 K. The step at 110 K in both the FC and ZFC magnetization curves is due to the Verwey transition [40], and is another strong indication for the presence of magnetite in our sample after annealing. The hysteresis plot in figure 3(b) measured at room temperature shows a typical SPM-like behavior with close to zero remanence and very low coercivity. The inset shows an enlargement of the low field region. 3. Polarized neutron reflectivity Figure 2. XRR measurements of vanadium film sputtered on
3.1. Scattering geometry
sapphire substrate (triangles) and after spin-coating NPs and annealing them in vacuum (circles). The reflectivities are offset with respect to each other by two orders of magnitude for clarity.
The PNR measurements were performed at the Super ADAM reflectometer stationed at the Institut Laue–Langevin (ILL), Grenoble, France [11]. The wavelength of neutrons selected by a HOPG monochromator was 0.441 nm, which corresponds to an energy of 4.22 meV or an equivalent temperature of 48.83 K. The incident polarization efficiency was about 98%.
2.3. Magnetization measurements
The magnetic characterization was performed with a superconducting quantum interference device (SQUID) 3
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Figure 4. Geometry of the PNR measurement. The incident and exit wave vectors are ki and kf , respectively, determined by incident and reflected angles of αi and αf with qz as the scattering vector. In the Cartesian axes the magnetic field H is directed along the Y -axis is the magnetization collinear with the neutron polarization axis. M vector, which may be tilted by an angle γ with respect to the Y -axis.
make an angle γ with the Y -axis. Then the Y -component, My = M cos γ , contributes to the NSF scattering (R ++ , R −− ), and the X-component, Mx = M sin γ , of the magnetization vector contributes to the SF scattering (R +− , R −+ ), even though the net magnetization of the sample, which is averaged over the whole surface, may be directed along the Y -axis [43]. The model reflectivities are captured in the following set of equations [43, 44]: 1 R ++ = (1) |R+ (1 + cos γ ) + R− (1 − cos γ )|2 4
Figure 3. (a) Magnetization versus temperature measurement under ZFC (solid circles) and FC (open circles) for monolayer of NPs annealed at 230 ◦ C in vacuum. The kink at 110 K is due to the Verwey transition and marks the presence of magnetite in the nanoparticles. (b) Hysteresis loop measured at room temperature. The inset shows a magnified plot at remanence.
R −− =
1 |R+ (1 − cos γ ) + R− (1 + cos γ )|2 4
(2)
1 (3) |R+ − R− |2 sin2 γ , 4 valid for ideal polarization Pi = Pf = 1, and where R+ and R− are the reflection amplitudes for two neutron spin states. The reflection amplitude appears due to scattering from the coherence ellipsoid and represents the average nuclear and magnetic scattering length density (nSLD and mSLD) over the ellipsoid. The coherence ellipsoid originates from the three dimensional resolution function defined by the beam divergence and uncertainty in angles of neutron detection [43]. The resolution function is convoluted to the reflectivity and the resultant intensity is fitted. The coherence ellipsoid is highly anisotropic in nature due to the slit configuration and grazing incidence. As shown in figure 4 it extends over a few dozens of micrometers along the X-axis and a few nanometers along the Y - and Z-axes. We used a slit of width 1 mm (X-direction) and several mm in height (Y -direction). That gives relaxed resolution in the Y -direction and about 10–50 µm resolution along the X-axis. Correspondingly, the coherence area illuminated in our case is a few nm along the Y and Z direction and about 10–50 µm along the X direction, which corresponds to a Qx resolution of R +− = R −+ =
The polarization of the reflected beam was analyzed with an efficiency of about 99%. Four reflectivities were recorded with a position sensitive 3 He detector (PSD): two non spin flip, R ++ , R −− (NSF) and two spin flip, R +− , R −+ (SF). All the measurements were carried out at room temperature. First, the reflectivities were recorded at an applied field of 2 kOe or 5 kOe. In remanence a guiding field of 6 Oe was applied to maintain the neutron polarization along the same direction as in the high field case. The geometry of the experiment is shown in figure 4. Incident neutrons with wave vector ki impinge at a glancing angle αi onto the sample surface. The reflected neutrons have a wave vector kf , scattered at an angle αf . For specular scans αi = αf and qz is the scattering vector. The coherence ellipsoid subtended by the neutron waves are also shown in this figure. The dotted lines represent the three different axes, ly , lz lx , of the coherence ellipsoid along three different cartesian axes. The neutron polarization is directed along with, or opposite to, the Y -axis which is set collinearly with averaged over the external field H . The magnetization M one of the coherence ellipsoids indicated in the figure may 4
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(a)
Figure 5. PNR measurements at high field of 5 kOe from a NP monolayer deposited directly onto a silicon wafer. All four reflectivities: two NSF (R++ , R−− ) and two SF (R+− , R−+ ) are displayed, together with the fits shown by solid lines.
(b)
about ∼10−3 –10−4 nm−1 . The component along the Z-axis gives rise to thickness oscillations. This provides the lateral resolution and the average mSLD value over the ellipse. The coherence ellipsoid spans a very small part of the total illuminated area and hence the reflectivity can be calculated by taking an incoherent average over the total illuminated area. In case of homogeneous samples the situation is trivial as the neutrons are scattered homogenously from all coherence ellipsoids, and the final intensity is an incoherent sum of intensities from all coherence ellipsoids.
Figure 6. PNR measurements from a NP/V/Al2 O3 heterostructure: (a) at high field of 2 kOe and (b) at remanence, respectively. All four reflectiviies: two NSF (R++ , R−− ) and two SF (R+− , R−+ ) are displayed, together with the fits shown by solid lines.
3.2. PNR measurements
Figure 5 shows PNR data collected from the NP monolayer deposited directly onto a silicon wafer and subjected to 5 kOe magnetic field, while figures 6(a) and (b) present PNR results obtained from the NP/V/Al2 O3 heterostructure at high fields of 2 kOe and at remanence, respectively, along with fits to the data points (solid lines). All scans were performed at room temperature. The NP covered layers are intrinsically rough due to the spherical shape of the NPs. Nevertheless, the small size distribution of our NPs and their uniform coating results in only a small roughness variation over the entire surface and gives rise to specular reflection from the sample. It shows that a simple spin-coating process may produce rather well defined monolayers, albeit containing islands and defects as seen in the SEM images. The effects of the latter are seen in figures 5 and 6 as smearing of the critical edges for total reflection, as well as by the fast damping of the Kiessig fringes at high wave vector transfer qz = (4π/λ) sin α. In fact, only two NP layer thickness oscillations are visible in figure 5, while faster oscillations in figure 6 are mostly due to the 500 Å vanadium film on the Si substrate. Surprisingly, no SF scattering was observed other than that due to imperfect spin polarizing and analyzing efficiencies. From this we infer that the mean magnetization averaged over the coherence volume is either well collinear with the Y -axis in figure 4, or equal to zero. On the other hand, at high fields one
can clearly recognize in figure 5 a small spin splitting between the critical edges of the total reflection for two NSF curves. Such splitting is harder to recognize in figure 6(a), but it still can be observed in the amplitudes of the thickness oscillations. Both effects unambiguously indicate a finite magnetization in both samples. At remanence the splitting in figure 6(b) almost vanishes, showing that the sample at low fields approaches a demagnetized state. 3.3. PNR fitting results Fitting scheme. More details on the microscopic arrangement of magnetic states become available via fitting of the data to theoretical models. But before delving into that we will first explain the fitting routine in some more detail. Fitting of the data in figure 5 was performed by use of a three layer model, while the best fit of data in figure 6 assumes a five layer model excluding the substrate. All four reflectivities, SF and NSF, in each case were fitted simultaneously by varying the nuclear scattering length density (nSLD or N b) and the magnetic scattering length density (mSLD or Np), the layer thicknesses and the interfacial roughnesses. Here PNR exposes another advantage compared to other experimental techniques, since one can retrieve the structural, as well as
3.3.1.
5
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(a)
Figure 7. Model for the reflectivity fit. The right panel shows the parabolic nuclear SLD profile.
(b)
(a)
Figure 9. Same as in figure 8, but for the sample with the vanadium sublayer on sapphire.
(b)
and oleic acid averaged over the lateral coordinates at a fixed coordinate z, respectively. The area fraction of iron oxide max can be expressed as XIO (z) = XIO (1 − z2 /r 2 ), which is max parabolic in nature. XIO , the area fraction at the center of the sphere z = 0 is the maximum value of area fraction of iron oxide, which contributes to the total nSLD value in the middle layer. Consequently the area fraction XIO vanishes at z = ±r, where r is the radius of the spherical iron oxide NP and d = 2r is the thickness of the iron oxide layer. This ideal nSLD profile is smeared out because of NP size distribution, uncertainties in NP positioning and packing defects, giving rise to an effective roughness at the interfaces. The roughness can be approximated by a Debye–Waller like factor. We used the Parratt [30] super-recursion scheme [43] for fitting the data, taking into account the neutron spin states. The reflectance at each interface is modified due to the roughness, which was incorporated in the fitting model according to the N´evot–Croce ansatz [29].
Figure 8. Nuclear (top) and magnetic (bottom) profiles obtained from the fitting of data in figure 5. z = 0 corresponds to the top layer and positive z-direction represents the SLD towards the silicon substrate.
the magnetic depth profiles from the same scans. Here the model discussed is similar to the one reported by Mishra et al [25]. Each NP layer is subdivided into three layers consisting of top oleic acid layer (OLA1), middle NP core layer and bottom oleic acid layer (OLA2) as sketched in figure 7. The z dependence of the nSLD for an ideal spherical NP in the trilayer model is shown in figure 7 right hand panel. The NP nSLD follows a parabolic shape, which is represented by the following equation. NbIO/OLA (z) = N bIO × XIO (z) + N bOLA × XOLA (z),
3.3.2. Nuclear SLD. Figures 8 and 9 show the nuclear and magnetic SLD profiles as obtained from fitting of the data in figures 5 and 6, respectively. In both cases the data are well described by a model taking into account one complete NP layer at the substrate and an additional incomplete layer with reduced SLDs on top. Such reduction is due to the fact that the top layer forms islands as seen in the SEM images of figure 1, and that the lateral dimension of the islands is smaller than the coherence length of the neutrons. One can also recognize an additional surfactant layer with low SLD between the NP core layer and either silicon, or vanadium.
(4)
where NbIO is the nominal nSLD of iron oxide, N bOLA is the nominal nSLD of oleic acid, XIO (z) = XIO (x, y)lateral and XOLA (z) = 1 − XIO (z) are the area fractions of iron oxide 6
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However, the SLD profile for NPs deposited onto silicon does not reveal an intermediate layer with low SLD between the complete NP core layer and the incomplete top NP layer. Such intermediate layer is clearly seen in figure 9. Also, previously no intermediate layer could be discerned via XRR [25] from the same sample. This fact, as well as smaller overall thickness of the NP bi-layer on Si substrate, indicates that NPs on Si are more closely packed than NPs deposited onto metallic vanadium. In the latter case the top incomplete layer is less ordered, while in the former case top NPs occupy positions between NPs of the base core layer. Note that the vanadium layer in figure 9 has a negative nSLD, a thickness of 50.8 nm and a roughness of 2.1 nm as obtained from the fitting. This is followed by the Al2 O3 substrate with the highest nSLD and roughness of 1.5 nm. The volume fraction of NPs in a layer can be calculated by using the equation: XIO =
N bIO/OLA − N bOLA N bIO − N bOLA
competing dipole interaction between different pairs of NPs in a 2D lattice. Interestingly, the magnetic induction of NP layer on the vanadium film is B ≈ 0.2 T, which is close to what is estimated from the NP concentration and the magnetite saturation induction. This supports the hypothesis of the role of frustration which should be less pronounced when the interparticle distance increases. The profiles of mSLD are identical at high fields and at remanence and therefore we show here only one of them. The non-zero mSLD in remanence is surprising because the hysteresis curve at room temperature (figure 3(b)) does not show remanent magnetization at zero field. In fact, there is no splitting of reflectivities for up and down polarizations in remanence, clearly showing a demagnetized state over the macroscopic area. But the positions of the critical edges of the total reflection and hence mSLD values at high field and at remanence are almost identical. This contradicting feature can be understood if the parameter cγ = cos γ lateral and the concept of coherence ellipsoid are considered [43] in the fitting routine. The projection onto parameter cγ provides the magnetization M the Y -axis, while an additional parameter sγ2 = sin2 γ lateral accounts for the magnetization projection onto the X-axis and gives rise to SF scattering.
(5)
which immediately follows from equation (4), and the nominal values of nSLD NbIO = 6.91 × 10−6 Å−2 for iron oxide, NbOLA = 0.078 × 10−6 Å−2 for oleic acid, and the effective SLDs values determined by the fit. For the NP layer deposited onto the bare silicon substrate the core layer SLD N bIO/OLA = 4.6 × 10−6 Å−2 is found to be in excellent agreement with the value earlier determined [25] for a multilayer consisting of 5 NP layers deposited onto a silicon wafer. In accordance with equation (5) this gives the volume fraction of magnetite in the core layer of 65%. In case of deposition onto the vanadium layer N bIO/OLA = 2.2 × 10−6 Å−2 , and the volume fraction of iron oxide is of only 32%, showing that NPs are less densely packed in the layer, which is appreciably smeared out due to blurred interfaces between the NP layers. The nature of some swelling of the NP monolayer deposited onto a metallic sub-layer is not clear, but one may speculate on the role of diamagnetic currents induced by thermal fluctuations of the NP magnetic moments. Then the interaction between those currents and moments may lead to a repulsion in an analogy with the Casimir effect [9].
4. Discussions
The magnetic configuration of magnetic NPs is quite unique. When high fields are applied, the NPs are expected to be aligned along the field direction and the mean SLD over different coherence ellipsoids are nearly identical. That means an incoherent averaging over all coherence ellipsoids is trivial and leads to the model intensity: see equation (3). But at remanence the situation becomes more complex. Two distinct cases have to be distinguished. First, the average mSLD over each ellipsoid may be zero due to complete randomness in directions of the NP magnetic moments. In the second scenario the superspins are collinear within each coherence ellipsoid, but are random over the total illuminated area. In both cases the net magnetization will be zero and the NSF reflectivities will be unsplit, i.e. R ++ R −− . The second scenario may lead to SF reflectivity and can be measured by analyzing the polarization of the reflected beam. This has indeed been performed for our case, but no significant SF intensity was observed within the finite accuracy of the polarization analysis. This means that the mean value sγ2 = sin2 γ lateral ≈ 0, i.e. the magnetization vector within each of the coherence ellipsoids is almost collinear with the polarization axis, and hence γ ≈ 0, or γ ≈ π . Such a situation corresponds to the case of domains separated by 180◦ domain walls recently observed [41] by Lorentz microscopy and electron holography in dipolar ferromagnetic phase of Fe3 O4 nanoparticle arrays. These domain walls separate domains in which the magnetization is directed along with, or opposite to, the direction of external field formerly applied to the sample. If both types of domains are equally populated, then cγ = 0. Alternatively, cγ determines the population of one or the other type of domains and hence the net magnetization is finite.
Next we consider the variation of the mSLD, which provides detailed insight into the magnetic correlation in a monolayer system at the microscopic level. The mSLD profiles for high fields and for remanence are shown in figures 8 (b) and 9(b). For the NP monolayer on the Si substrate the magnetic induction of the core iron oxide layer is B ≈ 0.28 T, i.e. it is more than a factor of two smaller bulk ≈ 0.6 T of bulk magnetite. than the saturation induction Bsat The magnetic induction can be calculated from the following equation: B = µ0 M, where µ0 is the permeability of free space, M = CNp is the magnetization, the conversion factor C ≈ 344 according to [39], and Np is the magnetic SLD obtained from the fitting. The layer induction is still 25% lower than the value B ≈ 0.4 T which one can expect due to the volume fraction of iron oxide in the NP core layer. Similar reduction observed earlier [25] was ascribed to the frustration effect caused by 3.3.3. Magnetic SLD.
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From fitting we obtain that the value of cγ is 0.7 at 2 kOe, whereas it is 0.3 at remanence. From this we infer that at high fields some of the NPs are oriented along the field direction, although full saturation is not achieved, as already noted [25]. The sample is only 70% saturated. So even at relatively high fields there exist microscopic areas, where the NP magnetic moments deviate from the applied field direction. The smaller value of 30% magnetization at remanence indicates that the sample probably is divided into microscopic regions, or quasidomains, where magnetic moments are antiparallel to those in the adjacent region. The non-zero mSLD at remanence also implies that a finite magnetization persists over the coherence ellipsoid. The area of these correlated regions are of the order of dozens of micrometers and greater than the coherence ellipsoid. Therefore, we do not observe any offspecular scattering from quasi-domains. On the other hand, individual NPs are too small and therefore scatter at high angles inaccessible in reflectivity measurements, but can be seen in small angle scattering at grazing incidence [25, 26]. The physical origin of enhanced correlations between NPs, forming quasi-domains, comes from pure dipolar coupling. The dipolar coupling amongst the NPs is relatively strong and can be estimated from the following relationship [7]: Udd ≈
m2 , 4πµ0 r 3
high magnetic field is applied, the superspins in single domain NPs act as magnetic dipoles, which align along the field axis according to the classical Langevin function [8], overcoming the thermal energy. Once the field is removed, dipolar coupling among the NPs becomes dominant, suppressing thermal fluctuations and supporting long range ferromagnetic correlations. The net magnetization resulting from such correlations, however, vanishes when averaged over the entire surface, and the sample enters a partially demagnetized state with magnetic flux closed via large quasi-domains. The nanoparticle monolayer, as well as the multilayer studied earlier [25], resembles a soft superferromagnet, which is formed due to dipolar coupling only. The distinction between a superspin glass and superferromagnet behavior from PNR measurement is not trivial. In conclusion, we prepared hexagonal close-packed iron oxide NP monolayer films on silicon substrates and on vanadium films via spin-coating. The vanadium films are sputtered on sapphire substrate. Both types of NP monolayers can be measured with polarized neutron reflectivity with reasonable statistics, which allows for further quantitative analysis. Complete fits to all four NSF and SF reflectivities reveal the microscopic magnetic states in the NP monolayers at high fields and at remanence. After exposing the magnetic nanoparticles to high magnetic field, the dipolar coupling starts to dominate over the thermal energy and gives rise to long range magnetic order resembling a soft superferromagnetic state even at remanence. The NP self-assembly after spin coating on Si and Al2 O3 /V substrates shows remarkable differences. On the latter substrate the NPs are less densely packed in the layer than on the former substrate.
(6)
where, m = µ0 V Ms is the magnetic moment of the N P , V = 4/3π a 3 is the volume of the NP of radius a, Ms is the saturation magnetization of the material, µ0 is the permeability of vacuum, and r is the distance between the dipoles. For magnetite NPs Ms is 4.8 × 105 Am−2 (the value taken from [15]) and for a radius of 9 nm and a dipole to dipole distance of 20 nm the dipolar energy corresponds to a thermal energy of 1942 K, which is the ordering temperature for purely dipolar interacting NPs. Such a high dipolar ordering temperature can lead to enhanced magnetic order spanning several NPs and hence gives rise to finite mSLD even at remanence and at room temperature. We can neglect the possibility of any exchange interaction as the NPs are separated by an oleic acid shell. At remanence the dipolar coupling dictates the spin arrangement in the monolayer, within which the superspins of the NPs are correlated. Quasi-domains formed in remanence differ from normal domains in ferromagnets in many aspects. First, they form due to dipolar or higher pole interactions unlike exchange interaction and anisotropy. Second, the origin of domain walls [41] is very different. In ferromagnets domain walls develop in order to reduce the magnetic field energy and the magnetic domain wall width is determined by the competition between exchange interaction and crystal anisotropy. But for dipolarly coupled systems the driving mechanism for domain wall formation is mainly entropy. The assumption that the magnetization stays in-plane and the magnetic flux line closes only in the same layer probably holds good.
Acknowledgments
We would like to acknowledge Mrs S Erdt-B¨ohm for preparing the vanadium films. DM would like to acknowledge a scholarship from NRW Research School on Bio- and Nanosciences. Financial support from BMBF project 05K10PC1 (SuperADAM) is also gratefully acknowledged. References [1] Bader S D 2006 Colloquium: opportunities in nanomagnetism Rev. Mod. Phys. 78 1 [2] Bedanta S, Barman A, Kleemann W, Petracic O and Seki T 2013 Magnetic nanoparticles: a subject for both fundamental research and applications J. Nanomater. 2013 952540 [3] Bedanta S, Eim¨uller T, Kleemann W, Rehnsius J, Stromberg F, Amaladass E, Cardoso S and Freitas P P 2007 Overcoming the dipolar disorder in dense CoFe nanoparticle ensembles: superferromagnetism Phys. Rev. Lett. 98 176601 [4] Bedanta S and Kleemann W 2009 Supermagnetism J. Phys. D: Appl. Phys. 42 013001 [5] Bedanta S et al 2010 Single-particle blocking and collective magnetic states in discontinuous CoFe/Al2 O3 multilayers J. Phys. D: Appl. Phys. 43 474002 [6] Benitez M J, Mishra D, Szary P, Badini G A, Feyen M, Lu A H, Agudo L, Eggeler G, Petracic O and Zabel H 2011 Structural and magnetic characterization of self-assembled iron oxide nanoparticle arrays J. Phys.: Condens. Matter 23 126003
5. Summary and conclusion
In a nutshell, individual magnetic NPs in absence of a magnetic field follow a N´eel–Brown like thermal fluctuation. When a 8
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