Ultramicroscopy ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Probing buried magnetic interface structure with the quantum size effect in spin-dependent electron reflectivity Qiang Wu, M.S. Altman n Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 9 November 2014 Accepted 9 February 2015
The quantum size effect (QSE) in electron reflectivity from Fe thin films grown on a W(110) surface precovered with a two monolayer Cu film has been investigated using spin polarized low energy electron microscopy. Spin-dependent QSE-induced oscillations in the reflected intensity occur with energy and film thickness. The series of intensity peaks that is observed identifies spin-dependent quantum well resonances in the Fe film that are sensitive to electronic band structure and details of the buried interface. Information about the spin-dependent unoccupied bands of the Fe film in the ΓΝ direction normal to the film plane is obtained by analyzing the observed quantum well resonance conditions. The spin-split bands that are determined are uniformly shifted downward by 1.7 eV compared to bulk-like bands determined previously in Fe films on a bare W(110) substrate by the same method. Evidence is also obtained that the buried interface that defines the thin film quantum well boundary is located one layer above the W(110) surface. These results suggest that the Cu layer in direct contact with the substrate remains largely intact, but the weakly-bound second Cu layer mixes or segregates freely. & 2015 Elsevier B.V. All rights reserved.
Keywords: Quantum size effect Spin polarized low energy electron microscopy Thin film Electron reflectivity
1. Introduction The boundaries of an ultrathin film that are formed by the vacuum interface at its surface and the buried interface between the film and the supporting substrate are known to induce quantum well states due to one-dimensional quantum confinement of electrons below the Fermi level. Many different quantum size effects (QSEs) in film properties that occur due to this confinement have been studied using a variety of experimental techniques [1–9]. In elastic electron scattering experiments, the reflected electron intensity measured from spatially resolved regions of uniform film thickness using low energy electron microscopy (LEEM) and spin polarized LEEM (SPLEEM) show thickness and energy dependent oscillations due to the quantum well resonances above the vacuum level [10–14]. Classically, quantum well resonances can be understood as the interference of the electron waves reflected from the film surface and the buried interface. Consequently, they are only ever observed at very low energy when the inelastic mean free path of electrons is long. By analyzing the variation of the quantum well resonance conditions with film thickness and incident electron energy, information about the unoccupied band structure can be obtained. The quantum resonance conditions are also known to be sensitive to gaps in the substrate band structure, and may also be affected by other n
Corresponding author.
aspects of buried interface structure. In the present work, we have studied the QSE in electron reflectivity from Fe films grown on W(110) substrate precovered with a two monolayer (ML) Cu film using SPLEEM. The spin resolved reflected intensity spectra for different thicknesses were investigated to gain information about the spin-dependent unoccupied band structure of the Fe film. A close comparison with the QSE in Fe films on Cu(1 ML)/W(110) [14] and on the bare W (110) surface [10] reveals the impact of a Cu buffer layer inserted between the W(110) and Fe films on the spin-dependent QSE. We find that unoccupied spin-dependent bands in an Fe film that is grown on 2 ML Cu film are shifted uniformly to lower energy relative to their positions in bulk Fe. QSE-induced intensity oscillations are also observed that can only be understood if the first Cu layer in direct contact with the substrate defines the confining boundary at the buried interface. This result suggests that the more weakly-bound top Cu layer mixes with the Fe film during growth at room temperature.
2. Experimental details The experimental measurements were carried out using a SPLEEM. The working principle of SPLEEM has been described in many early reports [15–18]. The SPLEEM is a conventional low energy electron microscope that is equipped with a spin polarized electron gun and a spin manipulator, which enables orientation of
http://dx.doi.org/10.1016/j.ultramic.2015.02.006 0304-3991/& 2015 Elsevier B.V. All rights reserved.
Please cite this article as: Q. Wu, M.S. Altman, Probing buried magnetic interface structure with the quantum size effect in spindependent electron reflectivity, Ultramicroscopy (2015), http://dx.doi.org/10.1016/j.ultramic.2015.02.006i
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the spin of the incident electron beam in any arbitrary direction. In SPLEEM, magnetic measurements are carried out by acquiring images with oppositely polarized incident beams, called the spinup and spin-down images, and evaluating the exchange asymmetry pixel-by-pixel as it is defined Aex ¼ (1/P)(I↑–I↓)/(I↑ þI↓), where P is the spin polarization degree of the incident electron beam, I↑ and I↓ are the reflected electron intensities of the spin-up and spin-down images. The electron beam in our experiments is produced using a GaAs photocathode and has a polarization of about P E25%. Intensities in the exchange asymmetry image are proportional to the scalar product of the incident beam polarization and the sample magnetization. Furthermore, the subtraction of spin-up and spin-down images eliminates non-magnetic information that does not depend upon the incident spin direction. The base pressure of the instrument was in the upper 10 11 Torr range. Before the film growth, the W(110) substrate was cleaned using a standard method, by annealing in oxygen environment at 1400 K to remove the carbon and flash up to 2200 K to burn off the oxide. All the temperature measurements were performed using a type-D (W–3%Re/W-25%Re) thermocouple. Cu was deposited from an electron beam heated evaporator onto the clean W(110) surface at sample temperature 800 K and at a deposition rate of around 0.1 ML/min. Under this condition, highly ordered growth of a smooth 2 ML Cu film occurs. The Cu double layer has fcc(111)-like structure with Nishiyama–Wasseran orientation relative to the substrate that is expanded by nearly 20% with respect to the bulk Cu(111) plane [19]. The completion of the Cu 2 ML growth was controlled precisely by in-situ LEEM observation of the growth process, which has been reported previously [20].
a
d
b
e
c
f
3. Results and discussion 3.1. Fe film growth Fe was deposited onto the 2 ML Cu film at room temperature. Accurate knowledge of the Fe film thickness is crucial in our work since it defines the width of the quantum well. The deposition rate of the Fe source was calibrated by monitoring the growth of a pseudomorphic Fe layer on the clean W(110) surface at 800 K. The completion of the pseudomorphic Fe layer is easily identified at this temperature by in situ LEEM observations. Fe films of different integer layer thickness were grown on top of the Cu double layer using the calibrated source by controlling the deposition time precisely. Furthermore, growth was also monitored by measuring the exchange asymmetry continuously as a function of time, Aex(t), during Fe deposition (Figs. 1,2). A sequence of SPLEEM images that show the evolution of magnetic domains in the Fe film with Fe film thickness during deposition is shown in Fig. 1. Asymmetry in oppositely magnetized domains that are present in the images is averaged to reduce noise. As Fig. 2(a) shows, Aex(t) recorded at 4.0 eV during Fe deposition to different integer thicknesses exhibits consistent features. Following the reproducible onset of magnetic signal in different deposition sequences at 1.3 ML, the exchange asymmetry modulates quasi-periodically. This modulation exhibits a reproducible pronounced peak at 2.5 ML Fe coverage and an equally reproducible valley at 4.0 ML. Films that were prepared by depositions that did not exhibit these reproducible features were discarded. The onset of exchange asymmetry corresponds to the thickness that the Curie temperature just rises above room temperature due to the finite size effect [21]. The variations of the exchange asymmetry with thickness that follow have their origin in two factors: the strengthening of magnetism due to diminishing finite size effect, and modulations of the exchange asymmetry that are caused by the QSE. These modulations
Fig. 1. SPLEEM exchange asymmetry images at imaging energy of 4.0 eV during Fe deposition on Cu(2 ML)/W(110) at coverages (a) 1.5 ML, (b) 2.5 ML, (c) 3.5 ML, (d) 4 ML, (e) 5.5 ML, and (f) 6.5 ML. The white dot (○) indicates the same sample position in each image, which shifts due to image drift.
are seen in the dependence of exchange asymmetry on energy, Aex (E), that is presented in Fig. 2(b) for different integer layer thicknesses. These data were obtained using films prepared by the controlled depositions shown in Fig. 2(a). They demonstrate how the asymmetry peak that is initially at 4.0 eV grows with increasing thickness due to diminishing finite size effect. This is responsible for the initial rise of Aex during deposition shown in Figs. 2(a). The data in Fig. 2(b) also shows that the number of QSEinduced oscillations increases in step with the increasing number of atomic layers. This causes peaks and valleys to shift. For example, the peak and valley initially at 4.0 eV and 6.0 eV, respectively, for a 2 ML Fe film are shifted to 2.6 eV and 4.0 eV, respectively, for the 4 ML film. This explains the minimum of Aex that is recorded reproducibly at 4.0 eV during continuous deposition shown in Fig. 2(a). The reproducibility of features in Fig. 2 (a) confirms precise control of integer layer film thickness that is important to our investigations. 3.2. Quantum size effect in electron reflectivity QSE-induced oscillations of electron intensity reflected from Fe films with different integer layer thicknesses are analyzed to determine the magnetic spin-split Fe band structure above the
Please cite this article as: Q. Wu, M.S. Altman, Probing buried magnetic interface structure with the quantum size effect in spindependent electron reflectivity, Ultramicroscopy (2015), http://dx.doi.org/10.1016/j.ultramic.2015.02.006i
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Fig. 2. (a) Exchange asymmetry vs. film thickness measured at E¼ 4.0 eV during Fe deposition on Cu(2 ML)/W(110) up to different integer layer thicknesses of Fe. Each curve is offset vertically for clarity. (b) Exchange asymmetry vs. energy for different integer layer thicknesses of Fe, m (ML), on Cu(2 ML)/W(110). The vertical line in (b) at 4.0 eV corresponds to the energy that the asymmetry in (a) was measured. The energy zero in (b) is the vacuum level.
vacuum level. The experimentally recorded intensity vs. energy (I (V)) curves decreases sharply with increasing energy, representing the general trend of the I(V) curve for bulk Fe (see Fig. 3(a), for example). Additionally, moderate QSE-induced oscillations are also observed that depend on film thickness. In order to see the oscillations clearly, we subtract off the contribution of the spinaverage bulk I(V) sprectrum and correct for the partial polarization of the incident electron. The bulk-like spectrum was simulated by polynomial fitting to the average of the spin-up and spin-down I (V) curves. As shown in Fig. 3(b), quantum size oscillations in spinup and spin-down I(V) curves emerge remarkably following these procedures. This allows accurate identification of the energies that the intensity peaks and valley occur. The energy positions that were determined for Fe films from 2 ML to 7 ML are presented in Fig. 4. Note that the data points in Fig. 4 were shifted by þ 1.7 eV in energy scale for reasons that become clear in the following analysis. Key differences are seen in the amplitudes of the quantum oscillations and the energy positions of the intensity peaks and valleys for spin-up and spin-down electrons. The different amplitudes originate in the spin dependence the inelastic mean free
path, which is longer for spin-up than for spin-down electrons [22,23]. Diminishing quantum oscillation amplitude with increasing energy likewise reflects the energy dependence of the inelastic mean free path, which decreases with increasing energy. Differences in the energies of the peaks and valleys are attributed to the dependence of the spin polarized quantum well resonances [10,13,14] on the spin-dependent band structure [24]. The quantum well resonance conditions can be evaluated using the phase accumulation model [25]. According to this model, quantum well resonances occur when the phase accumulated by an electron that traverses the film from the surface to the buried interface and back is equal to an integral multiple of 2π. This condition of constructive interference is expressed as
2k (E) mt + Φ (E) = 2nπ ,
(1)
where k(E) is the wave vector of the electron that moves perpendicular to the film plane, m is the number of atomic layers of the film, t is the layer spacing, Φ(E) is the phase shift that occurs upon the reflection at the interface, and n is an integer number. Eq. (1) can be rewritten as
Fig. 3. (a) Raw experimental spin-up and spin-down I(V) curves for 4 ML Fe on Cu(2 ML)/W(110) and the polynomial fit to the spin averaged I(V) curve, labeled as spin averaged “bulk”. (b) The QSE oscillations in the reflected intensity after polarization correction and subtraction of the spin averaged “bulk”. The energy zero is the vacuum level.
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Fig. 4. Energies of quantum interference peak maxima (●) and minima (○) in the (a) spin-up and (b) spin-down reflectivity for Fe film thickness 2–7 ML on Cu(2 ML)/W(110). The experimental data are shifted by þ 1.7 eV (see the text). The energy zero is the vacuum level. The black horizontal lines connect the points at the same energy that are used in the analysis (see text). The solid and dashed lines connect the points with same integer and half-integer quantum number ν, respectively.
m=
Φ (E)/2π + ν , κ (E)/k BZ
(2)
where ν is a quantum number, ν ¼ m–n for intensity maxima and ν ¼m–n–1/2 for intensity minima, kBZ ¼ π/t is the wave vector at the Brillouin zone boundary perpendicular to the film plane, κ (E)¼ kBZ–k(E) is the wave vector measured from the zone boundary to the zone center, i.e. N point to Γ point for the case of bcc Fe (110). The solid and dashed lines in Fig. 4 only represent the predictions of Eq. (2) schematically for different integer and halfinteger quantum numbers. More accurate modeling of quantum well resonance conditions using Eq. (2) requires information on the interface scattering phase and band structure. Empirical models have been used that relate the interface scattering phase in different systems to band gaps in the underlying substrate, including W(110) [11,12,25]. To obtain the information directly about the band structures of Fe films grown on Cu(2 ML)/W(110), the interface scattering phase is eliminated by subtracting Eq. (2) for pairs of intensity peaks or valleys that occur at the same energy for different thickness. Pairs used in this analysis are connected by horizontal lines in Fig. 4. The subtraction yields an expression for κ(E) in terms of the quantum numbers and film thicknesses of the two points chosen
κ (E) =
k BZ (ν2 − ν1) . (m2 − m1)
(3)
The κ(E) points calculated by Eq. (3) using the data in Fig. 4 are plotted in Fig. 5 for both spin-up (●) and spin-down (○) electrons. Note that the points shown in Fig. 5 are shifted by þ1.7 eV in energy scale corresponding to the same shift that was applied in Fig. 4. This uniform shift brings the experimental data points into very good agreement with the theoretical spin-spilt Fe bands in the ΓΝ direction that were reported in Ref. [24], which are shown as solid lines in Fig. 5. For comparison, the spin-split bands obtained using the same method for Fe films on W(110) without a Cu buffer layer were consistent with the theoretical bands without introducing an artificial shift of the experimental results [10]. On the other hand, it was necessary to shift bands determined similarly for Fe films on W(110) precovered with 1 ML Cu by þ1.1 eV in order to bring them in them into perfect agreement with the theoretically predicted bands [14]. In Fig. 6, we also compare the spin-dependent quantum intensity oscillations for several Fe film thicknesses on
Fig. 5. Spin-split bands for spin-up (●) and spin-down (○) electrons determined from the data in Fig. 4 using Eq. (3). The solid lines are the theoretical spin-split bands of bulk Fe along the ΓN direction (Ref. [24]).
Cu(2 ML)/W(110) obtained in this work with similar spin-dependent spectra for Fe/Cu(1 ML)/W(110) reported previously in ref. [14]. It is seen that the QSE-induced oscillations for m-1 ML Fe films on Cu(2 ML)/W(110) exhibit the same number of oscillations as m ML Fe films on Cu(1 ML)/W(110) [14]. The aforementioned þ1.7 eV and þ 1.1 eV shifts applied in these two cases, respectively, bring the peak and valley positions into coincidence over the entire thickness range studied. This is of practical importance because it confirms the incremental deposition of integer layers in this work using a calibrated deposition source. Additional implications are discussed below. Finally, we note that the spin-dependent reflectivity (Figs. 3,6) and A(E) curves (Fig. 2(b)) for Fe/Cu (2 ML)/W(110) exhibit somewhat weaker QSE-induced oscillations than the pronounced oscillations presented in Fig. 6 and in ref. [14] for Fe/Cu(1 ML)/W(110). These comparisons suggest an interesting sensitivity of the quantum size effect in electron reflectivity to details of the buried interface. Foremost, the similarity of oscillations in spin-dependent reflectivity for m ML and m-1 ML Fe films that differ by 1 ML on Cu(1 ML)/W(110) and Cu(2 ML)/W(110), respectively, (Fig. 6) indicates that the confined Fe film is effectively 1 ML thicker when Fe is deposited on the 2 ML Cu buffer layer. The comparison of QSE-induced oscillations for Fe on clean W(110) [10] and on Cu
Please cite this article as: Q. Wu, M.S. Altman, Probing buried magnetic interface structure with the quantum size effect in spindependent electron reflectivity, Ultramicroscopy (2015), http://dx.doi.org/10.1016/j.ultramic.2015.02.006i
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Fig. 6. Comparison of QSE oscillations in reflected intensity of (a) spin-up and (b) spin-down electrons for Fe(m ML)/Cu(1 ML)/W(110) (dashed curves) and Fe(m-1 ML)/Cu (2 ML)/W(110) (solid curves) for the indicated Fe film thicknesses, m¼3–7. Each curve is offset vertically for clarity. The energy zero is the vacuum level.
(1 ML)/W(110) that was made earlier [14] revealed that the buried confining interface for Fe films on the 1 ML Cu buffer is located between the Fe film and Cu layer, not between the Cu layer and the W substrate. Therefore, the observations presented here convincingly place the uppermost layer of the 2 ML Cu buffer inside the quantum confined film. However, these observations do not tell us how the Cu atoms in this layer are distributed in the Fe film. The possibility that the upper Cu layer remains intact at its original position seems unlikely since it should be more weakly bound to the Cu layer underneath it than the lower Cu layer is bound to the W substrate, and because of the prevalence of intermixing during interface formation of Fe films on bulk Cu substrates [26,27]. Thus, it is likely that the upper Cu layer intermixes, at least partially, with the growing Fe film. It may even segregate to the surface of the growing film. The relatively weaker QSE-induced oscillations in the spin-dependent reflectivity and Aex that are observed in Fe/ Cu(2 ML)/W(110) compared to Fe/Cu(1 ML)/W(110) [14] likewise point to a buried interface that is perturbed by intermixing. The 1.1 eV shift of the spin-split bands in the Fe film on Cu (1 ML)/W(110) that was reported previously [14] was attributed to the presence of the Cu monolayer at the interface, although the mechanism responsible for this shift was not understood. The larger 1.7 eV shift determined here for Fe films grown on Cu (2 ML)/W(110) may have the same yet to be understood origin. Aside from the uniform offset, it is interesting that the bands determined are otherwise consistent with bulk bands. We believe that this signals that intermixing is relatively localized at the interface. A small magnetic moment may be induced on Cu in contact with or embedded in the Fe film at the interface [28] and the electronic structure localized in the interfacial region may deviate from the rest of the Fe film. However, the method outlined above only averages these localized effects with more bulk-like properties in the majority of the film. This shortcoming can be addressed in the future by adapting more sophisticated approaches to understand the effects of interfacial mixing, including multiple scattering calculations [29] or first principles density functional theory calculations of reflectivity spectra [30] that have previously demonstrated sensitivity to layer spacing and the presence of interlayer states at the buried interface.
4. Summary The quantum size effect in electron reflectivity was studied experimentally in Fe films grown on a W(110) surface pre-covered with a 2 ML Cu film using spin polarized low energy electron microscopy. A series of QSE-induced intensity peaks is observed in the spin-dependent reflectivity that identifies the dispersion of quantum well resonances as a function of thickness and energy above the vacuum level. Spin-split bands in the Fe film are determined using a simple phase accumulation model analysis of spin-polarized quantum well resonance conditions. The result agrees with bands in bulk Fe in the ΓN direction except for a uniform downward shift by 1.7 eV. This reveals an interesting trend beginning with no shift in Fe/W(110) and the 1.1 eV downward shift of bands in Fe/Cu(1 ML)/W(110) that were determined previously by the same method. Although the origin of the band offset caused by interface Cu may be the same in the two cases, it is still not well understood. We also find clear evidence in the QSEinduced intensity oscillations that the buried interface that defines the thin film quantum well boundary is located one layer above the W(110) surface. This is likewise similar to previous observations for Fe/Cu(1 ML)/W(110). It means that the Cu layer in contact with the W substrate remains intact, while the top Cu layer that is more weakly bound likely intermixes with the Fe film. The details of how the Cu atoms are distributed in the film cannot be ascertained because the current analysis only provides average information over the depth.
Acknowledgements Financial support from the Research Grants Council, University Grants Committee, Hong Kong under Grant HKUST600111 is gratefully acknowledged.
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Please cite this article as: Q. Wu, M.S. Altman, Probing buried magnetic interface structure with the quantum size effect in spindependent electron reflectivity, Ultramicroscopy (2015), http://dx.doi.org/10.1016/j.ultramic.2015.02.006i
Contents lists available at ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
Probing buried magnetic interface structure with the quantum size effect in spin-dependent electron reflectivity Qiang Wu, M.S. Altman n Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 9 November 2014 Accepted 9 February 2015
The quantum size effect (QSE) in electron reflectivity from Fe thin films grown on a W(110) surface precovered with a two monolayer Cu film has been investigated using spin polarized low energy electron microscopy. Spin-dependent QSE-induced oscillations in the reflected intensity occur with energy and film thickness. The series of intensity peaks that is observed identifies spin-dependent quantum well resonances in the Fe film that are sensitive to electronic band structure and details of the buried interface. Information about the spin-dependent unoccupied bands of the Fe film in the ΓΝ direction normal to the film plane is obtained by analyzing the observed quantum well resonance conditions. The spin-split bands that are determined are uniformly shifted downward by 1.7 eV compared to bulk-like bands determined previously in Fe films on a bare W(110) substrate by the same method. Evidence is also obtained that the buried interface that defines the thin film quantum well boundary is located one layer above the W(110) surface. These results suggest that the Cu layer in direct contact with the substrate remains largely intact, but the weakly-bound second Cu layer mixes or segregates freely. & 2015 Elsevier B.V. All rights reserved.
Keywords: Quantum size effect Spin polarized low energy electron microscopy Thin film Electron reflectivity
1. Introduction The boundaries of an ultrathin film that are formed by the vacuum interface at its surface and the buried interface between the film and the supporting substrate are known to induce quantum well states due to one-dimensional quantum confinement of electrons below the Fermi level. Many different quantum size effects (QSEs) in film properties that occur due to this confinement have been studied using a variety of experimental techniques [1–9]. In elastic electron scattering experiments, the reflected electron intensity measured from spatially resolved regions of uniform film thickness using low energy electron microscopy (LEEM) and spin polarized LEEM (SPLEEM) show thickness and energy dependent oscillations due to the quantum well resonances above the vacuum level [10–14]. Classically, quantum well resonances can be understood as the interference of the electron waves reflected from the film surface and the buried interface. Consequently, they are only ever observed at very low energy when the inelastic mean free path of electrons is long. By analyzing the variation of the quantum well resonance conditions with film thickness and incident electron energy, information about the unoccupied band structure can be obtained. The quantum resonance conditions are also known to be sensitive to gaps in the substrate band structure, and may also be affected by other n
Corresponding author.
aspects of buried interface structure. In the present work, we have studied the QSE in electron reflectivity from Fe films grown on W(110) substrate precovered with a two monolayer (ML) Cu film using SPLEEM. The spin resolved reflected intensity spectra for different thicknesses were investigated to gain information about the spin-dependent unoccupied band structure of the Fe film. A close comparison with the QSE in Fe films on Cu(1 ML)/W(110) [14] and on the bare W (110) surface [10] reveals the impact of a Cu buffer layer inserted between the W(110) and Fe films on the spin-dependent QSE. We find that unoccupied spin-dependent bands in an Fe film that is grown on 2 ML Cu film are shifted uniformly to lower energy relative to their positions in bulk Fe. QSE-induced intensity oscillations are also observed that can only be understood if the first Cu layer in direct contact with the substrate defines the confining boundary at the buried interface. This result suggests that the more weakly-bound top Cu layer mixes with the Fe film during growth at room temperature.
2. Experimental details The experimental measurements were carried out using a SPLEEM. The working principle of SPLEEM has been described in many early reports [15–18]. The SPLEEM is a conventional low energy electron microscope that is equipped with a spin polarized electron gun and a spin manipulator, which enables orientation of
http://dx.doi.org/10.1016/j.ultramic.2015.02.006 0304-3991/& 2015 Elsevier B.V. All rights reserved.
Please cite this article as: Q. Wu, M.S. Altman, Probing buried magnetic interface structure with the quantum size effect in spindependent electron reflectivity, Ultramicroscopy (2015), http://dx.doi.org/10.1016/j.ultramic.2015.02.006i
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the spin of the incident electron beam in any arbitrary direction. In SPLEEM, magnetic measurements are carried out by acquiring images with oppositely polarized incident beams, called the spinup and spin-down images, and evaluating the exchange asymmetry pixel-by-pixel as it is defined Aex ¼ (1/P)(I↑–I↓)/(I↑ þI↓), where P is the spin polarization degree of the incident electron beam, I↑ and I↓ are the reflected electron intensities of the spin-up and spin-down images. The electron beam in our experiments is produced using a GaAs photocathode and has a polarization of about P E25%. Intensities in the exchange asymmetry image are proportional to the scalar product of the incident beam polarization and the sample magnetization. Furthermore, the subtraction of spin-up and spin-down images eliminates non-magnetic information that does not depend upon the incident spin direction. The base pressure of the instrument was in the upper 10 11 Torr range. Before the film growth, the W(110) substrate was cleaned using a standard method, by annealing in oxygen environment at 1400 K to remove the carbon and flash up to 2200 K to burn off the oxide. All the temperature measurements were performed using a type-D (W–3%Re/W-25%Re) thermocouple. Cu was deposited from an electron beam heated evaporator onto the clean W(110) surface at sample temperature 800 K and at a deposition rate of around 0.1 ML/min. Under this condition, highly ordered growth of a smooth 2 ML Cu film occurs. The Cu double layer has fcc(111)-like structure with Nishiyama–Wasseran orientation relative to the substrate that is expanded by nearly 20% with respect to the bulk Cu(111) plane [19]. The completion of the Cu 2 ML growth was controlled precisely by in-situ LEEM observation of the growth process, which has been reported previously [20].
a
d
b
e
c
f
3. Results and discussion 3.1. Fe film growth Fe was deposited onto the 2 ML Cu film at room temperature. Accurate knowledge of the Fe film thickness is crucial in our work since it defines the width of the quantum well. The deposition rate of the Fe source was calibrated by monitoring the growth of a pseudomorphic Fe layer on the clean W(110) surface at 800 K. The completion of the pseudomorphic Fe layer is easily identified at this temperature by in situ LEEM observations. Fe films of different integer layer thickness were grown on top of the Cu double layer using the calibrated source by controlling the deposition time precisely. Furthermore, growth was also monitored by measuring the exchange asymmetry continuously as a function of time, Aex(t), during Fe deposition (Figs. 1,2). A sequence of SPLEEM images that show the evolution of magnetic domains in the Fe film with Fe film thickness during deposition is shown in Fig. 1. Asymmetry in oppositely magnetized domains that are present in the images is averaged to reduce noise. As Fig. 2(a) shows, Aex(t) recorded at 4.0 eV during Fe deposition to different integer thicknesses exhibits consistent features. Following the reproducible onset of magnetic signal in different deposition sequences at 1.3 ML, the exchange asymmetry modulates quasi-periodically. This modulation exhibits a reproducible pronounced peak at 2.5 ML Fe coverage and an equally reproducible valley at 4.0 ML. Films that were prepared by depositions that did not exhibit these reproducible features were discarded. The onset of exchange asymmetry corresponds to the thickness that the Curie temperature just rises above room temperature due to the finite size effect [21]. The variations of the exchange asymmetry with thickness that follow have their origin in two factors: the strengthening of magnetism due to diminishing finite size effect, and modulations of the exchange asymmetry that are caused by the QSE. These modulations
Fig. 1. SPLEEM exchange asymmetry images at imaging energy of 4.0 eV during Fe deposition on Cu(2 ML)/W(110) at coverages (a) 1.5 ML, (b) 2.5 ML, (c) 3.5 ML, (d) 4 ML, (e) 5.5 ML, and (f) 6.5 ML. The white dot (○) indicates the same sample position in each image, which shifts due to image drift.
are seen in the dependence of exchange asymmetry on energy, Aex (E), that is presented in Fig. 2(b) for different integer layer thicknesses. These data were obtained using films prepared by the controlled depositions shown in Fig. 2(a). They demonstrate how the asymmetry peak that is initially at 4.0 eV grows with increasing thickness due to diminishing finite size effect. This is responsible for the initial rise of Aex during deposition shown in Figs. 2(a). The data in Fig. 2(b) also shows that the number of QSEinduced oscillations increases in step with the increasing number of atomic layers. This causes peaks and valleys to shift. For example, the peak and valley initially at 4.0 eV and 6.0 eV, respectively, for a 2 ML Fe film are shifted to 2.6 eV and 4.0 eV, respectively, for the 4 ML film. This explains the minimum of Aex that is recorded reproducibly at 4.0 eV during continuous deposition shown in Fig. 2(a). The reproducibility of features in Fig. 2 (a) confirms precise control of integer layer film thickness that is important to our investigations. 3.2. Quantum size effect in electron reflectivity QSE-induced oscillations of electron intensity reflected from Fe films with different integer layer thicknesses are analyzed to determine the magnetic spin-split Fe band structure above the
Please cite this article as: Q. Wu, M.S. Altman, Probing buried magnetic interface structure with the quantum size effect in spindependent electron reflectivity, Ultramicroscopy (2015), http://dx.doi.org/10.1016/j.ultramic.2015.02.006i
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Fig. 2. (a) Exchange asymmetry vs. film thickness measured at E¼ 4.0 eV during Fe deposition on Cu(2 ML)/W(110) up to different integer layer thicknesses of Fe. Each curve is offset vertically for clarity. (b) Exchange asymmetry vs. energy for different integer layer thicknesses of Fe, m (ML), on Cu(2 ML)/W(110). The vertical line in (b) at 4.0 eV corresponds to the energy that the asymmetry in (a) was measured. The energy zero in (b) is the vacuum level.
vacuum level. The experimentally recorded intensity vs. energy (I (V)) curves decreases sharply with increasing energy, representing the general trend of the I(V) curve for bulk Fe (see Fig. 3(a), for example). Additionally, moderate QSE-induced oscillations are also observed that depend on film thickness. In order to see the oscillations clearly, we subtract off the contribution of the spinaverage bulk I(V) sprectrum and correct for the partial polarization of the incident electron. The bulk-like spectrum was simulated by polynomial fitting to the average of the spin-up and spin-down I (V) curves. As shown in Fig. 3(b), quantum size oscillations in spinup and spin-down I(V) curves emerge remarkably following these procedures. This allows accurate identification of the energies that the intensity peaks and valley occur. The energy positions that were determined for Fe films from 2 ML to 7 ML are presented in Fig. 4. Note that the data points in Fig. 4 were shifted by þ 1.7 eV in energy scale for reasons that become clear in the following analysis. Key differences are seen in the amplitudes of the quantum oscillations and the energy positions of the intensity peaks and valleys for spin-up and spin-down electrons. The different amplitudes originate in the spin dependence the inelastic mean free
path, which is longer for spin-up than for spin-down electrons [22,23]. Diminishing quantum oscillation amplitude with increasing energy likewise reflects the energy dependence of the inelastic mean free path, which decreases with increasing energy. Differences in the energies of the peaks and valleys are attributed to the dependence of the spin polarized quantum well resonances [10,13,14] on the spin-dependent band structure [24]. The quantum well resonance conditions can be evaluated using the phase accumulation model [25]. According to this model, quantum well resonances occur when the phase accumulated by an electron that traverses the film from the surface to the buried interface and back is equal to an integral multiple of 2π. This condition of constructive interference is expressed as
2k (E) mt + Φ (E) = 2nπ ,
(1)
where k(E) is the wave vector of the electron that moves perpendicular to the film plane, m is the number of atomic layers of the film, t is the layer spacing, Φ(E) is the phase shift that occurs upon the reflection at the interface, and n is an integer number. Eq. (1) can be rewritten as
Fig. 3. (a) Raw experimental spin-up and spin-down I(V) curves for 4 ML Fe on Cu(2 ML)/W(110) and the polynomial fit to the spin averaged I(V) curve, labeled as spin averaged “bulk”. (b) The QSE oscillations in the reflected intensity after polarization correction and subtraction of the spin averaged “bulk”. The energy zero is the vacuum level.
Please cite this article as: Q. Wu, M.S. Altman, Probing buried magnetic interface structure with the quantum size effect in spindependent electron reflectivity, Ultramicroscopy (2015), http://dx.doi.org/10.1016/j.ultramic.2015.02.006i
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Fig. 4. Energies of quantum interference peak maxima (●) and minima (○) in the (a) spin-up and (b) spin-down reflectivity for Fe film thickness 2–7 ML on Cu(2 ML)/W(110). The experimental data are shifted by þ 1.7 eV (see the text). The energy zero is the vacuum level. The black horizontal lines connect the points at the same energy that are used in the analysis (see text). The solid and dashed lines connect the points with same integer and half-integer quantum number ν, respectively.
m=
Φ (E)/2π + ν , κ (E)/k BZ
(2)
where ν is a quantum number, ν ¼ m–n for intensity maxima and ν ¼m–n–1/2 for intensity minima, kBZ ¼ π/t is the wave vector at the Brillouin zone boundary perpendicular to the film plane, κ (E)¼ kBZ–k(E) is the wave vector measured from the zone boundary to the zone center, i.e. N point to Γ point for the case of bcc Fe (110). The solid and dashed lines in Fig. 4 only represent the predictions of Eq. (2) schematically for different integer and halfinteger quantum numbers. More accurate modeling of quantum well resonance conditions using Eq. (2) requires information on the interface scattering phase and band structure. Empirical models have been used that relate the interface scattering phase in different systems to band gaps in the underlying substrate, including W(110) [11,12,25]. To obtain the information directly about the band structures of Fe films grown on Cu(2 ML)/W(110), the interface scattering phase is eliminated by subtracting Eq. (2) for pairs of intensity peaks or valleys that occur at the same energy for different thickness. Pairs used in this analysis are connected by horizontal lines in Fig. 4. The subtraction yields an expression for κ(E) in terms of the quantum numbers and film thicknesses of the two points chosen
κ (E) =
k BZ (ν2 − ν1) . (m2 − m1)
(3)
The κ(E) points calculated by Eq. (3) using the data in Fig. 4 are plotted in Fig. 5 for both spin-up (●) and spin-down (○) electrons. Note that the points shown in Fig. 5 are shifted by þ1.7 eV in energy scale corresponding to the same shift that was applied in Fig. 4. This uniform shift brings the experimental data points into very good agreement with the theoretical spin-spilt Fe bands in the ΓΝ direction that were reported in Ref. [24], which are shown as solid lines in Fig. 5. For comparison, the spin-split bands obtained using the same method for Fe films on W(110) without a Cu buffer layer were consistent with the theoretical bands without introducing an artificial shift of the experimental results [10]. On the other hand, it was necessary to shift bands determined similarly for Fe films on W(110) precovered with 1 ML Cu by þ1.1 eV in order to bring them in them into perfect agreement with the theoretically predicted bands [14]. In Fig. 6, we also compare the spin-dependent quantum intensity oscillations for several Fe film thicknesses on
Fig. 5. Spin-split bands for spin-up (●) and spin-down (○) electrons determined from the data in Fig. 4 using Eq. (3). The solid lines are the theoretical spin-split bands of bulk Fe along the ΓN direction (Ref. [24]).
Cu(2 ML)/W(110) obtained in this work with similar spin-dependent spectra for Fe/Cu(1 ML)/W(110) reported previously in ref. [14]. It is seen that the QSE-induced oscillations for m-1 ML Fe films on Cu(2 ML)/W(110) exhibit the same number of oscillations as m ML Fe films on Cu(1 ML)/W(110) [14]. The aforementioned þ1.7 eV and þ 1.1 eV shifts applied in these two cases, respectively, bring the peak and valley positions into coincidence over the entire thickness range studied. This is of practical importance because it confirms the incremental deposition of integer layers in this work using a calibrated deposition source. Additional implications are discussed below. Finally, we note that the spin-dependent reflectivity (Figs. 3,6) and A(E) curves (Fig. 2(b)) for Fe/Cu (2 ML)/W(110) exhibit somewhat weaker QSE-induced oscillations than the pronounced oscillations presented in Fig. 6 and in ref. [14] for Fe/Cu(1 ML)/W(110). These comparisons suggest an interesting sensitivity of the quantum size effect in electron reflectivity to details of the buried interface. Foremost, the similarity of oscillations in spin-dependent reflectivity for m ML and m-1 ML Fe films that differ by 1 ML on Cu(1 ML)/W(110) and Cu(2 ML)/W(110), respectively, (Fig. 6) indicates that the confined Fe film is effectively 1 ML thicker when Fe is deposited on the 2 ML Cu buffer layer. The comparison of QSE-induced oscillations for Fe on clean W(110) [10] and on Cu
Please cite this article as: Q. Wu, M.S. Altman, Probing buried magnetic interface structure with the quantum size effect in spindependent electron reflectivity, Ultramicroscopy (2015), http://dx.doi.org/10.1016/j.ultramic.2015.02.006i
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Fig. 6. Comparison of QSE oscillations in reflected intensity of (a) spin-up and (b) spin-down electrons for Fe(m ML)/Cu(1 ML)/W(110) (dashed curves) and Fe(m-1 ML)/Cu (2 ML)/W(110) (solid curves) for the indicated Fe film thicknesses, m¼3–7. Each curve is offset vertically for clarity. The energy zero is the vacuum level.
(1 ML)/W(110) that was made earlier [14] revealed that the buried confining interface for Fe films on the 1 ML Cu buffer is located between the Fe film and Cu layer, not between the Cu layer and the W substrate. Therefore, the observations presented here convincingly place the uppermost layer of the 2 ML Cu buffer inside the quantum confined film. However, these observations do not tell us how the Cu atoms in this layer are distributed in the Fe film. The possibility that the upper Cu layer remains intact at its original position seems unlikely since it should be more weakly bound to the Cu layer underneath it than the lower Cu layer is bound to the W substrate, and because of the prevalence of intermixing during interface formation of Fe films on bulk Cu substrates [26,27]. Thus, it is likely that the upper Cu layer intermixes, at least partially, with the growing Fe film. It may even segregate to the surface of the growing film. The relatively weaker QSE-induced oscillations in the spin-dependent reflectivity and Aex that are observed in Fe/ Cu(2 ML)/W(110) compared to Fe/Cu(1 ML)/W(110) [14] likewise point to a buried interface that is perturbed by intermixing. The 1.1 eV shift of the spin-split bands in the Fe film on Cu (1 ML)/W(110) that was reported previously [14] was attributed to the presence of the Cu monolayer at the interface, although the mechanism responsible for this shift was not understood. The larger 1.7 eV shift determined here for Fe films grown on Cu (2 ML)/W(110) may have the same yet to be understood origin. Aside from the uniform offset, it is interesting that the bands determined are otherwise consistent with bulk bands. We believe that this signals that intermixing is relatively localized at the interface. A small magnetic moment may be induced on Cu in contact with or embedded in the Fe film at the interface [28] and the electronic structure localized in the interfacial region may deviate from the rest of the Fe film. However, the method outlined above only averages these localized effects with more bulk-like properties in the majority of the film. This shortcoming can be addressed in the future by adapting more sophisticated approaches to understand the effects of interfacial mixing, including multiple scattering calculations [29] or first principles density functional theory calculations of reflectivity spectra [30] that have previously demonstrated sensitivity to layer spacing and the presence of interlayer states at the buried interface.
4. Summary The quantum size effect in electron reflectivity was studied experimentally in Fe films grown on a W(110) surface pre-covered with a 2 ML Cu film using spin polarized low energy electron microscopy. A series of QSE-induced intensity peaks is observed in the spin-dependent reflectivity that identifies the dispersion of quantum well resonances as a function of thickness and energy above the vacuum level. Spin-split bands in the Fe film are determined using a simple phase accumulation model analysis of spin-polarized quantum well resonance conditions. The result agrees with bands in bulk Fe in the ΓN direction except for a uniform downward shift by 1.7 eV. This reveals an interesting trend beginning with no shift in Fe/W(110) and the 1.1 eV downward shift of bands in Fe/Cu(1 ML)/W(110) that were determined previously by the same method. Although the origin of the band offset caused by interface Cu may be the same in the two cases, it is still not well understood. We also find clear evidence in the QSEinduced intensity oscillations that the buried interface that defines the thin film quantum well boundary is located one layer above the W(110) surface. This is likewise similar to previous observations for Fe/Cu(1 ML)/W(110). It means that the Cu layer in contact with the W substrate remains intact, while the top Cu layer that is more weakly bound likely intermixes with the Fe film. The details of how the Cu atoms are distributed in the film cannot be ascertained because the current analysis only provides average information over the depth.
Acknowledgements Financial support from the Research Grants Council, University Grants Committee, Hong Kong under Grant HKUST600111 is gratefully acknowledged.
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