Current-driven magnetization switching in ferromagnetic bulk Rashba semiconductor (Ge,Mn)Te
Abstract
Multiferroic materials with both ferroelectric and ferromagnetic orders provide a promising arena for the electrical manipulation of magnetization through the mutual correlation between those ferroic orders. Such a concept of multiferroics may expand to semiconductor with both broken symmetries of spatial inversion and time reversal, that is, polar ferromagnetic semiconductors. Here, we report the observation of current-driven magnetization switching in one such example, (Ge,Mn)Te thin films. The ferromagnetism caused by Mn doping opens an exchange gap in original massless Dirac band of the polar semiconductor GeTe with Rashba-type spin-split bands. The anomalous Hall conductivity is enhanced with increasing hole carrier density, indicating that the contribution of the Berry phase is maximized as the Fermi level approaches the exchange gap. By means of pulse-current injection, the electrical switching of the magnetization is observed in the (Ge,Mn)Te thin films as thick as 200 nm, pointing to the Rashba-Edelstein effect of bulk origin. The efficiency of this effect strongly depends on the Fermi-level position owing to the efficient spin accumulation at around the gap. The magnetic bulk Rashba system will be a promising platform for exploring the functional correlations among electric polarization, magnetization, and current.
INTRODUCTION
In semiconductors without inversion symmetry, spin-orbit interaction causes the spin splitting of the electronic band structure, as exemplified by Rashba (1, 2) and Dresselhaus (3) effects. By applying electric field to those spin-polarized bands, the nonequilibrium spin accumulation occurs, that is, Edelstein effect (4). After the initial observations of the Edelstein effect in inversion broken semiconductors with Rashba and Dresselhaus components (5, 6), the highly efficient spin-charge conversion by the Edelstein effect has been demonstrated for two-dimensional (2D) electronic systems such as interfaces with metal (7) or oxide (8) and surface states of topological insulators (9–15). Recently, the research field has expanded to 3D materials with bulk ferroelectric polarity. The characteristic materials endowed with the bulk Rashba effect are polar semiconductors, such as BiTeX (X = Cl, Br, I) (16, 17) and GeTe (18–20). Among them, the magnetic ion (Mn) doping in GeTe induces the ferromagnetism while keeping the polar crystal structure (Fig. 1A) (21, 22), which may enable the current-driven magnetization switching through the bulk Rashba-Edelstein effect. Although these experiments have been performed in magnetic semiconductors (5) and ferromagnetic metals without inversion symmetry (23), the ferromagnetic bulk Rashba system has an additional merit in terms of the spintronic functionality. The bulk ferroelectric polarity is characteristic of bulk Rashba systems and has a one-to-one correspondence with the spin-momentum locking manner of the Rashba effect; therefore, we can expect the electrical switching of the generated spin moments by switching of the ferroelectric polarity (24). In addition, ferromagnetism possibly causes the exchange-gap opening of the inner Rashba band with the originally massless Dirac dispersion (see Fig. 1B). This anticrossing-type gap formation is ubiquitous in itinerant magnets with spin-orbit interaction, where the Berry curvature governs the intrinsic anomalous Hall conductivity (σAHE) (25). Under this situation, σAHE is strongly enhanced as the Fermi level (EF) becomes close to the gap region—the original position of band-crossing point. The most typical example of this is the quantum anomalous Hall effect in magnetic topological insulators (26, 27). The emergence of large anomalous Hall effect and current-induced magnetization switching in the ferromagnetic Rashba system with EF in the gapped band-crossing point are viewed as the magnetoelectric effect in semiconductor multiferroics (28–30).
Fig. 1 Rashba-Edelstein effect in ferromagnetic Rashba semiconductor (Ge,Mn)Te.
(A) Crystal structure of (Ge,Mn)Te with polar broken inversion symmetry along [111] denoted as P. A unit cell of (Ge,Mn)Te is represented as red lines. (B) Rashba-type spin-polarized band (valence band) by opening the magnetization gap due to broken time-reversal symmetry by ferromagnetic order. Broken lines represent the band structure above the ferromagnetic transition temperature at which the magnetization gap is closed. (C) Principle of Edelstein effect: The application of electric field along the x direction causes the shift in Fermi surfaces (represented as Δkx), resulting in spin accumulation. The black solid and dotted lines represent the Fermi surfaces without and with the application of electric field, respectively. (D) Schematic illustration of magnetization switching in (Ge,Mn)Te caused by current-induced spin-orbit torque. (E) Top-view photograph of a Hall bar device and illustration of measurement configuration.
(Ge,Mn)Te is a suitable platform for the effect owing to concomitance of large spin-split band and ferromagnetic order. The parent compound GeTe is a semiconductor that lacks inversion symmetry by the polar distortion with the displacement of Ge and Te ions along the [111] direction (Fig. 1A). The structural/ferroelectric phase transition temperature TCFE is approximately 700 K (31). The polar crystal structure leads to the finite Rashba-type band splitting. The Rashba parameter of the valence band for GeTe is αR = 2 to 4 eV·Å (19, 32), which is as large as that of the representative polar semiconductor BiTeI (16). Here, because of the natural tendency of Ge deficiency, GeTe tends to be a p-type degenerate semiconductor. Besides its polar semiconducting feature, GeTe can be endowed with the ferromagnetic order by Mn doping. The ferromagnetic transition temperature TCFM depends on Mn content and degree of lattice distortion (22). The highest TCFM reaches 150 K with Mn content around 10%. The polar structure persists up to the critical Mn content, the value of which is approximately 30 and 12% for thin film and bulk crystal, respectively (21, 22).
The ferromagnetic order with the spin moments normal to the film plane modifies the Rashba-type splitting of the valence band, as schematically drawn in Fig. 1B. In the paramagnetic condition above TCFM, there is a degeneracy point where the two spin-split bands cross with each other (depicted as broken lines in Fig. 1B). Below TCFM, by contrast, breaking of time reversal symmetry opens a gap at the degeneracy point via the exchange coupling of the holes with the Mn spin moments, leading to the anticrossing of the two bands (solid lines in Fig. 1B). When EF locates above the anticrossing gap (gray line in Fig. 1B), which is a typical case in this compound, there are two Fermi circles with different radii as shown in Fig. 1C. When the electric field is applied along the x direction, the respective Fermi circles shift in the opposite directions (depicted as Δkx in Fig. 1C) owing to the opposite Fermi velocities between the inner and outer Fermi circles, resulting in the emergence of the nonequilibrium spin accumulation that can cause the current-induced magnetization switching (Fig. 1D). The total spin accumulation is the difference in contributions from the two bands. In this study, we examined the thickness and hole density dependence of the anomalous Hall conductivity and the efficiency of the Rashba-Edelstein effect in the ferromagnetic bulk Rashba semiconductor (Ge,Mn)Te thin films.
RESULTS
Transport properties and anomalous Hall effect
We have grown (Ge,Mn)Te thin films on InP (111) substrates by molecular beam epitaxy (MBE). The composition of Mn was set to 9.1 atomic % to induce the ferromagnetic order and to sustain the polar crystal structure. The Rashba parameter of this composition is evaluated as approximately 2 eV·Å by photoemission spectroscopy (32). The polar crystal structure of our samples was confirmed using x-ray diffraction (see fig. S1). Here, we inserted Sb2Te3 (1 nm) and GeTe (14 nm) as buffer layers to induce the rhombohedral lattice distortion in the Mn-doped films, which led to the higher TCFM of ~80 K than in films with the same Mn content grown directly on a substrate (22). Hole density p of the films unintentionally varies in the range of 1 × 1020 to 5 × 1020 cm−3 with the variation of film thickness, although the films with the thickness ranging from 22 to 192 nm were prepared at the identical growth condition. The difficulty in p control is probably linked to the fact that the Ge deficiency is sensitive to the growth condition such as thermal process and lattice distortion (21). The thickness was tuned by the growth duration by supplying identical Ge, Mn, and Te fluxes. The electrical transport properties were measured using the physical properties measurement system (PPMS; Quantum Design). The 10-μm-wide Hall bar devices (Fig. 1E) are defined using the photolithography technique (see Materials and Methods).
The Hall resistivity Ryx as a function of magnetic field B is exemplified in Fig. 2A for a 192-nm-thick sample. At T = 200 K, which is higher than TCFM, Ryx shows a negative slope below 0.2 T, with an ordinary positive slope at high magnetic field (black line in Fig. 2A). Such a behavior of Ryx typically originates from the coexistence of two types of charge carriers; electron-type (inner Fermi surface) and hole-type (outer Fermi surface) carriers contribute to Ryx in (Ge,Mn)Te when EF locates above the degeneracy point in the spin-split band, as shown in Fig. 1B (the detailed temperature dependence of Ryx is shown in the Supplementary Materials). This EF location is verified by a model calculation of the gapped Rashba band based on the recent results of photoemission spectroscopy (32) and hole density p (see fig. S2). When the system is ferromagnetic at T = 10 K, by contrast, Ryx (shown in red line) represents a clear hysteresis at a low magnetic field region, showing the anomalous Hall effect accompanied by the positive ordinary Hall response. The number of hole density p was evaluated from the slope at a high magnetic field region.
Fig. 2 Transport properties of (Ge,Mn)Te.
(A) Magnetic field dependence of Hall resistivity Ryx for a 192-nm-thick (Ge,Mn)Te film at temperatures of T = 10 K (<TCFM; red) and 200 K (>TCFM; black); the ferromagnetic transition temperature TCFM is approximately 80 K [see (D)]. (B) Magnetic field dependence of anomalous Hall component in Hall conductivity σAHE at T = 10 K for (Ge,Mn)Te thin films with thicknesses of 22, 74, 144, and 192 nm. (C) Top: Ferromagnetic Rashba band structures with EF above (left) and within (right) the exchange gap. Bottom: Hole concentration (p) dependence of spontaneous anomalous Hall conductivity σAHES at T = 10 K for all the measured samples with different thicknesses and p values. The inset shows the p dependence of the Hall angle tanθH. (D) Temperature dependence of σAHES normalized by the value at the lowest temperature T = 2 K for the films with various thicknesses.
To elucidate the anomalous Hall effect in the ferromagnetic Rashba system, we compared the anomalous Hall conductivity σAHE in Fig. 2B for 22-, 74-, 144-, and 192-nm-thick samples that have different carrier densities; here, the anomalous Hall conductivity σAHE is defined by the subtraction of ordinary Hall component from σxy (see fig. S3). The magnetic hystereses of the four samples have similar coercive fields HC ~ 0.15 T but have large differences in magnitude of σAHE. It is worth noting that the tiny humps are observed at around zero field; these may originate from the topological Hall effect that is characteristic of noncoplanar spin configuration with scaler spin chirality, like magnetic skyrmion, in the magnetic systems without inversion symmetry (33, 34). The hole density p dependence of the spontaneous component σAHES (defined as σAHE at B = 0) is summarized in Fig. 2C (see fig. S3 for other samples); σAHES shows a large variation ranging from 0.9 to 13 ohm−1 cm−1. The clear correlation between σAHES and p is in accord with the Berry phase scenario that the anomalous Hall conductivity is enhanced in magnitude as EF becomes close to the magnetization-induced gap (schematically depicted in the top right panel of Fig. 2C). Similar to σAHES, the anomalous Hall angle tanθH, defined as σAHES/σxx(0 T), shows the monotonic increasing behavior with p (shown in the inset of Fig. 2C). The value tanθH = 2 × 10−3 to 3 × 10−3 is a typical or slightly smaller value compared with other magnets such as elemental transition ferromagnets (25), permalloy (35), CoFeB (36), diluted magnetic semiconductor (37), and noncollinear antiferromagnet (38). The temperature dependence of σAHES for various samples (Fig. 2D) indicates that TCFM ~ 80 K is almost independent of samples. The minimal thickness dependence of HC and TCFM in the film ensures homogeneous quality of thin films along the thickness direction as well as little effect from the surface or interface. The notable EF-dependent variation in anomalous Hall conductivity verifies the dominant contribution of Berry phase generated at the magnetization-induced gap (band anticrossing point) in the ferromagnetic Rashba system.
Current-driven magnetization switching
One of the emergent functions of such a multiferroic semiconductor with ferromagnetic Rashba bands is the exertion of spin-orbit torque by the spin-polarized current, which may realize the current-driven magnetization switching (1, 9, 10, 12–15). The current-driven magnetization switching experiment was performed at T = 10 K (<TCFM). The spin accumulation was generated by the injection of pulse currents under the application of small in-plane magnetic field of 0.02 T, which was necessary to determine the final state of the magnetization (see Materials and Methods). To minimize the heating effect of the sample, we set the maximum current density to 6 × 106 A cm−2 in this experiment. After each pulse injection, the Hall resistivity Ryxpulse was measured by the small excitation current (see Materials and Methods) to remove the current-nonlinear contribution of magnon scattering that was pointed out for the case of a magnetic topological insulator (10). Figure 3A shows the change in Hall resistivity ΔRyxpulse for four different thickness samples as a function of the injected current density j (see fig. S5 for other samples). All the samples show similar behaviors. Upon the positive (negative) current pulse under positive 0.02 T (red lines), Ryxpulse starts to change at around j ~ +2 × 106 (−2 × 106) A cm−2 by opening a hysteresis in the reversed scan. The hysteresis direction is reversed when the in-plane magnetic field is reversed (blue lines), verifying that the magnetization is switched by the current-driven spin-orbit torque.
Fig. 3 Experimental observation of current-driven magnetization switching.
(A) Variation in Hall resistivity ΔRyxpulse by current pulse injection for (Ge,Mn)Te thin films with thicknesses of 22, 74, 144, and 192 nm. Red and blue traces correspond to the cases of the in-plane bias magnetic field of +0.02 and −0.02 T, respectively, which are applied along the current direction (depicted in Fig. 1D). (B) Top: Schematic view of the EF shift in ferromagnetic Rashba bands and change in Fermi surface at EF. Bottom: Hole concentration (p) dependence of switching ratio of Hall resistivity defined as ΔRyxpulse/RAHES.
In this measurement range, the maximum value of ΔRyxpulse is ~0.05 microhm·cm, which is approximately 10% of the full magnetization reversal (the Hall resistivity for the full magnetization is shown in the Supplementary Materials). One possible reason for the limited magnetization reversal is the insufficient current density used in this experiment to avoid the heating-induced damage in the thin film. Nevertheless, the sample temperature may increase at high j region, and an intermediate magnetic state may appear with randomly distributed domains, which leads to the saturation of ΔRyxpulse (Fig. 3A) and makes the full reversal difficult. However, the magnitude of j used in this experiment is an order of magnitude smaller than that used in other magnetic materials and 2D Rashba interfaces/surfaces. In addition to small j, because of the warping effect of the band dispersion in this material (Fig. 1C), the spin polarization of the band tends to cant to the out-of-plane direction (32), which may decrease the in-plane spin polarization and efficiency of spin-charge conversion (18). As for the warping effect of the Fermi surface, we have performed the current directional dependence but we observed no discernible difference (see fig. S6). The observation in the (Ge,Mn)Te film as thick as 200 nm exemplifies the bulk-origin Rashba-Edelstein effect, not from surface- or interface-originated one.
DISCUSSION
The Edelstein effect also depends on EF position in the ferromagnetic Rashba band, as shown in the top panel of Fig. 3B. The bottom panel of Fig. 3B shows the hole density dependence of the switching ratio, which is defined as the ratio between ΔRyxpulse at j = 6 × 106 A cm−2 and the spontaneous anomalous Hall resistivity RAHES (Ryx at B = 0 T). As an overall behavior, the switching ratio increases with increasing hole density. This also supports the change in EF position as discussed in Fig. 2C. As the hole density increases, EF becomes closer to the magnetization-induced gap in the inner Rashba band. This gives the shrinking of the inner Fermi surface that suppresses the cancellation of the spin accumulation from the inner and outer bands, as schematically shown in Fig. 3B. The EF-sensitive magnetization switching exemplifies the unique band structure of the ferromagnetic Rashba system to cause the Rashba-Edelstein effect.
In conclusion, we have successfully observed the current-driven magnetization switching in bulk Rashba ferromagnet (Ge,Mn)Te thin films. The injection of pulse current switches the bulk magnetization even in a 192-nm-thick film, which evidences the Rashba-Edelstein effect of bulk origin. Furthermore, the strong EF dependence of the anomalous Hall conductivity and the efficiency of magnetization switching are observed to reflect the bulk band structure of the ferromagnetic Rashba system. These results demonstrate the correlation between electric polarization and magnetization in the ferromagnetic Rashba system as a semiconductor multiferroic.
MATERIALS AND METHODS
Thin-film growth and device fabrication
(Ge,Mn)Te films were fabricated with buffer layers GeTe (14 nm)/Sb2Te3 (1 nm) on semi-insulating InP (111) substrates at 200°C by MBE. The epi-ready substrate was annealed at 340°C in vacuum before the epitaxy. The equivalent pressure of beam flux for Ge, Mn, and Te is 4.5 × 10−6 Pa, 5.0 × 10−7 Pa, and 5.0 × 10−5 Pa, respectively. The Mn composition of 9.1 atomic % was evaluated from the inductively coupled plasma mass spectroscopy measurement. The growth rate of (Ge,Mn)Te was approximately 2.5 nm/min. After the thin-film growth, Hall bar devices with 10 μm in both width and length were defined using ultraviolet photolithography and Ar ion milling. The electrodes Au (25 nm)/Ti (5 nm) were formed by electron beam deposition.
Transport measurement and magnetization switching
Transport measurements were conducted using the DC transport option of PPMS (Quantum Design). The procedure of magnetization switching was as follows. (i) The in-plane magnetic field of 3 T was applied for the initialization of the magnetization. (ii) Under a small in-plane magnetic field, a single pulse current with a duration of 1 ms was injected. (iii) The anomalous Hall resistance was measured with low current (1 mA). (iv) Steps (ii) and (iii) were repeated by varying the pulse height of (ii). We used the Keithley model 6221 as the current source and the Keithley model 2182A as the voltmeter. We made the correction of current density by considering the parallel conduction in buffer layers whose resistivity is 2.5 milliohm·cm at 10 K. Because the resistivity of semi-insulating InP substrate was 10 megohm·cm even at room temperature and became completely insulating at low temperature, we did not need to take into account any parallel conduction in the substrate. During the magnetization switching measurement, the sample temperature was kept at 10 K using the cooling system of PPMS.
Acknowledgments
We thank K. Kondou and M. Kawamura for fruitful discussion. Funding: This research was supported by JSPS/MEXT Grant-in-Aid for Scientific Research(s) (grant nos. 24224009, 24226002, JP17H04846, JP18H04229, and JP15H05853) and CREST, JST (grant no. JPMJCR16F1). Author contributions: Y.T. conceived the project. R.Y. performed the thin-film growth, device fabrication, DC transport measurements, and data analysis. R.Y. and K.Y. performed the magnetization switching measurement. R.Y., A.T., and Y.T. wrote the manuscript with contributions from all authors. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
Supplementary Material
Summary
Section S1. Determination of lattice constants for (Ge,Mn)Te thin films by x-ray diffraction
Section S2. Qualitative evaluation of EF in (Ge,Mn)Te
Section S3. Electronic transport properties of the (Ge,Mn)Te samples
Section S4. Temperature dependence of Hall resistivity
Section S5. Current-induced magnetization reversal for all samples
Section S6. Current-directional dependence of magnetization switching
Section S7. In-plane bias magnetic field dependence of magnetization switching
Section S8. Repeated injection of pulses lower than saturation current density
Section S9. The estimation of spin Hall efficiency
Section S10. Correction of current flow to buffer layers
Section S11. Magnetization measurement
Fig. S1. Reciprocal space analysis for the in- and out-of-plane lattice constants of (Ge,Mn)Te thin film.
Fig. S2. Calculated band structure of (Ge,Mn)Te for x = 0.08.
Fig. S3. Transport properties for all samples.
Fig. S4. Temperature dependence of Hall resistivity.
Fig. S5. Current-induced magnetization for all samples.
Fig. S6. Current-directional dependence of magnetization switching.
Fig. S7. In-plane bias magnetic field dependence of magnetization switching.
Fig. S8. Repeated injection of pulses lower than saturation current density.
Fig. S9. Second-harmonic Hall resistivity.
Fig. S10. Temperature dependence of resistivity of the GeTe/Sb2Te3 thin film.
Fig. S11. Magnetization measurement for 74- and 192-nm-thick samples.
Table S1. Physical parameters for the effective band model of (Ge,Mn)Te.
Table S2. Current ratio for all samples.
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Published In
Science Advances
Volume 4 | Issue 12
December 2018
December 2018
Copyright
Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).
This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.
Submission history
Received: 26 April 2018
Accepted: 6 November 2018
Acknowledgments
We thank K. Kondou and M. Kawamura for fruitful discussion. Funding: This research was supported by JSPS/MEXT Grant-in-Aid for Scientific Research(s) (grant nos. 24224009, 24226002, JP17H04846, JP18H04229, and JP15H05853) and CREST, JST (grant no. JPMJCR16F1). Author contributions: Y.T. conceived the project. R.Y. performed the thin-film growth, device fabrication, DC transport measurements, and data analysis. R.Y. and K.Y. performed the magnetization switching measurement. R.Y., A.T., and Y.T. wrote the manuscript with contributions from all authors. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
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