⇦Chinese Physics Letters, 2022, Vol. 39, No. 10, Article code 108501 Enhanced Anomalous Hall Effect of Pt on an Antiferromagnetic Insulator with Fully Compensated Surface Yu Bai1,3†, Zhe Wang3†, Na Lei6†, Wisal Muhammad1,3, Lifeng Xiang1,3, Qiang Li1,3, Huilin Lai1,3, Yinyan Zhu1,2,4, Wenbing Wang1,2,4, Hangwen Guo1,2,4, Lifeng Yin1,2,3,4,5,8*, Ruqian Wu7*, and Jian Shen1,2,3,4,5,8* Affiliations 1State Key Laboratory of Surface Physics and Institute for Nanoelectronics Devices and Quantum Computing, Fudan University, Shanghai 200433, China 2Shanghai Qi Zhi Institute, Shanghai 200232, China 3Department of Physics, Fudan University, Shanghai 200433, China 4Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai 201210, China 5Shanghai Research Center for Quantum Sciences, Shanghai 201315, China 6Fert Beijing Institute, BDBC, School of Electronic and Information Engineering, Beihang University, Beijing 100191, China 7Department of Physics and Astronomy, University of California, Irvine, California 92697, USA 8Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China Received 1 August 2022; accepted manuscript online 13 September 2022; published online 23 September 2022 †Yu Bai, Zhe Wang and Na Lei contributed equally to this work.
*Corresponding authors. Email: lifengyin@fudan.edu.cn; wur@uci.edu; shenj5494@fudan.edu.cn Citation Text: Bai Y, Wang Z, Lei N et al. 2022 Chin. Phys. Lett. 39 108501    Abstract We report a significantly enhanced anomalous Hall effect (AHE) of Pt on antiferromagnetic insulator thin film (3-unit-cell La$_{0.7}$Sr$_{0.3}$MnO$_{3}$, abbreviated as LSMO), which is one order of magnitude larger than that of Pt on other ferromagnetic (e.g. Y$_{3}$Fe$_{5}$O$_{12}$) and antiferromagnetic (e.g. Cr$_{2}$O$_{3}$) insulator thin films. Our experiments demonstrate that the antiferromagnetic La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ with fully compensated surface suppresses the positive anomalous Hall resistivity induced by the magnetic proximity effect and facilitates the negative anomalous Hall resistivity induced by the spin Hall effect. By changing the substrate's temperature during Pt deposition, we observed that the diffusion of Mn atoms into Pt layer can further enhance the AHE. The anomalous Hall resistivity increases with increasing temperature and persists even well above the Neel temperature ($T_{\rm N}$) of LSMO. The Monte Carlo simulations manifest that the unusual rise of anomalous Hall resistivity above $T_{\rm N}$ originates from the thermal induced magnetization in the antiferromagnetic insulator.
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 DOI:10.1088/0256-307X/39/10/108501 © 2022 Chinese Physics Society Article Text The anomalous Hall effect (AHE) often occurs in ferromagnetic materials with either intrinsic[1] or extrinsic[2,3] physical origins, which can be understood within the scope of momentum-space Berry curvatures.[4] Besides the conventional AHE in bulk ferromagnets, interfacial AHE can emerge in nonmagnetic/ferromagnetic metal (FMM) heterostructures due to interfacial scattering.[5-16] To suppress the contribution of bulk AHE from the FMM layer, ferromagnetic insulator (FMI) has been used to replace the conducting FMM layer and an AHE-like transverse contribution due to the spin Hall effect (SHE) was found in a Pt/Y$_{3}$Fe$_{5}$O$_{12}$ (YIG) heterostructure.[17] Follow-up works have revealed that both the magnetic proximity effect (MPE) and the SHE contribute to AHE of Pt/YIG.[18-22] The MPE induced anomalous Hall effect (MPE-AHE) is pronounced at low temperature, while the SHE induced anomalous Hall effect (SHE-AHE) dominates at elevated temperature. The MPE-AHE and the SHE-AHE have opposite signs and opposite temperature dependences, leading to a sign reversal around 50 K for the anomalous Hall resistance of the Pt/YIG heterostructure,[18,19] as shown in Fig. S1(b) in the Supplementary Information. Similar results have been reported in other systems, such as Pt/Y$_{3}$Fe$_{5-x}$Al$_{x}$O$_{12}$,[20] W/YIG,[21] and Pt/Tm$_{3}$Fe$_{5}$O$_{12}$ (TmIG).[22] To boost the SHE-AHE and thus the total anomalous Hall resistivity at elevated temperatures, it would be ideal to further suppress the MPE-AHE using antiferromagnetic insulator (AFMI) instead of FMI. Attempts were made using Cr$_{2}$O$_{3}$[23] as the AFMI to interface with Pt but no noticeable enhancement of total anomalous Hall resistivity was observed compared to that of the Pt/YIG.[19,20] This is not surprising considering the fact that the surface of the AFMI Cr$_{2}$O$_{3}$ has an uncompensated spin structure.[24] In this Letter, we use a 3-unit-cell (UC) La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ (LSMO) grown on SrTiO$_{3}$(100) substrate, which is known to have a fully compensated surface spin structure,[25-28] as the AFMI layer to interface with Pt. Remarkably, the anomalous Hall resistivity of Pt/3-UC LSMO is enhanced by one order of magnitude compared to that of Pt/YIG because the MPE-AHE is effectively suppressed. The total anomalous Hall resistivity is dominated by SHE-AHE and increases monotonically with temperature well above the Neel temperature ($T_{\rm N}$) of the 3-UC LSMO film. The Monte Carlo simulations indicate that such unusual temperature dependence of the anomalous Hall resistivity originates from the thermo-induced short-range magnetic order in AFMI. LSMO films were epitaxially grown on SrTiO$_{3}$ substrates using pulse laser deposition with an energy density of 2 J/cm$^{2}$ (248 nm, 2 Hz).[25,29] During the growth, the substrate was held at 800 ℃ in an oxygen (8% ozone) environment of $3.5 \times 10^{-3}$ Torr. The thickness and the growth quality of the films were monitored by reflection high energy electron diffraction (RHEED). After that, the LSMO films were transferred in situ into a molecular beam epitaxy chamber with base pressure of $1 \times 10^{-10}$ Torr for the deposition of 2 nm Pt thin films at room temperature. The Pt/LSMO heterostructures were patterned into the Hall-bar mesa geometry using photolithography and Ar ion beam milling. The sample dimension is shown in Fig. 1(a). The width $w$ of the Hall bar is 100 µm and the distance $l$ between two longitudinal pads is 600 µm. Transport and magnetic measurements were carried out using a Quantum Design physical property measurement system (PPMS) and a superconducting quantum interference device (SQUID), respectively. For transport measurements, the charge current density $j_{\rm e}$ was applied in the $x$-direction along the Hall bar, where $V_{xx}$ and $V_{xy}$ are the voltages along the $x$ and $y$ directions, respectively.
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Fig. 1. (a) Schematic of the Pt/LSMO Hall bar samples. (b) $M$–$T$ curves of LSMO measured by SQUID. (c) Hysteresis loops of 3-UC and 6-UC LSMO samples. (d) $\rho $–$T$ curves of pure LSMO films measured by PPMS. Both 3-UC and 6-UC LSMOs show insulator behavior. (e) $\rho $–$T$ curves of Pt/LSMO heterostructure measured by PPMS both show conductor behavior. (f) The temperature dependence of AMR of 2 nm Pt/3-UC LSMO and 2 nm Pt/6-UC LSMO from 10 K to 300 K.
The magnetization versus temperature ($M$–$T$) curves of 3-UC and 6-UC LSMO samples (without Pt) are shown in Fig. 1(b) with a 500 Oe magnetic field applied along the surface normal. The $M$–$T$ curve of the 6-UC LSMO suggests a ferromagnetic behavior with curie temperature ($T_{\rm C}$) around 125 K, and the hysteresis loop in Fig. 1(c) gives a saturation magnetic moment of 2 $\mu_{\scriptscriptstyle{\rm B}}$/Mn. The $M$–$T$ curve of the 3-UC LSMO only has a small upturn around 40 K, which is consistent with the previous observation of an antiferromagnetic behavior based on exchange bias measurements.[26] The resistivity versus temperature ($\rho $–$T$) curves in Fig. 1(d) increase quickly with cooling, and even beyond the limit of Keithley 2400 source meter at low temperature, which indicates that both samples are well defined insulators. In comparison, the resistivity of the 2 nm Pt capped LSMO films [Fig. 1(e)] drops by 7 orders of magnitude, which ensures that the electric current flows within the Pt layer. Figure 1(f) shows the result of anisotropic magneto resistance (AMR) measurement with 1.5 T magnetic field, calculated by ${\Delta \rho}_{xx} / \rho_{xx}$. According to the AMR results, there is no MPE in the case of Pt/3-UC LSMO, while MPE does exist in Pt/6-UC LSMO below $T_{\rm C}$ (125 K). The field-dependent Hall resistivity can be calculated by $\rho_{xy}=(V_{xy} / I_{xx})d_{\mathrm{Pt}}$, where $d_{\mathrm{Pt}}$ is the thickness of the Pt layer; $\rho_{xy}$ includes the ordinary Hall resistivity ($\rho_{_{\scriptstyle \mathrm{OHE}}}$) and the anomalous Hall resistivity ($\rho_{_{\scriptstyle \mathrm{AHE}}}$) and can be expressed as $\rho_{xy}=\rho_{_{\scriptstyle \mathrm{OHE}}} +\rho_{_{\scriptstyle \mathrm{AHE}}}$. After subtracting $\rho_{_{\scriptstyle \mathrm{OHE}}}$, we plot magnetic-field-dependent $\rho_{_{\scriptstyle \mathrm{AHE}}}$ of the Pt/3-UC LSMO measured at various temperatures from 10 K to 375 K in Fig. 2(a). It is clear that the sign of $\rho_{_{\scriptstyle \mathrm{AHE}}}$ remains negative in this temperature range, unlike the sign reversal of Pt/YIG at 50 K.[18] Since the MPE in Pt/3-UC LSMO is absent based on our AMR measurements in Fig. 1(f), we may conclude that the measured $\rho_{_{\scriptstyle \mathrm{AHE}}}$ mainly results from the SHE-AHE. In fact, $\rho_{_{\scriptstyle \mathrm{AHE}}}$ has negative sign even at 10 K, which is rescaled in Fig. 2(c) for a better view.
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Fig. 2. (a) and (b) Magnetic field dependence of $\rho_{_{\scriptstyle \mathrm{AHE}}}$, obtained from 10 K to 375 K with the magnetic field along $z$ direction from $-3$ T to 3 T of 2 nm Pt on 3-UC LSMO and 6-UC LSMO. (c) The field dependence of $\rho_{_{\scriptstyle \mathrm{AHE}}}$ of 2 nm Pt/3-UC LSMO and 2 nm Pt/6-UC LSMO at 10 K, which clearly show the sign reversal. (d) The temperature dependence of $\rho_{_{\scriptstyle \mathrm{AHE}}}$ of 2 nm Pt/3-UC LSMO and 2 nm Pt/6-UC LSMO from 10 K to 375 K.
Strikingly, as shown in Fig. 2(a), $\rho_{_{\scriptstyle \mathrm{AHE}}}$ of the Pt/3-UC LSMO increases with temperature even above $T_{\rm N}$, and finally saturates around 375 K. While such kind of temperature dependence is opposite to that of Pt/YIG,[30] similar behavior was also observed in Pt/Cr$_{2}$O$_{3}$,[23] implying that the interfacial AHE in Pt/AFMI may have a different physical origin. This is especially true considering the fact that the net magnetization of AFMI becomes vanishingly small above $T_{\rm N}$ as in the case of the present 3-UC LSMO system. For the 6-UC LSMO, although the global physical behavior is similar to that of an FMI, it has a more complicated magnetic configuration than the pure FMI state in YIG. According to our previous studies for 6-UC LSMO,[25] the bottom 3-UC LSMO is in the pure AFMI phase, while the topmost 3-UC is phase separated FMM domains inside an AFMI matrix. As shown in Fig. 2(c), the positive sign of $\rho_{_{\scriptstyle \mathrm{AHE}}}$ and the none zero coercivity field at 10 K clearly indicate the existence of MPE in Pt/6-UC LSMO, similar to that of Pt/YIG below 50 K.[18] The $\rho_{_{\scriptstyle \mathrm{AHE}}}$ at 50 K in Fig. 2(b) displays a butterfly-like behavior as a result of the competition between the SHE-AHE and the MPE-AHE. Further increasing temperature to 100 K (near $T_{\rm c}$), the MPE is vanishingly small and the total AHE is dominated by the SHE-AHE with a negative sign. Beyond 150 K, the $\rho_{_{\scriptstyle \mathrm{AHE}}}$ curves show a pronounced upturn at the saturation field, which appears to originate from the topological Hall effect (THE) due to the thermally driven spin chirality fluctuation near the domain boundary of the AFM phase and the FM phase in the 6-UC LSMO. Similar THE has also been observed in Pt on systems with complex magnetic configurations above their ordering temperature, such as Pt/TmIG[31] and Pt/Cr$_{2}$O$_{3}$.[23] Figure 2(d) shows the saturated $\rho_{_{\scriptstyle \mathrm{AHE}}}$ deduced from Figs. 2(a) and 2(b) under a magnetic field of 3 T as a function of temperature for Pt on the 3-UC and 6-UC LSMO films. With the increase of temperature, the magnitude of $\rho_{_{\scriptstyle \mathrm{AHE}}}$ of the Pt/3-UC LSMO sample increases from $1.0 \times 10^{-3}\,µ \Omega \cdot $cm at 10 K to $1.8 \times 10^{-2}\,µ \Omega \cdot$cm at 375 K, which is one order of magnitude larger than that of the Pt/YIG.[19,20] For the Pt/6-UC LSMO sample, $\rho_{_{\scriptstyle \mathrm{AHE}}}$ changes from about $2.1 \times 10^{-4}\,µ \Omega\cdot$cm at 10 K to $-1.2 \times 10^{-2}\,µ \Omega\cdot$cm at 375 K with a sign reversal. To show the enhancement, the Hall resistance and anomalous Hall resistance of Pt/YIG and Pt/LSMO are compared side by side in Fig. S1 in the Supplementary Information. To better understand the nature of the interfacial AHE in the Pt/LSMO system, we carried out several controlled experiments. Figures 3(a) and 3(b) show the $\rho_{_{\scriptstyle \mathrm{AHE}}}$ versus temperature for Pt grown at 75 K, 300 K and 370 K on the 3-UC and the 6-UC LSMO films, respectively. In general, higher growth temperature of Pt tends to generate more intermixing between Mn and Pt, which should affect the SHE-AHE accordingly. For both cases, $\rho_{_{\scriptstyle \mathrm{AHE}}}$ is larger when Pt is grown at higher temperature. For example, $\rho_{_{\scriptstyle \mathrm{AHE}}}$ of Pt deposited at 370 K is one order of magnitude larger than that of Pt deposited at 75 K for the measuring temperature of 375 K. This evidently indicates that the SHE-AHE is enhanced by the intermixing between Mn and Pt atoms. Figure 3(c) shows the Pt thickness dependence of $\rho_{_{\scriptstyle \mathrm{AHE}}}$ for Pt grown on the 3-UC LSMO. The $\rho_{_{\scriptstyle \mathrm{AHE}}}$ value decreases with increasing Pt thickness, confirming that the interfacial effect plays the key role. Indeed, insertion of a 2 nm Cu layer between Pt and 6-UC LSMO completely diminishes the AHE, with only ordinary Hall effect left as shown in Fig. 3(d). For comparison, the Hall resistivity $\rho_{xy}$ of 2 nm Pt/6-UC LSMO without the subtraction of $\rho_{_{\scriptstyle \mathrm{OHE}}}$ is also shown in Fig. 3(d), which exhibits the same linear slope. Results of these controlled experiments all prove that the AHE in the present Pt/LSMO systems originates from the interface of Pt/LSMO. To investigate the role of Mn impurities in Pt, we measured the Hall resistivity of 2 nm Pt$_{100}$Mn$_{1}$/SrTiO$_{3}$(001). As shown in Fig. S2(a) in the Supplementary Information, AHE is almost unvisitable, which proves that only the diluted Mn impurities in Pt at the interface are not sufficient to exhibit AHE, and it needs the help of underlying LSMO through the exchange interaction.
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Fig. 3. (a) and (b) Temperature dependence of $\rho_{_{\scriptstyle \mathrm{AHE}}}$ for 2 nm Pt/3-UC LSMO and 2 nm Pt/6-UC LSMO grown at substrate temperatures of 75 K, 300 K, and 370 K, respectively. (c) Temperature dependence of $\rho_{_{\scriptstyle \mathrm{AHE}}}$ of 1 nm, 2 nm and 3 nm Pt on 3-UC LSMO grown at 300 K. (d) Magnetic field dependence of $\rho_{xy}$ (without the subtraction of $\rho_{_{\scriptstyle \mathrm{OHE}}}$) of 2 nm Pt/6-UC LSMO and 2 nm Pt/2 nm Cu/6-UC LSMO deposited and measured at 300 K.
Another puzzle is the origin of AHE above $T_{\rm N}$ in our system. For finite size AFM systems such as nanoparticles, it has been reported that thermal fluctuation can induce a net magnetization.[32] The two spin sublattices in AFM nanoparticles exhibit asymmetric moment canting under an external magnetic field, resulting in a nonzero magnetization as sketched in Fig. 4(a). Thermal fluctuation in fact turns to increase the canting asymmetries and produces net moment in AFM systems. Such a thermal induced magnetization is shown to increase linearly with temperature. As a matter of fact, the existence short-range magnetic order in AFM manganites has been observed at temperatures as high as 530 K, which is 4.5 times higher than their $T_{\rm N}$.[33] To further prove this argument, we measured the Hall resistivity of 2 nm Pt/2 nm Mn/SrTiO$_{3}$(001). As shown in Fig. S2(b) in the Supplementary Information, although $T_{\rm N}$ of bulk Mn is 95 K, AHE clearly appears at 100 K and gets significantly enhanced at 300 K, which is the evidence of the existence of short-range magnetic order above $T_{\rm N}$. For the same reason, nonzero magnetization can be induced by the thermal fluctuation in the AFM LSMO layer in our samples. Such a thermal induced magnetization may modulate the AHE through two mechanisms. Firstly, the spin current reflection at the interface is enhanced, resulting in stronger SHE-AHE with increasing temperature. Secondly, there are diffused Mn atoms in the Pt layers near the interface region. The magnetic moments of these Mn impurities can be pinned through the exchange interaction with the underlying LSMO, producing extra berry-phase contribution toward the anomalous Hall resistivity. To demonstrate this, we performed systematic Monte Carlo (MC) simulations. Our MC simulations are based on a classical Heisenberg model described by the following Hamiltonian: \begin{eqnarray} H=-\frac{1}{2}\sum\limits_{ij} {J_{ij}S_{i}\cdot S_{j}} -K\sum\limits_i (S_{i}^{z})^{2} +g\mu_{\scriptscriptstyle{\rm B}}B\cdot S_{i}^{z}, \notag \end{eqnarray} where $J_{\mathrm{ij}}$ represents exchange interactions, $K$ is the single-ion magnetic anisotropy, $g = 2$ is the electron spin $g$ factor, $\mu_{\scriptscriptstyle{\rm B}}$ is the Bohr magneton, and $B$ is the external magnetic field. The model of Pt/LSMO interface is shown in Fig. 4(b), which contains 3-UC AFM LSMO and one layer of Mn impurities. Each layer of LSMO has $30 \times 30$ spins represented by a unit vector $S_{i}$, and the Mn impurity layer consists of evenly distributed $10 \times 10$ spins. To capture the C-AFM nature of the LSMO layer, its inter-layer exchange interaction was set to the corresponding bulk value, $J_{\bot}=22.5$ meV (FM), while the intra-layer exchange interaction was set to $J_{\parallel}=-10$ meV (AFM). The exchange interaction $J_{\mathrm{int}}$ between Mn in Pt and Mn in LSMO was assumed to be 20 meV. For the single-ion magnetic anisotropy of Mn in LSMO, we adopted a typical value of $K=0.1$ meV. An external magnetic field of $B = 3$ T was applied to lift the degeneracy. We used $10^{4}$ MC steps per site to equilibrate the system, and $10^{5}$ MC steps per site for statistical averaging.
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Fig. 4. (a) Schematic illustration of the two uniform precession modes exited by thermal fluctuations in AFM materials. The red and blue arrows are magnetization vectors of the sublattices, and the black arrow is the net magnetization. The two modes are degenerated without external magnetic fields. (b) Schematic model of our Monte Carlo simulations. (c) Magnetization of Mn in LSMO and Mn impurities in Pt as a function of temperature.
The simulated magnetization as a function of temperature is shown in Fig. 4(c), in which the blue and red lines represent net magnetic moments of Mn in LSMO and Mn in Pt, respectively. At zero temperature, the magnetic moments of both LSMO layer and Mn impurities are zero. When the temperature increases, a finite magnetization emerges and increases with temperature up to $T_{\rm N}$. This thermally induced magnetic moment decreases very slowly above $T_{\rm N}$, which may explain why the AHE of Pt/Cr$_{2}$O$_{3}$[23] and Pt/LSMO survive well above ordering temperature. Through the exchange interaction between Mn atoms across the interface, Mn-impurities embedded in Pt show larger magnetic moments, about 2.7 times higher compared to the largest magnetic moment of Mn atoms in the AFM LSMO layer. Obviously, the interdiffusion of Mn is another important factor that enhances the AHE of Pt/LSMO as observed in our experiments. In summary, a 3-UC LSMO/STO (100) thin film with fully compensated surface allows the observation of a pure SHE-AHE when interfaced with Pt. In addition, the diffusion of Mn atoms into the Pt layers near the interface can further enhance the SHE-AHE. These two effects make the anomalous Hall resistivity of Pt/3-UC LSMO one order of magnitude larger than that of Pt/YIG. Interestingly, the anomalous Hall resistivity increases with increasing temperature even beyond $T_{\rm N}$. Based on our Monte Carlo simulation, the temperature dependence is attributed to thermally induced magnetization in AFMI LSMO and adjacent Mn atoms. The significantly enhanced AHE at interfaces of heavy metal and AFMI above room temperature is highly valuable for applications of antiferromagnetic spintronics.[34] Acknowledgments. This work was supported by the National Key Research Program of China (Grant No. 2020YFA0309100), the National Natural Science Foundation of China (Grant Nos. 11991062, 12074075, 12074073, 12074071, and 11904052), the Shanghai Municipal Science and Technology Major Project (Grant No. 2019SHZDZX01), and the Shanghai Municipal Natural Science Foundation (Grant Nos. 20501130600, 22ZR1407400, and 22ZR1408100). References Hall Effect in FerromagneticsThe spontaneous hall effect in ferromagnetics IISide-Jump Mechanism for the Hall Effect of FerromagnetsAnomalous Hall effectMagnetoresistance and Hall effect in epitaxial Co-Au superlatticesTemperature and Co thickness dependent sign change of the anomalous Hall effect in Co/Pd multilayers: An experimental and theoretical studyExtraordinary Hall effect in Co-Pd bilayersReversal of the extraordinary Hall effect polarity in thin Co/Pd multilayersEffects of surface and interface scattering on anomalous Hall effect in Co/Pd multilayersMagnetic anisotropy and anomalous Hall effect of ultrathin Co/Pd bilayersScaling behavior of giant magnetotransport effects in Co/Cu superlatticesExtraordinary Hall effect in (111) and (100)-orientated Co/Pt superlatticesPolarity of anomalous Hall effect hysteresis loops in [Pt∕Co]15∕AF∕[Co∕Pt]15 (AF=FeMn, NiO) multilayers with perpendicular anisotropyExtraordinary Hall effect in thin magnetic films and its potential for sensors, memories and magnetic logic applicationsLarge extraordinary Hall effect in [ Pt / Co ] 5 / Ru / [ Co / Pt ] 5 multilayersAnomalous Hall effect in Fe/Gd bilayersSpin Hall Magnetoresistance Induced by a Nonequilibrium Proximity EffectTransport Magnetic Proximity Effects in PlatinumMagnetotransport in metal/insulating-ferromagnet heterostructures: Spin Hall magnetoresistance or magnetic proximity effectMagnetic Proximity Effect and Anomalous Hall Effect in Pt / Y 3 Fe 5 − x Al x O 12 HeterostructuresStatic and dynamic origins of interfacial anomalous Hall effect in W/YIG heterostructuresAnomalous Hall effect in magnetic insulator heterostructures: Contributions from spin-Hall and magnetic-proximity effectsEvidence of the Topological Hall Effect in Pt/Antiferromagnetic Insulator BilayersImaging and Control of Surface Magnetization Domains in a Magnetoelectric AntiferromagnetThickness-driven first-order phase transitions in manganite ultrathin filmsExchange bias coupling of Co with ultrathin La2/3 Sr1/3 MnO3 filmsInterface Effects in Perovskite Thin FilmsEvidence of Orbital Reconstruction at Interfaces in Ultrathin La 0.67 Sr 0.33 MnO 3 FilmsEmergent phenomena in manganites under spatial confinementSpin Hall magnetoresistance at high temperaturesSpin-Hall Topological Hall Effect in Highly Tunable Pt/Ferrimagnetic-Insulator BilayersThermoinduced Magnetization in Nanoparticles of Antiferromagnetic MaterialsEvidence for a High-Temperature Short-Range-Magnetic-Order Transition in MnO(001)Antiferromagnetic spintronics
[1] Karplus R and Luttinger J M 1954 Phys. Rev. 95 1154
[2] Smit J 1958 Physica 24 39
[3] Berger L 1970 Phys. Rev. B 2 4559
[4] Nagaosa N, Sinova J, Onoda S, MacDonald A H, and Ong N P 2010 Rev. Mod. Phys. 82 1539
[5] Vavra W, Lee C H, Lamelas F J, He H, Clarke R, and Uher C 1990 Phys. Rev. B 42 4889
[6] Keskin V, Schmalhorst B A J, Reiss G, Zhang H, Weischenberg J, and Mokrousov Y 2013 Appl. Phys. Lett. 102 022416
[7] Shaya O, Karpovski M, and Gerber A 2007 J. Appl. Phys. 102 043910
[8] Rosenblatt D, Karpovski M, and Gerber A 2010 Appl. Phys. Lett. 96 022512
[9] Guo Z B, Mi W B, Aboljadayel R O, Zhang B, Zhang Q, Barba P G, Manchon A, and Zhang X X 2012 Phys. Rev. B 86 104433
[10] Kou X L, Schmalhorst J M, Keskin V, and Reiss G 2012 J. Appl. Phys. 112 093915
[11] Tsui F, Chen B X, Barlett D, Clarke R, and Uher C 1994 Phys. Rev. Lett. 72 740
[12] Canedy C L, Li X W, and Xiao G 1997 J. Appl. Phys. 81 5367
[13] Christides C and Speliotis T 2005 J. Appl. Phys. 97 013901
[14] Moritz J, Rodmacq B, Auffret S, and Dieny B 2008 J. Phys. D 41 135001
[15] Zhao J, Wang Y J, Han X F, Zhang S, and Ma X H 2010 Phys. Rev. B 81 172404
[16] Xu W J, Zhang B, Liu Z X, Wang Z, Li W, Wu Z B, Yu R H, and Zhang X X 2010 Europhys. Lett. 90 27004
[17] Nakayama H, Althammer M, Chen Y T, Uchida K, Kajiwara Y, Kikuchi D, Ohtani T, Geprägs S, Opel M, Takahashi S, Gross R, Bauer G E W, Goennenwein S T B, and Saitoh E 2013 Phys. Rev. Lett. 110 206601
[18] Huang S Y, Fan X, Qu D, Chen Y P, Wang W G, Wu J, Chen T Y, Xiao J Q, and Chien C L 2012 Phys. Rev. Lett. 109 107204
[19] Zhou X, Ma L, Shi Z, Fan W J, Zheng J G, Evans R F L, and Zhou S M 2015 Phys. Rev. B 92 060402(R)
[20] Liang X, Shi G Y, Deng L J, Huang F, Qin J, Tang T T, Wang C T, Peng B, Song C, and Bi L 2018 Phys. Rev. Appl. 10 024051
[21] Ma L, Fu H R, Tang M, Qiu X P, Shi Z, You C Y, Tian N, and Zheng J G 2020 Appl. Phys. Lett. 117 122405
[22] Ding S L, Liang Z Y, Yun C, Wu R, Xue M Z, Lin Z C, Ross A, Becker S, Yang W Y, Ma X B, Chen D F, Sun K, Jakob G, Kläui M, and Yang J B 2021 Phys. Rev. B 104 224410
[23] Cheng Y, Yu S S, Zhu M L, Hwang J, and Yang F Y 2019 Phys. Rev. Lett. 123 237206
[24] Wu N, He X, Wysocki A L, Lanke U, Komesu T, Belashchenko K D, Binek C, and Dowben P A 2011 Phys. Rev. Lett. 106 087202
[25] Chen H Y, Yu Y, Wang Z, Bai Y, Lin H X, Li X L, Liu H, Miao T, Kou Y F, Zhang Y S, Li Y, Tang J, Wang Z C, Cai P, Zhu Y Y, Cheng Z H, Zhong X Y, Wang W B, Gao X Y, Yin L F, Wu R Q, and Shen J 2019 Phys. Rev. B 99 214419
[26] Shi Y J, Zhou Y, Ding H F, Zhang F M, Pi L, Zhang Y H, and Wu D 2012 Appl. Phys. Lett. 101 122409
[27] Lepetit M B, Mercey B, and Simon C 2012 Phys. Rev. Lett. 108 087202
[28] Tebano A, Aruta C, Sanna S, Medaglia P G, Balestrino G, Sidorenko A A, De Renzi R, Ghiringhelli G, Braicovich L, Bisogni V, and Brookes N B 2008 Phys. Rev. Lett. 100 137401
[29] Shen J, Ward T Z, and Yin L F 2013 Chin. Phys. B 22 017501
[30] Uchida K I, Qiu Z Y, Kikkawa T, Iguchi R, and Saitoh E 2015 Appl. Phys. Lett. 106 052405
[31] Ahmed A S, Lee A J, Bagués N, McCullian B A, Thabt A M A, Perrine A, Wu P, Rowland J R, Randeria M, Hammel P C, McComb D W, and Yang F Y 2019 Nano Lett. 19 5683
[32] Mørup S and Frandsen C 2004 Phys. Rev. Lett. 92 217201
[33] Hermsmeier B, Osterwalder J, Friedman D J, and Fadley C S 1989 Phys. Rev. Lett. 62 478
[34] Baltz V, Manchon A, Tsoi M, Moriyama T, Ono T, and Tserkovnyak Y 2018 Rev. Mod. Phys. 90 015005