Unidirectional Spin Hall Magnetoresistance Research Articles

Evaluation of Spin Hall Effect in Ferromagnets by Means of Unidirectional Spin Hall Magnetoresistance in Ta/Co Bilayers

Evaluation of Spin Hall Effect in Ferromagnets by Means of Unidirectional Spin Hall Magnetoresistance in Ta/Co Bilayers

Charge-to-spin conversion in fully epitaxial Ru/Cu hybrid nanolayers with interface control

The demonstration of the charge-to-spin conversion, especially with enhanced spin Hall conductivity, is crucial for the development of energy-efficient spintronic devices such as spin–orbit torque (SOT) based magnetoresistive random access memories. In this work, fully epitaxial Ru/Cu heterostructures were fabricated with interface engineering and nanolayer insertions consisting of Cu (1 nm)/Ru (1 nm) structures with different numbers of periods. The atomically controlled interface was confirmed by the high-resolution high-angle annular dark-field scanning transmission electron microscopy, and the epitaxial relationship persists even in the hybrid nanolayer insertion structures. The spin current generation was detected by the measurement of unidirectional spin Hall magnetoresistance, and the effective damping-like spin Hall efficiency (ξ DL) was further quantitatively evaluated by the spin-torque ferromagnetic resonance with thickness dependence of the ferromagnetic layer. It is found that the sharp interface Ru/Cu film has a sizeable ξ DL of −2.2% and the insertion of Cu/Ru nanolayers at the interface can increase the ξ DL value to −3.7%. The former could be attributed to the interface spin–orbit filtering effect and the latter may be further understood by the intrinsic contribution from the local electronic structure tuning due to the lattice distortion near the interface. A large effective spin Hall conductivity is achieved to be (3∼5) × 105 Ω−1 m−1 in the epitaxial Ru/Cu hybrid nanolayers, which is in the same range as that of platinum. This work indicates that the interfacial control with hybrid nanolayer structures can extend the SOT-based materials to highly conductive metals, even with weak spin–orbit interactions, toward high stability, low cost, and low energy consumption for spintronic applications.

Observation of the Unidirectional Magnetoresistance in Antiferromagnetic Insulator Fe2O3/Pt Bilayers

AbstractUnidirectional magnetoresistance (UMR) has been observed in a variety of stacks with ferromagnetic/spin Hall material bilayer structures. In this work, UMR in antiferromagnetic insulator Fe2O3/Pt structure is reported. The UMR has a negative value, which is related to interfacial Rashba coupling and band splitting. Thickness‐dependent measurement reveals a potential competition between UMR and the unidirectional spin Hall magnetoresistance (USMR). This work reveals the existence of UMR in antiferromagnetic insulators/heavy metal bilayers and broadens the way for the application of antiferromagnet‐based spintronic devices.

Effects of thermal annealing on the spin–orbit torque and unidirectional spin Hall magnetoresistance in Pt/CoFe/Ta trilayers

We investigated the spin–orbit torque (SOT) and unidirectional spin Hall magnetoresistance (USMR) in Pt/CoFe/Ta trilayer as well as Pt/CoFe and CoFe/Ta bilayers with in-plane magnetic anisotropy by performing transverse and longitudinal second harmonic resistance measurements. Compared to the two bilayers, we found that the trilayer exhibits enhanced SOT and USMR due to the opposite spin Hall angles of Pt and Ta, which work together to enhance the spin accumulation in the trilayer. Furthermore, we found that thermal annealing has a significant influence on the magnitude and sign of the SOT and USMR in the Pt/CoFe/Ta trilayers. Specifically, we observed that both the damping-like SOT and USMR of the trilayer decrease as the annealing temperature increases, and they even change signs at an annealing temperature between 235 and 265 °C. In contrast, the sign change of the SOT and USMR upon annealing is absent in the Pt/CoFe and CoFe/Ta bilayers. These findings suggest that the sign of the SOT and USMR in the Pt/CoFe/Ta trilayer can be easily manipulated by using an appropriate thermal annealing treatment, which has important implications for the development of novel spintronic devices.

Unidirectional Spin Hall Magnetoresistance in Antiferromagnetic Heterostructures.

Unidirectional spin Hall magnetoresistance (USMR) has been widely reported in the heavy metal/ferromagnet bilayer systems. We observe the USMR in Pt/α-Fe_{2}O_{3} bilayers where the α-Fe_{2}O_{3} is an antiferromagnetic (AFM) insulator. Systematic field and temperature dependent measurements confirm the magnonic origin of the USMR. The appearance of AFM-USMR is driven by the imbalance of creation and annihilation of AFM magnons by spin orbit torque due to the thermal random field. However, unlike its ferromagnetic counterpart, theoretical modeling reveals that the USMR in Pt/α-Fe_{2}O_{3} is determined by the antiferromagtic magnon number with a non-monotonic field dependence. Our findings extend the generality of the USMR which pave the ways for the highly sensitive detection of AFM spin state.

Enhancement of room-temperature unidirectional spin Hall magnetoresistance by using a ferromagnetic metal with a low Curie temperature

The unidirectional spin Hall magnetoresistance (USMR) effect is useful to detect the direction of magnetization in a ferromagnetic metal/nonmagnetic metal bilayer, which is the typical geometry used in a spin-orbit torque switching device. In this Letter, we demonstrate the enhancement of the USMR effect by reducing the Curie temperature ${T}_{\mathrm{C}}$ of the ferromagnetic (FM) layer in a FM/platinum bilayer. The USMR ratio was maximized when the thickness of each FM layer was consistent with the spin diffusion length. We found that the maximum USMR ratio can be doubled by replacing ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ (${T}_{\mathrm{C}}=854$ K) with ${\mathrm{Ni}}_{85}{\mathrm{Cu}}_{15}$ (${T}_{\mathrm{C}}=527$ K) as the FM. This enhancement of the USMR effect is attributed to an increase of electron-magnon scattering in accordance with Bloch law. We also found that the use of ferromagnets with face-centered-cubic structures, such as Ni, ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$, and ${\mathrm{Ni}}_{85}{\mathrm{Cu}}_{15}$, increased the USMR effect relative to that of body-centered-cubic Fe.

Observation of unidirectional spin Hall magnetoresistance in amorphous PtSn4/CoFeB bilayers

Unidirectional spin Hall magnetoresistance (USMR) is a magnetoresistance effect with potential applications to read two-terminal spin–orbit-torque (SOT) devices directly. In this work, we observed a large USMR value (up to 0.7 × 10−11 per A/cm2, 50% larger than reported values from heavy metals) in sputtered amorphous PtSn4/CoFeB bilayers. Ta/CoFeB bilayers with interfacial MgO insertion layers are deposited as control samples. The control experiments show that increasing the interfacial resistance can increase the USMR value, which is the case in PtSn4/CoFeB bilayers. The observation of a large USMR value in an amorphous spin–orbit-torque material has provided an alternative pathway for USMR application in two-terminal SOT devices.

Manipulation of spin Hall magnetoresistance and unidirectional spin Hall magnetoresistance in Ta/Pt/CoFeB multilayers

The interaction between spin current and magnetic moments in heavy metal (HM)/ferromagnetic (FM) structure results in the well-known spin orbit torque and the concomitant magnetoresistance effect: spin Hall magnetoresistance (SMR) and the unidirectional SMR (USMR). In this work, we simultaneously investigated the SMR and USMR in Ta/Pt/CoFeB/MgO multilayers with different Pt thickness (tPt) by the harmonic measurements. It is observed that at tPt≈0.9nm, the SMR is close to zero and the polarity of USMR reverses, which originate from the competition of the spin current from Ta and Pt layers. Under the theoretical framework of the spin diffusion equation, we derived the theoretical expressions of SMR and USMR in the tri-layer magnetic heterostructures. We found that the tPt dependences of the SMR and USMR can be well fitted by the expressions, from which the spin transport parameters of Pt were extracted. Our work provides a fundamental insight into spin transport in the system with two heavy-metal layers, and a possible way to control SMR and USMR of HM/FM systems.

Fluctuation theorem for spin transport at insulating ferromagnetic junctions

General relations for nonequilibrium spin transport at a magnetic junction between a normal metal and a ferromagnetic insulator are derived from the quantum fluctuation theorem. They include the extended Onsager relations between the spin conductance and the spin-current noise that hold for nonequilibrium states driven by an external current. These relations are valid for a general setup of spin Hall magnetoresistance (SMR) when the main contribution is due to the interfacial spin conductance. Unidirectional spin Hall magnetoresistance (UMR) in insulating ferromagnetic junctions can be understood in a similar way. Therefore, our work can provide a comprehensive viewpoint for understanding of SMR and UMR in insulating ferromagnetic junctions. Our result also predicts relations for higher-order coefficients with respect to the external current in terms of higher-order cumulants in a unified framework.

Unidirectional spin Hall magnetoresistance in epitaxial Cr/Fe bilayer from electron-magnon scattering

Unidirectional Spin Hall magnetoresistance (USMR) is a non-linear phenomenon recently observed in ferromagnet (FM)/nonmagnetic metal (NM) bilayer structures. Two very different mechanisms of USMR have been proposed; one relies on the current-direction-dependence of electron-magnon scattering in a FM layer, and the other on the current-direction-dependence of the spin accumulation at the FM/NM interface. In this study, we investigate the USMR in epitaxial Cr/Fe bilayers finding that the USMR is significantly enhanced when the Fe magnetization is aligned to a particular crystallographic direction where the magnon magnetoresistance (MMR) by the electron-magnon scattering becomes stronger. This highlights the importance of the electron-magnon scattering for the understanding of USMR in Cr/Fe bilayers. Our result also suggests a route to enhance the efficiency of magnon generation in the magnonic devices. Lastly, we discuss the Ising-type spin exchange as a possible origin of the crystallographic direction dependences of the USMR and the MMR.

Magnonic Unidirectional Spin Hall Magnetoresistance in a Heavy-Metal-Ferromagnetic-Insulator Bilayer.

We report the observation of the unidirectional spin Hall magnetoresistance (USMR), which depends on the current or magnetization direction, in heavy-metal-ferromagnetic-insulator bilayer, Pt-Y_{3}Fe_{5}O_{12} (YIG). This USMR is apparently not caused by the mechanisms established in metallic bilayer, in which the ferromagnetic layer is required to be electrically conductive. From the magnetic field, current, temperature, and YIG thickness dependent measurements, the USMR is attributed to the asymmetric magnon creation and annihilation induced by the spin-orbit torque. This asymmetry and the resultant USMR are further revealed by the micromagnetic simulations combined with the spin-orbit torque and the spin drift-diffusion model. Our finding exhibits a nonlinear manipulation of magnons with the charge current.

Coexistence of low-frequency spin-torque ferromagnetic resonance and unidirectional spin Hall magnetoresistance

We investigate the DC voltage under an applied microwave current for platinum(Pt)/cobalt(Co), tantalum(Ta)/Co, and tungsten(W)/Co bilayers, where the microwave-induced alternating magnetic field (${B}_{\mathrm{rf}}$) is parallel to an external static magnetic field (${B}_{\mathrm{ext}}$). Whereas spin torque ferromagnetic resonance (ST FMR) signals do not appear because of the parallel configuration of ${B}_{\mathrm{rf}}$ and the magnetization of the Co layer, we recently found a clear hysteresis signal around ${B}_{\mathrm{ext}}=0\phantom{\rule{0.16em}{0ex}}\mathrm{mT}$ only when the microwave frequency (${f}_{\mathrm{MW}}$) is low, typically less than 10 GHz. This low-frequency ST FMR (LFST FMR) signal enables us to detect magnetization switching induced by spin-orbit torque (SOT) with high sensitivity. In this study, we found an additional background (BG) signal superimposed on the LSFT FMR signal. The additional BG signal also has hysteresis behavior and appears even at high ${f}_{\mathrm{MW}}$, where the LSFT FMR signal completely disappears. The sign of the BG signal is changed by changing the nonmagnetic material from Pt to Ta or W. By measuring ${f}_{\mathrm{MW}}$, the microwave current, the temperature, and the magnetic field angle dependences, we conclude that the BG signal is induced by spin-dependent unidirectional spin Hall magnetoresistance (SD USMR), which is generated by a spin current induced by the spin Hall effect of nonmagnetic metals and spin-dependent electron mobility in ferromagnetic metals. The SD USMR signal appears in wide ranges of ${f}_{\mathrm{MW}}$ and ${B}_{\mathrm{ext}}$ because the SD USMR originates from the nonlinearity of current-dependent resistance and is not related to magnetization dynamics. From the magnitude of the BG signal, the spin Hall angles of Pt and Ta are calculated to be 0.026 \ifmmode\pm\else\textpm\fi{} 0.006 and \ensuremath{-}0.042 \ifmmode\pm\else\textpm\fi{} 0.006, respectively. In addition, we demonstrate SOT magnetization switching using the BG signal.

Large and robust charge-to-spin conversion in sputtered conductive WTex with disorder

Topological materials with large spin-orbit coupling and immunity to disorder-induced symmetry breaking show great promise for efficiently converting charge to spin. Here, we report that long-range disordered sputtered WTex thin films exhibit local chemical and structural order as those of Weyl semimetal WTe2 and conduction behavior that is consistent with semi-metallic Weyl fermion. We find large charge-to-spin conversion properties and electrical conductivity in thermally annealed sputtered WTex films that are comparable with those in crystalline WTe2 flakes. Besides, the strength of unidirectional spin Hall magnetoresistance in annealed WTex/Mo/CoFeB heterostructure is 5 to 20 times larger than typical SOT layer/ferromagnet heterostructures reported at room temperature. We further demonstrate room temperature damping-like SOT-driven magnetization switching of in-plane magnetized CoFeB. These large charge-to-spin conversion properties that are robust in the presence of long-range disorder and thermal annealing pave the way for industrial application of a new class of sputtered semimetals.

Enhanced unidirectional spin Hall magnetoresistance in a Pt/Co system with a Cu interlayer

Spin-dependent scattering at the nonmagnet/ferromagnet interface plays a key role in determining the amplitude of unidirectional spin Hall magnetoresistance (USMR), similar to giant magnetoresistance (GMR). We report the enhancement of USMR by inserting a thin Cu interlayer into the Pt/Co interface, where the Cu/Co system is well known to exhibit a large GMR. A measurement of the spin-orbit torque shows that the spin current injection into the Co layer is not modulated by the Cu interlayer. In addition, USMR increases with the Cu thickness for the ultrathin regime as the Cu/Co interface is formed, reaching a peak before decreasing, owing to the shunting effect. Our results suggest an interfacial origin of the enhanced USMR and highlight the close similarities between USMR and GMR.

Large and Robust Charge-to-Spin Conversion in Sputtered Disordered WTe <sub>x</sub>

Topological insulators have recently shown great promise for ultralow-power spin-orbit torque (SOT) devices thanks to their large charge-to-spin conversion efficiency originating from the spin-momentum-locked surface states. Recently, Weyl semimetals emerge as an alternative SOT source with spin-polarized surface as well as bulk states, robustness against magnetic and structural disorder, and higher electrical conductivity for integration in metallic magnetic tunnel junctions. Here, we report that long-range disordered sputtered WTex thin films exhibit local chemical and structural order as those of Weyl semimetal WTe2 and conduction behavior that is consistent with semi-metallic Weyl fermion. We find large charge-to-spin conversion properties in thermally annealed sputtered WTex films that are comparable with those in crystalline WTe2 flakes. Besides, the strength of unidirectional spin Hall magnetoresistance in annealed WTex/Mo/CoFeB heterostructure is 5 to 20 times larger than typical SOT/ferromagnet bilayers reported at room temperature. We further demonstrate room temperature field-free magnetization switching at a current density of 1 – 2 MA/cm2. These large charge-to-spin conversion properties that are robust in the presence of long-range disorder and thermal annealing pave the way for industrial integration of such topological materials. Our results open a new class of sputtered semimetals for memory and computing based on magnetic tunnel junctions as well as broader planar heterostructures consisting of SOT layer/ferromagnet interfaces.

Giant unidirectional spin Hall magnetoresistance in topological insulator – ferromagnetic semiconductor heterostructures

The unidirectional spin Hall magnetoresistance (USMR) is one of the most complex spin-dependent transport phenomena in ferromagnet/nonmagnet bilayers, which involves spin injection and accumulation due to the spin Hall effect, spin-dependent scattering, and magnon scattering at the interface or in the bulk of the ferromagnet. While USMR in metallic bilayers has been studied extensively in very recent years, its magnitude (∼10−5) is too small for practical applications. Here, we demonstrate a giant USMR effect in a heterostructure of BiSb topological insulator – GaMnAs ferromagnetic semiconductors. We obtained a large USMR ratio of 1.1% and found that this giant USMR is governed not by the giant magnetoresistancelike spin-dependent scattering but by magnon emission/absorption and strong spin-disorder scattering in the GaMnAs layer. Our results provide new insights into the complex physics of USMR, as well as a strategy for enhancing its magnitude for device applications.

Spin-orbit torque and Nernst effect in Bi-Sb/Co heterostructures

Harmonic measurements of the longitudinal and transverse voltages in Bi-Sb/Co bilayers are presented. A large second harmonic voltage signal due to the ordinary Nernst effect is observed. In experiments where a magnetic field is rotated in the film plane, the ordinary Nernst effect shows the same angular dependence in the transverse voltage as the damping-like spin-orbit torque and in the longitudinal voltage as the unidirectional spin-Hall magneto-resistance respectively. Therefore, the ordinary Nernst effect can be a spurious signal in spin-orbit torque measurements, leading to an overestimation of the spin-Hall angle in topological insulators or semimetals.

Unidirectional Spin Hall Magnetoresistance as a Tool for Probing the Interfacial Spin Polarization of Co2MnSi

Many Heusler compounds are predicted to be ferromagnetic half metals in the bulk, which makes them promising compounds for spintronics. However, for devices the transport spin polarization at specific interfaces requires optimization. We show that investigations of the unidirectional magnetoresistance provide an alternative approach to access this quantity. Based on a Wheatstone-bridge design we probed the unidirectional magnetoresistance of Co2MnSi/(Ag, Cu, or Cr)(0.5 nm)/Pt (or Ta) multilayers and separate the spin-dependent unidirectional spin Hall magnetoresistance from other contributions. We demonstrated that by the insertion of a thin epitaxial Ag layer the spin-dependent contribution is doubled corresponding to a significant increase of the transport spin polarization, which is discussed in the framework of highly spin polarized interface states.

Magnon contribution to unidirectional spin Hall magnetoresistance in ferromagnetic-insulator/heavy-metal bilayers

We develop a model for the magnonic contribution to the unidirectional spin Hall magnetoresistance (USMR) of heavy metal/ferromagnetic insulator bilayer films. We show that diffusive transport of Holstein-Primakoff magnons leads to an accumulation of spin near the bilayer interface, giving rise to a magnoresistance which is not invariant under inversion of the current direction. Unlike the electronic contribution described by Zhang and Vignale [Phys. Rev. B 94, 140411 (2016)], which requires an electrically conductive ferromagnet, the magnonic contribution can occur in ferromagnetic insulators such as yttrium iron garnet. We show that the magnonic USMR is, to leading order, cubic in the spin Hall angle of the heavy metal, as opposed to the linear relation found for the electronic contribution. We estimate that the maximal magnonic USMR in Pt|YIG bilayers is on the order of ${10}^{\ensuremath{-}8}$ but may reach values of up to ${10}^{\ensuremath{-}5}$ if the magnon gap is suppressed and can thus become comparable to the electronic contribution in, e.g., Pt|Co. We show that the magnonic USMR at a finite magnon gap may be enhanced by an order of magnitude if the magnon diffusion length is decreased to a specific optimal value that depends on various system parameters.

Unidirectional Magneto-Resistance in Modulation-Doped Magnetic Topological Insulators.

Nonlinear unidirectional spin Hall magnetoresistance (USMR) has been reported in heavy metal/ferromagnet bilayers, which could be employed as an effective method in detecting the magnetization orientation in spintronic devices with two-terminal geometry. Recently, another unidirectional magnetoresistance (UMR) was reported in magnetic topological insulator (TI)-based heterostructures at cryogenic temperature, whose amplitude is orders of magnitude larger than the USMR measured in heavy metal-based magnetic heterostructures at room temperature. Here, we report the UMR effect in the modulation-doped magnetic TI structures. This UMR arises due to the interplay between the magnetic dopant's magnetization and the current-induced surface spin polarization, when they are parallel or antiparallel to each other in the TI material. By varying the dopant's position in the structure, we reveal that the UMR is mainly originating from the interaction between the magnetization and the surface spin-polarized carriers (not bulk carriers). Furthermore, from the magnetic field-, the angular rotation-, and the temperature-dependence, we highlight the correlation between the UMR effect and the magnetism in the structures. The large UMR versus current ratio in TI-based magnetic bilayers promises the easy readout in TI-based spintronic devices with two-terminal geometry.