Theory of spin Hall magnetoresistance (SMR) and related phenomena

A theory of unusual anisotropic magnetoresistance in bilayer heterostructures

The observation of magnetoresistance (MR) varying with the rotation of magnetization in the plane perpendicular to the electric current is an important discovery in spintronics in recent years. The famous conventional anisotropic MR (AMR) says that the resistance of a polycrystalline magnetic material must depend on magnetization component along the current direction only, thus cannot account for this newly observed unusual AMR (UAMR). This UAMR leads to the notion of the spin-Hall MR (SMR) in the famous SMR theory. However, the SMR theory may only explain UAMR observed in heavy-metal/magnetic-insulator bilayers, not other types of bilayers. Here, we present a two-vector theory that can explain not only all existing experiments on the unusual angular dependence of longitudinal and transverse resistivity when the magnetization rotates in three mutually perpendicular planes, but also how three amplitudes of MR angular oscillation are related to each other. The theory is very general and its correctness depends only on the assumption that the magnetization and interfacial field are the only vectors affecting electron transport besides of other scalar variables such as the temperatures and impurities. Experiments that can test this theory against the SMR theory are also proposed.

Defect Nanostructure and its Impact on Magnetism of α-Cr2 O3 Thin Films

Thin films of the magnetoelectric insulator α-Cr₂ O₃ are technologically relevant for energy-efficient magnetic memory devices controlled by electric fields. In contrast to single crystals, the quality of thin Cr₂ O₃ films is usually compromised by the presence of point defects and their agglomerations at grain boundaries, putting into question their application potential. Here, the impact of the defect nanostructure, including sparse small-volume defects and their complexes is studied on the magnetic properties of Cr₂ O₃ thin films. By tuning the deposition temperature, the type, size, and relative concentration of defects is tailored, which is analyzed using the positron annihilation spectroscopy complemented with electron microscopy studies. The structural characterization is correlated with magnetotransport measurements and nitrogen-vacancy microscopy of antiferromagnetic domain patterns. Defects pin antiferromagnetic domain walls and stabilize complex multidomain states with a domain size in the sub-micrometer range. Despite their influence on the domain configuration, neither small open-volume defects nor grain boundaries in Cr₂ O₃ thin films affect the Néel temperature in a broad range of deposition parameters. The results pave the way toward the realization of spin-orbitronic devices where magnetic domain patterns can be tailored based on defect nanostructures without affecting their operation temperature.

Angle Resolved Relaxation of Spin Currents by Antiferromagnets in Spin Valves

We observe and analyze tunable relaxation of a pure spin current by an antiferromagnet in spin valves. This is achieved by carefully controlling the angle between a resonantly excited ferromagnetic layer pumping the spin current and the Néel vector of the antiferromagnetic layer. The effect is observed as an angle-dependent spin-pumping contribution to the ferromagnetic resonance linewidth. An interplay between spin-mixing conductance and, often disregarded, longitudinal spin conductance is found to underlie our observations, which is in agreement with a recent prediction for related ferromagnetic spin valves.

Impact of Symmetry on Anisotropic Magnetoresistance in Textured Ferromagnetic Thin Films

We report on the magnetoresistance of textured films consisting of 3d-ferromagnetic layers sandwiched by Pt. While the conventional cos^{2}φ behavior of the anisotropic magnetoresistance (AMR) is found when the magnetization M is varied in the film plane, cos^{2n}θ contributions (2n≤6) exist for rotating M in the plane perpendicular to the current. This finding is explained by the symmetry-adapted modeling of AMR of textured films demonstrating that the cos^{2}θ behavior cannot be used as a fingerprint for the presence of spin Hall magnetoresistance (SMR). Further, the interfacial MR contributions for Pt/Ni/Pt contradict the SMR behavior confirming the dominant role of AMR in all-metallic systems.

Effect of Interfacial Roughness Spin Scattering on the Spin Current Transport in YIG/NiO/Pt Heterostructures

Interfacial properties play a vital role in spin current injection from the ferromagnetic (FM) layer into the nonmagnetic (NM) layer. So far, impedance matching and spin-orbit coupling are two important, well-known factors in spin current transport in FM/NM heterostructures. In this work, the spin current transport in Y₃Fe₅O₁₂ (YIG)/NiO/Pt heterostructures was investigated by spin Hall magnetoresistance and inverse spin Hall effect measurements. By inserting a layer of antiferromagnetic insulator NiO, the magnetic proximity effect affecting the Pt atoms owing to YIG and the anomalous spin Hall voltage can be efficiently blocked. Ferromagnetic resonance and spin pumping measurements verified that the ferromagnetic/antiferromagnetic exchange coupling inhibits transmission of the spin current at the YIG/NiO interface when the NiO layer is thick. Atomic force microscopy and spherical aberration-corrected transmission electron microscopy proved that the strong interfacial roughness-enhanced spin scattering between NiO and Pt can greatly increase both the inverse spin Hall voltage and the spin Hall magnetoresistance when the NiO layer is thin or even discontinuous. This interface roughness-dominated spin scattering mechanism based on the YIG/NiO/Pt heterostructure is a new discovery, and there is significant potential for exploiting this mechanism in the construction of low-dissipation spintronic devices with an efficient spin current injection.

Anisotropic and Controllable Gilbert-Bloch Dissipation in Spin Valves

Spin valves form a key building block in a wide range of spintronic concepts and devices from magnetoresistive read heads to spin-transfer-torque oscillators. We elucidate the dependence of the magnetic damping in the free layer on the angle its equilibrium magnetization makes with that in the fixed layer. The spin pumping-mediated damping is anisotropic and tensorial, with Gilbert- and Bloch-like terms. Our investigation reveals a mechanism for tuning the free layer damping in situ from negligible to a large value via the orientation of fixed layer magnetization, especially when the magnets are electrically insulating. Furthermore, we expect the Bloch contribution that emerges from the longitudinal spin accumulation in the nonmagnetic spacer to play an important role in a wide range of other phenomena in spin valves.

Probing Magnetism in Insulating Cr2Ge2Te6 by Induced Anomalous Hall Effect in Pt

Two-dimensional ferromagnet Cr₂Ge₂Te₆ (CGT) is so resistive below its Curie temperature that probing its magnetism by electrical transport becomes extremely difficult. By forming heterostructures with Pt, however, we observe clear anomalous Hall effect (AHE) in 5 nm thick Pt deposited on thin (<50 nm) exfoliated flakes of CGT. The AHE hysteresis loops persist to ∼60 K, which matches well to the Curie temperature of CGT obtained from the bulk magnetization measurements. The slanted AHE loops with a narrow opening indicate magnetic domain formation, which is confirmed by low-temperature magnetic force microscopy (MFM) imaging. These results clearly demonstrate that CGT imprints its magnetization in the AHE signal of the Pt layer. Density functional theory calculations of CGT/Pt heterostructures suggest that the induced ferromagnetism in Pt may be primarily responsible for the observed AHE. Our results establish a powerful way of investigating magnetism in 2D insulating ferromagnets, which can potentially work for monolayer devices.

Interface-induced spin Hall magnetoresistance enhancement in Pt-based tri-layer structure

In this study, we integrated bilayer structure of covered Pt on nickel zinc ferrite (NZFO) and CoFe/Pt/NZFO tri-layer structure by pulsed laser deposition system for a spin Hall magnetoresistance (SMR) study. In the bilayer structure, the angular-dependent magnetoresistance (MR) results indicate that Pt/NZFO has a well-defined SMR behavior. Moreover, the spin Hall angle and the spin diffusion length, which were 0.0648 and 1.31 nm, respectively, can be fitted by changing the Pt thickness in the longitudinal SMR function. Particularly, the MR ratio of the bilayer structure (Pt/NZFO) has the highest changing ratio (about 0.135%), compared to the prototype structure Pt/Y₃Fe₅O₁₂ (YIG) because the NZFO has higher magnetization. Meanwhile, the tri-layer samples (CoFe/Pt/NZFO) indicate that the MR behavior is related with CoFe thickness as revealed in angular-dependent MR measurement. Additionally, comparison between the tri-layer structure with Pt/NZFO and CoFe/Pt bilayer systems suggests that the SMR ratio can be enhanced by more than 70%, indicating that additional spin current should be injected into Pt layer.

Generation of megahertz-band spin currents using nonlinear spin pumping

Spin pumping enables the generation of d.c. and gigahertz-band (GHz-band) voltages from an applied microwave via magnetization dynamics when combined with inverse spin Hall effects. However, generating such voltages in the in-between frequency region, or the megahertz (MHz) band, has been difficult since ferromagnetic resonance usually occurs in the GHz band. Here we show that in spite of GHz-band microwaves applied, MHz-band voltages can be generated by spin pumping with use of nonlinear magnetization dynamics in Y₃Fe₅O₁₂. The mechanism is ascribed to the MHz-band oscillation of the amplitude of the magnetization precession, which is projected onto a rectified voltage component via spin pumping. The present finding could be useful for frequency down-conversion thanks to the simple and durable structure, continuous-wave operation, and the tunability of an output frequency with low magnetic fields.

Influence of intermixing at the Ta/CoFeB interface on spin Hall angle in Ta/CoFeB/MgO heterostructures

When a current is passed through a non-magnetic metal with strong spin-orbit coupling, an orthogonal spin current is generated. This spin current can be used to switch the magnetization of an adjacent ferromagnetic layer or drive its magnetization into continuous precession. The interface, which is not necessarily sharp, and the crystallographic structure of the nonmagnetic metal can both affect the strength of current-induced spin-orbit torques. Here, we investigate the effects of interface intermixing and film microstructure on spin-orbit torques in perpendicularly magnetized Ta/Co40Fe40B20/MgO trilayers with different Ta layer thickness (5 nm, 10 nm, 15 nm), greater than the spin diffusion length. Effective spin-orbit torques are determined from harmonic Hall voltage measurements performed at temperatures ranging from 20 K to 300 K. We account for the temperature dependence of damping-like and field-like torques by including an additional contribution from the Ta/CoFeB interface in the spin diffusion model. Using this approach, the temperature variations of the spin Hall angle in the Ta underlayer and at the Ta/CoFeB interface are determined separately. Our results indicate an almost temperature-independent spin Hall angle of [Formula: see text] in Ta and a strongly temperature-dependent [Formula: see text] for the intermixed Ta/CoFeB interface.

Tunable Sign Change of Spin Hall Magnetoresistance in Pt/NiO/YIG Structures

Spin Hall magnetoresistance (SMR) has been investigated in Pt/NiO/YIG structures in a wide range of temperature and NiO thickness. The SMR shows a negative sign below a temperature that increases with the NiO thickness. This is contrary to a conventional SMR theory picture applied to the Pt/YIG bilayer, which always predicts a positive SMR. The negative SMR is found to persist even when NiO blocks the spin transmission between Pt and YIG, indicating it is governed by the spin current response of the NiO layer. We explain the negative SMR by the NiO "spin flop" coupled with YIG, which can be overridden at higher temperature by positive SMR contribution from YIG. This highlights the role of magnetic structure in antiferromagnets for transport of pure spin current in multilayers.

Multi-Terminal Spin Valve on Channels with Spin-Momentum Locking

It is experimentally established that charge current flowing in a channel with spin-momentum locking such as topological insulator surface states or Rashba interfaces induces a spin voltage, which can be electrically measured with a ferromagnetic contact along the current path. Using this fact in conjunction with Onsager reciprocity arguments, we make the surprising prediction that the anti-parallel resistance of a spin valve can be either larger or smaller than the parallel resistance depending on the direction of spin flow relative to the direction of spin-momentum locking. However, we argue that this remarkable signature of spin-momentum locking can only be observed in multi-terminal measurements. Two-terminal measurements in the linear response regime, will show a single anti-parallel resistance larger than the parallel resistance as commonly observed in channels without spin-orbit coupling. We support this result with detailed numerical calculations based on a semiclassical model that provides insight into the underlying physics.