Paramagnetic spin Hall magnetoresistance

Vitaly Golovach

Paramagnetic spin Hall magnetoresistance

2020

Abstract

Spin Hall magnetoresistance (SMR) refers to a resistance change in a metallic film reflecting the magnetization direction of a magnet attached to the film. The mechanism of this phenomenon is spin exchange between conduction-electron spins and magnetization at the interface. SMR has been used to read out information written in a small magnet and to detect magnetization dynamics, but it has been limited to magnets; magnetic ordered phases or instability of magnetic phase transition has been believed to be indispensable. Here, we report the observation of SMR in a paramagnetic insulator Gd_3Ga_5O_12 (GGG) without spontaneous magnetization combined with a Pt film. The paramagnetic SMR can be attributed to spin-transfer torque acting on localized spins in GGG. We determine the efficiencies of spin torque and spin-flip scattering at the Pt/GGG interface, and demonstrate these quantities can be tuned with external magnetic fields. The results clarify the mechanism of spin-transport at a m...

spin-polarized currents. In recent years, however, the flow of pure spin currents has received much interest [1,2] in the quest of novel and low-energy consumption devices. [3] A key discovery was reported in 2013, when Nakayama et al. [4] and Hahn et al. [5] found out a new kind of magnetoresistance that appears in a nonmagnetic metal (NM) when placed in contact with a ferromagnetic insu-lator (FMI). It turned out that the resistance of the NM varies with the direction in which the FMI is magnetized. The observed effect relies on two ingredients. [6] The first one, so-called spin Hall effect (SHE), in which a charge current (J C), due to spin-orbit coupling, creates a flow of spins (J S) perpendicular to J C and produces a spin accumulation at sample edges with a polarization (σ) which is normal to both J C and J S (Figure 1a,b,e). The charge-to-spin current conversion is given by the spin Hall angle θ SH of the NM layer. Additionally, the created J S is converted back to J C by the inverse spin Hall effect (ISHE) which is the reciprocal effect to SHE, in which a spin current generates a transverse charge current. This is thus a second-order effect in θ SH that lowers the base resistivity of the NM layer with respect to its Drude resis-tivity. The second ingredient is the transport of spins across the NM/FMI interface, which is quantified by the spin-mixing interfacial conductance (G ↑↓). When a charge current is applied along the NM, the transverse spin current may be absorbed by the FMI depending on the direction of σ with respect to the direction of the magnetization (M) of the FMI. When σ is parallel to M, the spin current cannot be absorbed via spin transfer torque into the FMI and thus the electrical resistance of the NM layer remains unaltered; in contrast, when σ is perpendicular to M, spin torque occurs and J S is partially absorbed into the FMI (spin excitations) producing a loss of spin accumulation in the metal and thus a reduction of J C which is equivalent to an increase of resistance. Therefore, the resistance of the NM depends on the direction of M of the neighboring FMI, which can be controlled by appropriate external magnetic field, thus giving rise to the so-called spin Hall magnetoresistance (SMR) [4,7] (Figure 1a,b and Figure 2 (central panel)). Angular-dependent magnetore-sistance measurements (ADMR) and field-dependent magne-toresistance may allow observation of SMR. The magnitude of the observed SMR is determined by θ SH and G ↑↓. Spin currents have emerged as a new tool in spintronics, with promises of more efficient devices. A pure spin current can be generated in a nonmagnetic metallic (NM) layer by a charge current (spin Hall effect). When the NM layer is placed in contact with a magnetic material, a magnetoresistance (spin Hall magnetoresistance) develops in the former via the inverse spin Hall effect (ISHE). In other novel spin-dependent phenomena, such as spin pumping or spin Seebeck effect, spin currents are generated by magnetic resonance or thermal gradients and detected via ISHE in a neighboring normal metal layer. All cases involve spin transport across interfaces between nonmagnetic metallic layers and magnetic materials; quite commonly, magnetic insulators. The structural, compositional, and electronic differences between these materials and their integration to form an interface, challenge the control and understanding of the spin transport across it, which is known to be sensitive to sub-nanometric interface features. Here, the authors review the tremendous progress in material's science achieved during the last few years and illustrate how the spin Hall magnetoresistance can be used as a probe for surface magnetism. The authors end with some views on concerted actions that may allow further progress.

We observe an unusual behavior of the spin Hall magnetoresistance (SMR) in Pt deposited on a tensile-strained LaCoO3 (LCO) thin film, which is a ferromagnetic insulator with the Curie temperature Tc=85K. The SMR displays a strong magnetic-field dependence below Tc, with the SMR amplitude continuing to increase (linearly) with increasing the field far beyond the saturation value of the ferromagnet. The SMR amplitude decreases gradually with raising the temperature across Tc and remains measurable even above Tc. Moreover, no hysteresis is observed in the field dependence of the SMR. These results indicate that a novel lowdimensional magnetic system forms on the surface of LCO and that the LCO/Pt interface decouples magnetically from the rest of the LCO thin film. To explain the experiment, we revisit the derivation of the SMR corrections and relate the spin-mixing conductances to the microscopic quantities describing the magnetism at the interface. Our results can be used as a technique to probe quantum magnetism on the surface of a magnetic insulator. Introduction.-Magnetoresistance has been key for understanding spin-dependent transport in solids [1]. In the last years, new magnetoresistance phenomena were discovered in thin ferromagnetic/normal metal(FM/NM)-based heterostructures [2-18], which originate from the interplay of the spin currents generated in the heterostructure (via the spin Hall effect [19-22] or the Rashba-Edelstein effect [23,24]) with the magnetic moments of the FM layer. Among 2 many applications, these magnetoresistance effects have been used for quantifying spin transport properties such as the spin diffusion length  and the spin Hall angle SH of different NM layers, or the spin-mixing conductance ↑↓ of FM/NM interfaces. More interestingly, unlike other surface-sensitive techniques that suffer from a bulk contribution due to a finite penetration depth, the spin Hall magnetoresistance (SMR) [4-11] uses the spin accumulation at interfaces for sensing the magnetic properties of the very first atomic layer of magnetic insulators (MIs) [25,26]. For instance, SMR has been employed for probing the surface of complex magnetic systems such as ferrimagnetic spinel oxides [11,27], spin-spiral multiferroics [28,29], canted ferrimagnets [30], Y3Fe5O12/antiferromagnetic (YIG/AFM) bilayers [31,32], and synthetic AFMs [33]. LaCoO3 (LCO) presents an intriguing magnetic behavior, which has been studied for decades and is still under debate [34-49]. Bulk LCO is a diamagnetic insulator at low temperature, owing to the low-spin (LS) configuration of Co 3+. The relatively small crystal-field splitting of the Co 3+ 3d-shell results in an increasing population of high-spin (HS) Co 3+ with temperature, reaching 1:1 (LS:HS) above ~150K. The close proximity between crystal-field splitting and exchange energy makes the magnetic properties of LCO particularly susceptible to small changes in inter-ionic distances and coordination. For this reason, tensile-strained LCO thin films grown on particular substrates [such as SrTiO3 (STO)] exhibit FM order at low temperatures [42-49]. However, the magnetic properties of the surface of these films-where the crystal-field symmetry is lowered because of a different stoichiometry at the surface-have not been addressed yet. In this letter, we take the first steps towards understanding the magnetic behavior of the surface of strained LCO films by performing magnetoresistance measurements in STO/LCO/Pt. We find that SMR depends strongly on the magnetic field at all temperatures, both above and below the Curie temperature (Tc) of the film, and more strikingly, no hysteresis in the magnetoresistance is observed. These observations clearly show that the surface magnetism of the LCO film is radically different from its bulk counterpart. We support our measurements with a theoretical model that extends the known expressions for SMR [7,50] and HMR [51,52] in MI/NM bilayers for an arbitrary magnetic ordering (para-, ferri-, ferro-, antiferro-magnet) of the localized magnetic moments at the MI/NM interface. We provide expressions for ↑↓ Gr+iGi [25,53] and the effective spin conductance Gs [54,55] in terms of surface spincorrelators. The experimental data evidence that the surface of LCO behave as a lowdimensional Heisenberg FM. Experimental details.-Growth of epitaxial LCO thin films via polymer-assisted deposition on (001) STO substrates, as well as their structural, electrical, and magnetic characterization, is described in Ref. [46]. The LCO films exhibit a tetragonal distortion, which induces FM ordering below Tc~85K and with a coercive field below 1T at 10K, in agreement to other reports [43-45,47,56]. The films exhibit low surface roughness (<1nm) and are insulating [46]. Pt Hall bar structures (width W 100m, length L 800m and thickness dN 7nm) were

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