In solid-state materials with strong relativistic spin-orbit coupling, charge currents generate transverse spin currents. The associated spin Hall and inverse spin Hall effects distinguish between charge and spin current where electron charge is a conserved quantity but its spin direction is not. This review provides a theoretical and experimental treatment of this subfield of spintronics, beginning with distinct microscopic mechanisms seen in ferromagnets and concluding with a discussion of optical-, transport-, and magnetization-dynamics-based experiments closely linked to the microscopic and phenomenological theories presented.

Spin Hall effects

Through combined ferromagnetic resonance, spin pumping, and inverse spin Hall effect experiments in $\mathrm{Co}|\mathrm{Pt}$ bilayers and $\mathrm{Co}|\mathrm{Cu}|\mathrm{Pt}$ trilayers, we demonstrate consistent values of ${\ensuremath{\ell}}_{\mathrm{sf}}^{\mathrm{Pt}}=3.4\ifmmode\pm\else\textpm\fi{}0.4\text{ }\text{ }\mathrm{nm}$ and ${\ensuremath{\theta}}_{\mathrm{SHE}}^{\mathrm{Pt}}=0.056\ifmmode\pm\else\textpm\fi{}0.010$ for the respective spin diffusion length and spin Hall angle for Pt. Our data and model emphasize the partial depolarization of the spin current at each interface due to spin-memory loss. Our model reconciles the previously published spin Hall angle values and explains the different scaling lengths for the ferromagnetic damping and the spin Hall effect induced voltage.

Spin Pumping and Inverse Spin Hall Effect in Platinum: The Essential Role of Spin-Memory Loss at Metallic Interfaces

We use electrical detection, in combination with microwave transmission, to investigate both resonant and nonresonant magnon-photon coupling at room temperature Spin pumping in a dynamically coupled magnon-photon system is found to be distinctly different from previous experiments Characteristic coupling features such as modes anticrossing, linewidth evolution, peculiar line shape, and resonance broadening are systematically measured and consistently analyzed by a theoretical model set on the foundation of classical electrodynamic coupling Our experimental and theoretical approach paves the way for pursuing microwave coherent manipulation of pure spin current via the combination of spin pumping and magnon-photon coupling

https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.114.227201

Spin Pumping in Electrodynamically Coupled Magnon-Photon Systems

We reveal the cooperative effect of coherent and dissipative magnon-photon couplings in an open cavity magnonic system, which leads to nonreciprocity with a considerably large isolation ratio and flexible controllability. Furthermore, we discover unidirectional invisibility for microwave propagation, which appears at the zero-damping condition for hybrid magnon-photon modes. A simple model is developed to capture the generic physics of the interference between coherent and dissipative couplings, which accurately reproduces the observations over a broad range of parameters. This general scheme could inspire methods to achieve nonreciprocity in other systems.

pdf/nonreciprocity-and-unidirectional-invisibility-in-cavity-53hg5rdoxj.pdf

Nonreciprocity and Unidirectional Invisibility in Cavity Magnonics.

Three-dimensional (3D) topological insulators are known for their strong spin-orbit coupling (SOC) and the existence of spin-textured surface states that might be potentially exploited for "topological spintronics." Here, we use spin pumping and the inverse spin Hall effect to demonstrate successful spin injection at room temperature from a metallic ferromagnet (CoFeB) into the prototypical 3D topological insulator Bi2Se3. The spin pumping process, driven by the magnetization dynamics of the metallic ferromagnet, introduces a spin current into the topological insulator layer, resulting in a broadening of the ferromagnetic resonance (FMR) line width. Theoretical modeling of spin pumping through the surface of Bi2Se3, as well as of the measured angular dependence of spin-charge conversion signal, suggests that pumped spin current is first greatly enhanced by the surface SOC and then converted into a dc-voltage signal primarily by the inverse spin Hall effect due to SOC of the bulk of Bi2Se3. We find that the FMR line width broadens significantly (more than a factor of 5) and we deduce a spin Hall angle as large as 0.43 in the Bi2Se3 layer.

/pdf/giant-spin-pumping-and-inverse-spin-hall-effect-in-the-4s3li2c7a1.pdf

Giant Spin Pumping and Inverse Spin Hall Effect in the Presence of Surface and Bulk Spin−Orbit Coupling of Topological Insulator Bi2Se3

Using electrical detection of a strongly coupled spin-photon system comprised of a microwave cavity mode and two magnetic samples, we demonstrate the long distance manipulation of spin currents. This distant control is not limited by the spin diffusion length, instead depending on the interplay between the local and global properties of the coupled system, enabling systematic spin current control over large distance scales (several centimeters in this work). This flexibility opens the door to improved spin current generation and manipulation for cavity spintronic devices.

Cavity Mediated Manipulation of Distant Spin Currents Using a Cavity-Magnon-Polariton.

We experimentally examine the topological nature of a strongly coupled spin-photon system induced by damping The presence of both spin and photonic losses results in a non-Hermitian system with a variety of exotic phenomena dictated by the topological structure of the eigenvalue spectra and the presence of an exceptional point (EP), where the coupled spin-photon eigenvectors coalesce By controlling both the spin resonance frequency and the spin-photon coupling strength we observe a resonance crossing for cooperativities above one, suggesting that the boundary between weak and strong coupling should be based on the EP location rather than the cooperativity Furthermore, we observe dynamic mode switching when encircling the EP and identify the potential to engineer the topological structure of coupled spin-photon systems with additional modes Our work therefore further highlights the role of damping within the strong coupling regime, and demonstrates the potential and great flexibility of spin-photon systems for studies of non-Hermitian physics

Topological properties of a coupled spin-photon system induced by damping

An approach to directly measure the nonlinear foldover effect for cavity magnon polaritons is demonstrated by placing a nonlinear medium (yttrium iron garnet) into a Fabry-Perot-like microwave cavity. The resulting bistability features can exhibit clockwise, counterclockwise, and butterflylike hysteresis loops and are solely dependent on the relative weight of the magnonlike and photonlike components. In addition to accurately describing our experimental observations, our model also allows us to calculate the crucial system conditions required to produce photonlike foldover effects. Though the photon subsystem has no nonlinear components of its own, these photonlike foldover effects are produced through light-matter interactions with a nonlinear magnetic subsystem. Our model's description of these nonlinear light-matter interactions and their effects is not limited to ferromagnetic systems and should be generally applicable to other coherent coupled systems.

Direct measurement of foldover in cavity magnon-polariton systems

We experimentally realize an indirect coupling between two cavity modes via strong coupling with ferromagnetic resonance in Yttrium Iron Garnet. We find that some indirectly coupled modes of this system can have a higher microwave transmission than the individual uncoupled modes. Using a coupled harmonic oscillator model, the influence of the oscillation phase difference between the two cavity modes on the nature of the indirect coupling is revealed. The properties of the indirectly coupled modes can be controlled using an external magnetic field or by tuning the cavity height. The relation between cavity transmission and the relative phase difference between cavity modes should be useful for developing tunable optical devices and improved information processing technologies.

Indirect coupling between two cavity modes via ferromagnetic resonance

Spin rectification in a single crystal Fe/Au/Fe sandwich is electrically detected for collinear and non-collinear magnetization and external magnetic field configurations. The line shape, line width and signal polarity are analysed. The spin rectication theory has been much extended by taking the magneto-crystalline anisotropy and shape anisotropy into account, which explained non-collinear resonances and agrees very well with experimental data. Thus, a comprehensive understanding of spin rectification in ferromagnetic metal was demonstrated in this work.

/pdf/spin-rectification-for-collinear-and-noncollinear-2yl4yixtk2.pdf

Spin rectification for collinear and noncollinear magnetization and external magnetic field configurations

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