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The intrinsic spin Hall effect plays an important role in spintronics applications, such as spin-orbit torque-based memory. The bulk space group symmetry determines the form of the bulk spin current conductivity tensor. This paper considers materials for which the local point group symmetry of individual atoms is lower than the global (bulk) symmetry. This enables a position-dependent spin current response, with additional tensor components allowed relative to the bulk response. We present a general method to compute the position-dependent intrinsic spin Hall conductivity, with similar computational effort relative to computing the bulk spin Hall conductivity. We also present the general symmetry-constrained form of the position-dependent spin current response. We apply this method to 1T-WTe$_2$, which exhibits a conventional spin Hall conductivity tensor component $sigma^y_{xz}$ and a staggered unconventional component $sigma^z_{xz}$. The magnitude of these two components, around 100 and 20 $(rm Omegacdot cm)^{-1}$, respectively, are comparable to the spin-orbit torque exerted on adjacent ferromagnets in experiments. We then consider orthorhombic PbTe, in which both uniform and staggered spin current conductivity are one order of magnitude larger.
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The coupling of the spin and the motion of charge carriers stems directly from the atomic structure of a conductor. It has become an important ingredient for the emergence of topological matter, and, in particular, topological superconductivity which could host non-abelian excitations such as Majorana modes or parafermions. These modes are sought after mostly in semiconducting platforms which are made of heavy atoms and therefore exhibit naturally a large spin-orbit interaction. Creating domain walls in the spin orbit interaction at the nanoscale may turn out to be a crucial resource for engineering topological excitations suitable for universal topological quantum computing. For example, it has been proposed for exploring exotic electronic states or for creating hinge states. Realizing this in natural platforms remains a challenge. In this work, we show how this can be alternatively implemented by using a synthetic spin orbit interaction induced by two lithographically patterned magnetically textured gates. By using a double quantum dot in a light material -- a carbon nanotube -- embedded in a microwave cavity, we trigger hopping between two adjacent orbitals with the microwave photons and directly compare the wave functions separated by the domain wall via the light-matter coupling. We show that we can achieve an engineered staggered spin-orbit interaction with a change of strength larger than the hopping energy between the two sites.
We measure the low-frequency thermal fluctuations of pure spin current in a Platinum film deposited on yttrium iron garnet via the inverse spin Hall effect (ISHE)-mediated voltage noise as a function of the angle $alpha$ between the magnetization and the transport direction. The results are consistent with the fluctuation dissipation theorem in terms of the recently discovered spin Hall magnetoresistance (SMR). We present a microscopic description of the $alpha$ dependence of the voltage noise in terms of spin current fluctuations and ISHE.
Time-reversal (T) symmetry breaking is a fundamental physics concept underpinning a broad science and technology area, including topological magnets, axion physics, dissipationless Hall currents, or spintronic memories. A best known conventional model of macroscopic T-symmetry breaking is a ferromagnetic order of itinerant Bloch electrons with an isotropic spin interaction in momentum space. Anisotropic electron interactions, on the other hand, have been a domain of correlated quantum phases, such as the T-invariant nematics or unconventional superconductors. Here we report discovery of a broken-T phase of itinerant Bloch electrons with an unconventional anisotropic spin-momentum interaction, whose staggered nature leads to the formation of two ferromagnetic-like valleys in the momentum space with opposite spin splittings. We describe qualitatively the effect by deriving a non-relativistic single-particle Hamiltonian model. Next, we identify the unconventional staggered spin-momentum interaction by first-principles electronic structure calculations in a four-sublattice antiferromagnet Mn5Si3 with a collinear checkerboard magnetic order. We show that the staggered spin-momentum interaction is set by nonrelativistic spin-symmetries which were previously omitted in relativistic physics classifications of spin interactions and topological quasiparticles. Our measurements of a spontaneous Hall effect in epilayers of antiferromagnetic Mn5Si3 with vanishing magnetization are consistent with our theory predictions. Bloch electrons with the unconventional staggered spin interaction, compatible with abundant low atomic-number materials, strong spin-coherence, and collinear antiferromagnetic order open unparalleled possibilities for realizing T-symmetry broken spin and topological quantum phases.
We report on the observation of the acoustic spin Hall effect that facilitates lattice motion induced spin current via spin orbit interaction (SOI). Under excitation of surface acoustic wave (SAW), we find a spin current flows orthogonal to the propagation direction of a surface acoustic wave (SAW) in non-magnetic metals. The acoustic spin Hall effect manifests itself in a field-dependent acoustic voltage in non-magnetic metal (NM)/ferromagnetic metal (FM) bilayers. The acoustic voltage takes a maximum when the NM layer thickness is close to its spin diffusion length, vanishes for NM layers with weak SOI and increases linearly with the SAW frequency. To account for these results, we find the spin current must scale with the SOI and the time derivative of the lattice displacement. Such form of spin current can be derived from a Berry electric field associated with time varying Berry curvature and/or an unconventional spin-lattice interaction mediated by SOI. These results, which imply the strong coupling of electron spins with rotating lattices via the SOI, show the potential of lattice dynamics to supply spin current in strong spin orbit metals.
Spin Hall effects intermix spin and charge currents even in nonmagnetic materials and, therefore, ultimately may allow the use of spin transport without the need for ferromagnets. We show how spin Hall effects can be quantified by integrating permalloy/normal metal (N) bilayers into a coplanar waveguide. A dc spin current in N can be generated by spin pumping in a controllable way by ferromagnetic resonance. The transverse dc voltage detected along the permalloy/N has contributions from both the anisotropic magnetoresistance (AMR) and the spin Hall effect, which can be distinguished by their symmetries. We developed a theory that accounts for both. In this way, we determine the spin Hall angle quantitatively for Pt, Au and Mo. This approach can readily be adapted to any conducting material with even very small spin Hall angles.
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