We review the recently discovered spin Hall magnetoresistance (SMR) and related effects from a theoretical point of view. The SMR is observed in bilayers of a magnetic insulator and a metal, in which spin currents aregenerated in the normal metal due
to the spin Hall effect. The associated angular momentum transfer to the ferromagnetic layer and thereby the electrical resistance is modulated by the angle between the applied current and the magnetization direction. The SMR provides a convenient tool to non-invasively measure the magnetization direction and spin-transfer torque to an insulator. We introduce the minimal theoretical instruments to calculate the SMR, i.e. spin diffusion theory and quantum mechanical boundary conditions. This leads to a small set of parameters that can be fitted to experiments. We discuss the limitations of the theory as well as alternative mechanisms such as the ferromagnetic proximity effect and Rashba spin-orbit torques, and point out new developments related to the SMR.
We present a theory of the spin Hall magnetoresistance (SMR) in multilayers made from an insulating ferromagnet F, such as yttrium iron garnet (YIG), and a normal metal N with spin-orbit interactions, such as platinum (Pt). The SMR is induced by the
simultaneous action of spin Hall and inverse spin Hall effects and therefore a non-equilibrium proximity phenomenon. We compute the SMR in F$|$N and F$|$N$|$F layered systems, treating N by spin-diffusion theory with quantum mechanical boundary conditions at the interfaces in terms of the spin-mixing conductance. Our results explain the experimentally observed spin Hall magnetoresistance in N$|$F bilayers. For F$|$N$|$F spin valves we predict an enhanced SMR amplitude when magnetizations are collinear. The SMR and the spin-transfer torques in these trilayers can be controlled by the magnetic configuration.
Spin properties of two interacting electrons in a quantum dot (QD) embedded in a nanowire with controlled aspect ratio and longitudinal magnetic fields are investigated by using a configuration interaction (CI) method and exact diagonalization (ED) t
echniques. The developed CI theory based on a three-dimensional (3D) parabolic model provides explicit formulations of the Coulomb matrix elements and allows for straightforward and efficient numerical implementation. Our studies reveal fruitful features of spin singlet-triplet transitions of two electrons confined in a nanowire quantum dot (NWQD), as a consequence of the competing effects of geometry-controlled kinetic energy quantization, the various Coulomb interactions, and spin Zeeman energies. The developed theory is further employed to study the spin phase diagram of two quantum-confined electrons in the regime of cross over dimensionality, from quasi-two-dimensional (disk-like) QDs to finite one-dimensional (rod-like) QDs.
We consider a quantum dot embedded in a three-dimensional nanowire with tunable aspect ratio a. A configuration interaction theory is developed to calculate the energy spectra of the finite 1D quantum dot systems charged with two electrons in the pre
sence of magnetic fields B along the wire axis. Fruitful singlet-triplet transition behaviors are revealed and explained in terms of the competing exchange interaction, correlation interaction, and spin Zeeman energy. In the high aspect ratio regime, the singlet-triplet transitions are shown designable by tuning the parameters a and B. The transitions also manifest the highly correlated nature of long nanowire quantum dots.
