Buckley Prize (2022): Spin-orbit coupling, spintronics, and topology

Spintronics is spin-based electronics facilitating electrical processing of information stored in electron spins. The underlying mechanism is spin-orbit coupling (SOC), a relativistic effect of the order of 1/c². SOC also produces topological phases of matter.

In nonmagnetic noncentrosymmetric crystals SOC originates from the gradient of electrical potential V(r) through the Thomas term. It results in spin splitting of energy bands across the Brillouin zone (BZ) due to the violation of Kramers degeneracy and, depending on crystal symmetry, consists of the Dresselhaus [1] and/or Rashba α(σ X k)·z [2] terms, k being electron momentum, σ the vector of Pauli matrices, z a unit vector along the symmetry axis, and α the SOC constant. Remarkably, SOC produces spin-momentum locking (SML).

In magnetic crystals and structures including magnetic elements time reversal symmetry is broken and energy bands are spin-split even in absence of electric SOC [3].  Magnetic mechanism of SOC develops because of the motion of electron magnetic moment μ across the fast-oscillating microscopic magnetic field h(r) of the magnetized m(r) background. It can split bands at time reversal invariant momenta (TRIM) at the surface of BZ, even at k=0. While generically it is of the same scale of 1/c²as electric mechanism, it dominates in compounds with small atomic numbers Z [4] and is enhanced across the BZ by eliminating zeros at TRIM points [5].

SOC is used for electrical manipulation of electron spins through electric dipole spin resonance (EDSR). SML promises applications such as spin transistor and current driven spin torques. SOC produces topological insulators and forms basis for normal and superconducting topological systems featuring Majorana fermions and Skyrmions, and it manifests itself in exotic transport phenomena such as weak antilocalization [6].