Signatures of relativistic spin-light coupling in magneto-optical pump-probe experiments

Achiral dipoles on a ferromagnet can affect its magnetization direction

We demonstrate the possibility of a coupling between the magnetization direction of a ferromagnet and the tilting angle of adsorbed achiral molecules. To illustrate the mechanism of the coupling, we analyze a minimal Stoner model that includes Rashba spin-orbit coupling due to the electric field on the surface of the ferromagnet. The proposed mechanism allows us to study magnetic anisotropy of the system with an extended Stoner-Wohlfarth model and argue that adsorbed achiral molecules can change magnetocrystalline anisotropy of the substrate. Our research aims to motivate further experimental studies of the current-free chirality induced spin selectivity effect involving both enantiomers.

Dynamics of the relativistic electron spin in an electromagnetic field

A relativistic spin operator cannot be uniquely defined within relativistic quantum mechanics. Previously, different proper relativistic spin operators have been proposed, such as spin operators of the Foldy-Wouthuysen and Pryce type, that both commute with the free-particle Dirac Hamiltonian and represent constants of motion. Here we consider the dynamics of a relativistic electron spin in an external electromagnetic field. We use two different Hamiltonians to derive the corresponding spin dynamics. These two are: (a) the Dirac Hamiltonian in the presence of an external field, and (b) the semirelativistic expansion of the same. Considering the Foldy-Wouthuysen and Pryce spin operators we show that these lead to different spin dynamics in an external electromagnetic field, which offers possibilities to distinguish their action. We find that the dynamics of both spin operators involve spin-dependent and spin-independent terms, however, the Foldy-Wouthuysen spin dynamics additionally accounts for the relativistic particle-antiparticle coupling. We conclude that the Pryce spin operator provides a suitable description of the relativistic spin dynamics in a weak-to-intermediate external field, whereas the Foldy-Wouthuysen spin operator is more suitable in the strong field regime.

Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms

The phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects. To include magnetic inertial effects the LLG equation has previously been extended with a supplemental inertia term; the arising inertial dynamics has been related to second-order relativistic effects. Here we start from the relativistic Dirac equation and, performing a Foldy-Wouthuysen transformation, derive a generalised Pauli spin Hamiltonian that contains relativistic correction terms to any higher order. Using the Heisenberg equation of spin motion we derive general relativistic expressions for the tensorial Gilbert damping and magnetic inertia parameters, and show that these tensors can be expressed as series of higher-order relativistic correction terms. We further show that, in the case of a harmonic external driving field, these series can be summed and we provide closed analytical expressions for the Gilbert and inertial parameters that are functions of the frequency of the driving field.

Toy model for uncommon spin-orbit-driven spin-torque terms

A toy model combining the angular magneto electric (AME) coupling Hamitonian (Mondal et al 2015 Phys. Rev. B 92 100402) with long-range magnetic dipolar interactions is used to investigate spin-torque phenomena in a magnetic spin valve. It is found that such model (1) gives rise to spin-torque expressions that are analogous in form to those of the common spin-transfer torques; but also (2) predicts additional spin-torque terms, which are generated by an electrical current oriented along unconventional, in-plane directions. The magnitude of the AME induced terms is estimated and the conditions under which they may contribute significantly are explored.