All-optical Magnetisation Switching in Two-dimensional Metallic Ferro- and Antiferromagnetic Systems
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Motivated by recent experimental and theoretical work on ultrafast optical switching of magnetic order in ferromagnetic and antiferromagnetic materials,we study the influence of polarised light on the spin polarisation of itinerant electrons in a two-dimensional model of a metallic ferromagnet with Rashba and linear Dresselhaus spin-orbit interactions, as well as a model of a metallic Rashba antiferromagnet on a square lattice.Circularly and linearly polarised light can induce a change in the spin polarisation of the itinerant electrons that can be interpreted in terms of an effective magnetic field.This effective magnetic field gives rise to a magnetic torque that is believed to play a central role in all-optical switching of magnetic order. We derive analytical expressions for the light-induced effective magnetic field in both the ferromagnetic and the antiferromagnetic model using perturbation theory in the non-equilibrium Keldysh formalism.The results are derived to second order in the electric field amplitude of the light for linear, left- and right-circular polarisations, which we refer to as the helicity of the light.We specifically consider the geometry of an out-of-plane magnetisation/Néel order parallel to the light propagation direction.\\ In accordance with a previous theoretical study of a Rashba ferromagnet, we find that the effective magnetic field in the ferromagnetic Rashba-Dresselhaus model points in the out-of-plane direction and consists of a helicity-dependent term that is even in the magnetisation,as well as a helicity-independent term that is odd in the magnetisation.These two terms are attributed to the inverse Faraday effect (IFE) and the inverse Cotton-Mouton effect (ICME), respectively.Compared with the Rashba-only ferromagnet, we find that the introduction of Dresselhaus spin-orbit interaction results in a wider range of optical frequencies that can induce effective fields.Furthermore, the helicity-dependent contribution to the effective field from the Dresselhaus interaction is opposite in sign to the Rashba interaction,leading to a vanishing helicity dependence and dominance by the ICME in the special case where the Rashba and Dresselhaus interactions are equal in strength.\\ In the antiferromagnetic Rashba model, we calculate both the real and the staggered effective magnetic fields.We find that the real effective magnetic field is determined solely by the IFE, while the staggered effective field is caused by the ICME alone. This is the sort of qualitative behaviour one would expect from two superimposed independent Rashba ferromagnets with oppositely pointing magnetisations of equal magnitude.