A new and simple model for magneto-optics uncovers an unexpected spin switching

Abstract

In magneto-optics the spin angular momentum Sz of a sample is indirectly probed by the rotation angle and ellipticity, which are mainly determined by the off-diagonal susceptibility χ (1) xy . A direct and analytic relation between Sz and χ (1) xy is necessary and of paramount importance to the success of magneto-optics, but is often difficult to acquire since quantum mechanically the relation is hidden in the sum-over-states. Here we propose a new and simple model to establish such a much needed relation. Our model is based on the Hookean model, but includes spin-orbit coupling. Under cw excitation, we show that χ (1) xy (ω) is indeed directly proportional to Sz for a fixed photon frequency ω. Such an elegant relation is encouraging, and we wonder whether our model can describe spin dynamics as well. By allowing the spin to change dynamically, to our surprise, our model predicts that an ultrafast laser pulse can induce a spin precession; with appropriate parameters, the laser can even reverse spin from one direction to another. This works for both the circularly and linearly polarized light. The spin reversal window is narrow. These unexpected results closely resemble all-optical helicity-dependent magnetic switching found in much more complicated ferrimagnetic rare earth compounds. Therefore, we believe that our spin-orbit coupled model may find some important applications in spin switching processes, a hot topic in femtomagnetism.Introduction. -Magneto-optical Faraday and Kerr techniques are indispensable to modern magnetism investigations [1,2]. Such a technique is an ideal tool to investigate both static and dynamic evolutions of spin [3][4][5][6], since it is a photon-in and photon-out technique and leaves the sample intact before and after the experimental measurement. The origin of the magneto-optics is rooted in the spin-orbit coupling and exchange interaction [7,8], where the rotational angle and ellipticity carry the information of the spin moment change. The classical understanding is developed through the harmonic oscillator model (Hookean model), augmented with the Lorentz force term [7,8],

Switching ferromagnetic spins by an ultrafast laser pulse: Emergence of giant optical spin-orbit torque

“…This finding appears to agree with the experimental results reasonably well [18]. If the laser field becomes too stronger, we are not completely confident whether our model can describe the physics correctly, though we did test the model in a single site case [24], where we found that the switching becomes highly nonlinear, and even the linearly polarized light can switch the spin. For this reason, our present paper exclusively focuses on the lower laser field limit and ferromagnets.…”

Spin-orbit torque-mediated spin-wave excitation as an alternative paradigm for femtomagnetism

“…1). We wonder whether our prior model that was developed for all-optical spin switching [37][38][39][40][41] could help. This model is very much similar to the traditional t − J model, where the spin degree of freedom is taken into account by the Heisenberg exchange interaction, and the charge degree of freedom is taken into account by the hopping term between neighboring atoms.…”

All-optical spin switching under different spin configurations

“…When we were investigating the magneto-optical effect, we accidentally discovered a model [19,20] that allows us to simulate spin reversal, without an effective magnetic field. Different from other studies, we augment a spin-orbit coupling term, λL i · S i , to the Heisenberg exchange model, where λ is the spin-orbit coupling constant, L i and S i are the orbital and spin angular momenta at site i.…”

“…Different from other studies, we augment a spin-orbit coupling term, λL i · S i , to the Heisenberg exchange model, where λ is the spin-orbit coupling constant, L i and S i are the orbital and spin angular momenta at site i. Our Hamiltonian is [15,[19][20][21]…”

“…The fourth term in Eq. 1 describes the interaction between the laser pulse E(t) and the system [19], so we do not have to employ an effective magnetic field approximation. The laser field, centered with respect to magnetic domains, propagates vertically down along the −z axis, with the electric field…”