Sagnac interferometry for high-sensitivity optical measurements of spin-orbit torque

Abstract

Sagnac interferometry can provide a substantial improvement in signal-to-noise ratio compared to conventional magnetic imaging based on the magneto-optical Kerr effect. We show that this improvement is sufficient to allow quantitative measurements of current-induced magnetic deflections due to spin-orbit torque even in thin-film magnetic samples with perpendicular magnetic anisotropy, for which the Kerr rotation is second order in the magnetic deflection. Sagnac interferometry can also be applied beneficially for samples with in-plane anisotropy, for which the Kerr rotation is first order in the deflection angle. Optical measurements based on Sagnac interferometry can therefore provide a cross-check on electrical techniques for measuring spin-orbit torque. Different electrical techniques commonly give quantitatively inconsistent results so that Sagnac interferometry can help to identify which techniques are affected by unidentified artifacts.

Using Rotations to Control Observable Relativistic Effects

“…This for a while led people to believe there must be something wrong with the postulates of relativity, which was Sagnac's original intention (see [2]). Nowadays the phenomenon is not only well integrated into SR but also plays a major role in laser interferometers and precise Doppler gyroscopes [3][4][5]. Another interesting discovery from the early days of relativity was the Thomas precession [6] explaining how electron spins are affected by acceleration in non-inertial frames.…”

“…We refer to [19][20][21][22] for a deeper investigation of the problem of rotating frames in relativity, both from a purely mechanical perspective and with an account of electromagnetic interactions. Instead of diving into the physics and various applications of this topic, the present study discusses a unified geometric approach based on the structure of proper Lorentz transformations SO + (3, 1) ∼ = SO(3, C) and the corresponding Wigner little groups, starting with the compact subgroup of euclidean rotations in R 3 . A convenient representation proposed by Rodrigues back in 1840, based on Clifford's geometric algebras but preceeding their invention (cf.…”