Electronic Theory for the Nonlinear Magneto-Optical Response of Transition-Metals at Surfaces and Interfaces: Dependence of the Kerr-Rotation on Polarization and on the Magnetic Easy Axis

TL;DR

This paper develops a theoretical framework for understanding how the nonlinear magneto-optical Kerr effect depends on polarization and magnetic easy axis orientation at surfaces and interfaces, enabling detailed magnetic structure analysis.

Contribution

It extends previous models to include polarization dependence and provides a microscopic analysis of phase differences in tensor elements affecting nonlinear Kerr rotation.

Findings

Nonlinear Kerr rotation is sensitive to electromagnetic field components, not just intensities.

The direction of magnetization and easy axis can be deduced from polarization dependence.

The phase difference between tensor elements is 90 degrees, contrasting linear magneto-optics.

Abstract

We extend our previous study of the polarization dependence of the nonlinear optical response to the case of magnetic surfaces and buried magnetic interfaces. We calculate for the longitudinal and polar configuration the nonlinear magneto-optical Kerr rotation angle. In particular, we show which tensor elements of the susceptibilities are involved in the enhancement of the Kerr rotation in nonlinear optics for different configurations and we demonstrate by a detailed analysis how the direction of the magnetization and thus the easy axis at surfaces and buried interfaces can be determined from the polarization dependence of the nonlinear magneto-optical response, since the nonlinear Kerr rotation is sensitive to the electromagnetic field components instead of merely the intensities. We also prove from the microscopic treatment of spin-orbit coupling that there is an intrinsic phase difference of 90$^{\circ }$ between tensor elements which are even or odd under magnetization reversal in contrast to linear magneto-optics. Finally, we compare our results with several experiments on Co/Cu films and on Co/Au and Fe/Cr multilayers. We conclude that the nonlinear magneto-optical Kerr-effect determines uniquely the magnetic structure and in particular the magnetic easy axis in films and at multilayer interfaces.