Substrate effects in the magneto-optical second-harmonic generation from first principles: Fe/Cu(001)

TL;DR

This study uses first-principles calculations to analyze how substrate layers of copper influence the magneto-optical second-harmonic generation in an iron monolayer, revealing significant magnetic contributions to the nonlinear optical response.

Contribution

It provides a detailed ab initio analysis of substrate effects on nonlinear magneto-optical responses, including convergence behavior with increasing copper layers.

Findings

Magnetic tensor elements are comparable to nonmagnetic ones in nonlinear response.

Adding Cu layers converges the nonlinear susceptibility to a stable value.

The nonlinear optical response is significantly influenced by substrate-induced d-band states.

Abstract

We compute the nonlinear optical response of an Fe monolayer placed on top of 1 to 4 monolayers of Cu(001). Our calculation is based on ab initio eigenstates of the slab, which are obtained within the full-potential linearized augmented plane-wave method. The ground-state spin-polarized electronic structure is converged self-consistently to an accuracy better than 0.1 mRy. Subsequently, we take the spin-orbit interaction into account within a second variational treatment. The new set of eigenstates allows us to calculate the magneto-optical transition matrix elements. The second-harmonic response is determined in the reflection geometry with magnetization perpendicular to the surface (the so-called polar configuration) using the surface-sheet model. Adding layers of a noble metal (Cu) to the Fe monolayer gives a new degree of freedom for the inclusion of nonmagnetic Cu d bands to the nonlinear magneto-optical response of the slab, and the energy bands show that such an addition converges essentially to an addition of d states and a small broadening of the d band with growing number of Cu layers. The screened nonlinear optical susceptibility is calculated and converges quite well with a growing number of Cu layers. Our first-principles results confirm that the magnetic tensor elements of the nonlinear optical response tensor are roughly of the same order of magnitude as the nonmagnetic ones (in contrast to linear optics, where the magnetic response is only a minor correction).