Anisotropic spin fluctuations in Sr$_2$RuO$_4$: role of spin-orbit coupling and induced strain

TL;DR

This study investigates the spin anisotropy of magnetic susceptibility in Sr$_2$RuO$_4$, revealing how spin-orbit coupling and strain influence magnetic fluctuations and anisotropy, with implications for understanding its magnetic properties.

Contribution

The paper provides a detailed analysis of spin anisotropy in Sr$_2$RuO$_4$ considering spin-orbit coupling and strain effects, highlighting the orbital anisotropy and magnetic fluctuation behavior.

Findings

In-plane polarization of low ${f q}$ magnetic fluctuations.

Out-of-plane polarization at the nesting wave vector ${f Q}_1$.

Strong Ising-like ferromagnetic fluctuations near the Lifshitz transition.

Abstract

We analyze the spin anisotropy of the magnetic susceptibility of Sr$_2$RuO$4$ in presence of spin-orbit coupling and anisotropic strain using quasi-two-dimensional tight-binding parametrization fitted to the ARPES results. Similar to the previous observations we find the in-plane polarization of the low ${\bf q}$ magnetic fluctuations and the out-of-plane polarization of the incommensurate magnetic fluctuation at the nesting wave vector ${\bf Q}_1 = (2/3 \pi ,2/3 \pi)$ but also nearly isotropic fluctuations near ${\bf Q}_2=(\pi/6,\pi/6)$. Furthermore, one finds that apart from the high-symmetry direction of the tetragonal Brillouin zone the magnetic anisotropy is maximal, i.e. $\chi^{xx} \neq \chi^{yy} \neq \chi^{zz}$. This is the consequence of the orbital anisotropy of the $xz$ and $yz$ orbitals in the momentum space. We also study how the magnetic anisotropy evolves in the presence of the strain and find strong Ising-like ferromagnetic fluctuations near the Lifshitz transition for the $xy$-band.