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

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 $\mathbf{q}$ magnetic fluctuations and the out-of-plane polarization of the incommensurate magnetic fluctuation at the nesting wave vector ${\mathbf{Q}}_1=(2/3\pi ,2/3\pi )$ but also nearly isotropic fluctuations near ${\mathbf{Q}}_2=(\pi /6,\pi /6)$. Furthermore, one finds that apart from the high-symmetry direction of the tetragonal Brillouin zone the magnetic anisotropy is maximal, i.e. ${\chi }^{xx}\ne {\chi }^{yy}\ne {\chi }^{zz}$. 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.

6 pages, 4 figures

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