Competition between spin-orbit coupling and magnetic exchange splitting in Ca${}_{2}$RuO${}_{4}$

Competition between spin-orbit coupling and magnetic exchange splitting in Ca $_{2}$ RuO $_{4}$

Guo-Qiang Liu

Phys. Rev. B 88, 104428 – Published 30 September 2013

Abstract

The ferromagnetic phase of Ca $_{2}$ RuO $_{4}$ has been puzzling because the observed magnetic moment $m$ $\approx$ 0.4 $μ_{B}$ /Ru is surprisingly small, compared with the predicted 2 $μ_{B}$ /Ru. This discrepancy is resolved by considering the interplay of the spin-orbit coupling and Coulomb repulsion, which results in a large enhancement of the spin-orbit splitting. A simple tight-binding formula shows that the moment reduction originates in the competition between the spin-orbit coupling and magnetic exchange splitting. This competitive picture provides a unified explanation for the complicated phase diagram of Ca $_{2}$ RuO $_{4}$ , including the antiferromagnetic insulating, paramagnetic insulating, and ferromagnetic metallic phase.