Pressure-dependent magnetism of the Kitaev candidate Li$_2$RhO$_3$
We use magnetization measurements under pressure along with \textit{ab initio} and cluster many-body calculations to investigate magnetism of the Kitaev candidate Li$_2$RhO$_3$. Hydrostatic compression leads to a decrease in the magnitude of the nearest-neighbor ferromagnetic Kitaev coupling $K_1$ and the corresponding increase in the off-diagonal anisotropy $\Gamma_1$, whereas the experimental Curie-Weiss temperature changes from negative to positive with the slope of +40~K/GPa. On the other hand, spin freezing persists up to at least 3.46~GPa with the almost constant freezing temperature of 5~K that does not follow the large changes in the exchange couplings and indicates the likely extrinsic origin of spin freezing. Magnetic frustration in Li$_2$RhO$_3$ is mainly related to the interplay between ferromagnetic $K_1$ and antiferromagnetic $\Gamma_1$, along with the weakness of the third-neighbor coupling $J_3$ that would otherwise stabilize zigzag order. The small $J_3$ distinguishes Li$_2$RhO$_3$ from other Kitaev candidates.