Metamagnetism and tricriticalilty in the heavy-fermion ferromagnet URhGe

URhGe is a ferromagnetic superconductor with a distinctive magnetic behavior. In a field $H\ensuremath{\parallel}b$ applied perpendicular to the easy axis, URhGe exhibits an abrupt orientational transition of the magnetization with a reentrant superconducting phase emerging close to the transition field ${H}_{m}$. We develop a theoretical description of the magnetic properties of URhGe by considering a spin model with competing magnetic anisotropies. The model is analyzed both analytically at zero temperature and with Monte Carlo simulations at finite temperatures. The constructed ${H}_{b}$--$T$ phase diagram features a tricritical point on the line ${H}_{m}(T)$ and is in a good quantitative agreement with the experimental diagram of URhGe. We demonstrate that the asymptotic tricritical behavior of the order parameter and the correlation length is described by the mean-field critical exponents. The derived microscopic parameters suggest that URhGe is an $XY$-like ferromagnet with an additional weak in-plane anisotropy in the $bc$ plane.