Novel critical behavior of magnetization in URhSi: Similarities to the uranium ferromagnetic superconductors UGe2 and URhGe

Abstract

We study the critical behavior of dc magnetization in the uranium ferromagnet URhSi around the paramagnetic to ferromagnetic phase transition at ${T}_{\mathrm{C}}\ensuremath{\sim}10$ K with a modified Arrott plot, a Kouvel-Fisher plot, the critical isotherm analysis, and the scaling analysis. URhSi is isostructural to uranium ferromagnetic superconductors URhGe and UCoGe. The critical exponent $\ensuremath{\beta}$ for the temperature dependence of the spontaneous magnetization below ${T}_{\mathrm{C}}$, $\ensuremath{\gamma}$ for the magnetic susceptibility, and $\ensuremath{\delta}$ for the magnetic isotherm at ${T}_{\mathrm{C}}$ in URhSi have been determined as $\ensuremath{\beta}=0.300\ifmmode\pm\else\textpm\fi{}0.002$, $\ensuremath{\gamma}=1.00\ifmmode\pm\else\textpm\fi{}0.02$, and $\ensuremath{\delta}=4.38\ifmmode\pm\else\textpm\fi{}0.04$ by the scaling analysis and the critical isotherm analysis. These critical exponents fulfill the Widom scaling law $\ensuremath{\delta}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}1+\phantom{\rule{0.16em}{0ex}}\ensuremath{\gamma}/\ensuremath{\beta}$. Magnetization has strong uniaxial magnetic anisotropy in the ferromagnetic state of URhSi. However, the universality class of the ferromagnetic transition does not belong to the three-dimensional Ising system with short-range exchange interactions between magnetic moments ($\ensuremath{\beta}=0.325$, $\ensuremath{\gamma}=1.241$, and $\ensuremath{\delta}=4.82$). The obtained exponents in URhSi are similar to those in the uranium ferromagnetic superconductors ${\mathrm{UGe}}_{2}$ and URhGe, and uranium ferromagnets UIr and $\mathrm{U}({\mathrm{Co}}_{0.98}{\mathrm{Os}}_{0.02}$)Al. We have previously reported the unconventional critical behavior of magnetization in the uranium ferromagnetic superconductors [N. Tateiwa et al., Phys. Rev. B 89, 064420 (2014)]. The universality class of the ferromagnetic transition in URhSi may belong to the same one in the uranium ferromagnetic superconductors and the uranium ferromagnets. The unconventional critical behavior of the magnetization in the uranium compounds cannot be understood with previous theoretical interpretations of critical phenomena. The absence of the superconductivity in URhSi is discussed from several viewpoints. The improvement of the sample quality in URhSi could provide a good opportunity to gain a deeper understanding of the ferromagnetic superconductivity in the uranium ferromagnets.