Transverse and longitudinal magnetic-field responses in the Ising ferromagnets URhGe, UCoGe, and UGe${}_2$

The field dependence of the electronic specific heat $\gamma (H)$ of URhGe is determined using temperature-dependent magnetization measurements and Maxwell’s relation for all three orthorhombic directions. A large ($\approx$40%) enhancement of $\gamma (H)$ is found at the reorientational transition $H_R$ for fields applied along the $b$ hard axis, which we argue occurs when the field-induced moment is of the same size as the zero-field ordered moment $M_0$. Fields applied along the easy direction, on the other hand, lead to a rapid suppression of $\gamma (H)$. We emphasize that this behavior is also applicable to the closely related ferromagnetic superconductors UCoGe and UGe${}_2$ and discuss implications for the field-induced/enhanced superconductivity in these materials.

Figure 1

Magnetization as a function of temperature for URhGe in different fields applied parallel to the crystal $b$ hard axis. The continuous transition line, $T_{\mathrm{Curie}}(H)$, appears as a maximum in the magnetization (red symbols).

Figure 2

Field dependence of $(\partial \gamma /\partial H){}_T$ derived from the Maxwell relation [Eq. (3)] applied to the magnetization curves, for all three directions. The inset illustrates the low-temperature $T^2$ behavior of $M(T,H)$ for several values of field parallel to $b$.

Figure 3

(a) Field dependence of $T_{\mathrm{Curie}}(H)$ (black symbols, left-hand scale) and $T_c(H)$ (blue symbols and right-hand scale, taken from Ref. 6) for $H$ $\Vert$ $b$ obtained from magnetization and transport measurements, respectively. (b) Zero-temperature magnetization curves for $H$ $\Vert$ $a$, $b$, and $c$. (c) Field dependence of $\gamma (H)$ derived using the Maxwell relation for $H$ $\Vert$ $a$, $b$, and $c$. The inset shows the specific heat for $H=0$. The solid line is a fit to $\gamma (m_b)+B_3{T}^2$ for $T$ $>$ $T_{\mathrm{Curie}}$.

Figure 4

Comparison of the field dependence of the effective mass $m^{*}$ for $H$ $\Vert$ $b$ and $H$ $\Vert$ $c$ obtained from magnetization, specific-heat, and transport measurements.