Strong magnetic anisotropy and unusual magnetic field reinforced phase in URhSn with a quasi-kagome structure

The physical properties of URhSn with quasi-kagome structure are studied using single-crystalline samples via electrical resistivity, magnetic susceptibility, heat capacity, thermal expansion, and high-field magnetization measurements. Remarkable magnetic anisotropy is found in the ferromagnetic (FM) state below $T_{\mathrm{C}}=16\mathrm{K}$ as well as in the ordered state between $T_{\mathrm{C}}$ and $T_{\mathrm{O}}=54\mathrm{K}$, where the easy and hard magnetization directions are the hexagonal [0001] and $\left[10\overline{1}0\right]$ axes. In the paramagnetic state, the magnetic susceptibility shows a Curie-Weiss behavior; the Weiss temperatures are positive and negative for [0001] and $\left[10\overline{1}0\right]$, respectively, indicating the presence of both FM and antiferromagnetic (AFM) correlations. The entropy release for $5f$ electrons is approximately $R\ln 3$ at $T_{\mathrm{O}}$. The thermal expansion coefficient is strongly anisotropic around $T_{\mathrm{O}}$ between the hexagonal basal plane and the [0001] axis, indicating its remarkable anisotropic magnetoelastic response and uniaxial stress dependences. Interestingly, the magnetic field response of the higher-temperature ordered state is unusual: $T_{\mathrm{O}}\left(H\right)$ increases and the heat-capacity jump is enhanced with the magnetic field for $H\left|\right|\left[0001\right]$. Based on the established thermodynamic evidence for the second-order transition at $T_{\mathrm{O}}\left(H\right)$, a plausible scenario is the occurrence of a canted AFM ordering or a conical state under magnetic fields, which is stabilized when coupled with field-induced magnetic moments along the [0001] axis. Another possibility is the occurrence of quadrupole ordering at $T_{\mathrm{O}}\left(H\right)$.

Figure 1

The ZrNiAl-type hexagonal structure of URhSn, shown (a) for the $\left(1\overline{1}00\right)$, which is equivalent to the $\left(10\overline{1}0\right)$, and (b) for the (0001) planes. In the basal plane, the uranium atoms form a quasi-kagome structure. (c) Laue x-ray photograph for the (0001) plane of the annealed single-crystalline URhSn.

Figure 2

(a) The temperature dependence of electrical resistivity $\rho \left(T\right)$ for the annealed single-crystalline URhSn at zero field for electric currents along $J\left|\right|\left[11\overline{2}0\right]$ and [0001]. (b) $\rho \left(T\right)$ vs $T^2$. (c) $\rho \left(T\right)$ below 20 K, where the solid line is the fitting result assuming the anisotropic FM spin wave, and the phonon contribution is derived from the resistivity data of a polycrystalline ThRhSn.

Figure 3

(a) $M\left(T\right)/H$ of the annealed URhSn at 2 kOe under the FC condition for the [0001] and $\left[10\overline{1}0\right]$ axes in logarithmic scales. (b) The inverse susceptibility $H/M\left(T\right)$ of URhSn for [0001] and $\left[10\overline{1}0\right]$, where the solid lines are the results of fitting (see text). Here, the data for the as-grown sample are also plotted for [0001].

Figure 4

The magnetization $M\left(T\right)$ of the annealed single-crystalline URhSn, measured at 10, 30, 50, and 70 kOe for the easy magnetization axis [0001] under the FC condition. The inset shows the temperature derivative of magnetization, $dM/dT$.

Figure 5

(a) $M\left(T\right)/H$ for the annealed single-crystalline URhSn at 1, 2, 10, and 50 kOe applied along the hard magnetization axis $\left[10\overline{1}0\right]$ under the FC condition. (b) The enlarged $M\left(T\right)/H$ measured at 1, 2, 10, 20, 30, and 50 kOe (with shifted traces), where arrows indicate the FM transition at $T_{\mathrm{C}}$, the broad anomaly at $T_{\mathrm{M}}^{*}$, and the higher-$T$ order at $T_{\mathrm{O}}$.

Figure 6

(a) $M\left(H\right)$ curves of the annealed single-crystalline URhSn for [0001] at 4.2, 13 ($T<T_{\mathrm{C}}$), 25 ($T<T_{\mathrm{O}}$), and 60 K in the paramagnetic (PM) state, where diamond markers indicate the data for the as-grown sample. (b) $M\left(H\right)$ curves of the annealed single-crystalline URhSn for $\left[10\overline{1}0\right]$ at 4.2, 25, and 60 K.

Figure 7

(a) The magnetization curves for the annealed single-crystalline URhSn up to 560 kOe for [0001] at 1.4, 10, 30, 40, 50, 55, 62, 70, 80, and 100 K. (b) The differential magnetic susceptibility, $dM/dH$, at temperatures from 55 to 62 K (in 1 K steps) for [0001]. Here, the vertically shifted values are indicated for clarity.

Figure 8

The heat capacity $C\left(T\right)/T$ at zero field (in the semilogarithmic scale) for the annealed single-crystalline URhSn and polycrystalline ThRhSn. Inset: $C\left(T\right)/T$ below 2 K for the as-grown single-crystalline URhSn and polycrystalline ThRhSn.

Figure 9

(a) The magnetic contribution of heat capacity $C_{5f}\left(T\right)/T\equiv [C_{\mathrm{URhSn}}\left(T\right)-C_{\mathrm{ThRhSn}}\left(T\right)]/T$ in URhSn at zero field. (b) The obtained entropy of $S_{5f}$ in URhSn, divided by the gas constant $R$.

Figure 10

(a) The temperature dependence of the linear thermal expansion $\mathrm{\Delta }L/L$ for the $\left[10\overline{1}0\right]$, $\left[11\overline{2}0\right]$, and [0001] axes, for the annealed URhSn, measured at zero field. (b) The temperature dependence of the linear thermal expansion coefficient ${\alpha }_{\mathrm{L}}\left(T\right)\equiv d(\mathrm{\Delta }L/L)/dT$. Here, the transition temperatures, $T_{\mathrm{C}}$ and $T_{\mathrm{O}}$, defined as the peaks of $\mathrm{\Delta }{\alpha }_{\mathrm{L}}\left(T\right)$, are indicated by upper arrows and dashed lines.

Figure 11

(a) $C\left(T\right)/T$ of the annealed single-crystalline URhSn measured at 0, 40, 60, and 90 kOe for [0001], where the inset shows the enlarged figure around $T_{\mathrm{O}}$ (at 0, 40, 50, 60, 70, 80, and 90 kOe). The heat-capacity jump at $T_{\mathrm{O}}$ in URhSn, $\mathrm{\Delta }C/T_{\mathrm{O}}$, as a function of (b) magnetic field $H$ and (c) $H^2$, where the solid line is the result of linear fitting.

Figure 12

$H\text{−}T$ phase diagram of the annealed URhSn for [0001] and $\left[10\overline{1}0\right]$, where the dashed lines are guides to the eyes. The inset shows the enlarged figure around $T_{\mathrm{O}}\left(H\right)$.