Pressure dependence of the magnetization of $\mathrm{U}{\mathrm{Ru}}_2{\mathrm{Si}}_2$

The ground state of $\mathrm{U}{\mathrm{Ru}}_2{\mathrm{Si}}_2$ changes from so-called hidden order (HO) to large-moment antiferromagnetism (LMAF) upon applying hydrostatic pressure in excess of $\sim 14\mathrm{kbar}$. We report the dc magnetization $M(B,T,p)$ of $\mathrm{U}{\mathrm{Ru}}_2{\mathrm{Si}}_2$ for magnetic fields $B$ up to $12\mathrm{T}$, temperatures $T$ in the range $2–100\mathrm{K}$, and pressure $p$ up to $17\mathrm{kbar}$. Remarkably, characteristic scales such as the coherence temperature $T^{*}$, the transition temperature $T_0$, and the anisotropy in the magnetization depend only weakly on the applied pressure. However, the discontinuity in $\partial M∕\partial T$ at $T_0$, which measures the magnetocaloric effect, decreases nearly 50% upon applying $17\mathrm{kbar}$ for $M$ and $B$ parallel to the tetragonal $c$ axis, while it increases 15-fold for the $a$ axis. Our findings suggest that the HO and LMAF phases have an astonishing degree of similarity in their physical properties, but a key difference is the magnetocaloric effect near $T_0$ in the basal plane.

Figure 1

(Color online) Magnetization $M$ of $\mathrm{U}{\mathrm{Ru}}_2{\mathrm{Si}}_2$ versus temperature $T$ in the range $2–100\mathrm{K}$, for a field of $B=12\mathrm{T}$ applied along the tetragonal $c$ axis. Curve $a$, Ambient pressure; curve $b$, $p=15.9\mathrm{kbar}$. The inset displays typical data of $M\left(B\right)$ for $T=20\mathrm{K}$, where the nonlinearity in curve $b$ is due to the suppression of $T_0$ under magnetic field.

Figure 2

(Color online) $M∕B$ near $T_0$ for the tetragonal $c$ axis (a), and basal-plane $a$ axis (b), at ambient pressure. Data for both directions display a sharp kink at $T_0$ that signals the formation of a spin gap.

Figure 3

(Color online) Typical numerical derivative $\partial M∕\partial T$ vs $T$ of $M\left(T\right)$ measured experimentally for various fields at ambient pressure for the $c$ axis (a), and the $a$ axis (b). The discontinuous steps are purely due to the method of calculation. (Note that the data are normalized to the applied field, and the curves have been shifted by arbitrary constants for clarity.)

Figure 4

(Color online) Typical numerical derivative $\partial M∕\partial T$ vs $T$ of $M\left(T\right)$ measured for various fields at high pressure for the $c$ axis (a) and for the $a$ axis (b). For the $c$ axis additional structure, which emerges with increasing magnetic field, is seen. This indicates a more complex magnetic state at high pressure. (As in Fig. 3, the data are normalized to the applied field, and the curves have been shifted by arbitrary constants for clarity.)

Figure 5

(Color online) Normalized field dependence of $T_0$ at ambient pressure and high pressure (above $p_c$) for the $c$ and $a$ axes. As transition temperature $T_0$ we take the onset of the transition upon decreasing temperature. The additional structure for the $c$ axis at $15.9\mathrm{kbar}$ and $12\mathrm{T}$ shown in Fig. 4a is not represented here. We find that the suppression of $T_0$ with $B$ along the $c$ axis is mostly unchanged upon applying pressure, as discussed in the text.

Figure 6

Pressure dependencies of the coherence temperature $T^{*}$, the transition temperature $T_0$, and the total height of the anomaly in $\partial M∕\partial T$. Lines are guides to the eye. (a) The temperature $T^{*}$ of the maximum in $M\left(T\right)$ increases nearly 50% under pressure up to $\sim 20\mathrm{kbar}$. (b) The transition temperature $T_0$ increases weakly under pressure, with a pronounced change of slope around $14\mathrm{kbar}$. The change of slope suggests that the border between HO and LMAF is crossed, and may be used to define $p_c\approx 14\mathrm{kbar}$. (c) The total height of the anomaly at $T_0$ seen in $\partial M∕\partial T$. For the $c$ axis $\partial M∕\partial T$ decreases by nearly 50%, while $\partial M∕\partial T$ increases nearly 15-fold for the basal plane $a$ axis. It is interesting to note that the height of the anomaly in $\partial M∕\partial T$ for the $a$ axis is already maximal below $p_c$ and remains constant between 12 and $17\mathrm{kbar}$. The data point for the $a$ axis at $p=0$ was recorded without pressure cell (cf. Fig. 3).