Acoustic signatures of the phase transitions in the antiferromagnet ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$

We report on ultrasound measurements in a single crystal of the antiferromagnet ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ as a function of temperature and magnetic field. We find pronounced anomalies in the sound velocity at the Néel temperature, 25 K, and at the field-induced spin-flop-like transition at 22.5 T, which points to a strong magnetoelastic coupling. Additionally, we find that in the paramagnetic regime the temperature dependence of the magnetic susceptibility and the field dependences of the magnetization and sound velocity of transverse acoustic waves can be well described assuming a localized character of the $5f$ electrons. Using this premise, the crystal-electric-field scheme of ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ has been determined.

Figure 1

Temperature dependences of (a) the magnetic susceptibility, $\chi =M/H$, in 1 T; (b) the specific heat, $C$; and (c) the relative sound-velocity changes, $\mathrm{\Delta }v/v$, for the acoustic modes $C_{11},C_{33},C_{44}$, and $C_{66}$ in zero field.

Figure 2

(a) Magnetization, $M$, and (b) relative sound-velocity changes, $\mathrm{\Delta }v/v$, for the acoustic modes $C_{11}$ and $C_{44}$ measured in pulsed magnetic fields up to 58 T at 2 K.

Figure 3

Relative sound-velocity changes, $\mathrm{\Delta }v/v$, for the acoustic modes (a) $C_{11}$ and (b) $C_{44}$ measured in pulsed magnetic fields up to 58 T between 2 and 30 K.

Figure 4

Magnetic phase diagram of ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ for field applied along the [001] axis. The line is a guide to the eye.

Figure 5

(a) Temperature dependences of the magnetic susceptibility, $\chi$; (b) and (c) field dependences of the magnetization, $M$, and relative sound-velocity changes, $\mathrm{\Delta }v/v$, for $C_{44}$; and (d) CEF level scheme of a ${\mathrm{U}}^{4+}$ ion in ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ obtained from the CEF parameters listed in Table 1. In panels (a), (b), and (c), the symbols and solid lines represent the experimental and calculated data, respectively. In panel (d), the thin lines represent singlets and the thick lines represent doublets.