Anisotropic physical properties of single-crystal ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ in high magnetic fields

We report on the crystal and magnetic structures, magnetic, transport, and thermal properties of ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ single crystals studied in part in high magnetic fields up to 58 T. The material adopts a ${\mathrm{U}}_3{\mathrm{Si}}_2$-related tetragonal crystal structure and orders antiferromagnetically below $T_N=25$ K. The antiferromagnetic structure is characterized by a propagation vector $\mathit{k}=\left(00\frac{1}{2}\right)$. The magnetism in ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ is found to be associated mainly with $5f$ states. However, both unpolarized and polarized neutron experiments reveal at low temperatures in zero field non-negligible magnetic moments also on Rh sites. U moments of 0.50(2) ${\mu }_B$ are directed along the tetragonal axis while Rh moments of 0.06(4) ${\mu }_B$ form a noncollinear arrangement confined to the basal plane. The response to applied magnetic field is highly anisotropic. Above $\sim 15\mathrm{K}$ the easy magnetization direction is along the tetragonal axis. At lower temperatures, however, a stronger response is found perpendicular to the $c$ axis. While for the $a$ axis no magnetic phase transition is observed up to 58 T, for the field applied at 1.8 K along the tetragonal axis we observe above 22.5 T a field-polarized state. A magnetic phase diagram for the field applied along the $c$ axis is presented.

Figure 1

Crystal structure of ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ as determined from neutron data projected along the $a$ axis (a) and the $c$ axis (b). Sn, U, and Rh atoms are shown by large, intermediate, and small spheres, respectively. A sublattice formed by U atoms projected along the tetragonal axis is shown in (c). The thick (blue) lines connect the next-nearest uranium neighbors (at a distance $d_1=3.622\AA$) and the thin line (red) the second-next-nearest neighbors (at a distance $d_2=3.902\AA$). Corresponding exchange interactions are denoted as $J$ and $J^{\prime }$, respectively. The nearest U neighbors (at a distance $d_0=3.586\AA$) are found along the $c$ axis. The rectangle represents one crystallographic unit cell projected along the $c$ axis. U atoms form effectively a Shastry-Sutherland lattice as shown in (d). Rh atoms form this type of lattice as well.

Figure 2

Temperature dependence of the magnetic susceptibility $\chi \left(T\right)$ with a field of 1 T applied along the two principal directions (a). The inset magnifies the area around $T_N$ showing also the data taken in 14 T. Panel (b) shows the temperature dependence of the inverse magnetic susceptibility (open points) together with the best fits to a modified Curie-Weiss law (full lines).

Figure 3

Magnetization measurements as a function of magnetic field applied along the $a$ axis (a) and along the $c$ axis (b) at various temperatures measured using PPMS magnetometer.

Figure 4

High-field magnetization curves obtained at 2 K in pulse fields applied along [100], [110], and [001] directions together with the data (shown as full points) taken in static fields using PPMS. In the inset we show the magnetization curve obtained at 640 mK along the $c$ axis using a magnet with a significantly longer pulse duration.

Figure 5

High-field magnetization in increasing pulse fields applied along the $c$ axis direction measured at different temperatures.

Figure 6

The temperature dependence of the specific heat $C$ of ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ single crystal measured in zero magnetic field. The solid line through measured data is the estimation of the phonon background as described in the main text. The lower inset shows the temperature development of the magnetic entropy $S_{mag}$. The top inset shows the low temperature part of the specific heat in the $C/T\text{vs}{T}^2$ representation together with the best fit to formula given in the main text.

Figure 7

The temperature dependence of the specific heat $C$ of ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ single crystal measured in applied magnetic field up to 14 T directed along the tetragonal axis. In the inset we show the variation of the specific heat recorded at 2.9 K with field applied along the $c$ axis.

Figure 8

Electrical resistivity of ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ single crystal measured along the $c$ axis. The inset shows the low-temperature detail of the electrical resistivity curve to focus on the anomaly caused by the onset of antiferromagnetism and the best fit to the expression described in the main text.

Figure 9

Magnetic phase diagram of ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ for field applied along the $c$ axis determined from high field pulse measurements (HLD) and magnetization and specific heat measurements using static fields. The magnetic phase boundary for field applied along the $a$ axis is shown by the broken, nearly vertical line.

Figure 10

Rocking curves through the (1 1 $\frac{l}{2}$) magnetic Bragg reflection collected at 2.4 K and at 26 K (just above the magnetic phase transition) in zero field and at 2.4 K in a field of 14.5 T applied along the $\left[\overline{1}10\right]$ direction.

Figure 11

Schematic representation of the AF structure of ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ as determined from the best fit of our neutron diffraction data taken at 2.4 K in zero external field to the model assuming the existence of only U moments (a). AF structure of ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ assuming the existence of both U and Rh moments is shown in (b). Rh moments were multiplied by a factor of five. Both structures are shown in two projections: along the tetragonal axis (top) and along the $a$ axis (lower panel). Only half one magnetic unit cells are shown. Moment directions in the adjacent cells along the $c$ axis are reversed.

Figure 12

Temperature dependence of the (1 1 $\frac{1}{2}$) magnetic Bragg reflection recorded with increasing temperature in zero field and in the field of 14.5 T applied along the $\left[\overline{1}10\right]$ direction. The arrow in the main panel denotes conditions under which a field scan shown as a color coded map (shown in the inset) of intensities taken at the same reflection has been taken with decreasing field.

Figure 13

Projection of the spin distribution in ${\mathrm{U}}_2{\mathrm{Rh}}_2\mathrm{Sn}$ onto a plane perpendicular to the $c$ axis as obtained from the maximum entropy reconstruction from data collected at 30 K with a field of 6.2 T applied along the tetragonal axis. Only half of the unit cell along the c direction is projected. Densities around magnetic moments are restricted by an isosurface value of 0.01 ${\mu }_B/{\AA }^3$. Densities below this level are not shown.