NdRhSn: A ferromagnet with an antiferromagnetic precursor

NdRhSn has a ferromagnetic ground state [$T_t=7.6(1)$ K] with a magnetic moment equal to 2/3 of the free Nd${}^{3+}$-ion moment. Upon cooling from the paramagnetic state, the ferromagnetism is preceded by an incommensurate antiferromagnetic state between $T_N=9.8(1)$ K and $T_t$. In both magnetic phases the magnetic moments are locked along the $c$ axis, which is the easy-magnetization axis of the system. We have investigated this unusual situation by measuring anomalies of several bulk physical properties characteristic for the magnetic phase transitions at $T_N$ and $T_t$ and the response of these properties to an applied magnetic field. Neutron-diffraction experiments have been also performed at low temperatures. Furthermore, in order to understand better the physical properties of NdRhSn, single crystals have been studied under external hydrostatic and uniaxial pressure and in high magnetic fields. An antiferromagnetic phase with a propagation vector (0 0 1/11) has been found between $T_N$ and $T_t$. The magnetic-ordering temperatures $T_N$ and $T_t$ are sensitive to both hydrostatic and uniaxial pressures, but in a different manner. Application of hydrostatic pressure leads to a reduction of the ordering temperatures at rates $\Delta T_N/\Delta p=-0.76(5)$ K/GPa and $\Delta T_t/\Delta p=-0.9(2)$ K/GPa while uniaxial pressure applied along the $c$ axis leads to an increase of the ordering temperatures at rates $\Delta T_N/\Delta p=+1.2(5)$ K/GPa and $\Delta T_t/\Delta p=+2.7(4)$ K/GPa. No considerable influence of pressure on the antiferromagnetic propagation vector has been found. The peculiar evolution of magnetism in NdRhSn with temperature indicates a complex hierarchy of exchange interactions.

Figure 1

(a) Temperature dependence of the specific heat of NdRhSn measured on a single crystal and polycrystal compared with the specific heat of LaRhSn. The NdRhSn single-crystal data are taken from Mihalik et al. (Ref. 11) and the LaRhSn data are taken from Mihalik et al. (Ref. 7). (b) The calculated magnetic entropy where LaRhSn has been used as a nonmagnetic analog.

Figure 2

Relative electrical resistivity and magnetoresistivity of NdRhSn for (a) $\rho \left|\right|a$ axis, $B\left|\right|c$ axis and (b) $\rho \left|\right|c$ axis, $B\left|\right|a$ axis. The dashed lines represent the positions of $T_N$ and $T_t$. All data were obtained during the increasing of the temperature.

Figure 3

Magnetization at $T$ $=$ 4.2 K in fields up to 50 T.

Figure 4

Representative powder neutron-diffraction patterns of NdRhSn at (a) 14 K and (b) 4.3 K. The circles represents the experimental data, the line through circles represents the best Rietveld fit, and the line below the circles represents the difference.

Figure 5

Cut from the neutron Laue pattern of NdRhSn: (a) Temperature evolution; (b) indexed cut at 8.5 K.

Figure 6

Temperature evolution of the integrated intensities of representative reflections. The intensity of the magnetic satellites has been multiplied by a factor of 1000 to match the scale of the plot. The dashed lines indicate $T_N$ and $T_t$.

Figure 7

Relative thermal expansion of NdRhSn in various magnetic fields up to 1 T applied along the $c$ axis: (a) Measurement along the $a$ axis, (b) measurement along the $c$ axis, and (c) volume evolution as calculated using the $a$- and $c$-axis data.

Figure 8

(a) $a$- axis and (b) $c$-axis relative magnetostriction of NdRhSn. The reference points are the values measured at 0 T and 20 K. (c) Calculated relative change of the volume using the $a$- and $c$-axis data. In all cases, the magnetic field was applied along the $c$ axis.

Figure 9

Evolution of the magnetic-transition temperatures $T_N$ and $T_t$ of NdRhSn under applied hydrostatic pressure. The filled symbols represent the results from experiment No. 1 and the open symbols represent the results from experiment No. 2. In both cases, the data have been taken at $B=0.01$ T with $B\left|\right|c$ axis.

Figure 10

Evolution of the transition temperatures $T_N$ and $T_t$ of NdRhSn at $B=0.01$ T under uniaxial pressure. The data have been taken for the experimental configuration $B\left|\right|p\left|\right|c$ axis.

Figure 11

Comparison of the evolution of the metamagnetic transition in NdRhSn at $T=8.2$ K with the field applied parallel to the $c$ axis under hydrostatic and uniaxial pressure. The data under hydrostatic pressure are from experiment No. 2 and the zero-pressure data have been obtained in the same hydrostatic-pressure experiment in the unclamped hydrostatic-pressure cell.

Figure 12

First-quadrant part of the hysteresis loops of NdRhSn at 2 K measured at different hydrostatic pressures, together with hysteresis loops at a uniaxial pressure of 0.11 GPa along the $c$ axis at 8.2 and 9.3 K. In all cases, the magnetic field was applied along the $c$ axis. The hydrostatic pressure data were obtained in experiment No. 1.

Figure 13

The sketch of the proposed local RKKY interaction (thick lines) acting along the $c$ axis. The changes of the local interaction according to the hydrostatic (H) and uniaxial (U) pressure are plotted as small arrows.

Figure 14

Temperature evolution of the integrated intensity of (a) the nuclear (2 0 0) reflection of NdRhSn and (b) its magnetic satellite. The lines are guides to the eye.

Figure 15

Magnetic-field evolution at 9 K of the integrated intensity of (a) the nuclear (2 0 0) reflection and (b) its magnetic satellite. In all cases, the magnetic field was applied along the $c$ axis. The lines are guides to the eye.