Spin rotation induced by applied pressure in the Cd-doped ${\mathrm{Ce}}_2{\mathrm{RhIn}}_8$ intermetallic compound

The pressure evolution of the magnetic properties of the ${\mathrm{Ce}}_2{\mathrm{RhIn}}_{7.79}{\mathrm{Cd}}_{0.21}$ heavy fermion compound was investigated by single crystal neutron magnetic diffraction and electrical resistivity experiments under applied pressure. From the neutron magnetic diffraction data, up to $P=0.6\mathrm{GPa}$, we found no changes in the magnetic structure or in the ordering temperature $T_N=4.8\mathrm{K}$. However, the increase of pressure induces an interesting spin rotation of the ordered antiferromagnetic moment of ${\mathrm{Ce}}_2{\mathrm{RhIn}}_{7.79}{\mathrm{Cd}}_{0.21}$ into the $ab$ tetragonal plane. From the electrical resistivity measurements under pressure, we have mapped the evolution of $T_N$ and the maximum of the temperature dependent electrical resistivity ($T_{\mathrm{MAX}}$) as a function of the pressure ($P\lesssim 3.6\mathrm{GPa}$). To gain some insight into the microscopic origin of the observed spin rotation as a function of pressure, we have also analyzed some macroscopic magnetic susceptibility data at ambient pressure for pure and Cd-doped ${\mathrm{Ce}}_2{\mathrm{RhIn}}_8$ using a mean-field model including tetragonal crystalline electric field (CEF). The analysis indicates that these compounds have a Kramers doublet ${\mathrm{\Gamma }}_7^{-}$-type ground state, followed by a ${\mathrm{\Gamma }}_7^{+}$ first excited state at ${\mathrm{\Delta }}_1\sim 80\mathrm{K}$ and a ${\mathrm{\Gamma }}_6$ second excited state at ${\mathrm{\Delta }}_2\sim 270\mathrm{K}$ for ${\mathrm{Ce}}_2{\mathrm{RhIn}}_8$ and ${\mathrm{\Delta }}_2\sim 250\mathrm{K}$ for ${\mathrm{Ce}}_2{\mathrm{RhIn}}_{7.79}{\mathrm{Cd}}_{0.21}$. The evolution of the magnetic properties of ${\mathrm{Ce}}_2{\mathrm{RhIn}}_8$ as a function of Cd doping and the rotation of the direction of the ordered moment for the ${\mathrm{Ce}}_2{\mathrm{RhIn}}_{7.79}{\mathrm{Cd}}_{0.21}$ compound under pressure suggest important changes of the single ion anisotropy of ${\mathrm{Ce}}^{3+}$ induced by applying pressure and Cd doping in these systems. These changes are reflected in modifications in the CEF scheme that will ultimately affect the actual ground state of these compounds.

Figure 1

(a) Magnetic specific-heat data ($C_{\mathrm{mag}}=C_T$ - $C_{\mathrm{latt}}$) divided by temperature as a function of temperature for the pure compound (triangles) and doped compound (circles) ($x=0.21$). The inset presents the evolution of $T_N$ (open triangles) and $T_{\mathrm{MAX}}$ (closed triangles) as a function of the Cd concentration, extracted from the temperature dependence of $C_{\mathrm{mag}}$ and electrical resistivity $\rho \left(T\right)$. (b) Temperature dependence of $\rho \left(T\right)$ in the low-$T$ region for the pure (triangles) and doped (circles) ($x=0.21$) single crystals. The inset in panel (b) shows $\rho \left(T\right)$ from 2.0 to about 300 K for both samples. The arrows indicate the temperatures $T_N$ and $T_{\mathrm{MAX}}$, where the electrical resistivity has a maximum.

Figure 2

(a) Temperature dependence of $\rho \left(T\right)/{\rho }_{300\mathrm{K}}$ in the low-$T$ region for selected applied pressures. Typical resistivity values for those samples are about $80\mu \mathrm{\Omega }\mathrm{cm}$. (b) $T_N$ (open symbols) and $T_{\mathrm{MAX}}$ (closed symbols) as a function of the applied pressure for ${\mathrm{Ce}}_2{\mathrm{RhIn}}_{7.79}{\mathrm{Cd}}_{0.21}$. Error bars indicated one standard deviation. The first run (circles) was performed in the clamp-type cell, and the second run (squares) was performed in the indenter-type cell. Each run was performed with different single crystals. $T_{\mathrm{MAX}}$ was determined from the peaks in the derivative of $\rho \left(T\right)$. The dotted lines are a guide to the eyes.

Figure 3

Temperature dependence of the neutron integrated intensity of the $\left(\frac{1}{2},\frac{1}{2},1\right)$ magnetic reflection measured under 0.3 GPa (open squares) and 0.6 GPa (open circles) during heating the sample in the temperature range between $T=2.0\mathrm{K}$ and $T=6.0\mathrm{K}$ for ${\mathrm{Ce}}_2{\mathrm{RhIn}}_{7.79}{\mathrm{Cd}}_{0.21}$. Error bars indicated one standard deviation. The ambient pressure measurement (open diamonds) was adapted from Ref. [10]. The solid curves are a fit to the data using the expression $I/I_0={(1-T/T_N)}^{\beta }$, which yields $I_0=820\left(50\right)$ cts/min, $\beta =0.5\left(4\right)$, $T_N=4.8\left(1\right)\mathrm{K}$ for $P=0$; $I_0=680\left(30\right)$ cts/min, $\beta =0.6\left(3\right)$, $T_N=4.8\left(2\right)\mathrm{K}$ for $P=0.3\mathrm{GPa}$; and $I_0=570\left(40\right)$ cts/min, $\beta =0.7\left(6\right)$, $T_N=5.0\left(4\right)\mathrm{K}$, for $P=0.6\mathrm{GPa}$. These values of $T_N$ are in agreement with resistivity and specific heat measurements.

Figure 4

$l$ dependence (in reciprocal lattice units) of $\sigma \left(Q\right)$ for the magnetic peaks $\left(\frac{1}{2},\frac{1}{2},l\right)$ measured with the neutron energy of 35 meV at $T=2.0\mathrm{K}$ for (a) ambient pressure ${\mathrm{Ce}}_2{\mathrm{RhIn}}_{7.79}{\mathrm{Cd}}_{0.21}$ (open diamonds) and with applied pressures of (b) 0.3 GPa (open squares) and (c) 0.6 GPa (open circles). The solid lines in each panel represent the best fit using the model discussed in Eqs. (1, 2, 3).

Figure 5

Magnetic suceptibility data obtained at ambient pressure in an applied field of 0.1 T parallel to the $c$ axis (open symbols) and to the $ab$ plane (closed symbols). The solid lines are the corresponding fits to the CEF model discussed in the text for (a) Cd-doped ${\mathrm{Ce}}_2{\mathrm{RhIn}}_{7.79}{\mathrm{Cd}}_{0.21}$ (circles) and (b) pure ${\mathrm{Ce}}_2{\mathrm{RhIn}}_8$ (squares). The $\eta$ angles in the figures were used as a constraint in the CEF fit. Note: 1 emu/(mol Oe) = $4\pi \times {10}^{-6}{\mathrm{m}}^3/\mathrm{mol}$.