Evolution of the magnetic properties in the antiferromagnet Ce2RhIn8 simultaneously doped with Cd and Ir

Abstract

We report the evolution of the magnetic properties of ${Ce}_2{Rh}_{1-x}{Ir}_x{In}_{8-y}{Cd}_y$ single crystals. In particular, for ${Ce}_2{Rh}_{0.5}{Ir}_{0.5}{In}_8$ ($T_N=2.0K$) and ${Ce}_2{Rh}_{0.5}{Ir}_{0.5}{In}_{7.79}{Cd}_{0.21}$ ($T_N=4.2K$), we have solved the magnetic structure of these compounds using single-crystal neutron magnetic diffraction experiments. Taking the magnetic structure of the ${Ce}_2{RhIn}_8$ heavy-fermion antiferromagnet as a reference, we have identified no changes in the $q=\left(\frac{1}{2},\frac{1}{2},0\right)$ magnetic wave vector; however, the direction of the ordered Ce³⁺ moments rotates toward the $ab$ plane, under the influence of both dopants. By constraining the analysis of the crystalline electric field (CEF) with the experimental ordered moment's direction and high-temperature magnetic-susceptibility data, we have used a mean-field model with tetragonal CEF and exchange interactions to gain insight into the CEF scheme and anisotropy of the CEF ground-state wave function when Cd and Ir are introduced into ${Ce}_2{RhIn}_8$. Consistent with previous work, we find that Cd doping in ${Ce}_2{RhIn}_8$ tends to rotate the magnetic moment toward the $ab$ plane and lower the energy of the CEF excited states' levels. Interestingly, the presence of Ir also rotates the magnetic moment towards the $ab$ plane although its connection to the CEF overall splitting evolution for the y = 0 samples may not be straightforward. These findings may shed light on the origin of the disordered spin-glass phase on the Ir-rich side of the phase diagram and also indicate that the ${Ce}_{2}M{In}_8$ compounds may not follow exactly the same Rh-Ir CEF effects trend established for the ${Ce}_{2}M{In}_5$ compounds.

FIG. 1.

Magnetic specific-heat data divided by temperature as a function of temperature for the (a) pure and (b) Cd-doped (y = 0.21) compounds. (c) Data adapted from Ref. [34] presenting the evolution of $T_N$ and $T_{\mathrm{MAX}}$ as a function of the Cd concentration for ${\mathrm{C}\mathrm{e}}_2{\mathrm{R}\mathrm{h}}_{0.5}{\mathrm{I}\mathrm{r}}_{0.5}{\mathrm{I}\mathrm{n}}_{8-y}{\mathrm{C}\mathrm{d}}_y$. The dashed curves are guides to the eyes. x evolution of $T_N$ and the freezing temperature $T_g$ for (d) pure and (e) Cd-doped samples, as a function of Ir concentration. (f) Sommerfeld coefficient $\gamma$ roughly estimated from the data in (a) and (b), using an entropy-balance construction. Vertical error bars indicate one standard deviation.

FIG. 2.

(a) Temperature dependence of the neutron integrated intensity (square of the sublattice magnetization) of the $\left(\frac{1}{2},\frac{1}{2},1\right)$ magnetic reflection measured for the pure and Cd-doped ${\mathrm{C}\mathrm{e}}_2{\mathrm{R}\mathrm{h}}_{0.5}{\mathrm{I}\mathrm{r}}_{0.5}{\mathrm{I}\mathrm{n}}_8$. The incident neutron beam energy was 14.7 and $35\mathrm{m}\mathrm{e}\mathrm{V}$, respectively. Error bars indicate one standard deviation. The solid curves are a fit to the data using the expression $I/I_0={\left(1-T/T_N\right)}^{2\beta }$, in the case of the undoped sample, and the data from the Cd-doped sample were fit considering a combination of two order-parameter expressions due to the presence of different grains. (b) $\theta$ scans (sample rotation) of the same reflection for both studied samples at 0.3 and $1.4\mathrm{K}$, respectively. The solid curves are fits using Voigt functions, to extract the integrated intensity. Their FWHMs are $0.36(4{)}^{\circ }$ for ${\mathrm{C}\mathrm{e}}_2{\mathrm{R}\mathrm{h}}_{0.5}{\mathrm{I}\mathrm{r}}_{0.5}{\mathrm{I}\mathrm{n}}_8$ and $0.29(2{)}^{\circ }$ for ${\mathrm{C}\mathrm{e}}_2{\mathrm{R}\mathrm{h}}_{0.5}{\mathrm{I}\mathrm{r}}_{0.5}{\mathrm{I}\mathrm{n}}_{7.79}{\mathrm{C}\mathrm{d}}_{0.21}$.

FIG. 3.

l dependence [in reciprocal lattice units (r.l.u.)] of $\sigma (Q)$ for the magnetic peaks $\mathbf{Q}=\left(\frac{1}{2},\frac{1}{2},l\right)$ measured with (a) the neutron energy of 14.7 meV at T = 0.3 K for ${\mathrm{C}\mathrm{e}}_2{\mathrm{R}\mathrm{h}}_{0.5}{\mathrm{I}\mathrm{r}}_{0.5}{\mathrm{I}\mathrm{n}}_8$, for reflections with $h=\frac{1}{2}$ and $h=\frac{3}{2}$, and (b) the neutron energy of 35 meV at T = 1.4 K for the magnetic reflections with $h=\frac{1}{2}$ of ${\mathrm{C}\mathrm{e}}_2{\mathrm{R}\mathrm{h}}_{0.5}{\mathrm{I}\mathrm{r}}_{0.5}{\mathrm{I}\mathrm{n}}_{7.79}{\mathrm{C}\mathrm{d}}_{0.21}$. The curves in each panel represent the best fit using the model discussed in the text, and the errors bars represent one standard deviation.

FIG. 4.

Magnetic-susceptibility data obtained at ambient pressure in an applied field of $0.1\mathrm{T}$ parallel to the $c$ axis (open symbols) and to the $ab$ plane (closed symbols). The solid curves are the corresponding fits to a CEF mean-field model for (a) ${\mathrm{C}\mathrm{e}}_2{\mathrm{R}\mathrm{h}}_{0.5}{\mathrm{I}\mathrm{r}}_{0.5}{\mathrm{I}\mathrm{n}}_8$, (b) ${\mathrm{C}\mathrm{e}}_2{\mathrm{R}\mathrm{h}}_{0.5}{\mathrm{I}\mathrm{r}}_{0.5}{\mathrm{I}\mathrm{n}}_{7.79}{\mathrm{C}\mathrm{d}}_{0.21}$, (c) ${\mathrm{C}\mathrm{e}}_2{\mathrm{I}\mathrm{r}\mathrm{I}\mathrm{n}}_8$, and (d) ${\mathrm{C}\mathrm{e}}_2{\mathrm{I}\mathrm{r}\mathrm{I}\mathrm{n}}_{7.79}{\mathrm{C}\mathrm{d}}_{0.21}$. The dashed curves in (c) correspond to a speculated CEF scheme explained in the text. The $\eta$ angles in the figures were used solely as a constraint in the CEF fit. Note that $1\mathrm{e}\mathrm{m}\mathrm{u}/\left(\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{O}\mathrm{e}\right)=4\pi \times {10}^{-6}{\mathrm{m}}^3/\mathrm{m}\mathrm{o}\mathrm{l}$.

FIG. 5.

Proposed CEF schemes for ${\mathrm{C}\mathrm{e}}_2{\mathrm{R}\mathrm{h}}_{1-x}{\mathrm{I}\mathrm{r}}_x{\mathrm{I}\mathrm{n}}_{8-y}{\mathrm{C}\mathrm{d}}_y$ compounds, along with their magnetic structures. $†$ Data extracted from Ref. [27]. For ${\mathrm{C}\mathrm{e}}_2{\mathrm{I}\mathrm{r}\mathrm{I}\mathrm{n}}_8$, we display both the CEF scheme originated from fit and the scheme marked as $\mathrm{*}$ that follows the trend discussed in the text.