Magnetic properties of ${\mathrm{CeRh}}_3{\mathrm{B}}_2$ investigated by muon spin rotation spectroscopy

We report on positive muon spin rotation $\left({\mu }^{+}\mathrm{SR}\right)$ measurements on hexagonal ${\mathrm{CeRh}}_3{\mathrm{B}}_2$ single crystals. This ferromagnetic material, with the high Curie temperature of $T_C\approx 120\mathrm{K}$, shows anomalous magnetic properties. In the magnetically ordered state, two spontaneous ${\mu }^{+}$-precession frequencies are observed in zero applied magnetic field. The peculiar temperature dependence of these frequencies shows that a magnetization is found on Ce and, over a wide temperature range, on the Rh atoms. There is a strong indication that a significant negative fraction of the magnetization connected to the Ce atoms is delocalized on the $c$-axis $\mathrm{Ce}\text{−}\mathrm{Ce}$ chains. The analysis renders it necessary to allow for an unusual temperature dependence of the Rh-sublattice magnetization, deviating significantly from the Ce-sublattice magnetization. This points to a temperature dependent exchange coupling between the Ce and Rh $4f$ and $4d$ states. Transverse-field measurements above $T_C$ allow one to specify the interstitial sites occupied by the muons and indicate the presence of long-range ${\mu }^{+}$ diffusion for $T>125\mathrm{K}$.

Figure 1

Crystal-orientation dependence of the unique TF-$\mu \mathrm{SR}$ frequency shift in ${\mathrm{CeRh}}_3{\mathrm{B}}_2$ at $125\mathrm{K}$. The crystal is rotated about its $\left[10\overline{1}0\right]$ axis, which is kept perpendicular to ${\mathit{H}}_{\mathrm{ext}}$. The abscissa parameter is $\Theta +90°$, with $\Theta$ the angle between the applied field and the crystallographic $c$ axis. $\times$: Raw frequency-shift data, $•$ : Knight-shift data after demagnetization- and Lorentz-field corrections. Dash-dotted and full curves: ${\cos }^2\left(\Theta \right)$ fits to the raw and corrected data points, respectively. The dashed curves indicate limits of the maximum possible systematic errors in the Knight shift due to demagnetization-correction uncertainties.

Figure 2

Temperature dependence of the ${\mu }^{+}$ Knight shift for three orientations of the ${\mathrm{CeRh}}_3{\mathrm{B}}_2$ crystal. $\times$ for $\mathit{H}\Vert \left[11\overline{2}0\right]$ and $+$ for $\mathit{H}\Vert \left[10\overline{1}0\right]$ (both with $K_{\mu }>0$), and I for $\mathit{H}\Vert \mathit{c}$ $(K_c<0)$.

Figure 3

(Color online) Unit cell of ${\mathrm{CeRh}}_3{\mathrm{B}}_2$, containing one Ce ion at the 1a site, three Rh atoms at the 3g sites, and two B atoms at the 2c sites—the crystallographic axes are specified in the inset. Two ${\mu }^{+}$-site candidates are indicated: The 2d site between two B atoms, and the 1b site between two Ce atoms. Magnetic moments are essentially on Ce ions—parallel to the basal plane in the ordered state. A negative magnetic density is possibly found on Rh atoms or delocalized on the $\left[0001\right]$ $\mathrm{Ce}\text{−}\mathrm{Ce}$ chains (e.g., around the 2e sites, tiny spheres).

Figure 4

Muon Knight shift $K_{\mu }$ vs bulk magnetic susceptibility $\chi$ (Clogston-Jaccarino plot) for three crystal orientations, $\mathit{H}\Vert \left[11\overline{2}0\right]$ $(\times )$ and $\mathit{H}\Vert \left[10\overline{1}0\right]$ $(+)$, both with $K_{\mu }>0$, and $\mathit{H}\Vert \left[0001\right]$ (I) with $K_c<0$. Right panel: full $\chi$ range, left panel: expanded low-$\chi$ range. The linear scaling indicated by the dashed and solid straight lines is retained to determine the ${\mu }^{+}$ site.

Figure 5

ZF $\mu \mathrm{SR}$ signals in the “backward” positron detector for ${\mathrm{CeRh}}_3{\mathrm{B}}_2$ at $90\mathrm{K}$, with the incident-muon polarization either parallel or perpendicular to the crystallographic $c$ axis. The data are fitted with two frequencies and, for ${\mathit{P}}_{\mu }\left(0\right)\perp \mathit{c}$, an additional nonprecessing contribution.

Figure 6

Temperature dependence of the ZF spontaneous ${\mu }^{+}$ precession frequencies ${\nu }_2$ (a), ${\nu }_1$ (b), and the related relaxation rates $\lambda$ or $\sigma$ (c) and (d) in ${\mathrm{CeRh}}_3{\mathrm{B}}_2$. The solid and dashed curves in (a) and (b) are the mean $\nu \left(T\right)$ dependencies assumed for the Osaka and Grenoble single crystals, respectively. The polycrystalline-sample data from Reichl (Ref. 24) and Cooke et al. (Ref. 14) are also shown. The symbols used in all panels are explained in (a).

Figure 7

(Color online) Comparison of $B_{\perp }\left(T\right)$ from nuclear magnetic resonance (NMR) (Ref. 2) left, supposed to be proportional to $\mid \mathit{M}\left(T\right)\mid$, with $B^{\mathrm{Lor}}\left(T\right)=(4\pi ∕3\left)M\right(T)$ from magnetization measurements (Ref. 1), right (two finely dashed curves for $\mathit{H}$ in the $ab$ plane and the dash-dotted curve for $\mathit{H}\Vert \mathit{c}$). The thin solid curve is the ZF $B^{\mathrm{Lor}}\left(T\right)$ as assumed for solutions VD and VM, and the coarsely dashed curve is solution Pd calculated from the $\mu \mathrm{SR}$ frequencies, see Sec. 4C.

Figure 8

(Color online) Field contributions to $B_1^{\mu }$ and $B_2^{\mu }$ [Eqs. (16, 17)] and magnetization parameters from solutions VD and Pd (Table ) in ferromagnetic ${\mathrm{CeRh}}_3{\mathrm{B}}_2$ (labels in the upper right corner of the field panels, lines explained in the top panels). $f_{n,i}=(A_{n,i}^{\mathrm{dip}}+b_{n,i}^{\mathrm{c}})$ for $n=\mathrm{Ce}$,Rh and $i=1\mathrm{b}$,2d.

Figure 9

(Color online) Fields and magnetization parameters from solutions VM and Pe. For explanation, see Fig. 8.