Microscopic origin of hard-plane antiferromagnetism in the Kondo lattice Ce2Rh3Ge5

Abstract

Hard plane antiferromagnetic order where ordered moments lie perpendicular to the single-ion crystal electric field easy axis is rare in Ce-based Kondo lattices and is a subject of active interest. Here we show that Ce$_2$Rh$_3$Ge$_5$ realizes a hard-plane antiferromagnetic state in which partial delocalization of the local moment gives rise to an RKKY exchange that overturns the single-ion easy-axis preference. Neutron diffraction reveals moments in the $ab$ plane, while inelastic neutron scattering and susceptibility establish a magnetic easy axis along $c$ in the paramagnetic regime, highlighting a clear inversion between single-ion and ordered-state anisotropies. In this work, we establish a unified microscopic framework to consistently account for partial $4f$-moment delocalization, enhanced in-plane RKKY exchange, and the resulting hard-plane antiferromagnetic order. Ce$_2$Rh$_3$Ge$_5$ thus provides a benchmark system in which single-ion anisotropy, Kondo screening, and RKKY exchange compete on comparable energy scales, revealing a cooperative route to hard-axis ordering in strongly hybridized Kondo lattices.

Figures (9)

• Figure 1: Magnetic structure revealed by neutron diffraction: (a) Rietveld-refined NPD pattern of Ce$_2$Rh$_3$Ge$_5$ measured at room temperature on the D2B diffractometer at ILL using a wavelength $\lambda = 1.594$ Å. Red circles represent the experimental data, the black line is the calculated pattern for the orthorhombic U$_2$Co$_3$Si$_5$-type structure, green vertical ticks mark the Bragg reflection positions, and the blue line at the bottom shows the difference between observed and calculated intensities. The inset illustrates the crystal structure, emphasizing the local coordination around the Ce site within the three-dimensional Rh--Ge framework. The blue, green, and gray spheres represent Ce, Rh, and Ge atoms, respectively. (b) Refinement of the temperature-difference diffraction pattern (1.6 K-10 K), where a constant offset of 60000 counts was added to shift all the data to positive values. The scale factor was fixed based on the refinement of the paramagnetic phase at 10 K. The solid black line represents the calculated magnetic intensity assuming a propagation vector $\mathbf{k} = (0, 0, 0)$ with AFM coupling in the $ab$ plane, as depicted in panel (c). The blue line indicates the difference between observed and calculated intensities, and green vertical ticks denote the positions of magnetic Bragg reflections. (c) Crystal and magnetic structure of Ce$_2$Rh$_3$Ge$_5$, showing AFM alignment of Ce moments along both $a$ and $b$ axes. No ordered magnetic moment component along the $c$ axis is detected within experimental uncertainty.
• Figure 2: Crystal field excitations revealed by inelastic neutron scattering: Color-coded INS intensity maps of Ce$_2$Rh$_3$Ge$_5$ after phonon subtraction using La$_2$Rh$_3$Ge$_5$ at 4 K, plotted as a function of energy and momentum transfer, measured with incident neutron energies of (a) $E_i$ = 10 meV, (b) 18 meV, (c) 60 meV, and (d) 150 meV. Intensities are shown in arbitrary units.
• Figure 3: Crystal electric field Hamiltonian - modeling and fits to experimental data: (a) Inverse magnetic susceptibility of single-crystal Ce$_2$Rh$_3$Ge$_5$ measured at $H = 0.1$ T along the $a$, $b$, and $c$ axes PhysRevB.64.144412. Solid curves represent fits to the CEF model. Inset: Magnetization isotherms measured along the three principal crystallographic directions at $T = 2$ K. (b) Magnetic INS response after phonon subtraction using La$_2$Rh$_3$Ge$_5$, measured with $E_i = 60$ meV and $Q$-integrated over $0$-$3$$\text{\AA}^{-1}$ at selected temperatures in the paramagnetic state. Solid curves are fits to the CEF model. (c) Schematic CEF level scheme of Ce$^{3+}$ ($J$=5/2) showing the splitting into three Kramers doublets.
• Figure 4: Zero-field $\mu$SR results for Ce$_2$Rh$_3$Ge$_5$: (a) ZF-$\mu$SR spectra recorded at 1.85 and 5.5 K. Symbols represent experimental data, while the solid red lines show fits using Eq. (\ref{['eq:musr1']}). (b) Temperature dependence of the internal local field $B_{\text{loc}}$; the solid line shows a phenomenological fit using Eq. (\ref{['eq:musr2']}). The inset shows the magnetic volume fraction (MVF) derived from the oscillating asymmetry. (c) Transverse relaxation rate $\lambda_{\text{osc}}$, associated with the oscillatory component in Eq. (\ref{['eq:musr1']}), vs temperature. Inset: Longitudinal relaxation rate $\lambda_{\text{L}}$ (associated with the non-oscillatory component in Eq. (\ref{['eq:musr1']})) vs temperature. (d) Visualization of muon stopping sites within the crystallographic unit cell. The four potential muon stopping sites in this structure, marked A, B, C and D, are adopted from the isostructural compound Pr$_2$Pd$_3$Ge$_5$ Ref. PhysRevB.107.104412.
• Figure 5: Electronic properties of Ce$_2$Rh$_3$Ge$_5$ across different temperature regimes: Panels (a)–(d) display the total, atomic, and orbital-projected density of states (DOS) per primitive unit cell. Panels (e) and (f) show the spectral functions in the vicinity of the Fermi level ($E_F$), with insets providing magnified views of the regions indicated by the dotted rectangles. In all panels, zero energy corresponds to the $E_F$, which is also marked by a horizontal dotted line in (e) and (f). The arrows in these panels highlight the Kondo resonances arising from the $j = 5/2$ and $j = 7/2$ electronic states.