Evidence for easy-plane XY ferromagnetism in heavy-fermion quantum-critical CeRh6Ge4

TL;DR

The study addresses quantum-critical ferromagnetism in the heavy-fermion compound CeRh$_6$Ge$_4$, where a FM transition at ambient pressure can be tuned toward a QCP at $P_C \sim 0.8\,\mathrm{GPa}$. Using $^{73}$Ge NQR/NMR, the authors map electric-field-gradient tensors and hyperfine couplings for the two Ge sites Ge(1) and Ge(2), and extract a microscopic order parameter. They find a small in-plane ordered moment of $m \approx 0.26\,\mu_B$/Ce with uniform XY-type ferromagnetism, and observe critical slowing down with $1/T_1$ diverging near $T_C = 2.51\,\mathrm{K}$; the paramagnetic state shows local-moment fluctuations and a Knight shift that deviates below $T^* \approx 25\,\mathrm{K}$ due to CEF/Kondo effects. These results support an easy-plane anisotropy dominated by in-plane 4f moments, and indicate a nontrivial interplay between Kondo hybridization and local moments in this quantum-critical heavy-fermion FM, informing theories of FM QCPs in correlated electron systems.

Abstract

We report $^{73}$Ge nuclear quadrupole resonance (NQR) and magnetic resonance (NMR) spectroscopy in the heavy-fermion quantum-critical ferromagnet CeRh$_6$Ge$_4$. NQR and NMR spectral measurements at the two non-equivalent Ge sites reveal electric field gradient tensors and the directions of their principal axes relative to the hexagonal basal plane. The spin-lattice relaxation rate $1/T_1$ experiments reveal a clear critical slowing down approaching the ferromagnetic transition. $1/T_1$ in the paramagnetic state is found to be predominantly caused by fluctuating 4$f$-local moments. The Knight shift shows Curie-Weiss behavior at high temperature and a deviation from this below $T^\ast$ $\approx$ 25 K possibly due to a mixture of crystalline electric field effects and Kondo screening. Order-parameter-like behavior of hyperfine fields at the Ge sites and ferromagnetic signal enhancement are observed in Zeeman-perturbed NQR, with uniform ferromagnetic order and a small ordered moment of $\approx$ 0.26 $μ_B$/Ce confined within the $ab$-plane. The ordered moment shows a notable in-plane magnetic stiffness against out-of-plane radiofrequency fields and has an (XY-type) in-plane isotropic nature. Our results reveal a strong easy-plane anisotropy of 4$f$-electron moment and suggest an involved interplay of hybridization and local moment physics in this quantum critical heavy-fermion ferromagnet.

Figures (7)

• Figure 1: Hexagonal crystal structure of CeRh$_6$Ge$_4$ seen from side (a) and from top (b) views. Yellow balls stand for Ce atoms; gray balls are Rh atoms; and blue and red balls are the two non-equivalent Ge atoms, Ge(1) and Ge(2), respectively.
• Figure 2: Zero-field $^{73}$Ge NQR spectra of CeRh$_6$Ge$_4$ at 4.0 K in the PM state. The spectrum for (a) Ge(1) and (b) Ge(2) are depicted. The lowest-frequency (1$\nu_{\mathrm{Q}}$) line for Ge(1) (expected at 0.246 MHz) is missing due to the frequency limitation of our spectrometer.
• Figure 3: $^{73}$Ge NMR spectrum of CeRh$_6$Ge$_4$ recorded at 4.0 K under 12 T using powdered samples that are self-aligned to $H$$||$$ab$ due to the easy-plane anisotropy. Nine peaks from the axially-symmetric Ge(1) site (blue) is visible, with evenly spaced lines separated by 0.123 MHz. The overall background signal and the lowest-frequency peak (red) originate from the Ge(2) site (see the SM for details SM).
• Figure 4: $^{73}$Ge NMR spectrum of CeRh$_6$Ge$_4$ (red) using single crystal samples that are aligned along the $c$-axis, recorded at 9.70 MHz and 5.0 K for $H$$||$$c$. Shaded pattern (gray) gives the calculated single-crystalline spectrum of Ge(2) by exact diagonalization of Eq. (\ref{['eq_NQR_Zeeman']}), assuming $\nu_{\mathrm{Q}}^\mathrm{Ge(2)} = 1.615$ MHz, $\eta^\mathrm{Ge(2)} = 0.365$, $V_{zz}^\mathrm{Ge(2)}$$\parallel$$ab$, $V_{yy}^\mathrm{Ge(2)}$$\parallel$$ab$, and $V_{xx}^\mathrm{Ge(2)}$$\parallel$$c$. The $I_z = -9/2 \leftrightarrow -7/2$ and $9/2 \leftrightarrow 7/2$ lines as well as the Ge(1) signal are missing due to the low signal-to-noise ratio and field range (see the SM for details SM).
• Figure 5: Zero-field $^{73}$Ge NQR $1/T_1$ of CeRh$_6$Ge$_4$ at Ge(2) plotted as a function of temperature, determined from the $I_z = \pm 5/2 \leftrightarrow \pm 7/2$ line (see the SM SM for details). The bold horizontal line is a guide to the eyes, and the vertical dashed line indicates the FM transition temperature $T_\mathrm{C}$ ($=$ 2.51 K).