Anisotropic spin fluctuations in the triangular Kondo lattice compound CePtAl$_4$Ge$_2$ probed by site-selective $^{27}$Al NMR

TL;DR

This work uses site-selective $^{27}$Al NMR to study the frustrated Kondo lattice CePtAl$_4$Ge$_2$, with two inequivalent Al sites identified via EFG calculations and site-resolved Knight shifts and spin-lattice relaxation. The hyperfine couplings are predominantly transferred (RKKY) rather than dipolar, and the paramagnetic state exhibits strongly anisotropic, in-plane spin fluctuations that weaken below the Kondo-coherence scale, suggesting a spin gap of about $E_g/k_B\sim 10$ K. In zero field the material orders antiferromagnetically with an incommensurate, longitudinal SDW that is consistent with a field-tunable triple-$k$ spin texture; the momentum structure of fluctuations is shaped by the triangular Ce lattice and the Fermi surface. Overall, CePtAl$_4$Ge$_2$ serves as a clean platform to explore how geometric frustration and Kondo coherence intertwine in $f$-electron systems, with implications for related triangular Kondo lattices.

Abstract

A site-selective $^{27}$Al nuclear magnetic resonance (NMR) study is carried out on the Kondo lattice compound CePtAl$_4$Ge$_2$, which crystallizes in a rhombohedral lattice with quasi-two-dimensional Ce layers forming a triangular lattice network. Two inequivalent Al sites, Al(1) and Al(2), are unambiguously assigned by comparing measured nuclear quadrupole parameters with electric field gradients obtained from electronic structure calculations. Knight shift analysis yields distinct hyperfine coupling constants, revealing that they arise predominantly from RKKY-type transferred hyperfine fields through conduction electrons. Spin-lattice relaxation measurements reveal pronounced anisotropic spin fluctuations, and comparison of the relaxation rates between the two Al sites clarifies the momentum-space structure of these fluctuations. At low magnetic fields, $(T_1T)^{-1}$ is strongly enhanced on cooling toward the Néel temperature, indicating the growth of in-plane antiferromagnetic correlations in the paramagnetic state.

Figures (6)

• Figure 1: (a) Crystal structure of CePtAl$_4$Ge$_2$, consisting of alternating Ce layers and PtAl$_4$Ge$_2$ slabs stacked along the $c$ axis. (b) Extracted Ce sublattice highlighting the two-dimensional triangular lattice network. (c) Local environments of the two inequivalent Al sites, Al(1) and Al(2). Pt and Ge atoms are omitted for clarity.
• Figure 2: $^{27}$Al NMR spectra of CePtAl$_4$Ge$_2$ at 20 K under a magnetic field of $\mu_0H_0 = 2.8993$ T. (a) Field-swept spectra measured with $H_0 \parallel a$ and $H_0 \parallel c$. The two sets of lines are assigned to the Al(1) and Al(2) sites based on comparisons with electric field gradient parameters estimated from band structure calculations. Gray shaded regions indicate spectral blind spots due to $^{63,65}$Cu NMR signals from the NMR coil and $^{23}$Na NMR signals from the glass strip used to mount the crystal. (b) Polar-angle ($\Theta$) dependence of the resonance frequencies for $H_0$ rotated within the $ac$ plane. Blue circles and red squares represent experimental data, while the bold blue dashed and red solid lines are simulations for the Al(1) and Al(2) sites, respectively, obtained by exact diagonalization of the nuclear spin Hamiltonian. Horizontal dashed lines mark the positions of extrinsic $^{63,65}$Cu and $^{23}$Na NMR signals. (c) Azimuthal-angle ($\Phi$) dependence of the resonance frequencies for $H_0$ rotated within the $ab$ plane ($H_0 \perp c$).
• Figure 3: (a) Temperature dependence of the Knight shifts $K_a$ and $K_c$ for the Al(1) and Al(2) sites in CePtAl$_4$Ge$_2$, measured at $\mu_0H_0 = 2.8993$ T. (b) Knight shifts plotted against the bulk magnetic susceptibility $\chi$ in the paramagnetic state Shin2018Synthesis-and-c, demonstrating linear $K$–$\chi$ relations. The inset schematically illustrates the RKKY-type hyperfine coupling between the Ce and Al sites.
• Figure 4: Temperature dependence of the nuclear spin-lattice relaxation rate $1/T_1$ for the Al(1) and Al(2) sites in CePtAl$_4$Ge$_2$, measured under a magnetic field of $\mu_0H_0 = 2.8993$ T applied along the $a$ and $c$ axes. The Kondo coherence temperature $T^\ast$, as reported by resistivity measurements Shin2018Synthesis-and-c, is indicated by the vertical arrow.
• Figure 5: (a) Temperature dependence of the fluctuation amplitude $R_i / |A_i|^2$ ($i=a, c$) at the Al(1) and Al(2) sites. (b) Temperature dependence of the anisotropy ratio $\Gamma_c / \Gamma_a$ for spin fluctuations at each Al site. The quantity $\Gamma_i$ represents the characteristic energy scale of spin fluctuations along the $i$-axis; see main text for definition. The hyperfine form factor $|f(\bm{q})|^2$ for (c) Al(1) and (d) Al(2) sites, respectively, are illustrated in the $q_x$–$q_y$ plane. Red arrows indicate the specific point at $\bm{Q}_0 = (\frac{1}{3}, \frac{1}{3})$.