Hidden symmetry-breaking in a kagome Ising ferromagnet

TL;DR

TbV$_6$Sn$_6$ is studied as a kagome system with Ising Tb moments, addressing whether time-reversal symmetry breaking can coexist with ferromagnetism. Using inelastic neutron scattering, the authors observe two spin-flip excitations $E_1$ and $E_2$ near the nominal spin-flip energy $Δ_{SF}$, indicating two inequivalent Tb sites. They rule out hyperfine coupling and lattice distortions as the origin of the splitting and attribute it to a staggered internal field that breaks translational and time-reversal symmetry, likely arising from subtle V-layer magnetism. The work combines INS, NMR, XRD, and DFT+$U$ calculations to establish rare-earth local moment spectroscopy as a sensitive probe of hidden symmetry breaking and to reveal a link between kagome magnetism and rare-earth moments.

Abstract

Kagome metals can host unconventional electronic phenomena that emerge from their frustrated lattice geometry and associated band topology. Correlated electronic orders, such as charge-density waves and superconductivity, are observed to intertwine with subtle time-reversal symmetry breaking whose microscopic origin is not currently understood. Here, we provide evidence for such time-reversal symmetry breaking in the kagome metal TbV$_6$Sn$_6$ arising from staggered magnetic moments within the kagome layers. TbV$_6$Sn$_6$ consists of metallic V kagome layers separated by Tb triangular layers that host Ising ferromagnetic order. Deep in the ferromagnetic state, the Tb Ising doublet ground state should display a single, dispersionless spin-flip excitation. Instead, inelastic neutron scattering reveals two sharp excitations associated with inequivalent Tb sites, demonstrating that a symmetry-broken phase coexists with Ising ferromagnetism. No additional structural or magnetic phase transitions are detected, and first-principles calculations rule out lattice distortions as the origin of the splitting. We attribute this effect to time-reversal symmetry breaking encoded by small V moments that couple to the Tb sublattice and leave a measurable spectral fingerprint. Our results establish rare-earth local moment spectroscopy as a sensitive probe of subtle broken symmetries and highlight an unexpected interplay between kagome magnetism and rare-earth local moment magnetism.

Figures (4)

• Figure 1: Spin-flip excitations in an Ising ferromagnet. (a) Expected spin-flip excitation spectrum within the $\ket{\pm 6}$ doublet in the FM ordered state. The spectrum should consist of a single peak at $\Delta_{SF}\approx 1.3$ meV. (b) Schematic diagram of the spin-flip excitation. (c) Inelastic neutron scattering data from TbV$_6$Sn$_6$ at $T=1.7$ K showing two spin-flip excitations labeled $E_1$ and $E_2$. (d) Full $Q-E$ neutron spectrum of TbV$_6$Sn$_6$ at 1.7 K.
• Figure 2: Temperature evolution of spin-flip excitations in TbV$_6$Sn$_6$. (a) Inelastic neutron scattering data showing two spin-flip excitations at energies of $E_1$ and $E_2$ at temperatures above and below $T_\text{C}$. (b) Temperature dependence of $E_1$ and $E_2$, average value ($\Delta_{SF}$), and splitting parameter ($2\delta=E_2-E_1$) as obtained from fitting INS spectra similar to panel (a). (c) Temperature dependence of $2 \delta$ and Lorentzian full-width $\Gamma$ of the excitations. (d) The temperature dependence of the area of each peak along with the ratio of the areas $A_1/A_2$. (e) Schematic level diagrams for two inequivalent Tb ions with different spin-flip energies caused by symmetry-breaking energy $\delta$. In panels (b)-(d), different shading of symbols indicates independent measurements of different samples.
• Figure 3: Crystallographic-symmetry breaking. (a) A possible crystallographic-symmetry breaking scenario showing inequivalent Tb sites with equal multiplicities caused by $(0,0,1/2)$ distortion. The displacement of the atoms in dashed boxes creates inequivalent Tb$_1$ (light blue atoms) and Tb$_2$ (dark blue) local environments with Tb-Sn layer distances $d_0\pm\epsilon$ and can be understood as a local $\Delta~c/c$ distortion. (b) The change of $B_{l}^m$ parameters with $\Delta~c/c$ lattice distortion using the point charge model (dots) and the DFT calculation (triangle with dashed lines) up to $\Delta~c/c = 4\%$. (c) Evolution of the doublet splittings $E_1$ and $E_2$ in a molecular field along the $c$-axis in the presence of a large local distortion ($\Delta c/c = 3\%$) that generates Tb$_1$ and Tb$_2$ ions with $B_6^6$ values shifted $\pm 30\%$. The lower panel shows that the zero-field shift $2\delta < 0.015$ meV is suppressed by the molecular field. (d) Temperature-dependent strain ($\Delta L/L$) and X-ray diffraction measurements ($\Delta c/c$). The inset shows a spontaneous magnetostriction of $\Delta L/L \sim 0.002\%$ is observed below $T_\text{C}$. (e) Logarithm of XRD intensity along $(0~0~L)$ direction at $8$ K. No half-integer $L$ peaks are observed that correspond to ${\bf q}=(0,0,1/2)$ symmetry breaking. The Bragg peak corresponding to the Sn impurity is colored in gray. The shoulders next to the Bragg peaks are from Cu-K$\alpha_2$ incident X-ray.
• Figure 4: Time-reversal symmetry breaking. Different magnetic environments of Tb$_1$ and Tb$_2$ ions due to (a) stripe-like antiferromagnetic order within the V kagome layer and (b) up-up-down-down AFM stacking of FM V layers.