Multipolar fluctuations from localized 4f electrons in CeRh2As2

TL;DR

This work uses DFT+DMFT to derive momentum-dependent multipolar susceptibilities and intersite interactions for CeRh$_2$As$_2$, treating the Ce 4f electrons as localized and incorporating CEF splitting. The calculations reveal a dominant two-dimensional checkerboard antiferromagnetic order of $M_z$ at $\mathbf{q}=(1/2,1/2,0)$, with field-induced electric quadrupoles providing anisotropic responses that help reconcile the $T$–$H$ phase diagram. Higher-order multipoles become active through mixing with the first excited CEF doublet, but quadrupole-only scenarios fail to reproduce the observed anisotropy in the Phase I transition. The study demonstrates how first-principles methods, combined with symmetry analysis, can identify the plausible order parameter in a complex, non-centrosymmetric heavy-fermion system and explains the phase diagram via coupling to induced multipoles.

Abstract

The heavy-fermion superconductor CeRh2As2 exhibits a non-superconducting phase transition that precedes the emergence of superconductivity. The nature of the corresponding order parameter remains under debate, with competing proposals involving magnetic dipoles or electric quadrupoles. We derive the momentum-dependent multipolar susceptibilities and effective interactions among the localized 4f electrons, based on the framework of density functional theory combined with dynamical mean-field theory. Magnetic fluctuations within the crystalline-electric-field (CEF) ground-state doublet are dominated by q=(1/2,1/2,0), corresponding to a two-dimensional checkerboard configuration of the magnetic moment M_z along the c axis. Hybridization between the CEF ground state and the first-excited doublet gives rise to leading magnetic octupole fluctuations of z(x^2-y^2) symmetry, followed by electric quadrupole fluctuations of x^2-y^2 and {yz, zx} symmetries. By taking into account the anisotropic magnetic-field dependence of the transition temperature T_0, we conclude that an antiferromagnetic order of M_z at q=(1/2,1/2,0) is consistent with the experiments, owing to the enhancement of T_0 caused by fluctuations of the field-induced quadrupole of {yz, zx} type under an in-plane magnetic field.

Figures (15)

• Figure 1: (a) Crystal structure of CeRh2As2 and schematic $T$--$H$ phase diagrams based on experimental results in magnetic field applied along (b) the $c$-axis Semeniuk2023 and (c) the in-plane direction Hafner2022.
• Figure 2: (a) Fully relativistic band structure of CeRh2As2 calculated by FPLO package. The black lines represent the DFT result, and the red lines represent the tight-binding bands obtained from projective Wannier functions. (b) Density of states. The black and green lines show the total and Ce $4f$ contributions, respectively. (c) The high-symmetry points in the Brillouin zone.
• Figure 3: The CEF level schemes of $j=5/2$ of $4f$ electrons. (a) The experimental one Hafner2022, and (b) the DFT result. $\Delta_1$ and $\Delta_2$ denote the energy of $\Gamma_6$ and $\Gamma_7^{(2)}$ states, respectively, relative to $\Gamma_7^{(1)}$ state.
• Figure 4: (a) The single-particle excitation spectrum $A(\bm{k},\omega)$ and (b) the $\bm{k}$-integrated spectrum $A(\omega)$ computed in DFT+DMFT method.
• Figure 5: Eigenvalues $\chi^{(\xi)}(\bm{q})$ of the susceptibility for $T=0.01$ eV. The numbers on the right indicate the number of eigenmodes included in the group.