Theory of unconventional magnetism in a Cu-based kagome metal

TL;DR

The paper investigates itinerant magnetism on the Cu-based kagome lattice using CsCu3Cl5 as a realistic platform. By combining ab initio Wannier modeling, cRPA-derived interaction estimates, and functional renormalization group analysis, it identifies a cooperative mechanism between on-site and nearest-neighbor repulsions that stabilizes a spin-density and spin-bond order, onset at the M-point nesting. A Ginzburg-Landau treatment reveals a uniaxial 3Q magnetic state that can couple to spin current order, predicting an emergent spin-orbit–like effect and, deeper in the phase, an octahedral spin configuration with coexisting spin currents. The work demonstrates a bona fide itinerant mechanism for complex magnetic order in kagome metals and highlights the role of m-type van Hove filling and sublattice interference in shaping correlated states with potential experimental relevance.

Abstract

Kagome metals have established a new arena for correlated electron physics. To date, the predominant experimental evidence centers around unconventional charge order, nematicity, and superconductivity, while magnetic fluctuations due to electronic interactions, i.e., beyond local atomic magnetism, have largely been elusive. We find the challenge of locating the appropriate parameter regime for such exotic order to center around two aspects. First, the correlations implied by low-energy orbitals have to be sufficiently large to yield a dominance of magnetic fluctuations and weak to retain an itinerant parent state. Second, the kinematic kagome profile at the Fermi level demands an efficient mitigation of sublattice interference causing the suppression of magnetic fluctuations descending from electronic on-site repulsion. We elucidate our methodology by analyzing the potential copper-based kagome compound CsCu$_3$Cl$_5$: From ab initio design and many-body analysis, we develop a model framework of realistic Cu-based kagome materials the simulations of which reveal unconventional magnetic order in a kagome metal.

Figures (12)

• Figure 1: Crystal structure of pristine CsCu3Cl5. (a) Top view showing the Cu kagome lattice highlighted by blue bonds. Turquoise, blue and pink spheres represent Cs, Cu and Cl atoms. The unit cell is delimited by black lines. (b) Side view of the unit cell. The blue plane contains the Cu kagome lattice and additional Cl atoms, while the pink planes above and below contain a hexagonal lattice of Cl atoms. (c) Electronic band structure with projected orbital weights featuring distinct kagome bands and an $m$-type vHS close to $E_F$.
• Figure 2: Wannier orbital centered at the Cu site seen from (a) top and (b) side view of the pristine structure. The site-local reference axis $\mathbf{\hat{z}}$ is pointing towards the center of the hexagonal plaquettes. Purple/yellow orbital lobes indicate the phase of the MLWF. (c) Comparison of the DFT band dispersion (gray) with bands obtained from the Wannier three-orbital tight-binding model (yellow). (d) Fermi surface in the $k_z = 0$ plane for the non-interacting bandstructure at the upper vH filling and dominant nesting vectors. The colors indicate the eigenstate contributions on the three different sublattices. At the three $M$ points, i.e. the vH points, the state is equally composed of two sublattices given by the sublattice labels.
• Figure 3: Magnetic ordering vector of the Cu kagome network as obtained from combined FRG + GL analysis at $m$-type vH filling. The order parameter blends an collinear antiferromagnetic arrangement of local magnetic moments given in Eq. \ref{['eqn:SDW']} (left) and NN spin bond terms of Eq. \ref{['eqn:SBO']} (right) reminiscent of a tri-hexagonal pattern. Here, red/blue denote spin up/down on the indicated sites and bonds along the chosen quantization axis. While the relative strength of on-site ($\vec{\Delta}^{SDW}$) and bond magnetization ($\vec{\Delta}^{SBO}$) is dependent on the interaction parameter, their relative sign is fixed by the many-body analysis.To maintain vanishing net magnetization, the spin polarization on the $\downarrow$ bonds surpasses the value on the $\uparrow$ bonds by a factor of 3, as indicated by the line thickness.
• Figure S1: Top view of the kagome plane (left) highlighting the three copper atoms with the local reference frame around each Cu atom (right).
• Figure S2: Energy profiles of the pristine, breathing and twisted configurations for different interpolating geometries and unit cell's sizes. (a) Total free energy as a function of an isotropic change of volume, for all three discussed configurations. The twisted configuration is the most favourable one in a wide range of volume variations. (b) For a unit cell with constant volume, the energy is plotted across varying degrees of interpolation between the pristine and breathing cases, as well as between the pristine and the twisted ones. The twisted configuration stands out as the most energetically favourable.