Orbital-specific Itinerancy and Localization in a Kagome Magnet

Abstract

The kagome lattice naturally hosts flat bands, Dirac fermions, and van Hove singularities, yet whether its geometry can stabilize orbital-selective phases - a hallmark of Hund's physics in multi-orbital correlated systems - has remained an open question. Here, we combine resonant inelastic X-ray scattering with density functional theory and dynamical mean-field theory to demonstrate that YMn$_6$Sn$_6$ exhibits a spontaneous orbital differentiation into coexisting itinerant and localized electrons within the same Mn $3d$ manifold. Orbitals directed along Mn-Mn bonds provide coherent quasiparticles and metallic bands, while those pointing toward ligands become strongly correlated and display non-Fermi-liquid behavior. Hund's intra-atomic exchange suppresses orbital fluctuations, stabilizing this dichotomy and providing a natural double-exchange-like mechanism for the observed ferromagnetic bilayer coupling. Our work establishes YMn$_6$Sn$_6$ as a kagome platform where orbital selectivity, flat-band topology, and Hund's metallicity converge - revealing that geometric frustration and correlation-driven orbital differentiation can cooperatively design exotic quantum phases beyond the canonical paradigms of Mott physics or band topology alone.

Figures (5)

• Figure 1: Mn $L_3$-edge XAS and RIXS of YMn$_6$Sn$_6$. (a) Mn $L_3$-edge XAS data recorded at a temperature of 300 K. (b) RIXS intensity map plotted in the plane of energy loss vs. incident X-ray energy. The energy of incident $\pi$-polarized X-ray was tuned across the $L_3$-edge. The incident and scattering angles were 20 and 90 degrees, respectively.
• Figure 2: Calculated RIXS spectra obtained using ligand-field multiplet calculations. The calculations were carried out with $Quanty$ within an octahedral ($O_h$) crystal-field symmetry, characterized by a crystal-field splitting parameter of 10$Dq = 0.45$ eV. The intra-atomic exchange interaction (Hund’s coupling) was included through the Slater integrals $F^2$ and $F^4$, which were reduced to 78% of their Hartree–Fock values to account for configuration-interaction effects. The charge-transfer energy was set to $\Delta = 2.5$ eV. The hybridization strength between Mn $3d$ and ligand $2p$ orbitals was described by the Slater–Koster parameters ($pd\sigma$ and $pd\pi$), with hybridization energies $V_{e_g} = 2.06$ eV and $V_{t_{2g}} = 1.21$ eV.
• Figure 3: Partial densities of states (DOS) for Mn $3d$ orbitals in non-magnetic DFT calculations (see figure for color coding). Inset shows Mn 3$d$, Y 4$d$ and Sn 5$p$, by red, green and blue colors, respectively. The Fermi level is at zero.
• Figure 4: (a)-(e) Mn $3d$ orbitals obtained by the diagonalization of the local part of the corresponding DFT Hamiltonian. Mn atoms are shown by dark gray and Sn by violet balls. One can see that $i$ orbital is directed along Mn-Mn bonds, in contrast $t_{1,2}$ orbitals look mostly to Sn.
• Figure 5: Results of the ferromagnetic DFT+DMFT calculation at $U=3.75$ eV, $J_{\rm H}=0.81$ eV, and $T=386$ K. a) -- spin and orbital resolved spectral functions for Mn 3$d$ states; b) -- corresponding imaginary parts of self-energy. We note, that since RIXS is described by two-particle processes, these spectral functions can not be directly compared with the experimental results.