Correlated electronic structure and local spin in lead-copper-vanadium-bromine apatite: a DMFT study

TL;DR

This work investigates Pb$_9$Cu(VO$_4$)$_6$Br$_2$ with DFT+DMFT on a two-orbital Cu-centered model to characterize correlated electronic structure and local spin dynamics. It finds sustained metallicity around the stoichiometric filling $n \simeq 3$, with spectral weight shifting into Hubbard-like features upon doping away from $n \simeq 3$, and identifies a narrow spin-freezing crossover near $n \approx 2.94$ marked by enhanced spin fluctuations. The results place this Cu-apatite among promising candidates in the family and suggest Hund-metal physics may be relevant, potentially linking spin dynamics to unconventional pairing while acknowledging DMFT's limitation in capturing long-range order. The study combines $U$ and $J$ values from cRPA with a robust DMFT treatment to map the interplay between metallicity, spectral function evolution, and spin dynamics in a strongly correlated, copper-doped apatite system.

Abstract

We study the correlated electronic structure and local spin behaviour of the copper-substituted lead-vanadium bromine apatite Pb$_9$Cu(VO$_4$)$_6$Br$_2$ using DFT+DMFT with a two-orbital Cu-centred low-energy model. Simulations are done for several temperatures (20, 60, 100 K) and a broad range of band fillings 2.46 $\leq$ n $\leq$ 3.54. We find that the present compound stays metallic even once correlations are treated dynamically around the stoichiometric filling (n $\simeq$ 3). Away from n $\simeq$ 3, both hole and electron doping drive the system toward non-Fermi-liquid behaviour, and spectral weight is transferred from the low-energy peak into upper and lower Hubbard-like features. By analysing the low-frequency self-energy exponent and the dynamical part of the local spin susceptibility, we identify a narrow window of enhanced spin fluctuations on the slightly hole-doped side (n $\simeq$ 2.94), i.e. a spin-freezing-crossover regime of the kind reported in the literature for multiorbital Hund metals. This places Pb$_9$Cu(VO$_4$)$_6$Br$_2$ among the promising members of the Cu-substituted apatite family.

Figures (6)

• Figure 1: a) A schematic view of the crystal structure of Pb$_9$Cu(VO$_4$)$_6$Br$_2$. b) Near-Fermi DFT band structure and densities of states corresponding to Wannier projections.
• Figure 2: Imaginary part of the self-energy as a function of Matsubara frequencies for various doping levels and temperatures.
• Figure 3: Absolute value of the local Green's function at half the inverse temperature - a probe of the spectral weight at $E_F$ - for different fillings and temperatures.
• Figure 4: Analytically continued spectral function for T = 20 K and various fillings.
• Figure 5: Non-Fermi-liquid exponent factor $\gamma$ and the local spin susceptibility $\chi$. Highlighted in gradient are the regions of suspected spin-freezing crossover as suggested by the plotted values.