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

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.