Magnetic excitations and exchange parameters of a nickel chain compound PbMn$_2$Ni$_6$Te$_3$O$_{18}$: Neutron scattering and density functional theory studies

We have investigated the quasi-one dimensional Ni-chain compound PbMn$_2$Ni$_6$Te$_2$O$_{18}$ using theoretical DFT calculations, inelastic neutron scattering and optical spectroscopy in order to understand the nature of magnetic exchange interactions. Our inelastic neutron scattering study at 5 K on a powder sample reveals two bands of magnetic excitations, the first near 8 meV and the second near 18 meV originating from the antiferromagnetic zone center near $Q$ = 1~\AA. On the other hand at 100 K (which is above T$_N$ = 86 K) a broad diffuse scattering signal is observed indicating the presence of short range magnetic correlations. We have analyzed the magnetic excitations based on the Linear Spin Wave Theory (LSWT) and compared the experimentally estimated exchange parameters with the DFT calculations. Our analysis reveals that the value of the exchange parameter at the larger distance (d=3.654 $\AA$) $J_3$=4.21(8) meV between Ni-Ni (from inter-chain) is the strongest amongst the allowed six exchange parameters, which suggests that this system is not really a quasi-one-dimensional and confirmed by the absence of a Haldane gap. We have also presented the electronic structure calculations. The spin-polarized partial density of states (DOS) projected onto the Mn-d and Ni-d orbitals reveals that the Ni-d$_{x^2-y^2}$ contribution is dominant below the Fermi level in the spin-up and spin-down channel, while a minimal contribution from spin-up Mn states in the occupied region, suggesting a nearly high-spin state. The estimated N\'eel temperature, based on experimental exchange parameters is found to be in close agreement with the experimental value.