Valence and spin fluctuations in the Mn-doped ferroelectric ${\mathrm{BaTiO}}_3$

We study Mn substitution for Ti in ${\mathrm{BaTiO}}_3$ with and without compensating oxygen vacancies using density functional theory (DFT) in combination with dynamical mean-field theory (DMFT). We find strong charge and spin fluctuations. Without compensating oxygen vacancies, the ground state is found to be a quantum superposition of two distinct atomic valences, $3d^4$ and $3d^5$. Introducing a compensating oxygen vacancy at a neighboring site reduces both charge and spin fluctuations due to the reduction of electron hopping from Mn to its ligands. As a consequence, valence fluctuations are reduced, and the valence is closely fixed to the high spin $3d^5$ state. Here we show that inclusion of charge and spin fluctuations is necessary to obtain an accurate ground state of transition metal-doped ferroelectrics.

Figure 1

(a) Schematic representation of the structure for Mn-doped (at Ti site) ${\mathrm{BaTiO}}_3$ without any compensating oxygen vacancy. Isosurface plot of electron density difference between (b) DFT and DFT+U, (c) DFT and DFT+DMFT, and (d) DFT+U and DFT+DMFT methods. The green or red means increase or decrease of $0.85\times {10}^{-3}$ $e$/Å${}^3$ upon the DMFT calculation.

Figure 2

Spin decomposed total and projected densities of states (DOS) computed in (a) DFT, (b) DFT+U, and (c) DFT+DMFT methods for Mn substitution of Ti in ${\mathrm{BaTiO}}_3$ without any compensating oxygen vacancy (${\mathrm{Mn}}_{\text{Ti}}$). (d) Computed spin density (${\rho }_{\uparrow }-{\rho }_{\downarrow }$) with DFT and DFT+U for the same system.

Figure 3

DFT+DMFT computed atomic histogram of the Mn $3d$ shell for Mn substituted ${\mathrm{BaTiO}}_3$ (left) without (${\mathrm{Mn}}_{\text{Ti}}$) and (right) with (${\mathrm{Mn}}_{\text{Ti}}{\mathrm{V}}_{\text{O}}$) compensating oxygen vacancy: (a) and (b) Decomposed in number of particles $N$ and (inset) spin-state ($S_Z$); probability distribution for all $2^{10}$ (=1024) atomic configurations sorted for each $N$ (c) and (d) and for each spin state (e) and (f). $N$ and $S_Z$ values are denoted with various colors.

Figure 4

DFT+DMFT computed squared fluctuating local moment or the averaged spin-spin correlation function (a) for Mn substituted ${\mathrm{BaTiO}}_3$ without (${\mathrm{Mn}}_{\text{Ti}}$) and (b) with compensating oxygen vacancy (${\mathrm{Mn}}_{\text{Ti}}{\mathrm{V}}_{\text{O}}$).