Berry flux diagonalization: Application to electric polarization
John Bonini, David Vanderbilt, Karin M. Rabe
Abstract
The switching polarization of a ferroelectric is determined by the current that flows as the system is switched between two variants. Computation of the switching polarization in crystal systems has been enabled by the modern theory of polarization, where it is expressed in terms of a change in Berry phase from the initial state to the final state. It is straightforward to compute this change of phase modulo $2\ensuremath{\pi}$, thus requiring a branch choice to specify the predicted switching polarization. The measured switching polarization depends on the actual path along which the system is switched, which in general involves nucleation and growth of domains and is therefore quite complex. In this work we present a first-principles approach for predicting the switching polarization that requires only knowledge of the initial and final states based on the empirical observation that for most ferroelectrics, the observed polarization change is the same as that for a path involving minimal evolution of the state. To compute the change along a generic minimal path, we decompose the change of Berry phase into many small contributions, each much less than $2\ensuremath{\pi}$, allowing for a natural resolution of the branch choice. We show that for typical ferroelectrics, including those that would have otherwise required a densely sampled path, this technique allows the switching polarization to be computed without any need for intermediate sampling between oppositely polarized states.