Translation domains in multiferroics

Abstract

We describe the behavior of translation domains – that is domains resulting from the breaking of translation rather than point symmetries – in multiferroics with simultaneous magnetic and ferroelectric order. First, we review the structure of order parameters describing translation domains. Then, we report our spatially resolved measurements of translation domains using piezoresponse force microscopy and optical second harmonic generation in two types of multiferroics. In the split-order-parameter multiferroic hexagonal YMnO₃, we show that commensurate structural translation domains are rigidly coupled to the ferroelectric orientation domains so that the orientation domains adopt the translation domain structure. In contrast, in the joint-order-parameter multiferroic MnWO₄, incommensurate magnetic translation domains are largely decoupled from the ferroelectric orientation but nevertheless limited by stability criteria. These pronounced manifestations of the generally ‘hidden’ translation domains emphasize that their presence should be taken into account when discussing the physical properties and functionalities of multiferroics.

Keywords:

• multiferroics
• domains
• order parameter
• antiferromagnetic
• improper ferroelectric

Acknowledgments

The authors thank Pierre Tolédano and Morgan Trassin for many fruitful discussions and helpful comments. M.F. thanks the IMI Program of the National Science Foundation under Award No. DMR-0843934, managed by the International Center for Materials Research, UC Santa Barbara, for sabbatical support. D.M. acknowledges support by the Alexander von Humboldt Foundation and the NSF Science and Technology Center (E3S). M.F. and M.L. thank the SFB 608 of the DFG for financial support.