Phenomenological theory of phase transitions in multiferroic MnWO₄: magnetoelectricity and modulated magnetic order

Abstract

The phenomenological theory of phase transitions in multiferroic MnWO₄ is suggested. The theoretical model uses the assumption that the magnetic order is driven by the instability in the (1/4;1/2;1/2) point of the Brillouin zone, which is justified by the symmetry of the low-temperature magnetic phase. It is shown that the experimentally observed incommensurate magnetic order is due to the Lifshitz invariants allowed for the corresponding order parameters. Invariants responsible for the magnetoelectric interaction are found and a schematic phase diagram is calculated. The influence of the magnetic field on the phase transition sequence is also analyzed. It is suggested that the description of the phase transitions in MnWO₄ starting from the orthorhombic praphase significantly simplifies the approach and allows us to draw important conclusions.

Interpretation of magnetoelectric phase states using the praphase concept and exchange symmetry

“…The magnetic phase transitions in wolframite were studied theoretically in a number of works [16,18,19,37,38]. In [16,18] the authors developed phenomenological models of phase transitions in MnWO 4 starting with the order parameters belonging to the incommensurate wave vector k inc .…”

“…In our previous work [19] we developed a phenomenological model of phase transitions using magnetic order parameters belonging to the k c point of the Brillouin zone and accounted for the incommensurate phases by means of Lifshitz invariants. We also suggested that the phase transitions in wolframite be described starting from the orthorhombic praphase [19,20].…”

“…We also suggested that the phase transitions in wolframite be described starting from the orthorhombic praphase [19,20]. In this section using the praphase concept and exchange symmetry we discuss the magnetic structures of the magnetic field-induced phases HF, IV, and V and the magnetic field-induced flop of electric polarization (with magnetic field applied along the easy axis).…”

“…In [19] we developed a phenomenological model of magnetic phase transitions in wolframite starting from the monoclinic structure P 2/c. The magnetically ordered phases are described by the order parameters belonging to the star of wave vector k c .…”

“…In the case when a commensurate magnetically ordered phase is present in the phase diagram, the order parameters belonging to its wave vector are chosen and the incommensurate phases are found to be well described by the existing Lifshitz invariants. This is, for example, the case of RMn 2 O 5 [15], MnWO 4 [15,19], and CuO [20]. In other cases (such as, for example, in CuCl 2 [21]), when the magnetic order does not lock-in to a commensurate structure, one may choose the commensurate wave vector closest to that of the incommensurate phases to define the order parameters.…”