X phase of ${\mathrm{MnWO}}_4$

A long-standing issue, the magnetic structure of the so-called X phase of ${\mathrm{MnWO}}_4$, has been solved by single-crystal neutron diffraction. Emerging from the well-known ferroelectric phase which presents an electric polarization $P//b$ and which is induced by a cycloidal magnetic order called AF2, this phase is reached by application of a magnetic field along the $b$ axis and is characterized by a flop of the electric polarization towards the $a$ axis. We have identified this new phase as a reoriented cycloidal spin structure, AF2', and its evolution from the AF2 phase has been thoroughly described. Unlike for the usual magnetic-field-induced spin-flop transitions, this high-field flopped phase does not directly develop from the low-field phase but emerges via the nonpolar collinear commensurate AF1 phase, which creeps in between. This evolution is in good agreement with the observed field-induced change in $P_b$ and $P_a$ electric polarization as well as with magnetic susceptibility data.

Figure 1

Magnetic phase diagram for a magnetic field applied along the b axis as determined in this work by susceptibility data (circles) and from polarization and magnetization data reported in Ref. [17] (squares). Solid and open symbols denote data recorded on increasing and decreasing field and on increasing and decreasing temperature in the susceptibility and in the polarization experiments, respectively. The pink circled crosses present the neutron results from the present work. The lines and the textured areas are guides to the eyes, schematically tracing phase boundaries and coexisting phases. The dashed ellipse indicates the part of the phase diagram on which our neutron diffraction study is focused. CM = commensurate; ICM = incommensurate.

Figure 2

Field dependence of the magnetic satellites at 9.5(2) and 10.6(2) K: (a) at 9.5(2) K, a unique magnetic transition is observed from AF2 to AF1, and the X phase is not reached up to 12 T. (b) At 10.6(2) K, the magnetic reflection associated with AF2 disappears, and the one corresponding to AF1 appears around 10.5 T. A further increase of the field induces a second transition in which the later reflection disappears and the one characteristic of the X phase emerges. The top panels correspond to rocking curves $(\omega$ scans) of magnetic reflections at fixed magnetic fields, whereas the bottom panels are projections of all the rocking curves as a function of the applied field.

Figure 3

Magnetic structures under (a) zero field and (b) 10 T, (c) 10.8 T, and (d) 12 T field applied along the $b$ axis at 10.6(2) K. Since the monoclinic angle $\beta \sim {91}^{\circ }$ is close to ${90}^{\circ }$, an orthorhombic cell has been used in the plots.

Figure 4

Electric polarization $P$ along the $a$ and $b$ crystallographic directions at 10.5 K as a function of field applied along the $b$ axis. The inset shows the field derivative of the polarization.