Absence of commensurate ordering at the polarization flop transition in multiferroic $\mathrm{Dy}\mathrm{Mn}{\mathrm{O}}_3$

Ferroelectric spiral magnets $\mathrm{Dy}\mathrm{Mn}{\mathrm{O}}_3$ and $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_3$ show similar behavior of electric polarization in applied magnetic fields. Studies of the field dependence of lattice modulations on the contrary show a completely different picture. Whereas in $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_3$ the polarization flop from $P\parallel c$ to $P\parallel a$ is accompanied by a sudden change from incommensurate to commensurate wave vector modulation, in $\mathrm{Dy}\mathrm{Mn}{\mathrm{O}}_3$ the wave vector varies continuously through the flop transition. This smooth behavior may be related to the giant magnetocapacitive effect observed in $\mathrm{Dy}\mathrm{Mn}{\mathrm{O}}_3$.

Figure 1

(Color online) Temperature dependence of (a) the incommensurability $\delta$ and (b) the respective intensities of the (0, $4\text{−}2\delta$, 0) structural reflection. Data are shown for ${\mu }_{0}H=0\mathrm{T}$ and ${\mu }_{0}H\Vert b=10\mathrm{T}$ for decreasing (open symbols) and increasing (closed symbols) temperature. In (c) and (d), $\delta$ and intensity variations as function of magnetic field, respectively, are shown for a sample temperature of $T=2\mathrm{K}$, in the same axes range as in (a) and (b). In the inset, spontaneous electric polarization $P\Vert c$ is shown as function of temperature for magnetic-field orientation $H\Vert b$. Temperature dependence of (e) wave vector and (f) the respective intensities for ${\mu }_{0}H\Vert b=2.5\mathrm{T}$ and wave vectors (0, $\delta$, 5), (0, $2\delta$, 5), and (0, $4\text{−}2\delta$, 0) for decreasing (open symbols) and increasing (closed symbols) temperature. The (0, $2\delta$, 5) intensities in (f) are multiplied by a factor of 10.

Figure 2

(Color online) Field dependences with field $H\Vert a$ of (a) the incommensurability and (b) the integrated intensity measured at $T=8\mathrm{K}$. The error bars in (a) represent the half-width at half maximum of the superlattice reflection. In the inset, spontaneous electric polarization $P\Vert c$ is shown as function of temperature for magnetic field $H\Vert a$.

Figure 3

(Color online) (a) Scans along (0, $k$, 5) at $T=3\mathrm{K}$ for different applied magnetic fields with intensity in logarithmic scale. (b) Temperature dependence as function of field $H\Vert a$ of the integrated intensity of the superlattice reflections (0, 0.9, 5) in the Dy ordered phase and the second-harmonic reflection (0, $2\delta$, 5) due to Mn order. Open and closed symbols represent increasing and decreasing temperature, respectively. In (c) the wave vector of the (0, 0.9, 5) reflection is shown as function of temperature for different fields. The inset shows magnetization data of $\mathrm{Dy}\mathrm{Mn}{\mathrm{O}}_3$ for $H\Vert a$ and $H\Vert b$.