Neutron diffraction, magnetic, and magnetoelectric studies of phase transitions in multiferroic Mn${}_{0.90}$Co${}_{0.10}$WO${}_4$

We have studied various spontaneous and magnetic-field-induced phase transitions in single crystals of multiferroic Mn${}_{0.9}$Co${}_{0.1}$WO${}_4$ using magnetic and magnetoelectric measurements and neutron diffraction. Compared to pure MnWO${}_4$, our data consistently confirm that the anisotropic Co${}^{2+}$ ions induce reorientation of the spin cycloid structure to the $ac$ plane and reveal $P_a$ and $P_c$ components of spontaneous electric polarization. Field-induced phase transitions accompanied by anomalies of magnetic susceptibility and suppression of both $P_a$ and $P_c$ polarizations have been observed for $H$$\parallel$$c$ ($\sim$3 T) and $H$$\parallel$$a$ ($\sim$8.5 T). Neutron diffraction has revealed that in both cases the spin cycloid plane flops in direction almost perpendicular to $H$, i.e., close to the $ab$ and $bc$ planes, respectively. Parameters describing the magnetic structures including wave vectors, orientations of the main elliptical axes, etc., have been determined in all spontaneous and field-induced states.

Figure 1

(a) Temperature dependence of dc susceptibility at a field of 1 kOe applied along the principle crystallographic directions. (b) Temperature dependence of the inverse susceptibility. $T_N$ and $\theta$${}_P$ stand for Neél and asymptotic paramagnetic temperatures, respectively, while $T_{N2}$ refers to the small change in the susceptibility slope, tentatively ascribed to a second transition.

Figure 2

Integrated intensities of magnetic satellites in zero applied field monitored as the temperature increases. (a) Magnetic satellites that corresponds to k $=$ [$-$0.222(1) 0.5 0.472(1)]. The error bars are inside the symbols. Vertical lines indicate the two magnetic transitions. (b) Integrated intensity of $\left(\frac{1}{2}00\right)$ characteristic of the AF4 commensurate phase.

Figure 3

Agreement plot of the refinements in zero field for (a) the nuclear structure at 17 K, in the paramagnetic phase, (b) the AF3 magnetic phase at 12 K, (c) the AF2${}^{\prime }$ magnetic phase at 9 K, and (d) the AF2${}^{\prime }$ magnetic phase at 2 K. The calculated structure factors are plotted against the experimental ones. The agreement factors $R_{F^{2}w}$ and $\chi$${}^2$ are shown. The corresponding magnetic structures are shown in Fig. 4.

Figure 4

Magnetic structures of Mn${}_{0.9}$Co${}_{0.1}$WO${}_4$ in zero field, projected in the $ac$ plane. (a) Sinusoidal collinear AF3 magnetic phase at 12 K. AF2${}^{\prime }$ multiferroic phase (b) at 9 K and (c) at 2 K. The circles in the octahedra (green) correspond to (Mn,Co) atoms, circles between the octahedra (blue) are W atoms and the smallest circles (red) are O atoms. Their relative sizes are not real in the figure for clarity reasons. Distorted (Mn,Co)O${}_6$ octahedra are shown in purple. The thin gray lines illustrate the crystallographic unit cell. The corresponding magnetic models are described in the text and in Table .

Figure 5

Temperature dependence of spontaneous electric polarization along the principle crystallographic directions which appeared below $T_{N2}$ in the AF2${}^{\prime }$ cycloidal phase. The insert shows the anomalies of dielectric constants along the $a$ and $c$ axes at $T_{N2}$ measured at 16 kHz.

Figure 6

Magnetization curves along the principle crystallographic directions.

Figure 7

(a) Real component of ac susceptibility along the $a$ axis as a function of superimposed dc field amplitude. (b) The same for the $c$ axis. The insets are zooms of the susceptibility maxima. The arrows indicate the direction of changing the field.

Figure 8

(a) Evolution of the integrated intensity of (0 0 1)${}^{-}$ magnetic satellite with the magnetic field applied parallel to the $c$ axis ($H$$\parallel$$c$). (b) Similar plot for the (0 1 0)${}^{+}$ satellite when the magnetic field is applied parallel to the $a$ axis ($H$$\parallel$$a$). The error bars are inside the symbols.

Figure 9

Magnetic structure of Mn${}_{0.9}$Co${}_{0.1}$WO${}_4$ determined at 2 K and 5 T with the magnetic field applied parallel to the $c$ axis ($H\parallel$$c$). The structure is represented by the same color/size code as in Fig. 4a. A projection in the $ac$ plane of the spin order. (b) Projection of the magnetic structure in the $ab$ plane. The spin rotation plane is shown in light purple in the magnetic phases induced by the external field. The thin gray frame illustrate the crystallographic unit cell.

Figure 10

Magnetic structure of Mn${}_{0.9}$Co${}_{0.1}$WO${}_4$ determined at 2 K and 11 T with the magnetic field applied along $a$ ($H$$\parallel$$a$). Projection of the magnetic structure in the $ac$ plane (a) and in the $bc$ plane (b). The structure is represented by the same color/size code as in Figs. 4 and 9.

Figure 11

Agreement plot of the magnetic refinements under the magnetic field in Mn${}_{0.9}$Co${}_{0.1}$WO${}_4$ at 2 K. (a) Magnetic structure with $H$$\parallel$$c$ ($H=5$ T). (b) Magnetic structure with $H$$\parallel$$a$ ($H=11$ T). The calculated structure factors are plotted against the experimental ones. The agreement magnetic factors $R_{F^{2}w}$ factor and ${\chi }^2$ are given. The corresponding magnetic models are shown in Figs. 9 and 10.

Figure 12

(a) Dependence of the electric polarization along the $a$, $b$, and $c$ axes under the magnetic field along the $c$ axis. The insert shows the evolution of the critical field as a function of the temperature, $H_{cr}$-$T$ diagram, obtained from electric polarization and magnetization data. Green stars correspond to magnetic measurements, black squares to $P_a$, blue triangles to $P_b$, and red circles to $P_c$. (b) $P_a$ component of the electric polarization in pulsed magnetic field along the $a$, $b$, and $c$ axes, exhibiting a suppression of $P_a$ for $H$$\parallel$$a$ and $H$$\parallel$$c$. Almost nothing changes for $H$$\parallel$$b$.