Crystal structure, incommensurate magnetic order, and ferroelectricity in ${\mathrm{Mn}}_{1-x}{\mathrm{Cu}}_x\mathrm{WO}{}_4 \left(0 \le x\le 0.19\right)$

We have carried out a systematic study on the effect of Cu doping on nuclear, magnetic, and dielectric properties in ${\mathrm{Mn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{WO}}_4$ for $0\le x\le 0.19$ by a synergic use of different techniques, viz, heat capacity, magnetization, dielectric, and neutron powder diffraction measurements. Via heat capacity and magnetization measurements we show that with increasing Cu concentration magnetic frustration decreases, which leads to the stabilization of commensurate magnetic ordering. This was further verified by temperature-dependent unit cell volume changes derived from neutron diffraction measurements which was modeled by the Grüneisen approximation. Dielectric measurements show a low temperature phase transition below about 9–10 K. Furthermore, magnetic refinements reveal no changes below this transition indicating a possible spin-flop transition which is unique to the Cu doped system. From these combined studies we have constructed a magnetoelectric phase diagram of this compound.

Figure 1

The temperature dependence of specific heat $C_{\mathrm{P}}$ of ${\mathrm{Mn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{WO}}_4$. Different curves are vertically offset by 8 units along the $C_{\mathrm{P}}$ axis, zero for each curve is defined by the horizontal dashed lines. Vertical dashed lines are a guide to the eyes indicating transitions $T_{\mathrm{N}1}$ and $T_{\mathrm{N}2}$.

Figure 2

Temperature dependence of dielectric constant at 105 kHz, for ${\mathrm{Mn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{WO}}_4$ with: (a) $x=0.05$, (b) $x=0.1$, and (c) $x=0.19$. The arrows in (a) and (b) indicate the dielectric anomalies and the arrows in (c) indicate the anomalies seen in specific heat measurement of the sample with $x=0.19$.

Figure 3

(a) Susceptibility calculated from the magnetization data measured after a field cooling cycle with an applied magnetic field of 1 kOe. (b) Curie-Weiss fit (red lines) to the inverse susceptibilities, a deviation from linear nature is seen below magnetic ordering temperature. (c) The frustration parameter as a function of composition. Inset shows the Curie-Weiss temperature as a function of composition obtained from the Curie-Weiss fits. Straight lines are a guide to the eyes.

Figure 4

(a) Temperature evolution of diffraction patterns of ${\mathrm{Mn}}_{0.95}{\mathrm{Cu}}_{0.05}{\mathrm{WO}}_4$. Magnetic phase transition is discernible with the appearance of additional incommensurate Bragg peaks around 13.5 K (horizontal dashed line). (b) Temperature evolution of part of the diffraction patterns of ${\mathrm{Mn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{WO}}_4$. Magnetic phase transition is discernible with the appearance of additional incommensurate Bragg peaks around 14 K. (c) Temperature dependence of diffraction patterns of ${\mathrm{Mn}}_{0.8}{\mathrm{Cu}}_{0.19}{\mathrm{WO}}_4$. Two magnetic phase transitions are discernible at $\sim 17$ and $\sim 11.5$ K.

Figure 5

(a) Unit cell volume and monoclinic angle as a function of Cu concentration at temperature 300 K, lines are only guides. (b)–(d) The temperature dependence of unit cell volume for the Cu compositions $x=0.05$, 0.1, and 0.19. The curves are fits to Eq. (2) with the Grüneisen approximation for the zero pressure equation. Insets in (b)–(d) show the deviation of unit cell volume from the fitted data at low temperatures. In the second inset of (d) the unit cell volumes are plotted together, to compare the magnitude of negative thermal expansion close to ordering temperature the $y$ axes of $x=0.1$ and 0.19 are scaled by adding 0.375 and $1.155 \AA {}^3$, respectively, to match the value of the sample $x=0.05$ at 100 K. The lines are guides to the eyes.

Figure 6

Observed and calculated diffractions patterns and their difference for (a) ${\mathrm{Mn}}_{0.95}{\mathrm{Cu}}_{0.05}{\mathrm{WO}}_4$ at 1.5 K, (b) ${\mathrm{Mn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{WO}}_4$ at 1.5 K, (c) ${\mathrm{Mn}}_{0.81}{\mathrm{Cu}}_{0.19}{\mathrm{WO}}_4$ at 1.5 K, and (d) ${\mathrm{Mn}}_{0.81}{\mathrm{Cu}}_{0.19}{\mathrm{WO}}_4$ at 13.4 K. Circles are the measured intensities and the curve is the calculated pattern. Top and bottom vertical bars mark the positions of the nuclear and magnetic Bragg reflections, respectively. Bottom curve is the difference between the measured and calculated patterns.

Figure 7

Temperature variation of components of incommensurate propagation vector along $x \left(k_x\right)$ and $z \left(k_z\right)$ axes for (a) ${\mathrm{Mn}}_{0.95}{\mathrm{Cu}}_{0.05}{\mathrm{WO}}_4$, (b) ${\mathrm{Mn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{WO}}_4$, and (c) ${\mathrm{Mn}}_{0.81}{\mathrm{Cu}}_{0.19}{\mathrm{WO}}_4$. Component of propagation vector along $y$ is $k_y=0.5$.

Figure 8

(a) ICM structure of ${\mathrm{Mn}}_{0.81}{\mathrm{Cu}}_{0.19}{\mathrm{WO}}_4$ with propagation vector $\mathbf{k}=(-0.225,\frac{1}{2},0.531)$, the number of visible unit cells along $a,b$, and $c$ directions are 5, 2, and 20, respectively. (b) High temperature CM structure of ${\mathrm{Mn}}_{0.81}{\mathrm{Cu}}_{0.19}{\mathrm{WO}}_4$ with propagation vector (0.5, 0, 0), two unit cells along all three axes are shown. Gray box indicates one unit cell.

Figure 9

Tentative phase diagram of ${\mathrm{Mn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{WO}}_4$ with phase boundaries obtained from specific heat (asterisk), NPD (inverted triangle), and dielectric (circle) measurements. The symbols in black, red, and green corresponds to the transitions $T_{\mathrm{N}1},T_{\mathrm{N}2}$, and $T_{\mathrm{X}}$, respectively. Blue asterisk indicates the transition from AF2 to AF1 phase in ${\mathrm{MnWO}}_4$. (PM—paramagnet, CM—commensurate magnet, ICM—incommensurate magnet, FE—ferroelectric, and PE—paraelectric.)