Magnetocapacitance effect and magnetoelectric coupling in type-II multiferroic ${\mathrm{HoFeWO}}_6$

We have investigated the multiferroicity and magnetoelectric (ME) coupling in $\mathrm{Ho}\mathrm{Fe}\mathrm{W}{\mathrm{O}}_6$. With a noncentrosymmetric polar structure (space group Pna$2_1$) at room temperature, this compound shows an onset of electric polarization with an antiferromagnetic ordering at the Néel temperature ($T_N$) of 17.8 K. The magnetic properties of the polycrystalline samples were studied by DC and AC magnetization and heat capacity measurements. The metamagnetic behavior at low temperatures was found to be directly related to the dielectric properties of the compound. In particular, field-dependent measurements of capacitance show a magnetocapacitance (MC) effect with double-hysteresis loop behavior in direct correspondence with the magnetization. Our x-ray diffraction results show the Pna$2_1$ structure down to 8 K and suggest the absence of a structural phase transition across $T_N$. Soft x-ray absorption spectroscopy and soft x-ray magnetic circular dichroism (XMCD) measurements at the Fe $L{}_{2,3}$ and Ho $M{}_{4,5}$ edges revealed the oxidation state of Fe and Ho cations to be $3+$. Fe $L{}_{2,3}$ XMCD further shows that ${\mathrm{Fe}}^{3+}$ cations are antiferromagnetically ordered in a noncollinear fashion with spins arranged ${90}^{\circ }$ with respect to each other. Our findings show that $\mathrm{Ho}\mathrm{Fe}\mathrm{W}{\mathrm{O}}_6$ is a type-II multiferroic exhibiting a MC effect. The observed MC effect and the change in polarization by the magnetic field, as well as their direct correspondence with magnetization, further support the strong ME coupling in this compound.

Figure 1

(a) Rietveld refinement of the room-temperature synchrotron XRD data for $\mathrm{Ho}\mathrm{Fe}\mathrm{W}{\mathrm{O}}_6$. Crosses: measurement data; red solid line: calculated profile; green solid line: the difference between the observation and the calculated profile; and vertical bars: positions of Bragg peaks. Inset: magnified view of the main peaks. (b) Crystal structure of $\mathrm{Ho}\mathrm{Fe}\mathrm{W}{\mathrm{O}}_6$.

Figure 2

(a) Fe $L{}_{2,3}$ XAS spectrum of $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$, (b) Fe $L{}_{2,3}$ XAS (blue) and XMCD (red) spectra of $\mathrm{Ho}\mathrm{Fe}\mathrm{W}{\mathrm{O}}_6$ measured at 2 K under a magnetic field of 6 T, (c) calculated XAS and XMCD spectra for noncollinear AFM order, and (d) calculated XMCD spectrum for collinear AFM order. The XMCD spectra are scaled by a factor of 10 for a clearer view. (e) Ho $M{}_{4,5}$ XAS (blue dots) and XMCD (red dots) spectra of $\mathrm{Ho}\mathrm{Fe}\mathrm{W}{\mathrm{O}}_6$ measured at 2 K under a magnetic field of 6 T, together with the calculated XAS (solid blue line) and XMCD (solid red line) of ${\mathrm{Ho}}^{3+}$. (f) Total density of states for $\mathrm{Ho}\mathrm{Fe}\mathrm{W}{\mathrm{O}}_6$. Dashed line: Fermi energy. Highlighted region: insulating gap of $\sim 3.7$ eV.

Figure 3

(a) Heat capacity, (b) (molar) magnetic susceptibility, and (c) dielectric constant as functions of temperature. Heat capacity and dielectric constant were measured during warming without the presence of a magnetic field and magnetic susceptibility was measured under the field-cooled condition and in the presence of $H=1$ T. (d) Real part of AC magnetic susceptibility, ${\chi }_{\mathrm{AC}}\left(T\right)$, measured under the frequency of $f=1$ kHz and a time-varying magnetic field of $H_{\mathrm{AC}}=2$ Oe and under different external magnetic fields. (e) Electric polarization as a function of temperature, $\mathrm{\Delta }P\left(T\right)$, under different magnetic fields. To measure the $\mathrm{\Delta }P\left(T\right)$, the sample was cooled down from 20 K to the base temperature of 2 K in the presence of the poling field E. The $\mathrm{\Delta }P\left(T\right)$ was then measured after removing E and applying the magnetic field while warming the sample at the rate of 2 K/min.

Figure 4

(a) Field-dependent DC magnetization $M\left(H\right)$ at different temperatures and (b) its derivative. For clarity, the derivatives are shifted in the vertical direction.

Figure 5

(a) Temperature-dependent dielectric constant under different magnetic fields measured under the field-cooled condition, with the tangent loss, $\mathrm{Tan}(\delta$), in the inset. The data were collected at the frequency of $f=1$ kHz. (b) Field-dependent dielectric constant $\epsilon \left(H\right)$ at different temperatures, normalized by the expression $\left[\epsilon \right(H)/\epsilon (0)-1]\times 100$, (c) Derivative of $\epsilon \left(H\right)$ at different temperatures with respect to the field. The curves are shifted vertically by distances equal to their temperature differences for clarity. The arrow shows the linear shift in the hysteresis toward higher fields as the temperature is increased. (d) Electric polarization as a function of field, $\mathrm{\Delta }P\left(H\right)$, at different temperatures.