Multiferroic behavior in the double-perovskite Lu${}_2$MnCoO${}_6$

We present Lu${}_2$MnCoO${}_6$, a multiferroic member of the double perovskites that we have investigated using x-ray and neutron diffraction, specific heat, magnetization, electric polarization, and dielectric constant measurements. This material possesses a net electric polarization strongly coupled to a net magnetization below 35 K, despite the antiferromagnetic ordering of the $S=3/2$ Mn${}^{4+}$ and Co${}^{2+}$ spins in an $\uparrow \uparrow \downarrow \downarrow$ configuration along the $c$ direction. We discuss the magnetic order in terms of a condensation of domain boundaries between $\uparrow \uparrow$ and $\downarrow \downarrow$ ferromagnetic domains, with each domain boundary producing an electric polarization due to spatial inversion symmetry breaking. In an applied magnetic field the domain boundaries slide, controlling the size of the magnetization, electric polarization, and magnetoelectric coupling.

Figure 1

Derived $\uparrow \uparrow \downarrow \downarrow$ Mn${}^{4+}$ $S=3/2$ and Co${}^{2+}$ $S=3/2$ spin orientations along the $c$ axis at $T=4$ K. Domain boundaries refer to the boundary between $\uparrow \uparrow$ and $\downarrow \downarrow$. Two scenarios (left and right) for the location of domain boundaries are shown, along with possible resulting electric polarizations $P$. In the $a$-$b$ plane, an additional slow and incommensurate modulation of the spins occurs such that $\vec{k}=(0.0223\left(8\right),0.0098\left(7\right),0.5)$.

Figure 2

Monoclinic crystal structure of Lu${}_2$MnCoO${}_6$, showing the tilted oxygen octahedra surrounding alternating Mn${}^{4+}$ (dark blue) and Co${}^{2+}$ (light blue) ions. Yellow Lu ions are also shown. Oxygen ions are small red dots at the corners of the octahedra, and Lu ions are the largest yellow balls interstial between the octahedra.

Figure 3

Room-temperature SXRPD patterns of Lu${}_2$MnCoO${}_6$ and corresponding Rietveld refinement. Key: Observed (dots), calculated (solid line), and difference (at the bottom) profiles. The tick marks indicate the positions of the allowed Bragg reflections.

Figure 4

Elastic neutron-diffraction data for polycrystalline Lu${}_2$MnCoO${}_6$ at 100 K (a) and 4 K (b). The main panels show data taken with $\lambda =1.540\AA$ neutrons, while the inset to Fig. 4b shows data taken with $\lambda =2.079\AA$ neutrons. Red circles are experimental data, and the blue lines are fits to the data from Rietveld refinements. Ticks underneath the data indicate symmetry-allowed Bragg positions, and purple lines beneath the ticks show the differences between the data and fits.

Figure 5

Total specific heat $C$ vs temperature $T$ at various magnetic fields between 0 and 13 T for Lu${}_2$MnCoO${}_6$ showing a magnetic-ordering peak that broadens and evolves to higher temperatures in applied magnetic fields.

Figure 6

(a) dc magnetization $M_{\mathrm{dc}}$ vs temperature $T$ measured on warming in a 0.1 T magnetic field after zero magnetic-field cooling (ZFC) or magnetic-field cooling (FC) from room temperature. A kink near 43 K (marked by an arrow) indicates the magnetic ordering transition. The inset shows the inverse magnetic susceptibility $1/\chi \left(T\right)$ (magnetic-field cooled, red), which is fit by the Curie-Weiss relation (straight blue line) for $T>150$ K. This fit yields a Curie-Weiss temperature of 58 K and a magnetic moment of 5.5 ${\mu }_B$/formula unit. (b) ac susceptibility ${\chi }_{\mathrm{ac}}$ vs temperature $T$ at frequencies of $\sim$10, 100, and 1000 Hz in an applied oscillating magnetic field of $3\times {10}^{-4}$ T. The ordering peak near 43 K is independent of frequency, indicating long-range order (1 emu = 10${}^{-3}$ A m${}^2$).

Figure 7

Magnetic hysteresis loops measured in dc magnetic fields (a) and pulsed magnetic fields (b) with maximum pulses of 5, 15, and 60 T (see text). Thick arrows show the direction of the data. A coercive magnetic field of 1.21 T is observed in both data sets, and a magnetic moment of $\sim$6 ${\mu }_B$ is achieved by 0.5 K and 60 T, which would be expected from the combined Mn${}^{4+}$ $S=3/2$ and Co${}^{2+}$ $S=3/2$ moments (neglecting orbital effects). Thin arrows indicate a slight plateau in the magnetization.

Figure 8

(a) Measured change in electric polarization with time, $dP/dt$ as a function of magnetic field $H$ for various temperature $T$ during a rapid magnetic-field pulse for the geometry $\vec{P}\left|\right|\vec{H}$. Before measuring $dP/dt$, the sample was poled by applying an electric field of 2 MV/m in zero magnetic field while cooling from 70 K to the intended measuring temperature, at which point the electric field was removed and both sides of the sample were shorted. The inset shows data up to 60 T for $\vec{P}$ parallel and perpendicular to $\vec{H}$ at 4 K, with a 2 MV/m poling voltage. (b) $\Delta P\left(H\right)$ determined by integrating the data in (a). The inset shows $P(H=0\text{T})-P(H=15\text{T})$ as a function of temperature.

Figure 9

Influence of an external magnetic field $({\mu }_{\circ }H=14$ T) on the temperature dependence of the dielectric constant ${\epsilon }_r\left(T\right)$, measured at frequencies of 10 kHz and 1 MHz.