Ferroelectricity in spiral short-range-ordered magnetic state of spinel ${\mathrm{MnCr}}_2{\mathrm{O}}_4$: Significance of topological frustration and magnetoelastic coupling

We report the appearance of ferroelectricity below $T_S=18$ K, at which short-ranged spiral spin orders, suggesting that ${\mathrm{MnCr}}_2{\mathrm{O}}_4$ is an improper multiferroic material. Linear heat capacity data and zero-field-cooled memory effect verify reentrant spin-glass-like state below $T_S$. Synchrotron x-ray diffraction studies confirm significant magnetoelastic coupling at long-range ferrimagnetic order ($T_N=42$ K) and at $T_S$. We argue that the release of topological spin frustration, produced due to pyrochlore structure of Cr sublattice, is manifested through the significant magnetoelastic effect at $T_N$ and $T_S$ and holds the key for spiral spin order driven ferroelectricity in ${\mathrm{MnCr}}_2{\mathrm{O}}_4$.

Figure 1

(a) Corner sharing tetrahedra formed by $\mathrm{Cr}{}^{3+}$ sublattice in the spinel structure. (b) Example of antiferromagnetically coupled $\mathrm{Cr}{}^{3+}$ sublattice forming a tetrahedron and demonstrating strong magnetic frustration.

Figure 2

Thermal $\left(T\right)$ variation of (a) ZFC-FC magnetization measured with 100 Oe. Thermal hysteresis between FCC and FCH is also shown. Inset of (a) displays inverse susceptibility $\left({\chi }^{-1}\right)$ plot with $T$. (b) Thermal hysteresis of magnetization disappears for measurement at 500 Oe. Inset of (b) highlights the low-$T$ FC magnetization. (c) $T$ variation of ZFC-FC magnetization measured at 1 and 10 kOe. Inset of (c) highlights deviation between ZFC and FC magnetization at low $T$. (d) Magnetic hysteresis loops at 3, 35, and 50 K.

Figure 3

(a) $T$ variation heat capacity $\left(C_P\right)$. Inset shows linear dependence of $C_{\mathrm{mag}}$ at low temperature where straight line guides the linear dependence. (b) Thermal variation of field-cooled (FC) magnetization in different modes. The field is cut off during temporary stops at 30 and 12 K. Memory effect is demonstrated by a step above 12 K and is absent at 30 K. (c) Thermal variation of ZFC magnetization defined as $M_{\mathrm{ZFCH}}^{\mathrm{ref}}$ (reference) and ZFC memory defined as $M_{\mathrm{ZFCH}}^{\mathrm{mem}}$. Inset shows thermal variation of difference plot $\left(\Delta M\right)$ between $M_{\mathrm{ZFCH}}^{\mathrm{ref}}$ and $M_{\mathrm{ZFCH}}^{\mathrm{mem}}$, displaying convincing signature of memory effect at 12 K. (d) Time $\left(t\right)$ dependence of $M$ at 12 and 30 K in zero field after cooling the sample in 100 Oe.

Figure 4

(a) Thermal variations of real part $\left({\epsilon }^{\prime }\right)$ in left panel and imaginary part $\left({\epsilon }^{\prime \prime }\right)$ in right panel of dielectric permittivity at different $f$. (b) Electric polarization $\left(P\right)$ with $T$. Inset of (b) shows pyroelectric current $\left(I_p\right)$ with $T$.

Figure 5

Rietveld refinement of x-ray powder diffraction patterns (black symbols) at 10 (a) and 300 K (b). Solid curves demonstrate the fits. $T$ variations of (c) positional coordinate of O2 [$\mathrm{O}\left(x=y=z\right)$], (d) $a$, and (e) normalized integrated intensities of (220) peak. $T$ variations of (f) Cr–O, (g) Mn–O bond lengths, and (h) Cr–O–Cr $\left({\alpha }_1\right)$, (i) Mn–O–Cr $\left({\alpha }_2\right)$, and (j) Mn–O–Mn $\left({\alpha }_3\right)$ bond angles. Inset of (f) and (g) shows Cr octahedra and Mn tetrahedra displaying bond lengths and bond angles.

Figure 6

(a) Structure viewed along the conical spin modulation direction (110). The circles with inclined arrows indicate the spiral plane of the respective Mn, $\mathrm{Cr}\left(B1\right)$, and $\mathrm{Cr}\left(B2\right)$ spins with conical structure. (b) Possible direction of $\mathrm{O}{}^{2-}$ ion displacement driven by DM interaction between $i\mathrm{th} \left({\mathbf{S}}_i\right)$ and $j\mathrm{th} \left({\mathbf{S}}_j\right)$ spins according to inverse DM model. (c) Directions of the net magnetization M, the spiral spin modulation vector (110), and the induced polarization P for $B2$ site Cr chain.