Giant magnetoelectric effect in the $J_{\mathrm{eff}}=\frac{1}{2}$ Mott insulator ${\text{Sr}}_2{\text{IrO}}_4$

Our magnetic, electrical, and thermal measurements on single crystals of the $J_{\mathrm{eff}}=1/2$ Mott insulator, ${\text{Sr}}_2{\text{IrO}}_4$, reveal a giant magnetoelectric effect (GME) arising from a frustrated magnetic/ferroelectric state whose signatures are: (1) a strongly enhanced electric permittivity that peaks near an observed magnetic anomaly at 100 K, and (2) a large $\left(\sim 100\%\right)$ magnetodielectric shift that occurs near a metamagnetic transition. The GME hinges on a spin-orbit gapping of $5d$ bands rather than the magnitude and spatial dependence of magnetization, as traditionally accepted.

Figure 1

(Color online) (a) Field-cooled magnetization $M\left(T\right)$ and inverse susceptibility $\Delta {\chi }^{-1}\left(T\right)$ (right scale) at applied field ${\mu }_{\text{o}}H=0.2\text{T}$, (b) Specific heat $C\left(T\right)$, (c) resistivity $\text{log}\rho \left(T\right)$, and (d) thermoelectric power $S\left(T\right)$ for ${\text{Sr}}_2{\text{IrO}}_4$ as functions of temperature $T\le 600\text{K}$. Except for $C\left(T\right)$ $\left(H\perp \mathbf{c}\right)$, all properties are measured for $H$ along both $\mathbf{a}$ and $\mathbf{c}$ axes. Fig. 1b inset: C(T) vs $T^3$ for $T<11\text{K}$. Fig. 1d inset: Arrott plot ($M^2$ vs ${\mu }_{\text{o}}H/M$) shows a FM transition at $T_{\text{C}}\approx 240\text{K}$. Note: no anomaly is seen in $\rho \left(T\approx T_{\text{C}}\right)$ and $S\left(T\approx T_{\text{C}}\right)$.

Figure 2

(Color online) (a) Real part of ac susceptibility ${\chi }^{\prime }\left(T,\omega \right)$ along the $\mathbf{a}$ axis at ${\mu }_{\text{o}}H=0.1\text{T}$ and frequencies $\omega =0.8$ and 80 Hz. (b) dc magnetizations $M_{\text{a}}\left(T\right)$ and (c) $M_{\text{c}}\left(T\right)$ for various magnetic fields $H$. Note the $H$-dependent anomaly at $T_{\text{M}}$ (arrows) (d) $M\left(T\right)$ for ${\left({\text{Sr}}_{1-x}{\text{Ba}}_x\right)}_2{\text{IrO}}_4$ with $x=0.02$ for both the $\mathbf{a}$ and $\mathbf{c}$ axes. Note that $T_{\text{M}}$ and low-$T$ down turn are no longer visible. Fig. 2a inset: ${\chi }^{\prime }\left(T\right)$ for $\omega =8\text{Hz}$ at ${\mu }_{\text{o}}H=0.01$ and 0.1 T. Figs. 2b, 2c inset: Rotation scheme for ${\text{IrO}}_6$ octahedra.

Figure 3

(Color online) (a) Real part of the $\mathbf{c}$-axis dielectric constant ${\epsilon }_{\text{c}}^{\prime }\left(T\right)$ for representative frequencies $\omega$ (left scale), and $\mathbf{c}$-axis magnetization $M_{\text{c}}\left(T\right)$ (right scale); Fig. 3a inset: schematic change of O-Ir-O bond angle from region I to region II. (b) Real part of the $\mathbf{a}$-axis dielectric constant ${\epsilon }_{\text{a}}^{\prime }\left(T\right)$ for representative $\omega$ (left scale), and $\mathbf{a}$ axis $M_{\text{a}}\left(T\right)$ (right scale). (c) Electric polarization $P$ vs voltage $V$ for temperature $T=13.3\text{K}$ (low $V$, left scale) and 4.3 K (high $V$, right scale).

Figure 4

(Color online) (a) Magnetoelectric effect $\Delta {\epsilon }_{\text{c}}^{\prime }\left(H\right)/{\epsilon }_{\text{c}}^{\prime }\left(0\right)$ along $\mathbf{c}$ axis at temperatures $T=50$ and 110 K versus applied field $H$ for a few representative frequencies $\omega$ and ${\mu }_{\text{o}}H\le 10\text{T}$ applied along $\mathbf{c}$ axis; Right scale: the $\mathbf{c}$ axis $M_{\text{c}}\left(H\right)$ vs $H$ at 1.7 K; (b) the $\mathbf{c}$-axis $M_{\text{c}}\left(H\right)$ at various $T$. Note parallel behavior of ${\epsilon }_{\text{c}}$ and $M_{\text{c}}$ near the metamagnetic transition field, $H_{\text{c}}$.