Two-Dimensional Heisenberg Behavior of $J_{\mathrm{eff}}\mathbf{=}1/2$ Isospins in the Paramagnetic State of the Spin-Orbital Mott Insulator ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$

The dynamical correlations of $J_{\mathrm{eff}}=1/2$ isospins in the paramagnetic state of spin-orbital Mott insulator ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ were revealed by resonant magnetic x-ray diffuse scattering. We found a two-dimensional antiferromagnetic fluctuation with a large in-plane correlation length exceeding 100 lattice spacings at even 20 K above the magnetic ordering temperature. In marked contrast to the naive expectation of the strong magnetic anisotropy associated with an enhanced spin-orbit coupling, we discovered an isotropic isospin correlation that is well described by the two-dimensional $S=1/2$ quantum Heisenberg model. The estimated antiferromagnetic coupling constant as large as $J\sim 0.1\mathrm{eV}$ that is comparable to the small Mott gap ($<0.5\mathrm{eV}$) points out the weak and marginal Mott character of this spin-orbital entangled system.

Figure 1

(a) Crystal and magnetic structures determined by nonresonant magnetic x-ray scattering of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. Magnetic moments lie within the $ab$ plane. (b) Polarization analysis of the Bragg ($T=220\mathrm{K}$, logarithmic scale) and diffuse ($T=233\mathrm{K}$) scatterings using $\pi -{\pi }^{\prime }$ and $\pi -{\sigma }^{\prime }$ detections by aligning crystalline $\overrightarrow{a}+\overrightarrow{b}$ direction to the scattering plane. (c)–(e): The intensity maps in the $h-l$ plane of the magnetic diffractions from that at 240 K ($T_N+11.5\mathrm{K}$) to 225 K ($T_N-3.5\mathrm{K}$). Note that the color scale in (e) is shrunk to those in (c) and (d) by a factor of 6, because the intensity of the magnetic Bragg reflection is much larger than that of diffuse scattering.

Figure 2

Resonant magnetic scattering profiles around (1, 0, 22) magnetic superlattice reflection along the in-plane (a) and the out-of-plane (b) directions between 227 K ($=T_N-1.5\mathrm{K}$) and 254 K ($=T_N+25.5\mathrm{K}$). Baselines of the profiles for $T\le 249\mathrm{K}$ (a) and $T\le 244\mathrm{K}$ (b) are shifted. Arrows in (a) indicate the half maximum for each diffuse scattering profile.

Figure 3

Temperature evolutions of in-plane (${\xi }_a$) and out-of-plane (${\xi }_c$) spin correlation lengths obtained by a Lorentzian fitting of scattering profiles shown in Fig. 2. Solid lines are fitted curves to theoretically obtained temperature dependence of ${\xi }_a$ in the square lattice antiferromagnet calculated by $S=1/2$ quantum Heisenberg model (Chakravarty et al. and Makivić [13, 14]) (red), Ising (blue), and $XY$ (green) models.