Dimensionality Driven Spin-Flop Transition in Layered Iridates

Using resonant x-ray diffraction, we observe an easy $c$-axis collinear antiferromagnetic structure for the bilayer ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$, a significant contrast to the single layer ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ with in-plane canted moments. Based on a microscopic model Hamiltonian, we show that the observed spin-flop transition as a function of number of ${\mathrm{IrO}}_2$ layers is due to strong competition among intra- and interlayer bond-directional pseudodipolar interactions of the spin-orbit entangled $J_{\mathrm{eff}}=1/2$ moments. With this we unravel the origin of anisotropic exchange interactions in a Mott insulator in the strong spin-orbit coupling regime, which holds the key to the various types of unconventional magnetism proposed in $5d$ transition metal oxides.

Figure 1

(a) Crystal structure of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ as reported in Ref. 17. Every neighboring ${\mathrm{IrO}}_6$ octahedra are rotated in opposite sense about the $c$ axis by $\simeq 12°$. (b) Magnetic order has a $c$-axis collinear $G$-type antiferromagnetic structure. The up and down magnetic moments correlate with counterclockwise and clockwise rotations of the ${\mathrm{IrO}}_6$ octahedra, respectively.

Figure 2

(a) $l$ scan measured in $\pi \mathrm{\text{−}}\sigma$ polarization channel showing magnetic Bragg peaks. (b) Integrated intensities at each peak obtained from rocking curves (red dots). Red solid (green dashed) line is bilayer structural factor expected for antiferromagnetic (ferromagnetic) alignment of two adjacent ${\mathrm{IrO}}_2$ planes in a bilayer expressed by ${cos}^2\frac{2\pi d}{c}$ (${sin}^2\frac{2\pi d}{c}$). (c) Temperature dependence of (0 1 19) peak.

Figure 3

Rocking curves measured in two polarization channels for (a) (1 0 18) reflection and (b) (0 1 19) reflections. The azimuth angle, defined with respect to the reference vector (1 0 0), was set at 0° for (1 0 18) reflection so that the scattering plane is defined by (1 0 0) and (1 0 18). Likewise, for (0 1 19) reflection azimuth angle was set at 90° so that the scattering plane is defined by (0 1 0) and (0 1 19).

Figure 4

(a) The ground state phase diagram of the Hamiltonian (1) in terms of $\eta =J_H/U$ and the tetragonal distortion parameter $\theta$ [the values of $\theta$ smaller (larger) than ${\theta }_0$ correspond to compressed (elongated) octahedra]. The solid (dashed) line marks the spin-flop transition in bilayer (single-layer) system. The shaded area indicates the parameter space for ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ constrained by experimental observations (see text). (b) The ratio of intensities at $L_2$ and $L_3$ calculated as a function of $\theta$. The experimental ratio of at most 1% provides the lower and upper bounds for $\theta$. Spin-orbital density map is shown for some values of $\theta$ with spin up (down) represented by light gray (dark gray) [orange (blue)]. (c) Energy scan of (0 1 19) reflection scanned around Ir $L_3$ and $L_2$ resonance. Red dots and black lines indicate scattering intensity and x-ray absorption spectra, respectively.