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Model analysis of magnetic susceptibility of Sr$_2$IrO$_4$ - 2D $J_{\rm eff}$ = 1/2 Heisenberg system with competing interlayer couplings

We report the analysis of magnetic susceptibility $χ$($T$) of Sr$_2$IrO$_4$ single crystal in the paramagnetic phase. We formulate the theoretical susceptibility based on isotropic Heisenberg antiferromagnetism incorporating the Dzyaloshinsky-Moriya interaction exactly, and include the interlayer couplings in a mean-field approximation. $χ$($T$) above $T_{\rm N}$ was found to be well described by the model, indicating the predominant Heisenberg exchange consistent with the microscopic theory. The analysis points to a competition of nearest and next-nearest neighbor interlayer couplings, which results in the up-up-down-down configuration of the in-plane canting moments identified by the diffraction experiments.