  The currently accepted magnetic ground state of Sr2IrO4 (the -++- state)
preserves inversion symmetry. This is at odds, though, with recent experiments
that indicate a magnetoelectric ground state, leading to the speculation that
orbital currents or more exotic magnetic multipoles might exist in this
material. Here, we analyze various magnetic configurations and demonstrate that
two of them, the magnetoelectric -+-+ state and the non-magnetoelectric ++++
state, can explain these recent second-harmonic generation (SHG) experiments,
obviating the need to invoke orbital currents. The SHG-probed magnetic order
parameter has the symmetry of a parity-breaking multipole in the -+-+ state and
of a parity-preserving multipole in the ++++ state. We speculate that either
might have been created by the laser pump used in the experiments. An
alternative is that the observed magnetic SHG signal is a surface effect. We
suggest experiments that could be performed to test these various
possibilities, and also address the important issue of the suppression of the
RXS intensity at the L2 edge.
