Iridates such as Sr2IrO4 have attracted considerable attention because they are 5d systems that exhibit a strong interplay between spin-orbit coupling and strong electronic correlations.
[See this earlier post].
Sr2IrO4 is a focus because it has been argued that it is a J=1/2 Mott insulator, just like La2CuO4, the parent compound for cuprate superconductors.
A current holy grail is to dope this material in the hope of producing high-Tc superconductivity. Many are trying. No one is succeeding.
There is actually a whole series of layered compounds, the Ruddlesden-Popper perovskites that differ, not just in their stoichiometry, but also their crystal structure, and consequently how the Iridium ions are coupled together. Sr_n+1Ir_nO_3n+1, where n is the number of SrIrO3 perovskite layers sandwiched between extra SrO layers.
Resonant-Inelastic-X-ray-Scattering (RIXS) experiments show that spin excitations in the Mott insulating phase of Sr2IrO4 appear to be well described by a spin-1/2 Heisenberg model with a small amount of spin anisotropy due to crystal field effects. However, for Sr3Ir2O7, RIXS suggests a large spin gap and spin anisotropy.However, a different experiment suggests a small anisotropy.
In contrast, SrIO3 is a metal.
A major theoretical challenge is describe this whole family of materials and the disparate results, starting just from the crystal structures.
This has been done in an impressive paper,
Effective J=1/2 insulating state in Ruddlesden-Popper iridates: An LDA+DMFT study
Hongbin Zhang, Kristjan Haule, and David Vanderbilt
The calculations are based on GGA+DMFT, and represent another landmark achievement for the combination of Dynamical Mean-Field Theory with Density Functional Theory methods.
A key ingredient to understanding the apparent inconsistency between the results of different experimental probes is that in the many-body treatment the matrix describing the hybridisation of the three d-orbitals is frequency dependent. This is in contrast to the static matrix associated with crystal field theory.
The X-ray and thermodynamic experiments probe the system on different time scales. Thus they are respectively, more sensitive to the high- and low-frequency part of the hybridisation matrix.
The Figure below shows the calculated optical conductivity for the first three compounds in the RP series.
They also show how 0.2 per cent epitaxial lattice strain can have a big effect. [Aside: These are the kind of calculations I would like to see to address thermal expansion in organic charge transfer salts.]
I thank Kristjan Haule for explaining this work to me.