Raman signatures of strong Kitaev correlations in iridate compounds: Theory

Sodium Iridate compounds of the form $Na_2 Ir O_3 $ are known to be magnetically ordered and show residual spin liquid behaviour at high temperatures. The Kitaev-Heisenberg model has been a strong contender for describing such systems. We decoupled the model using the Majorana mean field, thus allowing for both short range correlations and magnetic order. We first located a regime in parameter space where short-range correlations exist despite the magnetic order being non-zero. This is the zigzag phase with short range correlations. In this regime, close to the spin liquid boundary, that we computed the Raman Response for the model at zero temperature and found a broad band which is a signature of short range correlations. We also estimated the strength of the Kitaev term Jk using the Raman response. We found our results to be in good agreement with the experiments.

On the other hand in $Na_4 Ir_3 O_8$ no magnetic order was found down to 100 mK. Our calculations of the Raman response of the Kitaev-Heisenberg model on the hyperkagome lattice shows that the experimental observations are consistent with the calculated Raman response where the Kitaev exchange interaction (JK) is much larger than the Heisenberg term J1 (J1/JK?0.1).