Unique signatures of electronic nematic liquids via nonlinear Raman spectroscopy*

It was recently proposed that the observed splitting of optical phonon lines in the tetragonal phase of BaNi₂As₂ is related to strong fluctuations of an underlying orbital-nematic Ising order parameter, leading to a liquid nematic phase [1]. Characterizing the nematic liquid phase can be challenging since linear Raman responses give similar signatures as a solid nematic phase with broken Z₂ symmetry but coexisting Ising domains. To further corroborate this view, we propose using non-linear Raman spectroscopy to unambiguously differentiate the nematic liquid from a static phase with different domains, where the Z₂ symmetry is effectively restored in the response upon domain averaging.  By computing the higher-order response functions, we show that the dynamical nematic Ising degree of freedom leads to features in the multidimensional spectrum that are absent in the solid phase, reflecting the additional quantum coherence that is only present in the liquid phase.  We also discuss experimental ways of measuring such higher-order responses.

 [1] Y. Yao, R. Willa, T. Lacmann, S.-M. Souliou, M. Frachet, K. Willa, M. Merz, F. Weber, C. Meingast, R. Heid, A.-A. Haghighirad, J. Schmalian, and M. Le Tacon, Nature Communications 13, 4535 (2022).