Fast and slow sound excitations in nematic aerogel in superfluid He 3

Nematic aerogel (nAG) supports so-called polar phase in liquid 3He. The experiment [Dmitriev et al, JETP Lett. 112, 780 (2020)] showed that the onset of polar phase inside the nAG is accompanied by emergence of a sound wave with frequency quickly growing with cooling down from transition temperature and reaching a plateau. To describe this behavior, we start by calculating the elastic properties of the dry nematic AG that appear to depend only on Young's modulus of the parent material (e.g. mullite), the volume fraction of the solid phase and the aspect ratio of the representative volume of nAG. The elastic constants are then used to solve elasto-hydrodynamic equations for various sound vibrations of nAG filled with 3He. The (isotropic) first sound and anisotropic second sound in the polar phase are strongly hybridized with fourth sound and standard elastic modes in nAG. The hybrid second and the transverse fourth sound start with zero velocity at the transition, similar to pure 3He, and quickly grow with lowering temperature until they hit the sample finite size cutoff.