The Effect of Leggett–Takagi Relaxation on Vortex-Generated Spin Waves in Superfluid ³He-B

Vortices in the B phase of superfluid ³He can excite spin waves, leading to experimentally observable relaxation of uniformly precessing magnetisation [1,2,3]. Here, we study the phenomenon at intermediate temperatures T∼0.5 T_c within the framework of Leggett–Takagi theory [4] by solving the equations of spin dynamics for an isolated vortex line in the absence of spin diffusion and calculating the energy relaxation rate. There are two factors contributing to the relaxation: excitation of spin waves by the vortex and the intrinsic Leggett–Takagi mechanism stemming from conversion of spin between Cooper pairs and quasiparticles. Under conditions relevant to the experiment in Ref. [1], we find that spin wave radiation is the dominant effect. One noteworthy consequence of the Leggett–Takagi mechanism is attenuation of spin waves at distances less than the typical inter-vortex separation, justifying our assumption that vortices can be treated independently of each other.

[1] Y. Kondo et al., Phys. Rev. Lett. 67, 81 (1991).
[2] V. V. Zavjalov et al., Nat. Commun. 7, 10294 (2016).
[3] S. M. Laine and E. V. Thuneberg, Phys. Rev. B 98, 174516 (2018).
[4] A. J. Leggett and S. Takagi, Ann. Phys. (NY) 106, 79 (1977).