Impurity effects on the A₁ − A₂ splitting of superfluid ³He in aerogel

When liquid ³He is impregnated into silica aerogel a solid-like layer of ³He atoms coats the silica structure. The surface ³He is in fast exchange with the liquid on NMR time scales. The exchange coupling of liquid ³He quasiparticles with the localized ³He spins modifies the scattering of ³He quasiparticles by the aerogel structure. In a magnetic field the polarization of the solid spins gives rise to a splitting of the scattering cross section of for “up” vs “down” spin quasiparticles, relative to the polarization of the solid ³He. We discuss this effect, as well as the effects of nonmagnetic scattering, in the context of a possible splitting of the superfluid transition for ↑↑ vs ↓↓ Cooper pairs for superfluid ³He in aerogel, analogous to the A₁ − A₂ splitting in bulk ³He. Comparison with the existing measurements of T_c for B < 5 kG, which shows no evidence of the A₁ − A₂ splitting, suggests a liquid-solid exchange coupling of order J ≃ 0.1 mK. Measurements at higher fields, B ≳ 20 kG, should saturate the polarization of the solid ³He and reveal the A₁ − A₂ splitting.