Magnetic Relaxation and Minority Spin Condensate in Spin-Polarized Superfluid $^3$He A$_1$

The magnetic relaxation phenomena in superfluid $^3$He A$_1$ phase are studied using a magnetic fountain pressure detector in which a large reservoir is connected to a small sensor chamber through two superleak channels of height 18 $\mu$m. Superflow in simultaneous mass/spin current is driven by an externally applied magnetic field. Measurements of the relaxation of the induced fountain pressure are carried out under a variety of conditions including pressure(3 - 29 bar), temperature, static field(up to 8 T) and $^4$He(5 monolayers) coverage. The relaxation of the fountain pressure arises from the time dependent spin density in the sensor chamber. The observed relaxation time $\tau$ varies from 80 s near the upper transition temperature, T$_{c1}$, to less than 0.1 s near the lower transition temperature, T$_{c2}$. The measured relaxation rate increases starting near the middle of A$_1$ phase and more rapidly as the T$_{c2}$ is approached. The $^4$He coverage is observed not to affect the measured spin relaxation rate and this indicates that the relaxation is a bulk liquid effect. The rapid increase in relaxation rate is interpreted in terms of the Leggett-Takagi$^1$ mechanism of intrinsic spin relaxation arising from a small but increasing presence of minority spin pair condensate$^2$(with pair magnetic moment aligned in the opposite direction to the applied field) in A$_1$ phase as T$_{c2}$ is approached. It is concluded that the conventional view of the superfluid A$_1$ phase being composed of condensate pairs with magnetic moment aligned strictly along the applied field is inadequate. \newline $^1$ A.J. Leggett and S. Takagi, Ann. Phys. \textbf{106}, 79(1977). \newline $^2$ H. Monien and L. Tewordt, J. Low Temp. Phys. \textbf{60}, 323(1985).