Minority Spin Condensate in Spin-Polarized Superfluid $^3$He-A$_1$ Phase

The spin-polarized superfluid $^3$He A$_1$ phase, which forms below 3 mK in external magnetic field, serves as a material in which theoretical notions of fundamental magnetic processes and macroscopic quantum spin phenomena may be tested. Conventionally, the superfluid component of the A$_1$ phase is understood to contain only the majority spin condensate having energetically-favoured paired spins directed along the external field and no minority spin condensate having paired spins in the opposite direction. We have developed a novel mechanical spin density detector to measure the spin relaxation in the A$_1$ phase as functions of temperature, pressure and magnetic field. The mechanical spin detector is based in principle on the unique magnetic fountain effect occurring only in the A$_1$ phase (occurring between two transition temperatures, T$_{c1}$ and T$_{c2}$). Unexpectedly, the spin relaxation rate increases rapidly as the temperature is decreased towards T$_{c2}$. Our measurements, together with Leggett-Takagi and Monien-Tewordt theories, demonstrate that a minute presence of minority spin pairs is responsible for the unexpected spin relaxation phenomena in A$_1$ phase.