Using a glass-capacitance technique, we have measured the thermal-boundary resistance $R_K$ between liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and thin silver films on a flat glass substrate in the millikelvin regime. For $T>\mathrm{}30\mathrm{}$ mK, the experimental observations are in excellent agreement with the acoustic mismatch theory. For $T<\mathrm{}30\mathrm{}$ mK, we find concrete evidence supporting the magnetic coupling mechanism: (i) observation of a minimum in $R_K$ as a function of magnetic field, (ii) a decrease in $R_K$ as ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ pressure is increased, and (iii) a nearly order-of-magnitude increase in $R_K$ resulting from preplating the silver surface with monolayers of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ (with no such effect at $T>\mathrm{}30\mathrm{}$ mK).

• Received 2 February 1996

DOI:https://doi.org/10.1103/PhysRevB.54.R9639