Coefficient of ultrasound transmission from liquid helium to aluminum in the intermediate state at T ≈ 0.1 K

The coefficient α(θ) of ultrasound transmission from liquid 4He to an aluminum single crystal in intermediate, superconducting, and normal states at a temperature T ≈ 0.1 K is measured as a function of the polar angle θ at the azimuthal angle φ = 0. The experimental technique is based on the measurement of the Kapitza temperature jump at the interface between two media. The dependences of the transmission coefficient for the Rayleigh modes on the sound frequency (in the range 13–194 MHz) and the magnetic field strength are determined. It is demonstrated that the integrated transmission coefficient of the aluminum single crystal in the intermediate state at an angle θR larger than the critical value increases with an increase in the magnetic field strength. The integrals of the transmission coefficient in magnetic fields close to the field Hc are independent of the frequency. In the vicinity of H = 0, the transmission coefficient at ν > 39 MHz increases only slightly with increasing frequency. At the lowest frequencies, the transmission coefficient increases anomalously as the frequency decreases. The experimental data are compared with the results obtained in the framework of the Andreev theory. Numerical calculations are performed and the dependences α(θ, φ) for bulk modes in the range corresponding to angles smaller than the critical value are constructed for the three principal planes of the crystal, i.e., the (001), (011), and (111) planes. The dependence α(θ) is obtained for the azimuthal angle φ = 0. The width of the Rayleigh peak is estimated.