NMR experiments on rotating superfluid ³He-A and ³He-B and their theoretical interpretation

We have constructed a rotating nuclear demagnetization cryostat and used it for continuous-wave NMR experiments on superfluid³He-A and³He-B. The measurements were performed in a long cylindrical geometry of 5 mm diameter, with the cylinder axis parallel to the axis of rotation and with the external magnetic field H₀=284 or 142 Oe in the same direction. The angular velocity of rotation Ω was varied between 0.2 and 1.5 rad/sec, and the experiments were done under 29.3 bar pressure at temperatures between T_c=2.72 and about 1.4 mK. As a guide to the new and esoteric field of superfluid³He in rotation, we first review the general theory at some length in relatively simple terms. Pictorial explanations are often given. In³He-A, a rotation-dependent NMR satellite was found; its intensity a rotation-dependent NMR satellite peak was discovered; its relative intensity increases linearly with Ω. The position of the satellite is independent of Ω and H, and does not depend on whether the sample was cooled from the Fermi-liquid region to the A phase while rotating or at rest. At temperatures 0.1ct=0.86-1.1(1-T/T_c). Cooldown under rotation produced systematically larger satellite intensities than cooldown at rest. A second, metastable satellite, best seen at rest and disappearing in less than 30 min, was also discovered. Furthermore, the main NMR peak broadens during rotation, while the total NMR absorption remains the same. The behavior of the rotation-dependent satellite strongly supports the existence of vortices in³He-A, their number being proportional to Ω; the satellite is caused by localized spin wave modes trapped by vortex cores. Theoretical calculations agree quite well with our experimental data if continuous vortices, without a singularity in the order parameter, are assumed. Their presence is also responsible for the additional broadening of the main peak, due either to increased spin diffusion or to scattering of spin waves. The metastable satellite is caused by textural boundaries, probably by twist solitons in the superfluid, created by the rapid cooldown of the sample. In³He-B, a series of nearly equally spaced NMR satellites was found on the high-frequency side of the main peak with the cryostat at rest. Under rotation the separation between the satellites increases linearly with Ω. The spacing displays a jump, proportional to Ω, at 1-T/T_c=0.40. The discontinuity occurred only during start/stop experiments, not if the cryostat was continuously rotated while warming over the transition region. Immediately after rotation had been started the whole NMR spectrum shifted toward higher frequencies for about 30 sec; these transients were seen only at Ω>0.25 rad/sec. In³He-B, the order parameter is strongly influenced by the wall of the container, producing the so-called flareout texture, with the angle β between the {Mathematical expression} vector and H equal to 63° at the walls. The satellites can be explained as spin wave modes arising from an almost harmonic potential well formed by the {Mathematical expression} texture. The creation of vortices changes the texture and increases the steepness of the potential and therefore increases the satellite spacing during rotation. The vortices themselves perturb the {Mathematical expression} texture due to the long-range orientating effect of their cores on the order parameter. The discontinuity in the satellite splitting at 1-T/T_c=0.40 is explained as being due to a first-order phase change in the vortex core at this temperature. The transient shift in the NMR spectrum, immediately after the start of rotation when vortices are not yet present, is caused by the large superfluid vs. normal liquid counterflow; this phenomenon thus gives an estimate for the time needed to create vortices in³He-B.