Linear and nonlinear low-frequency electrodynamics of surface superconducting states in an yttrium hexaboride single crystal

Abstract

We report on the low-frequency dynamics of surface superconducting states in yttrium hexaboride single crystal. Tunneling and dc magnetization experiments demonstrate that ${\text{YB}}_{6}$ is a classical type-II BCS superconductor with a slightly suppressed order parameter near the surface. The ac response at frequencies 10--1500 Hz has been measured for fields ${H}_{0}$ parallel to the crystal surface. We found that for ${H}_{0}>{H}_{c2}$ the dc magnetic moment completely disappeared, while the ac response exhibited the presence of surface superconductivity. Increasing ${H}_{0}$ above ${H}_{c2}$ revealed the loss maximum in a field between ${H}_{c2}$ and ${H}_{c3}$ with a magnitude considerably larger than in mixed or normal states. In some dc fields the frequency dependence of the real part of the susceptibility is reminiscent of a spin-glass system. At the same time the imaginary component exhibits frequency dispersion which is not a typical feature of the classical spin-glass response. Analysis of the experimental data with the Kramers--Kronig relations showed the possible existence of the loss peak at very low frequencies. It was found that the amplitude of the third harmonic was not a cubic function of the ac amplitude (as it follows from the perturbation theory) even at very low excitation levels. It was shown that the critical state model cannot adequately describe the existing experimental data. The proposed model of a slow relaxing of the order parameter allows one to understand the origin of partial shielding and losses for ${H}_{0}>{H}_{c2}$.