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Ordinary magnetic measurements only see the surface of a superconductor, where barriers and viscous flows of magnetic field get in the way. Inside, in the so-called intermediate state, superconducting and normal domains coexist, separated by thin walls. These walls can oscillate, but hearing them directly has been difficult.

In the new work, instead of the magnetic response, they measured how a lead sample changes its length under an alternating magnetic field — an effect called magnetostriction. It turned out that the domain boundaries oscillate not with simple damping, as expected, but almost resonantly: the imaginary part of the response changes sign, and the real part behaves non-monotonically with frequency.

The authors attribute this to collective oscillations of the boundaries, pushed by eddy currents that arise in the normal domains. These currents, like whirlpools in a river, drag the walls and make them move in concert. The method turned out to be more sensitive than traditional magnetic measurements and for the first time allowed seeing this hidden channel of dynamics.

This approach is like a stethoscope applied to the internal boundaries of a superconductor. It opens the way to studying phases with spatial modulation in other materials, where boundaries may also hide their oscillations.

Original abstract

as written by the authors arXiv:2604.17333

The dynamics of phase boundaries, such as superconducting/normal (S/N) interfaces in type-I superconductors, are typically obscured in conventional magnetic measurements, which are dominated by surface barriers and over-damped flux processes. Here, we employ ac magnetostriction as a sensitive probe to reveal the distinct bulk dynamics of these domain walls in the intermediate state of lead. In contrast to the Debye-type relaxation observed in magnetic susceptibility, we discover a pronounced quasiresonant response characterized by a sign reversal of the imaginary component and a non-monotonic evolution of the real part with frequency. We attribute this behavior to the collective oscillations of S/N interfaces driven by eddy currents generated within the normal domains. This work uncovers a fundamental dynamical channel in superconducting modulated phases and establishes ac magnetostrictive coefficient as a powerful tool for probing hidden interface physics.