Frequency non-reciprocity of surface spin wave in Permalloy thin films

TL;DR

This study investigates the frequency non-reciprocity of surface spin waves in Permalloy thin films, revealing how it depends on film thickness and wave vector, and proposing its use as a probe for magnetic asymmetries.

Contribution

The paper introduces an analytical model explaining frequency non-reciprocity in thin films considering surface anisotropies and modal profiles, supported by experimental observations.

Findings

Frequency non-reciprocity scales linearly with wave vector at thin films.

Non-reciprocity scales quadratically with film thickness below 20 nm.

Complex behavior observed at larger film thicknesses.

Abstract

Surface spin waves in thin Permalloy films are studied by means of propagative spin wave spectroscopy. We observe a systematic difference of up to several tens of MHz when comparing the frequencies of counter-propagating waves. This frequency non-reciprocity effect is modeled using an analytical dipole-exchange theory that considers the mutual influence of non-reciprocal spin wave modal profiles and differences in magnetic anisotropies at the two film surfaces. At moderate film thickness (20 nm and below), the frequency non-reciprocity scales linearly with the wave vector and quadratically with the thickness, whereas a more complex non-monotonic behavior is observed at larger thickness. Our work suggests that surface wave frequency non-reciprocity can be used as an accurate spectroscopic probe of magnetic asymmetries in thin ferromagnetic films.