Measuring the dispersion relations of spin wave bands using time-of-flight spectroscopy

Abstract

We develop a generic all-inductive procedure to measure the dispersion relation of spin waves in a magnetic stripe. Our method works even if several spin wave branches coexist in the investigated frequency interval, provided that the branches possess sufficiently different group velocities. We first measure the microwave scattering matrix of a network composed of distant antennas inductively coupled to the spin wave bath of a magnetic stripe. The antenna-to-antenna coupling that is independent from the applied magnetic field are suppressed by an appropriate calibration to get the complex spin wave transmission coefficient versus frequency. A comparison with the expected contribution of when a single spin wave mode exists argues for the existence of several spin wave branches in the magnetic conduit (Fig. 1). After a mathematical transformation to the time-domain to get the transmission impulse response, the different spin wave branches are viewed as wavepackets that reach successively the receiving antenna after different travel times (Fig. 2) determined by their group velocities. In analogy with time-of flight spectroscopy, the wavepackets are then separated by time-gating. The time-gated responses are used to recalculate the contribution of each spin wave branch to the frequency domain scattering matrix. The dispersion relation of each branch stems from the absolute phase of the time-gated transmission parameter. The spin wave wavevector can be determined unambiguously if the results for several propagation distances are combined, so as to get the dispersion relations of each band, and in the end the full band structure of the spin waves [1].   Measuring the dispersion relations of spin wave bands using time-of-flight spectroscopy