Spin Wave Resonance

Spin wave resonance (SWR) consists of exciting waves of spins called magnons in thin magnetic films. For SWR, the field is applied normal to the film surface. For certain frequencies (harmonics), resonances are generated.

These resonance fields are analogous to the energy levels of a quantum well. The magnetization profile is analogous to the well potential.

SWR	Quantum Well
M(z)	V(x)

Hn	En

For a uniform magnetization (square well) the resonance spacing are quadratic in field. This produces the so-called Kittel modes. This the SWR spectrum of a magnetic thin film.

Indeed, the resonance positions vary quadratically with mode number. The slope of the line gives us the value of the spin wave stiffness, D, an essential parameter in any theory of magnetic materials.

For samples that have a magnetization which varies quadratically with position, the analogous problem in quantum mechanics is the simple harmonic oscillator (SHO). As we know that the energy levels in the SHO are evenly spaced, so are the resonance positions in such a film as seen from this spectrum:

There are other sorts of information one can retrieve from SWR, but its principle uses are the determination of the spin wave stiffness and the determination of magnetic profiles.

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