Magnon Gas Research Articles

Magnon-drag Peltier effect in a Ni-Cu alloy

Peltier-effect measurements to an accuracy of 1% have been made on ${\mathrm{Ni}}_{66}$${\mathrm{Cu}}_{34}$ and ${\mathrm{Ni}}_{69}$${\mathrm{Fe}}_{31}$ at 1.3-4.2 K and magnetic fields to 5.5 T. The Peltier coefficient $\ensuremath{\pi}$ is proportional to ${T}^{2}$ as expected for electron diffusion. However, the absolute value of $\ensuremath{\pi}$ decreases by 7% in Ni-Cu and 4% in Ni-Fe when the field is increased from just above ferromagnetic saturation to 5.5 T, at 4.2 K. This decrease is consistent with a magnon-drag contribution to the Peltier coefficient, which is quenched by the field, at least in the case of Ni-Cu. The magnitude of the contribution, when combined with Hall data, indicates that the magnon gas drifts at a speed close to that of the $4s$ electron gas. Using a simple kinetic theory this implies that magnons relax faster on $4s$ electrons than on impurities. Interpretation of Ni-Fe data is not so clear.

Longitudinal Susceptibility of a Planar Ferromagnet

The longitudinal susceptibility ${\ensuremath{\chi}}_{\mathrm{zz}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},\ensuremath{\omega})$ of a spin-\textonehalf{} planar ferromagnet is investigated. The random-phase approximation is used and particular emphasis is placed on the long-wave-length behavior. The static susceptibility for temperatures in the vicinity of the Curie point is calculated. Correlation lengths above and below ${T}_{C}$ are obtained. In the region below ${T}_{C}$ the expression for ${\ensuremath{\chi}}_{\mathrm{zz}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},\ensuremath{\omega})$ is compared with the susceptibility of an ideal magnon gas. Departures from ideal-gas behavior near the Curie point are studied. The relevance of the findings to recent hydrodynamic- and dynamic-scaling-law theories is discussed.

Hydrodynamic modes in a gas of magnons

Density waves analogous to second sound are studied in a gas of magnons. Quasiparticle interaction is considered for both equilibrium and non equilibrium thermodynamics. The non equilibrium theory is based on a Boltzmann equation for magnon-magnon scattering. Contrary to the total energy and magnetization, (quasi)-momentum is not strictly conserved. In the hydrodynamic regime, the transport equation is reduced to a set of two coupled equations for the magnetization and the local temperature. For low temperatures these have diffusive and propagating solutions while for high temperatures, where momentum is dissipated by Umklapp processes, the solutions are only diffusive. The magnetization response function and the corresponding spectral function are discussed for various wavenumbers and temperatures.

Magnon Density Fluctuations in the Heisenberg Ferromagnet

It is shown, by means of a decoupling procedure for the equations of motion of a spin system governed by the Heisenberg Hamiltonian, that the distribution of magnons in phase space satisfies the quantum-mechanical Boltzmann equation at low temperatures. We conclude from this that disturbances in the longitudinal component of the magnetization, which may be thought of as density fluctuations in the gas of magnons, propagate essentially undamped at long wavelengths, in complete analogy with the propagation of sound in a gas of real particles. The interaction of this hydrodynamic mode with phonons is considered, and the damping coefficient of the phonons when their velocity coincides with the magnon sound velocity is obtained.

Magnon-Density Fluctuations in the Heisenberg Ferromagnet

It is shown, by means of a decoupling procedure for the equations of motion of a spin system governed by the Heisenberg Hamiltonian, that the distribution of magnons in phase space satisfies the quantum-mechanical Boltzmann equation at low temperatures. We conclude from this that disturbances in the longitudinal component of the magnetization, which may be thought of as density fluctuations in the gas of magnons, propagate essentially undamped at long wavelengths, in complete analogy with the propagation of sound in a gas of real particles. The interaction of this hydrodynamic mode with phonons is considered, and the damping coefficient of the phonons when their velocity coincides with the magnon sound velocity is obtained.