We study the universal far from equilibrium dynamics of magnons in Heisenberg ferromagnets. We show that such systems exhibit universal scaling in momentum and time of the quasiparticle distribution function, with the universal exponents distinct from those recently observed in Bose-Einstein condensates. This new universality class originates from the SU(2) symmetry of the Hamiltonian, which leads to a strong momentum-dependent magnon-magnon scattering amplitude. We compute the universal exponents using the Boltzmann kinetic equation and incoherent initial conditions that can be realized with microwave pumping of magnons. We compare our numerical results with analytic estimates of the scaling exponents and demonstrate the robustness of the scaling to variations in the initial conditions. Our predictions can be tested in quench experiments of spin systems in optical lattices and pump-probe experiments in ferromagnetic insulators such as yttrium iron garnet.
Using a functional renormalization group approach we show that at low temperatures and in a certain range of magnetic fields the longitudinal dynamic structure factor of quantum Heisenberg ferromagnets in dimensions $D\leq 2$ exhibits a well-defined quasi-particle peak with linear dispersion that we identify as zero-magnon sound. In $D>2$ the larger phase space available for the decay into transverse spin waves leads only to a broad hump centered at zero frequency whose width scales linearly in momentum.
Thickness dependent Curie temperature and power-law behavior of layering transitions in ferromagnetic classical and quantum thin films described by Ising, XY and Heisenberg models
We characterize the universal far-from-equilibrium dynamics of the two-dimensional quantum Heisenberg magnet isolated from its environment. For a broad range of initial conditions, we find a long-lived universal prethermal regime characterized by self-similar behavior of spin-spin correlations. We analytically derive the spatial-temporal scaling exponents and find excellent agreement with numerics using phase space methods. The scaling exponents are insensitive to the choice of initial conditions, which include coherent and incoherent spin states with values of total magnetization and energy i…
Today, further downscaling of mobile electronic devices poses serious problems, such as energy consumption and local heat dissipation. In this context, spin wave majority gates made of very thin ferromagnetic films may offer a viable alternative. However, similar downscaling of magnetic thin films eventually enforces the latter to operate as quasi-two dimensional magnets, the magnetic properties of which are not yet fully understood, especially those related to anisotropies and external magnetic fields in arbitrary directions. To this end, we have investigated the behaviour of an easy-plane an…
The Quantum Heisenberg Ferromagnet can be naturally reformulated in terms of interacting bosons (called spin waves or magnons) as an expansion in the inverse spin size. We calculate the first order interaction correction to the free energy, as an upper bound in the limit where the spin size $S \to \infty$ and $βS$ is fixed ($β$ being the inverse temperature). Our result is valid in two and three spatial dimensions. We extrapolate our result to compare with Dyson's low-temperature expansion. While our first-order correction has the expected temperature dependance, in higher orders of the pertur…
The Monte Carlo method is a powerful technique for computing thermodynamic magnetic states of otherwise unsolvable spin Hamiltonians, but the method becomes computationally prohibitive with increasing number of spins and the simulation of real materials and nanostructures is cumbersome. This paper presents the acceleration of Monte Carlo simulations of the three-dimensional anisotropic Heisenberg model on Graphics-Processing Units (GPU). The GPU implementation of the method presented here provides an acceleration of two orders of magnitude over conventional implementations and enables the simu…
We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins $S\geq 1/2$. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution to the free energy at low temperatures. Our proof comes with explicit, constructive upper and lower bounds on the error term. It uses in an essential way the bosonic formulation of the model in terms of the Holstein-Primakoff representation. In this language, the model describes interacting bosons with a hard-core on-site repulsion and a nearest-neigh…
