A method for atomistic spin dynamics simulations: implementation and examples

We present a method for performing atomistic spin dynamic simulations. A comprehensive summary of all pertinent details for performing the simulations such as equations of motions, models for including temperature, methods of extracting data and numerical schemes for performing the simulations is given. The method can be applied in a first principles mode, where all interatomic exchange is calculated self-consistently, or it can be applied with frozen parameters estimated from experiments or calculated for a fixed spin-configuration. Areas of potential applications to different magnetic questions are also discussed. The method is finally applied to one situation where the macrospin model breaks down; magnetic switching in ultra strong fields.Comment: 14 pages, 19 figure

Microscopic Theory for Coupled Atomistic Magnetization and Lattice Dynamics

A coupled atomistic spin and lattice dynamics approach is developed which merges the dynamics of these two degrees of freedom into a single set of coupled equations of motion. The underlying microscopic model comprises local exchange interactions between the electron spin and magnetic moment and the local couplings between the electronic charge and lattice displacements. An effective action for the spin and lattice variables is constructed in which the interactions among the spin and lattice components are determined by the underlying electronic structure. In this way, expressions are obtained for the electronically mediated couplings between the spin and lattice degrees of freedom, besides the well known inter-atomic force constants and spin-spin interactions. These former susceptibilities provide an atomistic ab initio description for the coupled spin and lattice dynamics. It is important to notice that this theory is strictly bilinear in the spin and lattice variables and provides a minimal model for the coupled dynamics of these subsystems and that the two subsystems are treated on the same footing. Questions concerning time-reversal and inversion symmetry are rigorously addressed and it is shown how these aspects are absorbed in the tensor structure of the interaction fields. By means of these results regarding the spin-lattice coupling, simple explanations of ionic dimerization in double anti-ferromagnetic materials, as well as, charge density waves induced by a non-uniform spin structure are given. In the final parts, a set of coupled equations of motion for the combined spin and lattice dynamics are constructed, which subsequently can be reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations for spin dynamics and damped driven mechanical oscillator for the ...Comment: 22 pages, including 7 pages of Appendix and references, 6 figure

Atomistic spin dynamics of the CuMn spin glass alloy

We demonstrate the use of Langevin spin dynamics for studying dynamical properties of an archetypical spin glass system. Simulations are performed on CuMn (20% Mn) where we study the relaxation that follows a sudden quench of the system to the low temperature phase. The system is modeled by a Heisenberg Hamiltonian where the Heisenberg interaction parameters are calculated by means of first-principles density functional theory. Simulations are performed by numerically solving the Langevin equations of motion for the atomic spins. It is shown that dynamics is governed, to a large degree, by the damping parameter in the equations of motion and the system size. For large damping and large system sizes we observe the typical aging regime.Comment: 18 pages, 9 figure

Simulation of a spin-wave instability from atomistic spin dynamics

We study the spin dynamics of a Heisenberg model at finite temperature in the presence of an external field or a uniaxial anisotropy. For the case of the uniaxial anisotropy our simulations show that the macro moment picture breaks down. An effect which we refer to as a spin-wave instability (SWI) results in a non-dissipative Bloch-Bloembergen type relaxation of the macro moment where the size of the macro moment changes, and can even be made to disappear. This relaxation mechanism is studied in detail by means of atomistic spin dynamics simulations.Comment: 8 pages, 12 figures, submitted to PR

Dynamics of diluted magnetic semiconductors from atomistic spin dynamics simulations: Mn doped GaAs as a case study

The dynamical behavior of the magnetism of diluted magnetic semiconductors (DMS) has been investigated by means of atomistic spin dynamics simulations. The conclusions drawn from the study are argued to be general for DMS systems in the low concentration limit, although all simulations are done for 5% Mn-doped GaAs with various concentrations of As antisite defects. The magnetization curve, $M(T)$, and the Curie temperature $T_C$ have been calculated, and are found to be in good correspondence to results from Monte Carlo simulations and experiments. Furthermore, equilibrium and non-equilibrium behavior of the magnetic pair correlation function have been extracted. The dynamics of DMS systems reveals a substantial short ranged magnetic order even at temperatures at or above the ordering temperature, with a non-vanishing pair correlation function extending up to several atomic shells. For the high As antisite concentrations the simulations show a short ranged anti-ferromagnetic coupling, and a weakened long ranged ferromagnetic coupling. For sufficiently large concentrations we do not observe any long ranged ferromagnetic correlation. A typical dynamical response shows that starting from a random orientation of moments, the spin-correlation develops very fast ($\sim$ 1ps) extending up to 15 atomic shells. Above $\sim$ 10 ps in the simulations, the pair correlation is observed to extend over some 40 atomic shells. The autocorrelation function has been calculated and compared with ferromagnets like bcc Fe and spin-glass materials. We find no evidence in our simulations for a spin-glass behaviour, for any concentration of As antisites. Instead the magnetic response is better described as slow dynamics, at least when compared to that of a regular ferromagnet like bcc Fe.Comment: 24 pages, 15 figure

Simulation of a spin-wave instability from atomistic spin dynamics

We study the spin dynamics of a Heisenberg model at finite temperature in the presence of an external field or a uniaxial anisotropy. For the case of the uniaxial anisotropy our simulations show that the macro moment picture breaks down. An effect which we refer to as a spin-wave instability (SWI) results in a non-dissipative Bloch-Bloembergen type relaxation of the macro moment where the size of the macro moment changes, and can even be made to disappear. This relaxation mechanism is studied in detail by means of atomistic spin dynamics simulations.Comment: 8 pages, 12 figures, submitted to PR

Ultrafast cooling and heating scenarios for the laser-induced phase transition in CuO

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Exchange Coupling and Exchange Bias in FM/AFM Bilayers for a Fully Compensated AFM Interface

We address the interlayer coupling in a ferromagnet/antiferromagnet bilayer where the interface of the antiferromagnet is fully compensated. We discuss the role of different types of exchange interaction for the interlayer coupling and exchange bias. We propose two types of corrections to the ideal Heisenberg Hamiltonian which may explain exchange bias. The first is a correction for the angular dependence of the exchange interactions and the second a correction due to magnetostriction and interface imperfections. The first correction contributes to an anisotropy at the interface and favors either parallel or perpendicular coupling across the interface. The second correction contributes to the exchange bias. Our analysis is based on atomic spin dynamics simulations, and our results show that small corrections to the ideal Heisenberg Hamiltonian may have macroscopic consequences in systems with frustrated interatomic interactions

Ultrafast spin dynamics in multisublattice magnets

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