Adiabatic spin dynamics and effective exchange interactions from constrained tight-binding electronic structure theory: Beyond the Heisenberg regime

Abstract

We consider an implementation of the adiabatic spin dynamics approach in a tight-binding description of the electronic structure. The adiabatic approximation for spin-degrees of freedom assumes that the faster electronic degrees of freedom are always in a quasi-equilibrium state, which significantly reduces the numerical complexity in comparison to the full electron dynamics. Non-collinear magnetic configurations are stabilized by a constraining field, which allows to directly obtain the effective magnetic field from the negative of the constraining field. While the dynamics are shown to conserve energy, we demonstrate that adiabatic spin dynamics does not conserve the total spin angular momentum when the lengths of the magnetic moments are allowed to change, which is confirmed by numerical simulations. Furthermore, we develop a method to extract an effective two-spin exchange interaction from the energy curvature tensor of non-collinear states, which we calculate at each time step of the numerical simulations. We demonstrate the effect of non-collinearity on this effective exchange and limitations due to multi-spin interactions in strongly non-collinear configurations beyond the regime where the Heisenberg model is valid. The relevance of the results are discussed with respect to experimental pump-probe experiments that follow the ultra-fast dynamics of magnetism.

arXiv comment13 pages, 13 figures

References in corpus (28)

• Applications of a tight-binding total energy method for transition and noble metals: Elastic Constants, Vacancies, and Surfaces of Monatomic Metals
• Exchange interaction parameters and adiabatic spin-wave spectra of ferromagnets: A "renormalized magnetic force theorem"
• Microscopic origin of Heisenberg and non-Heisenberg exchange interactions in ferromagnetic bcc Fe
• Systematic derivation of realistic spin-models for beyond-Heisenberg solids
• Stable and fast semi-implicit integration of the stochastic Landau-Lifshitz equation
• Many-body theory of ultrafast demagnetization and angular momentum transfer in ferromagnetic transition metals
• Different dimensionality trends in the Landau damping of magnons in iron, cobalt and nickel: time dependent density functional study
• Magnetism of iron: from the bulk to the monoatomic wire
• Magnetic susceptibility, exchange interactions and spin-wave spectra in the local spin density approximation
• The exchange coupling and spin waves in metallic magnets: removal of the long-wave approximation
• Extension of the standard Heisenberg Hamiltonian to multispin exchange interactions
• Exchange interactions and magnetic force theorem
• Gilbert damping in noncollinear ferromagnets
• Prospecting chiral multi-site interactions in prototypical magnetic systems
• First-principles Dzyaloshinskii-Moriya interaction in a non-collinear framework
• {\it Ab initio} studies of spin-spiral waves and exchange interactions in 3{\it d} transition metal atomic chains
• Pressure induced bcc to hcp transition in Fe: Magnetism-driven structure transformation
• Magnetic interactions in strongly correlated systems: spin and orbital contributions
• Theory of non-collinear interactions beyond Heisenberg exchange; applications to bcc Fe
• Polarisation-dependent single-pulse ultrafast optical switching of an elementary ferromagnet
• Exchange coupling constants at finite temperature
• Gilbert damping in non-collinear magnetic system
• Equation of motion and the constraining field in ab initio spin dynamics
• Ultrafast spin dynamics in inhomogeneous systems: a density-matrix approach applied to Co/Cu interfaces
• Exchange constants for local spin Hamiltonians from tight-binding models
• Langevin spin dynamics based on ab initio calculations: numerical schemes and applications
• Spin dynamics from a constrained magnetic Tight-Binding model
• Generalization of the Landau-Lifshitz-Gilbert equation by multi-body contributions to Gilbert damping for non-collinear magnets