Algorithm for Molecular Dynamics Simulations of Spin Liquids

Omelyan, I. P.; Mryglod, I. M.; Folk, R.

doi:10.1103/physrevlett.86.898

Cited by 83 publications

(100 citation statements)

References 18 publications

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“…(2), we adopted an algorithm based on the second order Suzuki-Trotter (ST) decomposition of the non-commuting operators [33,50,51]. To obtain a reasonable level of accuracy as reflected by the energy and magnetization conservation, an integration time step of ∆t = 1 fs was used.…”

Section: Simulation Detailsmentioning

confidence: 99%

“…The idea of integrating spin dynamics with molecular dynamics was pioneered by Omelyan et al [33] in the context of a simple model for ferrofluids. The foundation of this combined molecular and spin dynamics (MD-SD) approach lies in the unification of an atomistic potential and a Heisenberg spin Hamiltonian, with the coupling between the atomic and spin subsystems established via a coordinate-dependent exchange interaction.…”

Section: Introductionmentioning

confidence: 99%

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Collective dynamics in atomistic models with coupled translational and spin degrees of freedom

et al. 2017

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Using an atomistic model that simultaneously treats the dynamics of translational and spin degrees of freedom, we perform combined molecular and spin dynamics simulations to investigate the mutual influence of the phonons and magnons on their respective frequency spectra and lifetimes in ferromagnetic bcc iron. By calculating the Fourier transforms of the space-and time-displaced correlation functions, the characteristic frequencies and the linewidths of the vibrational and magnetic excitation modes were determined. Comparison of the results with that of the standalone molecular dynamics and spin dynamics simulations reveal that the dynamic interplay between the phonons and magnons leads to a shift in the respective frequency spectra and a decrease in the lifetimes. Moreover, in the presence of lattice vibrations, additional longitudinal magnetic excitations were observed with the same frequencies as the longitudinal phonons.

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Section: Simulation Detailsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Collective dynamics in atomistic models with coupled translational and spin degrees of freedom

et al. 2017

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“…The development of efficient algorithms for solving the equations of motion in such systems should therefore impact a lot of fields of fundamental research. During the last decade a considerable activity [1][2][3][4][5][6][7][8][9] has been directed on the construction of symplectic time-reversible algorithms that employ decompositions of the evolution operators into analytically solvable parts. The decomposition algorithms exactly preserve all Poincaré invariants and, thus, are ideal for long-time integration in molecular dynamics [10] and astrophysical [11] simulations.…”

Section: Introductionmentioning

confidence: 99%

Construction of high-order force-gradient algorithms for integration of motion in classical and quantum systems

2002

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A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic algorithms are first derived up to the eighth order by direct decompositions of exponential propagators and further collected using an advanced composition scheme to obtain the algorithms of higher orders. Contrary to the scheme by Chin and Kidwell [Phys. Rev. E 62, 8746 (2000)], where high-order algorithms are introduced by standard iterations of a force-gradient integrator of order four, the present method allows to reduce the total number of expensive force and its gradient evaluations to a minimum. At the same time, the precision of the integration increases significantly, especially with increasing the order of the generated schemes. The algorithms are tested in molecular dynamics and celestial mechanics simulations. It is shown, in particular, that the efficiency of the new fourth-order-based algorithms is better approximately in factors 5 to 1000 for orders 4 to 12, respectively. The results corresponding to sixth-and eighthorder-based composition schemes are also presented up to the sixteenth order. For orders 14 and 16, such highly precise schemes, at considerably smaller computational costs, allow to reduce unphysical deviations in the total energy up in 100 000 times with respect to those of the standard fourth-order-based iteration approach.

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“…Due to the lack of thermal expansion coefficient data, C V values above 1000 K are not given [37]. For a fair comparison with the experimental results, we have added 3 2 k B to the DD and FS results to include the contribution of the kinetic energy based on the equipartition theorem. For the rigid lattice results, 3k B was added to include the contribution of both the kinetic energy and the lattice potential energy.…”

Section: Resultsmentioning

confidence: 99%

“…This demands sophisticated and improved magnetic models that are capable of providing a more realistic depiction of the material than that is possible with conventional spin models. A novel class of such improved models that continues to gain widespread attention are atomistic models that treat the dynamics of the translational (atomic) degrees of freedom on an equal footing with the spin (magnetic) degrees of freedom [1][2][3][4]. We will refer to such models as (coupled, dynamical) spin-lattice models.…”

Section: Introductionmentioning

confidence: 99%

Magnetic phase transition in coupled spin-lattice systems: A replica-exchange Wang-Landau study

2016

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Coupled, dynamical spin-lattice models provide a unique test ground for simulations investigating the finite-temperature magnetic properties of materials under the direct influence of the lattice vibrations. These models are constructed by combining a coordinate-dependent interatomic potential with a Heisenberg-like spin Hamiltonian, facilitating the treatment of both the atomic coordinates and spins as explicit phase variables. Using a model parameterized for bcc iron, we study the magnetic phase transition in these complex systems via the recently introduced, massively parallel replica-exchange Wang-Landau Monte Carlo method. Comparison with the results obtained from rigid lattice (spin only) simulations show that the transition temperature as well as the amplitude of the peak in the specific heat curve is marginally affected by the lattice vibrations. Moreover, the results were found to be sensitive to the particular choice of the interatomic potential.

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Algorithm for Molecular Dynamics Simulations of Spin Liquids

Cited by 83 publications

References 18 publications

Collective dynamics in atomistic models with coupled translational and spin degrees of freedom

Collective dynamics in atomistic models with coupled translational and spin degrees of freedom

Construction of high-order force-gradient algorithms for integration of motion in classical and quantum systems

Magnetic phase transition in coupled spin-lattice systems: A replica-exchange Wang-Landau study

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