An Efficient Geometric Integrator for Thermostatted Anti-/Ferromagnetic Models

Arponen, Teijo; Leimkuhler, Benedict

doi:10.1023/b:bitn.0000046812.08252.34

Cited by 7 publications

(9 citation statements)

References 24 publications

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“…indicates an average over possible realizations of the fluctuating field [17], δ α,β is Kronecker delta function and δ (t 1 − t 2 ) is a Dirac delta function. A semi-implicit method devised by Mentink et al [41] is adopted here to (i) properly integrate the LLG equation, which is a Stratonovich stochastic differential equation [17] (the need to properly integrate LLG equation is a pivotal point that has been discussed in several studies [17,[41][42][43][44][45]); and (ii) to enforce the conservation of the magnetic moments' magnitude. The Mentink algorithm is efficient by limiting the matrix inversion procedure -which is needed by an implicit integrator -for each magnetic moment at each time step.…”

Section: Lk13183 R Ementioning

confidence: 99%

Atomistic Molecular Dynamic Simulations of Multiferroics

2012

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A first-principles-based approach is developed to simulate dynamical properties, including complex permittivity and permeability in the GHz-THz range, of multiferroics at finite temperatures. It includes both structural degrees of freedom and magnetic moments as dynamic variables in Newtonian and Landau-Lifshitz-Gilbert (LLG) equations within molecular dynamics, respectively, with the couplings between these variables being incorporated. The use of a damping coefficient and of the fluctuation field in the LLG equations is required to obtain equilibrated magnetic properties at any temperature. No electromagnon is found in the spin-canted structure of BiFeO3. On the other hand, two magnons with very different frequencies are predicted via the use of this method. The smallest-in-frequency magnon corresponds to oscillations of the weak ferromagnetic vector in the basal plane being perpendicular to the polarization while the second magnon corresponds to magnetic dipoles going in and out of this basal plane. The large value of the frequency of this second magnon is caused by static couplings between magnetic dipoles with electric dipoles and oxygen octahedra tiltings.

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Section: Lk13183 R Ementioning

confidence: 99%

Atomistic Molecular Dynamic Simulations of Multiferroics

2012

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“…This way of thermostating the temperature was also applied to a spin system but was rarely tested in realistic spin dynamics. 61,62 Nevertheless, accelerated simulations of large systems have recently been investigated and proven to be competitive with the stochastic method. 63 In the stochastic approach, the particles are subject to some random process which alters their momenta.…”

Section: B Canonical Ensemble: Nvt Algorithmmentioning

confidence: 99%

Anisotropic magnetic molecular dynamics of cobalt nanowires

2012

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An investigation of thermally induced spin and lattice dynamics of a cobalt nanowire on a (111)Pt substrate is presented via magnetic molecular dynamics. This dynamical simulation model treats each atom as a particle supporting a classical spin. A coordinate dependent on both exchange and anisotropic functions ensures a minimal coupling between the spin and the lattice degrees of freedom to translate the magnetostrictive behavior of most magnetic materials. A spin-pair model of anisotropy is proposed to connect to the lattice thermodynamics. In order to solve linked spin-coordinate equations of motion, the efficiencies of algorithms based on SuzukiTrotter decompositions are compared. The temperature dependence of the magnetic behavior of Co nanowires is investigated through thermal stochastic connections with mechanical and spin Langevin noises. From a magnetic Hamiltonian parametrized on ab initio calculations, the size dependence of the energy barriers and characteristic time scales of the magnetization relaxation are computed. In the superparamagnetic limit, it is shown that all spins in a nanowire evolve in a coherent rotation. When the size of the single nanowire increases, nucleations of domain walls let the activation energy be independent of the length of the wire.

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“…To tackle this problem, Bulgac and Kusnezov (BK) introduced a deterministic constant-temperature dynamics [22][23][24] which can be applied to spins. A number of numerical approaches to integration of spin dynamics can be found in the literature [25][26][27][28]. However, BK dynamics, as any other deterministic canonical phase space flow, is able to correctly sample the canonical distribution only if the motion in phase space is ergodic on the timescale of the simulation.…”

Section: Introductionmentioning

confidence: 99%

Bulgac-Kusnezov-Nosé-Hoover thermostats

Sergi

Ezra

2010

Phys. Rev. E

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In this paper we formulate Bulgac-Kusnezov constant temperature dynamics in phase space by means of non-Hamiltonian brackets. Two generalized versions of the dynamics are similarly defined: one where the Bulgac-Kusnezov demons are globally controlled by means of a single additional Nosé variable, and another where each demon is coupled to an independent Nosé-Hoover thermostat. Numerically stable and efficient measure-preserving time-reversible algorithms are derived in a systematic way for each case. The chaotic properties of the different phase space flows are numerically illustrated through the paradigmatic example of the one-dimensional harmonic oscillator. It is found that, while the simple Bulgac-Kusnezov thermostat is apparently not ergodic, both of the Nosé-Hoover controlled dynamics sample the canonical distribution correctly. * Electronic address: sergi@ukzn.ac.za † Electronic address: gse1@cornell.edu

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An Efficient Geometric Integrator for Thermostatted Anti-/Ferromagnetic Models

Cited by 7 publications

References 24 publications

Atomistic Molecular Dynamic Simulations of Multiferroics

Atomistic Molecular Dynamic Simulations of Multiferroics

Anisotropic magnetic molecular dynamics of cobalt nanowires

Bulgac-Kusnezov-Nosé-Hoover thermostats

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