Magnetic Nanoparticles as Many-Spin Systems

Kachkachi, Hamid; Garanin, D. A.

doi:10.1007/0-387-26018-8_3

Cited by 19 publications

(15 citation statements)

References 38 publications

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“…This kind of structure has been the basis of many theoretical studies using the Heisenberg Hamiltonian (see, e.g., Refs. 7,14,17,18,20,21,23).…”

Section: A Computing Methodsmentioning

confidence: 99%

“…We consider the atomistic model of a magnetic nanoparticle consisting of N classical spins s i (with |s i | = 1) taking account of its lattice structure, shape, and size 7,12,[14][15][16][17][18][19][20][21] . The magnetic properties of the particle can be described by the anisotropic Heisenberg model…”

Section: From the Atomistic To The Effective Energymentioning

confidence: 99%

“…(9). One obtains 27 an additional mixed contribution that is second order in K s and first order in K c…”

mentioning

confidence: 99%

“…where g(m) is a function of m α which comprises, among other contributions, both the 2 nd -and 4 th -order contributions in spin components 27 . For example for sc lattice, g(θ, ϕ = 0) = − cos 2 θ +3 cos 4 θ −2 cos 6 θ, which is shown later to give agreement with numerical simulations.…”

mentioning

confidence: 99%

“…Thus we have seen that in most cases the effective anisotropy of a magnetic particle, considered as a single magnetic moment, can be approximately described as a combination of uniaxial and cubic anisotropies 18,21,27 . Consequently, collecting all these contributions and defining the EOSP energy as…”

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confidence: 99%

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Effective anisotropies and energy barriers of magnetic nanoparticles with Néel surface anisotropy

et al. 2007

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R. Evans and R. W. ChantrellDepartment of Physics, University of York, Heslington, York YO10 5DD, UKMagnetic nanoparticles with Néel surface anisotropy, different internal structures, surface arrangements and elongation are modelled as many-spin systems. The results suggest that the energy of many-spin nanoparticles cut from cubic lattices can be represented by an effective one-spin potential containing uniaxial and cubic anisotropies. It is shown that the values and signs of the corresponding constants depend strongly on the particle's surface arrangement, internal structure and elongation. Particles cut from a simple cubic lattice have the opposite sign of the effective cubic term, as compared to particles cut from the face-centered cubic lattice. Furthermore, other remarkable phenomena are observed in nanoparticles with relatively strong surface effects: (i) In elongated particles surface effects can change the sign of the uniaxial anisotropy. (ii) The competition between the core and surface anisotropies leads to a new energy that contributes to both the 2 nd − and 4 th −order effective anisotropies. We also evaluate energy barriers ∆E as functions of the strength of the surface anisotropy and the particle size. The results are analyzed with the help of the effective one-spin potential, which allows us to assess the consistency of the widely used formula ∆E/V = K∞ + 6Ks/D, where K∞ is the core anisotropy constant, Ks is a phenomenological constant related to surface anisotropy, and D is the particle's diameter. We show that the energy barriers are consistent with this formula only for elongated particles for which the surface contribution to the effective uniaxial anisotropy scales with the surface and is linear in the constant of the Néel surface anisotropy.

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“…This kind of structure has been the basis of many theoretical studies using the Heisenberg Hamiltonian (see, e.g., Refs. 7,14,17,18,20,21,23).…”

Section: A Computing Methodsmentioning

confidence: 99%