Thermodynamic properties of magneto-anisotropic nanoparticles

Abstract

The purpose of this paper is to study the thermodynamic equilibrium properties of a collection of non-interacting three-dimensional (3D) magnetically anisotropic nanoparticles in the light of classical statistical physics. Pertaining to the angular dependence (α) of the magnetic field with the anisotropy axis, energy landscape plots are obtained which reveal a continuous transition from a double well to a single well for [Formula: see text] and show an asymmetric bistable shape for other values of α. The present analysis is related to the interpretation of equilibrium magnetization and static susceptibility of a nanomagnetic system as a function of external magnetic field, B, and temperature, T. The magnetization and susceptibility confirm the non-Langevin behaviour of magneto-anisotropic monodomain particles. The susceptibility analysis establishes the ferromagnetic-, antiferromagnetic- and paramagnetic-like coupling for various α. This study reveals the essential role of magneto-anisotropic energy in the interpretation of the magnetic behaviour of a collection of non-interacting single-domain nanoparticles.

Biological Magnetometry: Torque on Superparamagnetic Beads in Magnetic Fields

“…1(e); Section 2 of [17]) will depend on the free energy [Eq. (2)], i.e., on expð−F=k B TÞ [27][28][29][30][31][32][33][34]. Finally, a recently proposed model [8] simplifies the SW model by reducing the continuous range of θ 1 to just two orientations aligned with the anisotropy axis ("two-stateflipping," 2SF), i.e., θ 1 ¼ nπ, where n is an integer.…”

Magnetic Materials Characterization and Modeling for the Enhanced Design of Magnetic Shielding of Cryomodules in Particle Accelerators

“…For this paper, we only consider the magnetocrystalline energy and Zeeman energy contributions (we note stress anisotropy and other contributions may be added where appropriate): Many prior models approximately employ the following approach or some variants thereof to model the magnetization behavior. The total energy density (E i ) corresponding to the magnetization orientation along a crystallographic direction ("i") as shown in figure 1.5.a is evaluated and the probability (p i ) of this state being occupied is calculated as [25][26][27][28][29][30][31][32][33]:…”

“…While there are others stochastic models for ferromagnetic materials [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], this model can comprehensively accommodate and effectively model both the effect of temperature and defects in such materials on their magnetization (M-H) curves. This is the uniqueness of this model compared to other magnetization models for ferromagnetic materials.…”

Energy based model for temperature dependent behavior of ferromagnetic materials

“…Many prior models approximately employ the following approach [6][7][8][9][10][11][12][13][14] or some variants thereof to model the magnetization behavior. The total energy density (E i ) corresponding to the magnetization orientation along a crystallographic direction ("i") as shown in Fig.…”

“…There have been many magnetization models for ferromagnetic materials such as Preisach model [1][2], Weiss model [3], Stoner-Wolfforth model [4], Brown's analysis of thermal fluctuation in singe domain particles [5], homogenized energy model [6], Jiles-Atherton model [7][8], energy weighted stochastic models [9][10][11][12][13], Globus model [14] other nonlinear constitutive [15] and phase field approaches [16]. While models such as the Preisach model are purely mathematical and do not actually addresses the underlying physics, later models attempt to incorporate specific exchange coupling, shape anisotropy, magnetoelastic anisotropy magnetocrystalline anisotropy and Zeeman energies in describing the magnetization behavior of bulk samples.…”