Geodesic
States, hysteresis and equilibrium properties of one-dimensional chains of magnetic dipoles
Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 1, pp. 82-97.

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A theoretical study of the magnetic properties of one-dimensional arrays of ferromagnetic nanoparticles was conducted. It is shown that in the Stoner-Wohlfarth model, depending on distance between the dipole-dipole interacting particles, the chain can show either soft magnetic or hard magnetic properties and behavior may vary from a Stoner-Wohlfarth-like to an Ising-like. The criteria of difference between strong and weak dipole interactions for one-dimensional arrays of single-domain ferromagnetic nanoparticles with uniaxial anisotropy were defined. By using numerical simulations magnetic states were obtained for 1D array for a set value of an external magnetic field. Staircase-shaped hysteresis curves obtained at orthogonality of the external magnetic field to the axis of the array are caused by weak magnetostatic interaction, which leads to the Ising-like behavior, and by a discrete set of the magnetic moment configurations. Using the Gibbs distribution, the magnetization curve is obtained for one-dimensional magnetic point dipoles Ising system in thermodynamic equilibrium state. The obtained results of the calculations are in agreement with the experimental data. 
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А. А. Peretyatko; V. A. Ivanov; A. G. Makarov; K. V. Nefedev. States, hysteresis and equilibrium properties of one-dimensional chains of magnetic dipoles. Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 1, pp. 82-97. http://geodesic.mathdoc.fr/item/DVMG_2017_17_1_a6/

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