Abstract
Magnetostatic dipolar anisotropy energy and the total dipolar anisotropy constant, , in periodic arrays of ferromagnetic nanowires have been calculated as a function of the nanowire radius, the interwall distance of the nanowires in the arrays and the geometry of the array (square or hexagonal), by using a realistic atomistic model and the Ewald method. The simulated nanowires have a radius size up to 175 Å that corresponds to 31 500 atoms, and the simulated nanowire arrays have interwall distances between 35 and 3000 Å. The dependence of total magnetostatic dipolar anisotropy constant on the nanowire radius, their interwall distance and the type of array symmetry has been analyzed. The total dipolar anisotropy constant, which is the sum of the intrananowire dipolar anisotropy constant, , due to the dipolar interactions inside an isolated nanowire and the main responsible of the shape anisotropy, and of the internanowire dipolar anisotropy constant, , due to the magnetostatic dipolar interactions among nanowires in the array, have been calculated and compared with the magnetocrystalline anisotropy constant for three nanowire compositions and their crystalline structures. The simulations of the nanowire arrays with large interwall distances have been used to calculate the intrananowire anisotropy constant, , and to analyze the competition between the intrananowire, internanowire and magnetocrystalline anisotropies. According to some magnetic theories, the ratio equals to the areal filling fraction of a nanowire array. Present calculations indicate that the equation for the areal filling fraction matches perfectly for any interwall distance and radius of Ni and Co nanowire arrays. This first equation is used to write a general equation that relates the radius and interwall distance of nanowire arrays with the intrananowire, internanowire and magnetocrystalline anisotropies. This general equation allows to design the geometry of nanowire arrays with the desired orientation of the easy magnetization axis.
Highlights
Introduction and motivationIn the last decades many research efforts have been focused on the synthesis and characterization of arrays of magnetic nanowires, due to the technological applications of these materials in diverse areas, such as: high density data storage [1], biosensors [2, 3], MRAM devices [4, 5], microwave electronics [6, 7], magnetic field sensors [8], permanent magnets [9, 10] and spin-torque nano-oscillators, STNO [11, 12], among others
According to the present calculations, the linear relationship between the ratio and the filling fraction given by the equations (8)–(10), is very accurate and it is valid to calculate the values of the radius and interwall distance necessary to obtain an array of nanowires with the desired direction of the easy magnetization axis
The present Ewald calculations of the total dipolar anisotropy constants in arrays of Ni and constant of fcc-Ni (Co) nanowires show that these constants for hexagonal and square arrays of fcc-Ni, fcc-Co and hcp-Co nanowires are very similar, except for narrow nanowires, with a radius below ≈20 Å and for arrays with short or medium interwall distances, i, below ≈1000 Å
Summary
In the last decades many research efforts have been focused on the synthesis and characterization of arrays of magnetic nanowires, due to the technological applications of these materials in diverse areas, such as: high density data storage [1], biosensors [2, 3], MRAM devices [4, 5], microwave electronics [6, 7], magnetic field sensors [8], permanent magnets [9, 10] and spin-torque nano-oscillators, STNO [11, 12], among others. Instead of the chain and macrodipole models, a more realistic atomistic model that considers the local magnetic dipoles of each atom of the nanowires in the array and periodic cells has been used in the present work to simulate the collective magnetic behaviour of an infinite array of ferromagnetic nanowires. This model has been applied to study nanowire arrays with any value of radius and interwall, and to study nanowire arrays with large radii and interwall distances, similar to the experimental values, which are relevant to study the dipolar interactions among nanowires. Details of this implementation and its application to any type of lattice, and especially to nanowire arrays, can be found elsewhere [48]
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