Dipolar magnetic interactions among magnetic microwires

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Abstract

This paper presents a brief review of experiments and simulations on dipole–dipole interacting magnetic microwires that form a linear chain. In particular, recent studies on (a) amorphous Fe77.5Si7.5B15 and (b) granular Cu45Ni25Co29Mn1 microwires are discussed. Hysteresis loops were performed at room temperature for an array of N microwires (N=1–5 for (a) and N=1–100 for (b)) and compared with Monte Carlo simulations. In the case of amorphous soft magnetic materials (a), clear steps and plateaux on the demagnetization are visible, each step corresponding to the magnetization reversal of an individual wire. In the case of CuNiCoMn microwires (b), that exhibit a granular structure and a nearly superparamagnetic behavior when isolated, it was found that the coercivity abruptly changes from 20 to 700 Oe for N around 10. Novel Monte Carlo simulations are presented, providing useful insights about the effect of long-range interactions that account for the interesting observed magnetic behaviors.

Introduction

Interactions among magnetic entities are being intensively investigated in both basic and applied aspects of novel magnetic materials. Advances in fabrication techniques (including chemical routes, electrodeposition and litography) have allowed the fabrication of nanostructured systems with very interesting physical properties. In particular, it is nowadays possible to obtain controlled arrays of magnetic wires with diameters of few nanometers, which are of practical interest in the design and optimization of magnetoresistive heads for ultrahigh-density data storage applications. In such systems, as in many other artificial magnetic structures, magnetostatic interactions can play a fundamental role in the magnetization reversal process and domain structures of the individual elements, which consequently would influence the macroscopic magnetic response of the system.

An intrinsic obstacle in the experimental study of magnetic interactions is the fact that it is extremely difficult to single out a magnetic element, even using the most sensitive magnetometry techniques. Also, the predictions of numerical simulations are intricate to compare with real systems, owing to the necessity to introduce several approximations in the modeled problem. However, a very interesting macroscopic analogous was recently found, placing together several ferromagnetic glass-covered microwires. The stray fields couple the magnetizations of the wires, affecting the magnetic state of each single wire. This system is relatively easy to study both experimentally and theoretically, and, in the case of few wires it was possible to obtain analytical solutions. The exact solutions and experimental data can be compared with Monte Carlo simulations, which are necessary to employ when the array is formed by a large number of wires. Although this system seems to be rather simple, it displays a variety of interesting aspects which apply to other physical systems.

This work will be organized as follows: a brief revision of the literature will be given in Section 2. This revision does not have the intention to be complete and extensive, but only to mention some recent results connected to dipole–dipole interactions among wires. The quantity of works on this subject is increasing day after day, and a complete revision of the related works is beyond the scope of this short review. Section 3 will discuss the properties of the materials used in our experiments. Section 4 will focus on experimental results recently obtained in linear arrays of glass-covered amorphous microwires (GCAW) by our group, showing the main experimental results and the simple models developed to understand the data. Section 5 will show several Monte Carlo simulations, including a novel approach developed to model and visualize the problem in an easier way.

Section snippets

General remarks

The magnetostatic interaction among magnetic entities have been a target of research for many years, mainly due to its importance in technological devices (see, for example the review by Yelon [1] for the case of multilayer films). In particular, the interest on dipole–dipole interactions in arrays of magnetic wires is becoming more and more intense in the last few years, owing to the strong interest in such systems as possible candidates for future magnetic recording media. The cylindrical

Materials and experiments

Amorphous wires have attracted substantial attention in the last years owing to their outstanding magnetic properties that make them very convenient to be used as sensing elements in sensor devices [14], [15]. Magnetostrictive amorphous wires can exhibit bistable magnetic behavior [16], characterized by a low-field squared hysteresis loop while wires with vanishing magnetostriction show the largest values for the giant magnetoimpedance effect [17]. In this context, amorphous microwires can be

Experimental results

Fig. 1 shows the experimental hysteresis loops measured on 5 mm long wires placed side by side forming an array with distance between the axes of the wires of around 20 μm [9]. In the case of a single wire (see Fig. 1) the hysteresis curve exhibits a typical square loop, with characteristic large Barkhausen jumps, as expected for high magnetostriction amorphous wires [14]. In the case of an array of two wires, the hysteresis loops exhibit two clear Barkhausen jumps and plateaux at zero

Monte Carlo simulations

As shown in the previous sections, it was experimentally found that an ensemble of microwires forming a linear chain shows characteristic hysteresis cycles, demonstrating the effect of dipole–dipole interaction among the magnetic wires.

For the case of bistable amorphous microwires, the authors have used Monte Carlo (MC) method based on a one-dimensional (1D) modified classical Ising model [9]. They considered a 1D array of magnetic moments interacting through the long-range dipole–dipole

Conclusions

It was shown that the long-range dipole–dipole interaction among ferromagnetic wires can be easily studied (both theoretically and experimentally) by means of glass-coated magnetic microwires placed side by side, which is analogous to an array of nanowires or even spins. In such cases, a macroscopic array of microwires can be regarded as a model system to verify the influence of dipolar interactions in the magnetic response of an array of dipoles, being possible to test micromagnetic

Acknowledgements

The authors acknowledge the financial support of CNPq, FAPESP, FAEP (UNICAMP), CAPES (Procad) and Vitae/Andes. Fondecyt (Chile) grants 1990812, 1010127 and ICM P99-135F are also acknowledged.

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