Size effect on the magnetic behavior of rapidly solidified cylin-drical amorphous nanowires

Abstract

Results on the influence of sample dimensions, specifically nanowire length, $L$, and diameter, $D$, on the magnetization processes taking place in cylindrical amorphous nanowires prepared by rapid quenching from the melt are reported. Nanowires with various compositions - (Co 0.94 Fe 0.06 ) 72.5 Si 12.5 B 15 and Fe 77.5 Si 7.5 B 15 - have been investigated in order to correlate their magnetic behavior with the dimensions, mainly to reveal the role played by the large aspect ratio of these novel nanowires, which can exhibit significant lengths, in their overall magnetic behavior. The approach taken was to simulate first the axial hysteresis loops of amorphous nanowires with different lengths, whilst keeping their diameter constant. The simulations have been performed in the micromagnetic approximation employing finite element discretization. This method allowed us to perform a unique study of the magnetization reversal process within this new type of cylindrical nanowires, starting from a fully saturated state $(+M_{S})$ with the nucleation of a domain with reverse magnetization, continuing with the depinning and propagation of the newly formed 180° domain wall until it reaches the opposite end of the nanowire, which is again fully saturated in the opposite direction $(- M_{S})$. The usual inductive hysteresis loops (experimental) are bypassing nucleation, since there already are end domains with reversed magnetization due to demagnetization, and magnetization reversal only consists in the depinning and propagation of the preexistent 180° domain wall. The results of micromagnetic simulations, illustrated in Figure 1 for the case of (Co 0.94 Fe 0.06 ) 72.5 Si 12.5 B 15 amorphous nanowire samples, which exhibit nearly zero magnetostriction, reveal the fact that the remanence to saturation ratio $M_{R}/ M_{S}$ increases with the nanowire length to diameter ratio $L/ D$. This dependence shows directly the critical effect of shape anisotropy, which also increases with the $L/ D$ ratio (aspect ratio). The relatively large coercivity of the calculated highfield loops is the result of the magnetization reversal mechanism described above, which begins with the nucleation of a reverse domain, requiring thus a quite large applied field. The inset of Figure 1 shows the region near the switching field for every value of the sample length. From the results illustrated in the inset, one can clearly observe that the remanence to saturation ratio $(M_{R}/ M_{S})$ varies monotonically with the sample length, showing that it is easier to nucleate domains with reversed magnetization in the shorter samples. In order to thoroughly understand the mechanisms of magnetization reversal, the visualization of the orientation of the magnetic moments within the sample at various stages is extremely helpful. Figure 2 shows the orientations of the magnetic moments for an amorphous nanowire sample with 2.7 mm in length and the diameter of 90 nm at various stages of the hysteresis loop. Magnetic moments are represented by red arrows when pointing in the direction of the applied field and by blue arrows when pointing in the opposite direction. The magnetization reversal process begins from both ends of the nanowire, with a small delay, the two domain walls propagating towards the middle of the wire. Here, the two domain walls collide, canceling out each other. Such behavior has been previously emphasized experimentally in the case of thicker amorphous glass-coated microwires subjected to large applied fields [1]. We have also simulated the axial hysteresis loops for amorphous nanowires with various diameters, whilst keeping a constant sample length. The results confirm that $M_{R}/ M_{S}$ increases with $L/ D$. The same result has been also confirmed experimentally, by means of inductive hysteresis loop measurements. Thus, shape anisotropy and the demagnetizing field play a key role in the magnetic behavior of rapidly solidified nanowires. Moreover, the correlation between the simulated loops and the experimental ones allows us to get a deeper insight into the magnetization reversal mechanism, and to analyze the two separate stages of axial magnetization switching, i.e., the nucleation of new domains with reversed magnetization, as indicated by the variation of the remanence to saturation ratio with the nanowire dimensions, and the propagation of the domain wall between the newly nucleated domains or pre-existent end domains and the rest of the nanowire, as shown by the changes in the value of the experimental switching field. The results are key for understanding and controlling the magnetization processes in these novel nanowires, with important application possibilities in new miniaturized sensing devices. Thus, it is possible to tailor a nanowire's anisotropy and magnetic characteristics (switching field, remanence, coercivity) by changing its dimensions (diameter and/or length).