We investigate the stability features of steady-states of a two-dimensional system of ferromagnetic nanowires.We constitute a systemwith the finite number of nanowires arranged on the (e⃗1, e⃗2) plane, where (e⃗1, e⃗2, e⃗3) is the canonical basis of ℝ3. We consider two cases: in the first case, each nanowire is considered to be of infinite length, whereas in the second case, we deal with finite length nanowires to design the system. In both cases, we establish a sufficient condition under which these steady-states are shown to be exponentially stable.
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Magneto-resistive nanostructures have been investigated. The structures were fabricated by electron beam lithography patterning and chemical etching from thin epitaxial layers of the ferromagnetic semiconductor (Ga,Mn)As, in shape of three nanowires joined in one point and forming three-terminal devices, in which an electric current can be driven through any of the three pairs of nanowires. In these devices, a novel magneto-resistive memory effect has been demonstrated, related to a rearrangement of magnetic domain walls between different pairs of nanowires in the device consisting in that its zero-field resistance depends on the direction of previously applied magnetic field. The nanostructures can thus work as twostate devices providing basic elements of nonvolatile memory cells.
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Simple magnetoresistive nanodevices formed by narrow constrictions of submicron width in the epitaxial film of a ferromagnetic (Ga,Mn)As semiconductor have been fabricated employing the electronbeam- lithography patterning and low-energy low-dose oxygen ion implantation. Low-temperature chargecarrier transport through the constrictions has been investigated and correlated with magnetic properties of the film. The constricted devices revealed abrupt jumps of a reduced resistance that appeared when the sweeping magnetic field crossed the regions of the coercive field of the film magnetization. In contrast, the non-constricted reference device displayed abrupt jumps of an enhanced resistance at the same values of magnetic field. We interpret the both features, whose positions on the magnetic-field scale reflect the hysteresis loop of magnetization, as manifestation of domain wall contribution to the (Ga,Mn)As film resistance. Presumably, the suppression of the weak localization effects by a domain wall located at the constriction results in a negative contribution of a domain wall to the resistance, while the spin-orbit interaction can be responsible for its positive contribution to the resistance.
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