The electrical resistance of a diffusive ferromagnet with magnetic domain walls is studied theoretically, taking into account the spatial dependence of the magnetization. The semiclassical domain wall resistance is found to be either negative or positive depending on the difference between the spindependent scattering lifetimes. The predictions can be tested experimentally by transport studies in doped ferromagnets. PACS numbers: 75.60.Ch, 73.50.Bk, A domain wall (DW) is the region between two ferromagnetic domains in which the direction of the magnetization rotates. A number of experiments have been conducted which show either an increase [1][2][3] or a decrease [4][5][6][7][8] of the resistance due to DWs compared to the resistance of a single-domain ferromagnet. These experiments have been done on thin films, structured thin films, and membranes in the diffusive transport regime, where the electron mean free path is shorter than the typical system size.In the diffusive limit, Cabrera and Falicov [9] calculated an increase of the resistance caused by the backreflection of electrons by the domain wall. The reflection probability was found to be exponentially small in the ratio of the DW width to the Fermi wavelength. An increase of the semiclassical resistance has also been predicted by Tatara and Fukuyama [10] by linear response calculations assuming spin-independent relaxation times. Levy and Zhang [11] obtained the DW resistance from a Boltzmann equation. They showed that spin-dependent relaxation times can enhance this positive DW resistance, depending on the ratio of relaxation times of the majority and minority spin electrons. Brataas et al. [12] calculated the domain wall resistance generalizing the approach of Tatara and Fukuyama to include spin-dependent lifetimes with qualitatively similar results to Levy and Zhang.The only intrinsic mechanism which explains a decrease of the resistance has been proposed by Tatara and Fukuyama [10], viz., the destruction of electron weak localization by the dephasing, caused by the domain wall, decreases the resistance. However, experimentally, the negative domain wall resistance persists up to relatively high temperatures [5,6], where localization does not play a role. Kent et al. [6] explain the negative DW resistance by an extrinsic effect: reduced surface scattering.It is the purpose of this Letter to show that the semiclassical DW resistance of diffusive ferromagnets can be negative as well as positive when the electronic structure of the domain wall is taken into account semiclassically. where m is the mass of the electron, e is the charge of an electron, n 1 ͑n 2 ͒ is the density of spin-up (spin-down) electrons, and t 1 ͑t 2 ͒ is the scattering relaxation time for the spin-up (spin-down) electrons which at low temperatures depends on the (spin-dependent) impurity potential and (spin-dependent) density of states. A redistribution of the electrons between the spin-up and spin-down bands (i.e., a change in magnetization) modifies the resistivity when t 1 fi ...
We perform detailed temperature dependent measurements of the magnetoresistance ͑MR͒ and its angular dependence of epitaxial Fe ͑110͒ films. The angular dependence of the MR at Hϭ10 kOe is found to change strongly when going from Tϭ4.2 K to Tϭ230 K. We analyze the data on the basis of Döring's equation. Second-and fourth-order angular dependent terms are found to be of equal importance, indicating strong deviations of the MR from a simple cos 2 dependence. One of the MR components is the ordinary or Lorentz magnetoresistance, which is strong at low temperatures and becomes smaller at higher temperatures, due to the reduction of the mean free path. By subtracting the ordinary magnetoresistance from the MR data we obtain the anisotropic magnetoresistance. We decompose the temperature dependent anisotropic magnetoresistance in the temperature dependent k constants of Döring's equation. These constants show a reduction between Tϭ20 K and Tϭ100 K, which reflects the observed decrease of the anisotropic magnetoresistance. We present arguments that the temperature dependence of the anisotropic magnetoresistance is most likely due to the change from defect-dominated scattering to phonon-dominated scattering, each of which has its own anisotropic magnetoresistance.
Room temperature magnetoresistance switching of Permalloy thin films induced by iron nanoparticles Appl. Phys. Lett. 92, 093121 (2008); Negative resistance contribution of a domain-wall structure in a constricted geometry
We have studied the giant magnetoresistance ͑GMR͒ in magnetic multilayer point contacts of three different types. The first generation contacts were made by deposition with molecular-beam epitaxy ͑MBE͒ of an uncoupled Co/Cu multilayer on a pre-etched hole in a thin membrane. These devices exhibited a GMR, but its ratio was low and, as deduced from finite element calculations, in many cases was dominated by the resistance of the multilayer electrode. When corrected for this, the maximum point-contact GMR was 3%. The multilayer structure at some depth in the constriction was disrupted, as observed by transmission electron microscopy. This was identified as a cause of the low GMR, together with contamination and an oxide layer in the constriction, resulting from ex situ sample rotation. The second generation was fabricated by sputtering of a coupled Co/Cu multilayer before etching of the nanohole, giving a proper multilayer at the constriction. Further, the GMR signal from the electrode was shorted by a thick Cu cap. This did not bring the expected increase of the GMR (ratioр5%), indicating that the so-called dead layers and the quality of the interface between the GMR system and the contacting metal were limiting. This interface quality was strongly improved for the third generation of contacts by using in situ rotation, while the question of multilayer quality was avoided by shifting to granular Co/Au. Granular Co/Au in the constriction was obtained by growing a discontinuous Co layer by MBE. The maximum GMR ratio of the granular contacts was 14%, an improvement of a factor 3. These contacts displayed small jumps in the GMR, two-level fluctuations in the resistance time trace and ballistic transport, the latter being evident from phonon peaks in the point-contact spectrum of a high resistance contact. ͓S0163-1829͑99͒01537-4͔
Influence of magnetic domain-wall width and shape on magnetoresistance measurementsWe study the magnetoresistance ͑MR͒ of Py/Py, Co/Py, Co/Co, Ni/Ni, and Co/Cu point contacts (PyϭpermalloyϭNi 80 Fe 20 ). These devices are narrow constrictions or channels ͑diameter, length Ϸ30 nm͒ between two thin film electrodes. Due to the small size of the constriction, which is comparable to a bulk domain-wall ͑DW͒ thickness, a DW can be caught in it. For almost all material combinations studied we find that low resistance contacts show an MR minimum at zero field (Hϭ0) of magnitude 0.4%-1.3%, for temperatures between 1.5 and 293 K. The minimum occurs for all field orientations with respect to the channel axis. When the contact resistance increases beyond the value set by a diameter-to-length ratio for the channel of about unity, the resistance minima at Hϭ0 evolve into a maximum/minimum combination as expected for a predominant anisotropic magnetoresistance ͑AMR͒ effect. We use micromagnetic calculations based on magnetostatic and exchange interactions to obtain the magnetization in the constriction. These calculations predict that, due to the finite channel length, there are two partial DWs at either side of the channel. For high resistance contacts this agrees with the observed AMR, which results from scattering in the homogeneously magnetized material in the channel. The MR minimum for low resistance contacts arises from the DWs, which cause a resistance decrease. We attribute this decrease to a change of spin-dependent diffuse scattering at the constriction boundary due to the DWs.
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