Resistivity due to Domain Wall Scattering

Abstract

Domain walls in ferromagnetic metals are known to be a source of resistance since the early experiments on iron whiskers. Recently it has been possible to identify this contribution from data on cobalt and nickel films which display stripe domains in which the current is driven normal to the domain walls. With the same Hamiltonian as used to explain giant magnetoresistance in structures with collinear magnetic alignments we have determined the spin flip, as well as nonflip, scattering present in domain walls. We calculate the resistivity in zero field, i.e., in the presence of striped domains, and at saturation to show the amount of magnetoresistance that is attributable to domain wall scattering.[S0031-9007(97)04820-5] PACS numbers: 73.40.Cg, 73.50.Bk, Since the early experiments on iron whiskers [1], it was recognized that walls between domains in ferromagnets are a source of electrical resistance in addition to that present in the domains. By applying magnetic fields to saturate magnetization, and thereby erase domains in an otherwise multidomain ferromagnet, the resistance of iron was found to drop significantly. Cabrera and Falicov [2] considered two mechanisms by which the walls produce additional scattering: paramagnetic effects from the reflection of incoming electron waves from the ferromagnetically ordered domains as they enter the twisted spin structure of a wall, and diamagnetic effects "due to the zigzagging character of the electron orbits when going between up and down regions of the magnetization." In metals with few impurities, such as iron whiskers, the relaxation times are sufficiently long, and Cabrera and Falicov concluded that these diamagnetic effects can account for the observed negative magnetoresistance (MR) [3]. Indeed, both Cabrera and Falicov, and Berger [4], found that the reflection for an electron at the Fermi surface from a 180 ± wall which is 10 nm thick is negligible; unless the walls are so abrupt to be of monolayer thickness, electron scattering from reflections do not contribute to the electrical resistance.While the resistivity of iron whiskers at low temperatures (about 4.2 K) is small, of the order of 0.01 mV cm, most of the ferromagnetic layers that are used in magnetoresistive elements, e.g., spin valves, have a considerably higher resistivity due to inherent defects such as grain boundaries and roughness at the boundaries of these thin layers. Recently Gregg et al. [5] obtained the first direct observation of ferromagnetic domain wall scattering by passing a current that is nominally perpendicular to a striped domain structure in thin films of cobalt (1000 A). The resistivity of their films was about 10 mV cm, so that the diamagnetic effects that are putatively responsible for the negative MR in pure iron whisker cannot be responsible. Also, as the thickness of the walls is estimated to be 15 nm, reflections of impinging electrons with the Fermi wavelength cannot account for the additional resis-tivity due to domain walls which was estimated to be about 0.52 mV cm. Greg...

Spin-dependent scattering of a domain wall of controlled size

“…With taking the values measured previously on multilayered nanowires obtained with the same electrodeposition method ρ = 10 −7 mΩ, β = 0.45, l sf = 20 nm [7,8] we have R GMR = 0.2 Ω. Unfortunately, the small δ range in Fig13 and the rough scaling procedure do not allow to differentiate between the predictions ∂R(δ) ∝ δ −2 (Levy and Zang in reference [10]) or ∂R(δ) ∝ δ −1 and ∂R(δ) ∝ −δ (van Hoof et al in reference [12]). …”

“…However, this relaxation takes place only in the case of an abrupt spatial change of the magnetization, namely a length smaller or equal to the spin diffusion length l sf (about 20 nm in Co measured with Co/Cu/Co multilayers) [7,8] . In the case of a smooth magnetic change, the polarization axis of the conduction electrons follows the local magnetic field adiabatically [9,10] and there is no relaxation.…”

“…However, in the case of non uniformly magnetized layers, or domain-walls (the so-called Domain-wall Scattering problem: DWS), the relaxation has not been evidenced clearly. Different theoretical models were proposed and are currently under development [10,[12][13][14]. Simply speaking, two regimes have to be considered depending on the domain-wall thickness δ.…”

Magnetic excitations in a nanocontact

“…For diffusive transport, the wall resistance is predicted to vary as ␦ Ϫ2 . 12 The change in wall resistance due to mode fluctuations may be a few percent.…”

Ballistic versus diffusive magnetoresistance of a magnetic point contact

“…A negative magnetoresistance can be due to scattering on domain walls (DW) and this effect has been considered in a number of works [5][6][7][8] giving typical values of MR in a range of few percents. Such considerably low values of the MR were obtained assuming that realistic widths of the DW were large, which resulted in a low scattering amplitudes.…”