Ballistic and diffuse transport through a ferromagnetic domain wall

Brataas, Arne; Tatara, Gen; Bauer, G.

doi:10.1103/physrevb.60.3406

Cited by 76 publications

(90 citation statements)

References 21 publications

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“…Since domain walls give observable corrections on the order of 1% to the resistance of ferromagnetic systems [55][56][57], we expect this also to be the case for the boundary-driven twist states discovered in this work. The texture-induced resistance has been extensively studied in the context of domain walls, where the spatially varying magnetization has been shown to produce a correction to the local resistivity proportional to (∂ i m) 2 in the diffusive regime [56].…”

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confidence: 82%

“…The texture-induced resistance has been extensively studied in the context of domain walls, where the spatially varying magnetization has been shown to produce a correction to the local resistivity proportional to (∂ i m) 2 in the diffusive regime [56]. In addition, there will be corrections from the anisotropic magnetoresistance (AMR) effect [57].…”

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confidence: 99%

“…Here, ρ 0 is the resistance for currents perpendicular to the magnetization in the absence of any twist state, δρ t parameterizes the resistivity caused by scattering at the magnetic texture, [56] and (∂zψ(z)) 2 determines the magnitude of the magnetization gradient (∂ i m) 2 .…”

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New Boundary-Driven Twist States in Systems with Broken Spatial Inversion Symmetry

Hals

Everschor-Sitte

2017

Phys. Rev. Lett.

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A full description of a magnetic sample includes a correct treatment of the boundary conditions (BCs). This is in particular important in thin film systems, where even bulk properties might be modified by the properties of the boundary of the sample. We study generic ferromagnets with broken spatial inversion symmetry and derive the general micromagnetic BCs of a system with Dzyaloshinskii-Moriya interaction (DMI). We demonstrate that the BCs require the full tensorial structure of the third-rank DMI tensor and not just the antisymmetric part, which is usually taken into account. Specifically, we study systems with C∞v symmetry and explore the consequences of the DMI. Interestingly, we find that the DMI already in the simplest case of a ferromagnetic thinfilm leads to a purely boundary-driven magnetic twist state at the edges of the sample. The twist state represents a new type of DMI-induced spin structure, which is completely independent of the internal DMI field. We estimate the size of the texture-induced magnetoresistance effect being in the range of that of domain walls.Over the past few years, there has been an increasing interest in magnets where interface-induced phenomena play a major role [1][2][3]. This includes the topics of magnetic heterostructures as well as thin films, where the main effects arise from the sample's boundary. Therefore, a rigorous understanding of the physical boundary conditions (BCs) is needed.The strong spin-orbit coupling (SOC) and broken spatial inversion symmetry of these nanostructures lead to an intricate interplay between spin, charge, and orbital degrees of freedom, which affect the magnetic equilibrium state as well as the current-driven spin phenomena. Important examples of the SOC effects include current-driven spin-orbit torques [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], charge-pumping via magnetization precession [8,[22][23][24][25][26], and the formation of topologically nontrivial skyrmion textures [27][28][29][30][31][32][33][34][35][36][37][38] and chiral domain walls [15,16,[39][40][41], as well as the multiferroic behaviour of chiral magnets [42,43] and the ferroelectricity of magnetic textures [41,44].The underlying mechanism being responsible for chiral skyrmions and domain walls is the Dzyaloshinskii-Moriya interaction (DMI) [45,46]. The DMI is a relativistic magnetic exchange interaction that originates from broken spatial inversion symmetry. Phenomenologically, the DMI is modeled by a free-energy density term, which is linear in the spatial variations of the magnetization. In its most general form, the term can be written asas discussed for example explicitly in Landau & Lifshitz, Ref.[47].Here, m is a unit vector pointing along the magnetization M = M s m, and D ijk is the DMI tensor, which is linear in the relativistic interactions. The particular form of the DMI tensor is determined by the point group of the system. Here, and in what follows, we use the convention of a summation of repeated indices. To avoid confusion with the...

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New Boundary-Driven Twist States in Systems with Broken Spatial Inversion Symmetry

Hals

Everschor-Sitte

2017

Phys. Rev. Lett.

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“…(14) has the advantage that the corresponding basis states can be found in closed form. 15,19 The local spin eigenstates |± (parallel and anti-parallel to the direction of f (z)) are position-dependent inside the domain wall. Denoting the spin basis states with respect to the fixed z-axis as |± z , we have…”

Section: B Electronic States In a Ballistic Domain Wallmentioning

confidence: 99%

Electron transport through disordered domain walls: Coherent and incoherent regimes

et al. 2006

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We study electron transport through a domain wall in a ferromagnetic nanowire subject to spindependent scattering. A scattering matrix formalism is developed to address both coherent and incoherent transport properties. The coherent case corresponds to elastic scattering by static defects, which is dominant at low temperatures, while the incoherent case provides a phenomenological description of the inelastic scattering present in real physical systems at room temperature. It is found that disorder scattering increases the amount of spin-mixing of transmitted electrons, reducing the adiabaticity. This leads, in the incoherent case, to a reduction of conductance through the domain wall as compared to a uniformly magnetized region which is similar to the giant magnetoresistance effect. In the coherent case, a reduction of weak localization, together with a suppression of spin-reversing scattering amplitudes, leads to an enhancement of conductance due to the domain wall in the regime of strong disorder. The total effect of a domain wall on the conductance of a nanowire is studied by incorporating the disordered regions on either side of the wall. It is found that spin-dependent scattering in these regions increases the domain wall magnetoconductance as compared to the effect found by considering only the scattering inside the wall. This increase is most dramatic in the narrow wall limit, but remains significant for wide walls.

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“…The extra resistivity arises since the channels exhibit unequal conductivities in a ferromagnet in the absence of the wall. (ii) A redistribution of the charge carriers between spin-majority and spin minority channels due to the domain wall scattering [4,5]. The works perform a diagrammatic evaluation of the Kubo's formula over the DW scattering potential.…”

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confidence: 99%