Theory of the Dzyaloshinskii domain-wall tilt in ferromagnetic nanostrips

Muratov, Cyrill B.; Slastikov, Valeriy; Kolesnikov, Alexander; Tretiakov, Oleg A.

doi:10.1103/physrevb.96.134417

Cited by 32 publications

(21 citation statements)

References 44 publications

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“…The interplay between the short-range and long-range interactions causes complex ordering processes [35][36][37][38][39][40] , and it is important for two-step SC transitions 30,[41][42][43][44][45][46][47][48][49][50][51] , in which the antiferromagnetic (AF) -like phase mostly appears as a medium-temperature phase.…”

Section: Introductionmentioning

confidence: 99%

Nontrivial phase diagram for an elastic interaction model of spin crossover materials with antiferromagnetic-like short-range interactions

2017

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We study the phase diagram of an elastic interaction model for spin crossover (SC) materials with antiferromagnetic-like short-range interactions. In this model, the interplay between the shortrange interaction and the long-range interaction of elastic origin causes complex phase transitions. For relatively weak elastic interactions, the phase diagram is characterized by tricritical points, at which antiferromagnetic (AF) -like and ferromagnetic (F) -like spinodal lines and a critical line merge. On the other hand, for relatively strong elastic interactions, unusual "horn structures," which are surrounded by the F-like spinodal lines, disorder (D) spinodal lines, and the critical line, are realized at higher temperatures. These structures are similar to those obtained in our previous study [Phys. Rev. B 93, 064109 (2016)] of an Ising antiferromagnet with infinite-range ferromagnetic interactions, and we find universal features caused by the interplay between the competing short-range and long-range interactions. The long-range interaction of elastic origin is irrelevant (inessential) for the critical line. In contrast, the AF-like, F-like, and D spinodal lines result from the long-range interaction of elastic origin. This difference causes qualitatively different features of domain formation or nucleation of the new phase: clustering occurs in the former case, while clustering is absent in the latter. Based on the phase diagrams, we discuss the patterns and clustering features of two-step SC transitions, in which the AF-like phase is realized in the intermediate temperature region. PACS numbers: 75.30.Wx 64.60.-i 75.60.-d 64.60.De

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Section: Introductionmentioning

confidence: 99%

Nontrivial phase diagram for an elastic interaction model of spin crossover materials with antiferromagnetic-like short-range interactions

2017

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“…Furthermore, the field-like component of the SOT may also induce a tilt of the DW, similar to the effect of an in-plane field orthogonal to the current. 16,25,29,30 The aim of this work is to reconcile these controversial observations by elucidating the timeresolved dynamics of tilted DWs in racetrack structures and investigate the influence of DW tilt and field-like torque on the velocity of the walls.We present a study of the current-driven dynamics of chiral DWs in heavy metal / ferromagnetic racetracks performed using micromagnetic simulations. As model system, we choose Pt/Co/AlO x stripes divided into 4 nm × 4 nm × 1 nm rectangular cells with the following material parameters: Co thickness 1 nm, saturation magnetization M s = 900 kA m −1 , exchange coupling A ex = 10 −11 J m −1 , effective uniaxial anisotropy energy K u = 657 kJ m −3 , DMI constant D = 1.2 mJ m −2 , and damping α = 0.5.…”

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confidence: 99%

Asymmetric velocity and tilt angle of domain walls induced by spin-orbit torques

Baumgartner

Gambardella

2018

Applied Physics Letters

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We present a micromagnetic study of the current-induced domain wall motion in perpendicularly magnetized Pt/Co/AlOx racetracks. We show that the domain wall velocity depends critically on the tilt angle of the wall relative to the current direction, which is determined by the combined action of the Dzyaloshinskii-Moriya interaction, damping-like, and field-like spin-orbit torques. The asymmetry of the domain wall velocity can be controlled by applying a bias-field perpendicular to the current direction as well as by the current amplitude. As the faster domain walls are expelled rapidly from the racetrack boundaries, we argue that the domain wall velocity and tilt measured experimentally depend on the timescale of the observations. Our findings reconcile the discrepancy between time-resolved and quasi-static domain wall measurements n which domain walls with opposite tilts were observed and are relevant to tune the velocity of domain walls in racetrack structures.The propagation of domain walls (DWs) plays a fundamental role in determining the efficiency and speed of current-induced switching of magnetic devices. 1-10 In the context of spin-orbit torques (SOTs), 11 DW propagation has been extensively studied by analytical 12-15 and micromagnetic models, 16-19 magneto-optical Kerr effect (MOKE), 4-9 nitrogen-vacancy magnetometry, 20 as well as x-ray imaging. 10,21 An important conclusion drawn from this extended body of work is that the DWs in perpendicular magnetized layers, such as Pt/Co/AlO x and Ta/CoFeB/MgO, are chiral Néel walls stabilized by the Dzyaloshinskii-Moriya interaction (DMI). The Néel wall magnetization points in-plane, perpendicular to the DW and hence parallel to the current direction, which maximizes the amplitude of the current-induced damping-like SOT and promotes very large DW displacement velocities v DW , of the order of 100 m s −1 for a current density j = 10 8 A cm −2 . This large v DW allows for high speed DW displacements in racetrack structures 4,8,9 as well as for sub-ns reversal of ferromagnetic dots. 10,22 Two prominent effects of the DMI in perpendicularly magnetized layers are the tilting of the DW 10,16,23-27 and the asymmetric v DW relative to the current direction. 9,26,28 These two effects are related by the DW dynamics under the combined action of DMI and damping-like SOT. 16,[25][26][27] Tilted DWs were first observed in Pt/Co/Ni/Co layers by imaging the magnetic domains after a sequence of current pulses using MOKE microscopy 23 and later reproduced by analytical and micromagnetic models. 16,25,27 Figure 1(a) illustrates the DW configurations reported in Ref. 23 for the four combinations of current (black arrows) and up/down, down/up domains propagating in a racetrack. The tilt angle is indicated by ψ and the propagation direction of the DW is given by the green arrows. These DW tilt symmetries are typical of perpendicularly magnetized films with a Pt underlayer. Recent time-resolved x-ray microscopy measurements on Pt/Co/AlO x dots, however, reported DWs rotated by about 9...

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“…We note that our variational setting could similarly be used to study the gradient flow dynamics governed by ( 4.2 ) (for a related study, see [ 40 ]). Other physical effects, however, need to be incorporated to account for some unusual properties of chiral domain walls such as their tilt in sufficiently strong external fields [ 22 , 35 ].…”

Section: Discussionmentioning

confidence: 99%

“…These walls play a crucial role in producing new types of magnetization patterns inside a ferromagnet. For instance, in the presence of a transverse applied field, chiral edge domain walls provide a mechanism for tilting of an interior domain wall in a ferromagnetic strip [ 22 , 35 ]. Moreover, they also significantly modify the dynamic behaviour of the interior domain wall under the action of current and an applied field [ 18 ].…”

Section: Introductionmentioning

confidence: 99%

Domain structure of ultrathin ferromagnetic elements in the presence of Dzyaloshinskii–Moriya interaction

Muratov

Slastikov

2017

Proc. R. Soc. A.

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Recent advances in nanofabrication make it possible to produce multilayer nanostructures composed of ultrathin film materials with thickness down to a few monolayers of atoms and lateral extent of several tens of nanometers. At these scales, ferromagnetic materials begin to exhibit unusual properties, such as perpendicular magnetocrystalline anisotropy and antisymmetric exchange, also referred to as Dzyaloshinskii–Moriya interaction (DMI), because of the increased importance of interfacial effects. The presence of surface DMI has been demonstrated to fundamentally alter the structure of domain walls. Here we use the micromagnetic modelling framework to analyse the existence and structure of chiral domain walls, viewed as minimizers of a suitable micromagnetic energy functional. We explicitly construct the minimizers in the one-dimensional setting, both for the interior and edge walls, for a broad range of parameters. We then use the methods of Γ-convergence to analyse the asymptotics of the two-dimensional magnetization patterns in samples of large spatial extent in the presence of weak applied magnetic fields.

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Theory of the Dzyaloshinskii domain-wall tilt in ferromagnetic nanostrips

Cited by 32 publications

References 44 publications

Nontrivial phase diagram for an elastic interaction model of spin crossover materials with antiferromagnetic-like short-range interactions

Nontrivial phase diagram for an elastic interaction model of spin crossover materials with antiferromagnetic-like short-range interactions

Asymmetric velocity and tilt angle of domain walls induced by spin-orbit torques

Domain structure of ultrathin ferromagnetic elements in the presence of Dzyaloshinskii–Moriya interaction

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