Understanding current-driven dynamics of magnetic Néel walls in heavy metal/ferromagnetic metal/oxide trilayers

Abstract

We consider analytically current-driven dynamics of magnetic Néel walls in heavy metal/ ferromagnetic metal/oxide trilayers where strong spin-orbit coupling and interfacial Dzyaloshinskii-Moriya interaction (i-DMI) coexist. We show that field-like spin-orbit torque (FL-SOT) with effective field along´n J(n being the interface normal andĴ being the charge current direction) and i-DMI induced torque can both lead to Walker breakdown suppression meanwhile leaving the wall mobility (velocity versus current density) unchanged. However, i-DMI itself can not induce the 'universal absence of Walker breakdown' (UAWB) while FL-SOT exceeding a certain threshold can. Finitelyenlarged Walker limits before UAWB are theoretically calculated and well explain existing data. In addition, change in wall mobility and even its sign-inversion can be understood only if the antidamping-like SOT is appended. For Néel walls in ferromagnetic-metal layer with both perpendicular and in-plane anisotropies, we have calculated the respective modifications of wall mobility under the coexistence of spin-transfer torque, SOTs and i-DMI. Analytics shows that in trilayers with perpendicular anisotropy strong enough spin Hall angle and appropriate sign of i-DMI parameter can lead to sign-inversion in wall mobility even under small enough current density, while in those with in-plane anisotropy this only occurs for current density in a specific range.Over the past decade, in heavy metal/ferromagnetic metal/oxide (HM/FMM/Oxide) trilayers, axial domain wall propagation in FMM layer with perpendicular magnetic anisotropy (PMA) or in-plane magnetic anisotropy (IPMA) driven by axial currents are experimentally observed [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. In certain case (Pt Co AlO x ), walls can move at a high velocity up to 400 m s -1 when current density is around -10 A cm 8 2 [37]. More interestingly, walls with certain polarity can even move in the direction of charge current [33][34][35][36][37][38][39][40][41], which is also confirmed by numerical simulations [42][43][44][45]. To understand these findings, spin-orbit torques (SOTs) from strong spin-orbit coupling (SOC) in these trilayers are proposed [46][47][48][49][50][51][52][53][54][55][56][57][58][59]. SupposeĴ is the charge current direction and n is interface normal. Mathematically, SOTs can be decomposed into two perpendicular components: (a) µ´(ˆ) m J n which is odd in magnetization direction m and usually referred to as field-like (FL) torque; (b) µ´´[ (ˆ)] m m J n which is even in m and usually called anti-damping-like (ADL) torque. Physically, two typical mechanisms are of most importance: the 'spin Hall torques' from the spin Hall effect (SHE) [60] in HM layer and the 'Rashba torques' from the structure inversion asymmetry (SIA) at the HM/ FMM interface. In early literatures, ADL-SOTs are believed to stem mostly from bulk SHE while field-like spinorbit torques (FL-SOTs) are mainly attributed to interfacial Rashba SOC. However, recent works based on scatt...

Chiral domain wall dynamics in magnetic heterostructures with bulk Dzyaloshinskii-Moriya interactions

“…For fixed b and κ, once the maximum absolute value of the function f , i.e. | f (ϕ)| max , is found for ϕ ∈ [0, 2π), the new Walker field then reads recovers the result in one of our recent works [6]. However, in real magnetic heterostructures, κ is generally the order of 1.…”

“…Recently, discussions about chiral magnetic solitons stabilized by the Dzyaloshinskii-Moriya interaction (DMI) become extraordinarily active. The most common examples are chiral domain walls (DWs) [1][2][3][4][5][6], skyrmions/antiskyrmions [7][8][9][10][11] and bimerons [12][13][14][15][16], etc. Historically, the bulk DMI (bDMI) was first proposed which should phenomenologically include an odd term of the spatial gradient of magnetization as a result of being an antisymmetric exchange coupling [17].…”

Determination of the Dzyaloshinskii-Moriya interactions

“…At last, in our theory "q − ϕ − ∆" model [29,30] is adopted. For ideal narrow-strip shaped heterostructures when considering the DMI-induced wall tiling χ [28] and canting θ ∞ [37] in domains from in-plane fields, a more complicated wall ansatz tan ϑ 2 = e R + tan(θ ∞ /2) 1 + e R tan(θ ∞ /2) , φ = ϕ(t) (10) can be proposed with R ≡ η[(x − q) cos χ + y sin χ]/∆. By integrating the resulting dynamical equations over strip surface in xy−plane, alternative Lagrangian-based collective coordinate models, such as the "q − ϕ − χ" [28] or "q − ϕ − χ − ∆" [38,39] models, emerge.…”

“…where an overdot means ∂ /∂t and X is a related coordinate. When X = θ (φ ), the familiar Landau-Lifshitz-Gilbert equation [10] is recovered. In principle, θ (r,t) and φ (r,t) vary from point to point, thus generates huge number of degrees of freedom.…”

“…The importance of DMI in manipulating magnetic structures and dynamics has been recognized and an upsurge of research was witnessed in the passing decades after a successful explanation of huge remanent magnetization enhancement due to the DMI induced by Au or Pt impurities in metallic spin glasses [3] and distinct features of chiral DW dynamics in ultrathin magnetic films [4]. The main consensuses of the community are: (i) DMI comes from the spin-orbit coupling in magnetic systems with broken inversion symmetry either in a bulk or at an interface; (ii) DMI is crucial for stabilizing chiral magnetic solitons, such as skyrmions [5,6] and chiral DWs [7,8]; (iii) DMI plays an important role in the dynamics of both magnetic chiral solitons [9,10] and spin waves [11]. Therefore precise determination of the nature and strength of a DMI is not only of a fundamental issue, but also practically important.…”