Time-dependent Ginzburg-Landau simulations of superconducting vortices in three dimensions

Lara, Antonio; González-Ruano, César; Aliev, F. G.

doi:10.1063/10.0000861

Cited by 11 publications

(5 citation statements)

References 30 publications

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“…Where N x and N y are the total number of cells in each dimension of the simulation, and F is a filter "Vortex generation function" that takes into account the simulated dependence of the number of vortices on the vertically applied field (Figure S13c). The vortices were simulated using the Time Dependent Ginzburg Landau code devel- ), simulated at T = 2 K by using the TDGL code described in [59]. The insert shows a typical image of the vortices at H=0.15Hc2 oped in Madrid described in [59].…”

Section: S6 Evaluation Of the Vortex Induced Pinning Of Domain Wallsmentioning

confidence: 99%

“…The vortices were simulated using the Time Dependent Ginzburg Landau code devel- ), simulated at T = 2 K by using the TDGL code described in [59]. The insert shows a typical image of the vortices at H=0.15Hc2 oped in Madrid described in [59]. The TDGL simulations took place in 5×5 µm 2 Vanadium samples with 200×200 cells, at T = 2 K, with a coherence length ξ 0 = 2.6×10 −8 based on our experimental estimations for the studied devices, κ = 3 and T C = 4 K. A uniform field was applied in the perpendicular direction, its magnitude varying from 0.1H C2 to 0.6H C2 , and the number of vortices generated in the relaxed state were counted.…”

Section: S6 Evaluation Of the Vortex Induced Pinning Of Domain Wallsmentioning

confidence: 99%

“…Indeed, our experiments show that magnetization, when locked below T C in the (π + π/4) angle, hardly depends on the absolute value of the external field along [110] varied between 0 and 100 Oe. Moreover, simulations of the vortex-DW interaction using MuMax3 [52] and TDGL codes [59] discard the vortex mediated DW pinning [26,27] scenario including when interfacial magnetic defects created by misfit dislocations [54] are considered (see Supplemental material S6 [49]). The vortex pinning mechanism also contradicts that only the (0 − π) field rotation span (Figure 2a) gets affected below T C /2.…”

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Superconductivity-induced change in magnetic anisotropy in epitaxial ferromagnet-superconductor hybrids with spin-orbit interaction

et al. 2020

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The interaction between superconductivity and ferromagnetism in thin film superconductor/ferromagnet heterostructures is usually reflected by a change in superconductivity of the S layer set by the magnetic state of the F layers. Here we report the converse effect: transformation of the magnetocrystalline anisotropy of a single Fe(001) layer, and thus its preferred magnetization orientation, driven by the superconductivity of an underlying V layer through a spin-orbit coupled MgO interface. We attribute this to an additional contribution to the free energy of the ferromagnet arising from the controlled generation of triplet Cooper pairs, which depends on the relative angle between the exchange field of the ferromagnet and the spin-orbit field. This is fundamentally different from the commonly observed magnetic domain modification by Meissner screening or domain wall-vortex interaction, and it offers the ability to fundamentally tune magnetic anisotropies using superconductivity-a key step in designing future cryogenic magnetic memories.

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Section: S6 Evaluation Of the Vortex Induced Pinning Of Domain Wallsmentioning

confidence: 99%

Section: S6 Evaluation Of the Vortex Induced Pinning Of Domain Wallsmentioning

confidence: 99%

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confidence: 99%

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Superconductivity-induced change in magnetic anisotropy in epitaxial ferromagnet-superconductor hybrids with spin-orbit interaction

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“…While TDGL simulations of microsized helical stripes are at the edge of the current computation capabilities, various aspects of TDGL simulations in 3D geometries are extensively discussed. [715,726,727] Recently, vortex patterns in nanostructured microhelices have been considered and quasi-degeneracy of vortex patterns has been revealed in the helical coils when the number of vortices is incommensurable with the total number of half-turns. [678] Experimentally, free-standing superconducting Nb nanohelices have recently been fabricated from a 50 nmthick Nb film rolled up into helices with diameters down to 6 μm, [29] see Figure 16c.…”

Section: Applications Of Superconducting 3d Nanoarchitecturesmentioning

confidence: 99%

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

et al. 2021

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condensed matter physics, including cell membranes, [1] nematic crystals, [2,3] superfluids, [4] semiconductors, [5][6][7][8] ferromagnets, [9] and superconductors. [10,11] Currently, much attention is paid to strongly correlated electronic systems, for example, ferromagnets and superconductors, as they provide a unique tool to manipulate the topology of coexisting vector and scalar fields, associated with geometries of conventional systems.Until recently, in the case of magnetism, the influence of the geometry on the spin vector fields was addressed primarily by the design of the sample boundaries. This approach naturally brings the shape anisotropy to the system and leads to the formation of specific spin textures, for example, magnetic vortices [12] and antivortices [13] as well as provides control over the dynamics of the topologically nontrivial magnetic solitons. [14][15][16][17][18] This discussion also tackles the state of the art in modern experimental antiferromagnetism, where the design of the sample topography and boundaries allows to control the domain wall states. [19][20][21][22] With the development of novel fabrication techniques allowing to realize complex 3D architectures, not only the boundary effects but also the extrinsic geometrical properties (e.g., local curvatures) can be addressed rigorously for the case of ferromagnets [23][24][25][26][27] as well as superconductors. [28][29][30] The explored effects are directly related to the interplay between the Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro-and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-...

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“…We simulated OOP hysteresis cycles where a correction to the applied field was added based on a typical Meissner effect (ME) hysteresis cycle (obtained from 36 , shown in Figure 6b inset), scaled for different values of field contribution from Meissner effect and adapted to the first and second critical fields of vanadium (correspondingly H c1 and H c2 ). The contribution from superconducting vortices was taken into account by using an in-group developed program that numerically solves the time dependent Ginzburg-Landau equations in order to simulate the behaviour of type II superconductors under magnetic fields 37 . The initial stray fields from an in-plane saturated FM simulation were used to generate a distribution of vortices, and then the fields generated by those vortices were calculated 38 and added into the corrected hysteresis cycle.…”

Section: Influence Of Meissner Effect On the Oop Magnetization Reorie...mentioning

confidence: 99%

Superconductivity assisted change of the perpendicular magnetic anisotropy in V/MgO/Fe junctions

González-Ruano,

Caso,

Johnsen

et al. 2021

Preprint

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Due to its technological importance, controlling the perpendicular magnetic anisotropy (PMA) in thin films has received considerable attention in recent years. PMA based devices usually involve heavy-metal (oxide)/ferromagnetic-metal bilayers, where, thanks to interfacial spin-orbit coupling (SOC), the in-plane (IP) stabilization of the magnetization is broken. Here we show experimentally that in V/MgO/Fe(001) epitaxial junctions with competing in-plane and out-of-plane (OOP) magnetic anisotropies, the SOC mediated interaction between a ferromagnet (FM) and a superconductor (SC) enhances the effective PMA below the superconducting transition. For the larger area junctions with more stable IP magnetization, the OOP anisotropy field can be increased either by the interaction between magnetic stray fields and superconducting vortices or decreased by an applied electric field. Our findings, supported by theoretical and numerical modelling of the ferromagnet-superconductor interaction, open pathways to active control of magnetic anisotropy in the emerging dissipation-free superconducting electronics involving spin.

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Time-dependent Ginzburg-Landau simulations of superconducting vortices in three dimensions

Cited by 11 publications

References 30 publications

Superconductivity-induced change in magnetic anisotropy in epitaxial ferromagnet-superconductor hybrids with spin-orbit interaction

Superconductivity-induced change in magnetic anisotropy in epitaxial ferromagnet-superconductor hybrids with spin-orbit interaction

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

Superconductivity assisted change of the perpendicular magnetic anisotropy in V/MgO/Fe junctions

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