The incorporation of the Cauchy stress matrix tensor in micromagnetic simulations

Dean, J.; Bryan, Matthew T.; Hrkac, G.; Goncharov, Alexander V.; Freeman, C. L.; Bashir, Muhammad; Schrefl, T.; Allwood, D. A.

doi:10.1063/1.3489969

Cited by 12 publications

(9 citation statements)

References 25 publications

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“…By varying the values of cubic anisotropy energy densities K1 and K2, introducing negative uniaxial anisotropy, or including magnetoelastic effects in the model 53 , the interplay between the MCA and shape anisotropy can be tuned to produce a variety of magnetic configurations. Figures 9a,b show a vortex domain formation which develops at room temperature when a negative uniaxial anisotropy is introduced to the system, with anisotropy energy densities Ku = -0.01 Merg/cm 3 and Ku = -1.0 Merg/cm 3 , respectively.…”

Section: Figure 6: Exploded Slices Of the Micromagnetic Configuration...mentioning

confidence: 99%

Periodic chiral magnetic domains in single-crystal nickel nanowires

Kan

Lubarda

Chan

et al. 2018

Phys. Rev. Materials

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We report on experimental and computational investigations of the domain structure of ~0.2 x 0.2 x 8 μm single-crystal Ni nanowires (NWs). The Ni NWs were grown by a thermal chemical vapor deposition technique that results in highly-oriented single-crystal structures on amorphous SiOx coated Si substrates. Magnetoresistance measurements of the Ni NWs suggest the average magnetization points largely off the NW long axis at zero field. X-ray photoemission electron microscopy images show a well-defined periodic magnetization pattern along the surface of the nanowires with a period of λ = 250 nm. Finite element micromagnetic simulations reveal that an oscillatory magnetization configuration with a period closely matching experimental observation (λ = 240 nm) is obtainable at remanence. This magnetization configuration involves a periodic array of alternating chirality vortex domains distributed along the length of the NW. Vortex formation is attributable to the cubic anisotropy of the single crystal Ni NW system and its reduced structural dimensions. The periodic alternating chirality vortex state is a topologically protected metastable state, analogous to an array of 360° domain walls in a thin strip. Simulations show that other remanent states are also possible, depending on the field history. Effects of material properties and strain on the vortex pattern are investigated. It is shown that at reduced cubic anisotropy vortices are no longer stable, while negative uniaxial anisotropy and magnetoelastic effects in the presence of compressive biaxial strain contribute to vortex formation.The investigation of magnetism in mesoscale structures has attracted considerable interest in recent years 1-6 . As the structural dimensions of materials are reduced down to typical length scales associated with ferromagnetic ordering, competitions between several magnetic interactions arise and can result in the formation of new, intricate magnetic configurations 7-11 . These new structures could offer a pathway towards future applications in high-density data storage 12-16 , compact magnetic sensors 17, 18 , high frequency nanoscale oscillators 19,20 , and magnetic logic [21][22][23][24] . For example, a competition between the

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Section: Figure 6: Exploded Slices Of the Micromagnetic Configuration...mentioning

confidence: 99%

Periodic chiral magnetic domains in single-crystal nickel nanowires

Kan

Lubarda

Chan

et al. 2018

Phys. Rev. Materials

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“…This experimental study demonstrates that it is possible to gradually change the coercive field by externally applying anisotropic strain to the patterned nanostructures. In addition, these experimental results are compared with an existing micromagnetic model originally proposed by Dean et al 17 incorporating finite element mechanical analysis. Our results shows that experimental data agree with the simulation when nonuniform strain distribution is incorporated into the micromagnetic simulation using a position dependant strain-induced magnetic anisotropy term.…”

Section: Introductionmentioning

confidence: 99%

Strain-induced magnetization change in patterned ferromagnetic nickel nanostructures

Bur

Hockel

et al. 2011

Journal of Applied Physics

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We report strain-induced coercive field changes in patterned 300 Â 100 Â 35 nm 3 Ni nanostructures deposited on Si/SiO 2 substrate using the magnetoelastic effect. The coercive field values change as a function of the applied anisotropy strain ($1000 ppm) between 390 and 500 Oe, demonstrating that it is possible to gradually change the coercive field elastically. While the measured changes in coercive field cannot be accurately predicted with simple analytical predictions, fairly good agreement is obtained by using a micromagnetic simulation taking into account the influence of nonuniform strain distribution in the Ni nanostructures. The micromagnetic simulation includes a position dependant strain-induced magnetic anisotropy term that is computed from a finite element mechanical analysis. Therefore, this study experimentally corroborates the requirement to incorporate mechanical analysis into micromagnetic simulation for accurately predicting magnetoelastic effects in patterned ferromagnetic nanostructures. V

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“…A finite element micromagnetic model [24,25] was used to solve the Landau-Lifshitz-Gilbert equation for smooth-sided wires containing either a vortex or a transverse domain wall.…”

Section: Finite Element Modellingmentioning

confidence: 99%

Transverse and vortex domain wall structure in magnetic nanowires with uniaxial in-plane anisotropy

Bryan

Bance

Dean

et al. 2011

J. Phys.: Condens. Matter

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Micromagnetic and analytical models are used to investigate how in-plane uniaxial anisotropy affects transverse and vortex domain walls in nanowires where shape anisotropy dominates. The effect of the uniaxial anisotropy can be interpreted as a modification of the effective wire dimensions. When the anisotropy axis is aligned with the wire axis (θ a = 0), the wall width is narrower than when no anisotropy is present. Conversely, the wall width increases when the anisotropy axis is perpendicular to the wire axis (θ a =π/2). The anisotropy also affects the nanowire dimensions at which transverse walls become unstable. This phase boundary shifts to larger widths or thicknesses when θ a = 0, but smaller widths or thicknesses when θ a = π/2.2

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The incorporation of the Cauchy stress matrix tensor in micromagnetic simulations

Cited by 12 publications

References 25 publications

Periodic chiral magnetic domains in single-crystal nickel nanowires

Periodic chiral magnetic domains in single-crystal nickel nanowires

Strain-induced magnetization change in patterned ferromagnetic nickel nanostructures

Transverse and vortex domain wall structure in magnetic nanowires with uniaxial in-plane anisotropy

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