Spin waves in circular soft magnetic dots at the crossover between vortex and single domain state

Aliev, F. G.; Sierra, Juan F.; Awad, Ahmad A.; Kakazei, G. N.; Han, Dong‐Soo; Kim, Sang Koog; Metlushko, V.; Ilić, B.; Guslienko, K. Yu.

doi:10.1103/physrevb.79.174433

Cited by 80 publications

(62 citation statements)

References 31 publications

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“…Also note that the calculated field has collective character -for each of the stripes it is a sum of the field produced by the eddy current in the stripe and of the fields of all its neighbours at the position of the stripe (see the summation sign in Eq. (8).) An example of calculation using Eq.…”

Section: Discussionmentioning

confidence: 99%

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Microwave magnetic dynamics in ferromagnetic metallic nanostructures lacking inversion symmetry

Kostylev

Yang

Maksymov

et al. 2016

Journal of Applied Physics

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In this work we carried out systematic experimental and theoretical investigations of the ferromagnetic resonance (FMR) response of quasi-twodimensional magnetic nano-objects -microscopically long nanostripes made of ferromagnetic metals. We were interested in the impact of the symmetries of this geometry on the FMR response. Three possible scenarios, from which the inversion symmetry break originated were investigated: (1) from the shape of the stripe crosssection, (2) from the double-layer structure of the stripes with exchange coupling between the layers, and (3) from the single-side incidence of the microwave magnetic field on the plane of the nano-pattern. The latter scenario is characteristic of the stripline FMR configuration. It was found that the combined effect of the three symmetry breaks is much stronger than impacts of each of these symmetry breaks separately. I. IntroductionFerromagnetic resonance (FMR) is a powerful tool for studying dynamic properties of metallic ferromagnetic thin films and nanostructures (see e.g., Refs. [1][2][3][4][5][6][7][8][9][10][11][12]). These materials are important for the emerging fields of magnonics [13], microwave spintronics [14][15][16][17], and for novel sensor applications [18][19][20][21].Macroscopically-long stripes with sub-micron cross-section made of ferromagnetic materials have attracted a lot of attention, because this geometry is a very convenient model object for studying the impact of geometric confinement on magnetization dynamics on the sub-micrometre and nanometer scales [22][23][24][25][26][27][28][29][30]. The main reasons for the attractiveness of this geometry are the practical absence of a static demagnetizing field H ds when the external field is applied along the stripes (i.e. along the axis y in Fig. 1(a)) and the quasi-two-dimensional (2D) character of the dynamics.The former property allows clear separation of the static and dynamic demagnetizing effects. Furthermore, because of the absence of H ds , the static magnetization configuration for the stripes is very simple. The static magnetization vector has the same magnitude -equal to the saturation magnetization for the material -and the same direction -along the stripe -for every point on the stripe crosssection. Due to strong shape anisotropy for this geometry, this configuration remains very stable even at remanence [29][30][31]. The simplicity of the magnetization ground state, together with the 2D character of the magnetization dynamics, results in simple analytical and quasi-analytical theoretical models able to deliver a clear physical

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Section: Discussionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10][11][12]). These materials are important for the emerging fields of magnonics [13], microwave spintronics [14][15][16][17], and for novel sensor applications [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Microwave magnetic dynamics in ferromagnetic metallic nanostructures lacking inversion symmetry

Kostylev

Yang

Maksymov

et al. 2016

Journal of Applied Physics

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“…11,16,18,[29][30][31][32][33]53 The magnetic parameters used in simulations were: the saturation magnetization M s = 800 emu/ cc, the exchange constant A =13ϫ 10 −12 J / m, the gyromagnetic ratio ␥ / 2 = 2.95 MHz/ Oe. 11,55 We use the code object oriented micromagnetic framework ͑OOMMF͒ 56 with the LLG equation of motion modified by a term that includes the interaction with a spin polarized current. 1 Using this code, magnetization dynamics can be explored as a function of current, applied magnetic field, and the sizes/shape of the free layer and polarizer.…”

Section: Appendixmentioning

confidence: 99%

“…The vortex magnetization distribution stability as well as the vortex excitations were studied in Refs. [5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Limits for the vortex state spin torque oscillator in magnetic nanopillars: Micromagnetic simulations for a thin free layer

Aranda

González

Val

et al. 2010

Journal of Applied Physics

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Anomalous magnetic properties of 7nm single-crystal Co3O4 nanowires J. Appl. Phys. 111, 013910 (2012) High field-gradient dysprosium tips for magnetic resonance force microscopy Appl. Phys. Lett. 100, 013102 (2012) Dipolar interactions in magnetic nanowire aggregates J. Appl. Phys. 110, 123924 (2011) Dielectric and spin relaxation behaviour in DyFeO3 nanocrystals J. Appl. Phys. 110, 124301 (2011) Finite size versus surface effects on magnetic properties of antiferromagnetic particles Appl. Phys. Lett. 99, 232507 (2011) Additional information on J. Appl. Phys. We report micromagnetic simulations of magnetization dynamics of a vortex state in the free layer of a circular nanopillar excited by the spin transfer torque effect of a perpendicular to the layer ͑dot͒ plane spin-polarized electrical current. The magnetization of the reference layer ͑polarizer͒ is assumed to be fixed. A new regime of the dynamic magnetization response to the current is reported: vortex expelling from the dot, subsequent in-plane magnetization oscillations in single domain state, and the vortex return with an opposite core polarization. We analyze conditions ͑limits of the vortex state as a nano-oscillator͒ to achieve steady magnetization oscillations corresponding to a gyrotropic motion of the vortex core in terms of the current intensity. These conditions are formulated via the critical currents and vary greatly with the magnetic damping parameter and the cell size used for micromagnetic simulations. The existing experiments on the current induced magnetization dynamics in nanopillars and nanocontacts are discussed.

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“…For in-plane magnetic driving field the azimuthal SW and GM mode ͑m = Ϯ 1͒ with nonzero dipolar moments can be only excited. 8,9,23 The azimuthal SW with m = Ϯ 1 having the same symmetry as the vortex background GM are especially important because they are responsible for the vortex-core distortion resulting in the core switching. 15 The component A z ‫ץ−=‬ ⌽ of the vector A plays crucial role in the dynamics, whereas the other components of A ϳ ‫ץ‬ ⌰ , related to the vortex core ͑the area where ⌰ / 2͒, can be neglected in the main approximation.…”

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confidence: 99%

Topological gauge field in nanomagnets: Spin-wave excitations over a slowly moving magnetization background

2010

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We introduce a topological gauge vector potential which influences spin-wave excitations over arbitrary nonuniform, slowly moving magnetization background. The time component of the gauge potential plays a principal role in the magnetization dynamics of typical magnetic nanostructures. As an example, we consider spin modes excited in the vortex-state magnetic dots. The vortex-spin-wave interaction is described as a consequence of the gauge field arising due to the moving vortex magnetization. The approach yields a giant frequency splitting of the spin waves having nonzero overlapping with the vortex background mode as well as a finite vortex mass of dynamical origin. DOI: 10.1103/PhysRevB.81.014414 PACS number͑s͒: 75.40.Gb, 75.40.Mg, 75.75.Ϫc In the recent years a lot of attention was paid to influence of the gauge fields on semiclassical equations of motion of quantum particles such as electrons in solids.1 It was shown within the local models of itinerant magnetism 2,3 and s-d exchange interaction 4 that a topological gauge field induced by a nonuniform magnetization acts on electron motion as a real external magnetic or electric field.5 From the other side, spin-polarized electric current can essentially contribute to the equation of motion of magnetization 6 transferring angular momentum. The conception of such gauge field has led to prediction and explanation of various observable magnetoelectric effects in patterned nanostructures related to spin angular momentum transfer ͑spin-Hall effect, magnetoresistance, spin pumping, domain-wall dynamics, etc.͒, for recent review see Ref. 1 and references therein.Precise knowledge of the dynamic processes in patterned nanomagnetic materials is important due to their applications in magnetic storage media, magnetic sensors, spintronic devices including microwave nano-oscillators, 7 etc. Understanding dynamic response of nanomagnets to external magnetic field 8,9 or spin-polarized current 10,11 involves rich underlying fundamental physics. Among the different patterned magnetic structures considered so far, flat ferromagnetic particles ͑dots͒ with submicron lateral sizes occupy a special place due to their unique, nonuniform vortex ground state.12 Regular arrays of such dots are being considered as a new high-density nonvolatile recording media 13 characterized by two Boolean variables: chirality and polarity of magnetic vortex core.12 Special interest in the vortex core, small area where magnetization deviates from the dot plane ͑ϳ10-15 nm in size 14 ͒, is inspired by the possibility of easy and fast switching its magnetization direction.15,16 The vortex-state dots as well as domain walls in magnetic nanostripes 5,11 represent the simplest patterned nanosystems with topologically nontrivial magnetization distribution. However, there is still lack of understanding of the spinwave dynamics in such strongly nonuniform ground states. The energy dissipation of moving one-dimensional domain wall in bulk anisotropic ferromagnet due to interaction with thermal magnons was...

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Spin waves in circular soft magnetic dots at the crossover between vortex and single domain state

Cited by 80 publications

References 31 publications

Microwave magnetic dynamics in ferromagnetic metallic nanostructures lacking inversion symmetry

Microwave magnetic dynamics in ferromagnetic metallic nanostructures lacking inversion symmetry

Limits for the vortex state spin torque oscillator in magnetic nanopillars: Micromagnetic simulations for a thin free layer

Topological gauge field in nanomagnets: Spin-wave excitations over a slowly moving magnetization background

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