Spin-Hall nano-oscillator with oblique magnetization and Dzyaloshinskii-Moriya interaction as generator of skyrmions and nonreciprocal spin-waves

Giordano, A.; Verba, Roman; Zivieri, R.; Laudani, Antonino; Puliafito, Vito; Gubbiotti, G.; Tomasello, Riccardo; Siracusano, Giulio; Azzerboni, B.; Carpentieri, Mario; Slavin, A. N.; Finocchio, G.

doi:10.1038/srep36020

Cited by 43 publications

(47 citation statements)

References 53 publications

(85 reference statements)

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“…Interestingly, the skyrmion modes are analog to the dynamical skyrmions discussed by Giordano et al . 24 . The dynamical skyrmions treated as non-linear gyrotropic rotations of the magnetic vortex core that give rise to spin-waves with spiral spatial profile.…”

Section: Numerical Resultsmentioning

confidence: 99%

Tunable odd-frequency triplet pairing states and skyrmion modes in chiral p-wave superconductor

Lou

Wen

Zha

et al. 2017

Sci Rep

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Bogliubov-de Gennes equations are solved self-consistently to investigate the properties of bound states in chiral p-wave superconductive disks. It shows that either an s-wave or the mixed d- and s-wave state with odd-frequency and spin-triplet symmetry is induced at the vortex core, depending both on the chirality of the pairing states and on the vortex topology. It is also found that the odd-frequency triplet even parity (OTE) bound state can be manipulated with a local non-magnetic potential. Interestingly, with an appropriate potential amplitude, the zero-energy OTE bound state can be stabilized at a distance from the vortex core and from the local potential. Possible existences of the Majorana fermion modes are expected if the particle-hole symmetry property is applied to the zero-energy OTE bound state. Moreover, skyrmion modes with an integer topological charge have been found to exist.

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Section: Numerical Resultsmentioning

confidence: 99%

Tunable odd-frequency triplet pairing states and skyrmion modes in chiral p-wave superconductor

Lou

Wen

Zha

et al. 2017

Sci Rep

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“…Ds, 76.50.+g, 75.78.Cd, 75.76.+j been shown that the i-DMI in STO and SHO results in the excitation of two-dimensional nonreciprocal spin waves, and, at a sufficient strength of the i-DMI, in the generation of spiral spin wave modes.The main purpose of this work is the development of an analytical model, which describes the excitation of two-dimensional nonreciprocal spin waves in a nanocontact SHO (the quasi-onedimensional case of a nanowire-based SHO has been already considered theoretically in Ref. [38]). Our approach is based on an approximate solution of the linearized Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation and, in fact, is a generalization of the Slonczewski's theory [14] to the case of the presence of the i-DMI.…”

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Theory of nonreciprocal spin-wave excitations in spin Hall oscillators with Dzyaloshinskii-Moriya interaction

et al. 2018

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A two-dimensional analytical model for the description of the excitation of nonreciprocal spin waves by spin current in spin-Hall oscillators in the presence of the interfacial Dzyaloshinskii-Moriya interaction (i-DMI) is developed. The theory allows one to calculate the threshold current for the excitation of spin waves, as well as the frequencies and spatial profiles of the excited spin wave modes. It is found, that the frequency of the excited spin waves exhibits a quadratic red shift with the i-DMI strength. At the same time, in the range of small and moderate values of the i-DMI constant, the averaged wave number of the excited spin waves is almost independent of the i-DMI, which results in a rather weak dependence on the i-DMI of the threshold current of the spin wave excitation. The obtained analytical results are confirmed by the results of micromagnetic simulations.PACS numbers: 75.30. Ds, 76.50.+g, 75.78.Cd, 75.76.+j been shown that the i-DMI in STO and SHO results in the excitation of two-dimensional nonreciprocal spin waves, and, at a sufficient strength of the i-DMI, in the generation of spiral spin wave modes.The main purpose of this work is the development of an analytical model, which describes the excitation of two-dimensional nonreciprocal spin waves in a nanocontact SHO (the quasi-onedimensional case of a nanowire-based SHO has been already considered theoretically in Ref. [38]).Our approach is based on an approximate solution of the linearized Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation and, in fact, is a generalization of the Slonczewski's theory [14] to the case of the presence of the i-DMI. The developed theory allows one to calculate profiles of the excited spin waves, which are approximately described by a combination of Laguerre's polynomials and Tricomi's hypergeometric functions, as well as to calculate the excitation threshold and frequency of excited spin waves, which both become lower with the increased i-DMI strength.The paper is organized as follows. Sections II describes the model system used in this study. In Sec. III a step-by-step derivation of the analytical formalism is presented. Analytically calculated results are compared with micromagnetic modeling in Sec. IV. Finally, conclusions are given in Sec. V. II. Device under study and micromagnetic simulationsThe device under investigation is shown in Fig. 1. It is a typical SHO, consisting of a ferromagnetic/ heavy metal bilayer. The current is injected locally in the bilayer by using a gold concentrator of a double-triangular shape with a distance d between the tips. The system is biased by an external magnetic field B ext , applied in the y-z plane and making the angle θ B with the film normal (axis z) ( Fig. 1(b)). The bias magnetic field is required in order to tilt the film static magnetization from the in-plane direction, and, if the angle θ M between the static magnetization and film normal is sufficiently small, the SHO supports excitation of propagating spin waves.

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“…Snapshots of the Oersted field in the ferromagnet are shown in Figs. 1(d)-(e) for the devices with two and five SHOs, respectively. These computations are based on the numerical framework already described in previous works 12, 37 and they have been performed within a parallel processing framework which has been designed and implemented for accelerating algorithms computation. Synchronization still takes place for any applied current also in presence of a small variation of out-of-plane amplitude and in-plane field angle (not shown).…”

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“…33 For the simulations including IDMI, we have chosen a value of 1.5mJ/m 2 for the parameter D. 37 An external field of 400mT, tilted 15° degrees with respect to the z-axis, is applied to the device and tilts the equilibrium magnetization at about 23° with respect to the z-axis. Snapshots of the Oersted field in the ferromagnet are shown in Figs. 1(d)-(e) for the devices with two and five SHOs, respectively.…”

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Scalable synchronization of spin-Hall oscillators in out-of-plane field

Puliafito

Giordano

Laudani

et al. 2016

Applied Physics Letters

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A strategy for a scalable synchronization of an array of spin-Hall oscillators (SHOs) is illustrated. In detail, we present micromagnetic simulations of two and five SHOs realized by means of couples of triangular golden contacts on the top of a Pt/CoFeB/Ta trilayer. Results highlight that the synchronization occurs for the whole current region that gives rise to the excitation of self-oscillations. This is linked to the role of the magnetodipolar coupling, which is the phenomenon driving the synchronization when the distance between oscillators is not too large. Synchronization turns out to be also robust against geometrical differences of the contacts, simulated by considering variable distances between the tips ranging from 100nm to 200nm. Besides, it entails an enlargement of the radiation pattern that can be useful for the generation of spin-waves in magnonics applications. Simulations performed to study the effect of the interfacial Dzyaloshinskii-Moriya interaction show nonreciprocity in spatial propagation of the synchronized spin-wave. The simplicity of the geometry and the robustness of the achieved synchronization make this design of array of SHOs scalable for a larger number of synchronized oscillators. a)

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Spin-Hall nano-oscillator with oblique magnetization and Dzyaloshinskii-Moriya interaction as generator of skyrmions and nonreciprocal spin-waves

Cited by 43 publications

References 53 publications

Tunable odd-frequency triplet pairing states and skyrmion modes in chiral p-wave superconductor

Tunable odd-frequency triplet pairing states and skyrmion modes in chiral p-wave superconductor

Theory of nonreciprocal spin-wave excitations in spin Hall oscillators with Dzyaloshinskii-Moriya interaction

Scalable synchronization of spin-Hall oscillators in out-of-plane field

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