Mode-coupling mechanisms in nanocontact spin-torque oscillators

Iacocca, Ezio; Dürrenfeld, Philipp; Heinonen, Olle; Åkerman, Johan; Dumas, Randy K.

doi:10.1103/physrevb.91.104405

Cited by 25 publications

(28 citation statements)

References 36 publications

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“…The same approach has been used and shown to be accurate in many dynamical regimes to date [37][38][39][40][41][42][43]. In this formalism, the Landau-Lifshitz equation of motion describing conservative magnetization dynamics is cast as a function of a complex amplitude a, using a Holstein-Primakoff transformation.…”

Section: Analytical Formalismmentioning

confidence: 99%

Reconfigurable wave band structure of an artificial square ice

et al. 2016

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Artificial square ices are structures composed of magnetic nanoelements arranged on the sites of a twodimensional square lattice, such that there are four interacting magnetic elements at each vertex, leading to geometrical frustration. Using a semianalytical approach, we show that square ices exhibit a rich spin-wave band structure that is tunable both by external magnetic fields and the magnetization configuration of individual elements. Internal degrees of freedom can give rise to equilibrium states with bent magnetization at the element edges leading to characteristic excitations; in the presence of magnetostatic interactions these form separate bands analogous to impurity bands in semiconductors. Full-scale micromagnetic simulations corroborate our semianalytical approach. Our results show that artificial square ices can be viewed as reconfigurable and tunable magnonic crystals that can be used as metamaterials for spin-wave-based applications at the nanoscale.

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Section: Analytical Formalismmentioning

confidence: 99%

Reconfigurable wave band structure of an artificial square ice

et al. 2016

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“…Spin-transfer torque was considered only in a cylindrical region defined by the NC of diameter d = 100 nm positioned in the geometrical center of the disk. We assumed a polarization consistent with a Co layer, P = 0.3, and a symmetric torque λ = 1, as has previously been shown to model similar devices with high accuracy [13,14]. The direction of the fixed layer was calculated numerically by solving the magnetostatic boundary conditions for a Co thin film with saturation magnetization μ o M P = 1.5 T. Both the external applied field and the current-generated Oersted field were included in the simulations.…”

Section: B Micromagnetic Simulationsmentioning

confidence: 99%

“…On the one hand, by using Co/Ni multilayers exhibiting perpendicular magnetic anisotropy, NC-STOs have been shown to support steady magnetization dynamics at low external fields [6] and even the excitation of localized modes known as magnetic dissipative droplets [7][8][9][10]. On the other hand, using soft magnets such as NiFe, the existence of propagating [11,12], localized [12][13][14][15], and vortex [16,17] modes has been demonstrated, depending on both the strength and the direction of the external magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Propagating spin waves excited by spin-transfer torque: A combined electrical and optical study

et al. 2015

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Nanocontact spin-torque oscillators are devices in which the generation of propagating spin waves can be sustained by spin transfer torque. In the present paper, we perform combined electrical and optical measurements in a single experimental setup to systematically investigate the excitation of spin waves by a nanocontact spin-torque oscillator and their propagation in a Ni 80 Fe 20 extended layer. By using microfocused Brillouin light scattering we observe an anisotropic emission of spin waves, due to the broken symmetry imposed by the inhomogeneous Oersted field generated by the injected current. In particular, spin waves propagate on the side of the nanocontact where the Oersted field and the in-plane component of the applied magnetic field are antiparallel, while propagation is inhibited on the opposite side. Moreover, propagating spin waves are efficiently excited only in a limited frequency range corresponding to wavevectors inversely proportional to the size of the nanocontact. This frequency range obeys the dispersion relation for exchange-dominated spin waves in the far field, as confirmed by micromagnetic simulations of similar devices. The present results have direct consequences for spin wave based applications, such as synchronization, computation, and magnonics.

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“…By solving the equations of motion for the amplitudes of the two modes, nonlinearly coupled by third order terms originating from four-magnon interactions, they concluded that, in steady state, only one mode will survive whereas the other will be extinguished. However, neither of these theories mentioned above can explain recent experimental observations of a variety of multi-mode dynamical effects in STOs such as mode-hopping [8][9][10], periodic mode transitions [11,12], and mode coexistence [13,14]. In addition to mode-hopping, Muduli et al [10] also noted a mode cross-over driven by temperature with other parameters, such as current and external magnetic field, kept fixed.…”

Section: Introductionmentioning

confidence: 99%

Tunable Mode Coupling in Nanocontact Spin-Torque Oscillators

2017

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Recent experiments on spin torque oscillators have revealed interactions between multiple magnetodynamic modes, including mode-coexistence, mode-hopping, and temperature-driven cross-over between modes. Initial multimode theory has indicated that a linear coupling between several dominant modes, arising from the interaction of the subdynamic system with a magnon bath, plays an essential role in the generation of various multimode behaviors, such as mode hopping and mode coexistence. In this work, we derive a set of rate equations to describe the dynamics of coupled magnetodynamic modes in a nano-contact spin torque oscillator. Expressions for both linear and nonlinear coupling terms are obtained, which allow us to analyze the dependence of the coupled dynamic behaviors of modes on external experimental conditions as well as intrinsic magnetic properties. For a minimal two-mode system, we further map the energy and phase difference of the two modes onto a two-dimensional phase space, and demonstrate in the phase portraits, how the manifolds of periodic orbits and fixed points vary with external magnetic field as well as with temperature.

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Mode-coupling mechanisms in nanocontact spin-torque oscillators

Cited by 25 publications

References 36 publications

Reconfigurable wave band structure of an artificial square ice

Reconfigurable wave band structure of an artificial square ice

Propagating spin waves excited by spin-transfer torque: A combined electrical and optical study

Tunable Mode Coupling in Nanocontact Spin-Torque Oscillators

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