Mode-coupling mechanisms in nanocontact spin-torque oscillators

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

Phys. Rev. B 91, 104405 – Published 11 March 2015

Abstract

Spin-torque oscillators (STOs) are devices that allow for the excitation of a variety of magnetodynamical modes at the nanoscale. Depending on both external conditions and intrinsic magnetic properties, STOs can exhibit regimes of mode hopping and even mode coexistence. Whereas mode hopping has been extensively studied in STOs patterned as nanopillars, coexistence has been only recently observed for localized modes in nanocontact STOs (NC-STOs), where the current is confined to flow through a NC fabricated on an extended pseudo spin valve. By means of electrical characterization and a multimode STO theory, we investigate the physical origin of the mode-coupling mechanisms favoring coexistence. Two coupling mechanisms are identified: (i) magnon-mediated scattering and (ii) intermode interactions. These mechanisms can be physically disentangled by fabricating devices where the NCs have an elliptical cross section. The generation power and linewidth from such devices are found to be in good qualitative agreement with the theoretical predictions, as well as provide evidence of the dominant mode-coupling mechanisms.

Received 18 December 2014
Revised 19 February 2015

DOI:https://doi.org/10.1103/PhysRevB.91.104405

Authors & Affiliations

Ezio Iacocca^1,2, Philipp Dürrenfeld¹, Olle Heinonen^3,4, Johan Åkerman^1,2,5, and Randy K. Dumas^1,2

¹Physics Department, University of Gothenburg, 412 96, Gothenburg, Sweden
²NanOsc AB, Electrum 205, 164 40, Kista, Sweden
³Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
⁴Northwestern-Argonne Institute for Science and Engineering, Evanston, Illinois 60208, USA
⁵Material Physics, School of ICT, Royal Institute of Technology, Electrum 229, 164 40, Kista, Sweden

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Vol. 91, Iss. 10 — 1 March 2015

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Images

Figure 1
Mode energy distribution for the bullet (a) and high-frequency (b) modes for a NC-STO with a circular NC. The relative orientation of the current-induced Oersted field (yellow) and in-plane applied field component (white) are indicated in (b). (c) Schematic representation of the local frequency landscape along the $Y$ direction in a NC-STO modified by the current-induced Oersted field (black line). The red dashed lines indicate the edges of the NC. The bullet mode, B (high-frequency mode, HF) sits at the local frequency minimum (maximum). Black arrows represent the possible flow of magnons due to the finite mode volume of both B and HF. (d) Generation linewidth due to magnon-mediated scattering and intermode exchange mechanisms, by virtue of Eq. (2). Inset: Magnon-scattering event between the dominant modes ( $ω_{1}$ and $ω_{2}$ ) and thermal magnons.
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Figure 2
Field angle dependent spectra obtained (a) experimentally and (b) numerically using an elliptical NC with tilt $ϕ_{N C} = 0^{\circ}$ and biased at $- 18$ mA. The ferromagnetic resonance (FMR) frequency is shown by a yellow solid line. In both cases, the critical angle $θ_{c} \approx 60^{\circ}$ defines the onset of mode-hopping regime, which coincides with the onset of the bullet mode. A second critical angle $θ_{L} \approx 42 . 5^{\circ}$ is also observed when both the bullet (B) and high-frequency (HF) modes are localized, corresponding to a coexistence regime. The inset in (a) shows an SEM image of a fabricated elliptical contact with a minor axis of 100 nm. The inset in (b) schematically shows the convention of $ϕ_{N C}$ with respect to the in-plane component of the applied field, $H_{∥}$ .
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Figure 3
Mode energy distribution for the bullet and high-frequency modes for NC-STOs with elliptical NCs tilted $ϕ_{N C} = 0^{\circ}, 45^{\circ}$ , and $90^{\circ}$ . The relative orientations of the current-induced Oersted (yellow) and in-plane field component (white) are indicated in the lower left panel.
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Figure 4
(a) Integrated power ratio between the high-frequency and bullet mode, $p_{I, H F} / p_{I, B}$ , for devices at $ϕ_{N C} = 0^{\circ}$ (blue circles), $45^{\circ}$ (red diamonds), and $90^{\circ}$ (black squares), biased at currents between $- 16$ and $- 26$ mA. The modes have an integrated power ratio close to 1, denoting mode coexistence. Above $θ = 40^{\circ}$ a divergence is observed, corresponding to the onset of a mode-hopping regime. (b) Linewidth of the high-frequency (HF) and bullet (B) mode for a particular device biased at $- 18$ mA. The HF mode exhibits variations between the devices with different $ϕ_{N C}$ , while the B mode remains mostly stable.
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Figure 5
Integrated power (a) and linewidth (b) at $θ = 30^{\circ}$ for devices with elliptical NCs satisfying $ϕ_{N C} = 0$ (blue circles) and $90^{\circ}$ (black squares). The data are obtained from averaging the results obtained from five nominally identical devices, exhibiting a similar threshold current of $\approx - 15$ mA. The integrated power in both cases decreases linearly, in agreement with the Oersted field induced mode separation. However, the linewidth exhibits different behaviors in correspondence with the mode-coupling mechanisms in these devices. In particular, for $ϕ = 90^{\circ}$ , the magnon-mediated scattering mechanism dominates, as observed from the average linewidth behavior.
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