Magnetic vortex oscillators are an ideal system to study the dynamics of magnetic systems at very small length scales and over a wide frequency range. Their dynamic behavior shows characteristics known from other fundamental physical systems like the harmonic oscillator [1] and is in many aspects well understood. Their lateral dimension vary from a few microns [2] down to the nanometer scale [3]. Due to their flux closure configuration they are magnetically stable and a potential candidate for high density magnetic logic devices and magnonic crystals [4]. The oscillations, which can be obtained in essentially zero external magnetic field (besides the driving field), exhibit a narrow line width and resonance frequencies starting from the MHz range up to GHz frequencies [5]. They can be excited using magnetic field pulses [6] and electric currents harnessing the Spin Transfer Torques (STT) [5].

Recently, the magnetization dynamics in neighbouring magnetic vortex oscillators coupled via their stray fields come into focus of research [7-10]. The system behaves like damped coupled harmonic oscillators. It has been shown that the dynamics of such systems is strongly influenced by the strength of the magnetostatic interaction given by the distance between the elements and the relative configuration of the core polarizations, e.g., the directions of the out-of-plane magnetization components [9].

Here we present a study of coupled vortices with Lorentz Transmission Electron Microscopy (LTEM) and Differential Phase Contrast Microcopy (DPC) at zero magnetic field. We show a novel technique to control the interaction of two or more vortex oscillators by directly influencing their resonance frequencies. The resonance frequencies depend on the saturation magnetization M_s of the magnetic material, in this case permalloy and is highly dependent on the temperature of the disk. We use Joule heating to electrically manipulate the resonance frequencies of one element to control its excitation by a second neighbouring disk. We systematically mapped the frequency response of both disks for different temperatures to fully understand the behavior of the system.

References
[1] S. Zhang and Z. Li, Phys. Rev. Lett. 93, 127204 (2004)
[2] T. Shinjo1, T. Okuno, R. Hassdorf, K. Shigeto, T. Ono, Science 11, 289, 930-932 (2000)
[3] A. Imre, G. Csaba, L. Ji, A. Orlov, G.H. Bernstein, W. Porod, Science 13, 311, 205-208 (2006)
[4] Anjan Barman, Saswati Barman, T. Kimura, Y. Fukuma and Y. Otani, Journal of Physics D: Applied Physics, 43, 422001 (2010)
[5] Matthias Noske, Ajay Gangwar, Hermann Stoll, Matthias Kammerer, Markus Sproll, Georg Dieterle, Markus Weigand, Manfred Fähnle, Georg Woltersdorf, Christian H. Back, and Gisela Schütz, Phys. Rev. B 90, 104415 (2014)
[6] Jung, Hyunsung and Yu, Young-Sang and Lee, Ki-Suk and Im, Mi-Young and Fischer, Peter and Bocklage, Lars and Vogel, Andreas and Bolte, Markus and Meier, Guido and Kim, Sang-Koog, Applied Physics Letters, 97, 222502 (2010)
[7] K. Yu. Guslienko, V. Novosad, Y. Otani, H. Shima, and K. Fukamichi, Phys. Rev. B 65, 024414 (2001)
[8] A. Vogel, M. Martens, M. Weigand, and G. Meier, Appl. Phys. Lett. 99, 042506 (2011)
[9] A. Vogel, A. Drews, T. Kamionka, M. Bolte, and G. Meier, Phys. Rev. Lett. 105, 037201 (2010)
[10] Satoshi Sugimoto, Yasuhiro Fukuma, Shinya Kasai, Takashi Kimura, Anjan Barman, and YoshiChika Otani PRL 106 (2011)

Figures:

Figure 1: DPC micrograph of a single magnetic vortex in a Py disk. The colors represent direction, brightness strength of the in-plane component of the magnetic induction. The local direction can be derived from the color wheel shown in the upper left.

Figure 2: LTEM image of two oscillating vortices. One vortex is driven by an AC-spin-polarzied current. The second vortex is driven by stray fields from the first one and has increased temperature due to Joule heating.

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EMC Abstracts - https://emc-proceedings.com/abstract/study-of-thermally-tunable-coupled-magnetic-vortex-oscillators-with-lorentz-transmission-electron-microscopy-and-differential-phase-contrast-microscopy/