Nonlinear Oscillations of Magnetization in a Tangentially Magnetized Ferromagnetic Film Resonator

Introduction. Resonators based on epitaxially grown single-crystal films of yttrium iron garnet are used in various applications of microwave electronics. It is known that with increasing of microwave power incident on a resonator, various nonlinear effects begin to manifest themselves. There are: bistability effect, nonlinear frequency shift, nonlinear damping, etc. By now, the listed nonlinear effects have been quite good studied experimentally. Previously, when describing oscillations of various dynamical systems, the nonlinear damping and the nonlinear frequency shift were usually considered separately. At the same time, it was known that, when studying nonlinear magnetization oscillations in ferromagnetic film resonators with an increase in oscillation amplitude, these effects could occur simultaneously.

Aim. Development of a model of magnetization oscillations taking into account the nonlinear frequency shift and nonlinear damping, as well as its experimental justification for a ferromagnetic film resonator.

Materials and methods. The development of the model was carried out by the method of slowly varying amplitudes. An experimental study was carried out with a ferromagnetic film resonator. For the measurements, we used Rohde & Schwarz ZVA 40 vector network analyzer. We measured the frequency dependence of the reflection coefficient of the microwave signal from the resonator.

Results. A model of nonlinear magnetization oscillations was developed taking into account both a nonlinear frequency shift and a nonlinear attenuation. The resonance curves were experimentally measured at various levels of the microwave power incident on the resonator. It was shown that nonlinear damping limits the nonlinear frequency shift of the magnetization oscillations in a tangentially magnetized ferromagnetic film resonator.

Conclusion. The developed model adequately describes behavior of the resonance curves of ferromagnetic film resonators at high microwave power levels. The nonlinear damping leads to broadening of the resonance curves, thereby increasing losses. This effect also increases the reflection coefficient of the microwave signal from the resonator.

1. Ishak W. S., Chang K-W. Tunable Microwave Resonators using Magnetostatic Wave in YIG films. IEEE Trans. on Microwave Theory and Techniques. 1986, vol. 34, no. 12, pp. 1383–1393. doi: 10.1109/TMTT.1986.1133553

2. Adam J. D., Davis L. E., Dionne G. F., Schloemann E. F., Stitzer S. N. Ferrite Devices and Materials. IEEE Trans. on Microwave Theory and Techniques. 2002, vol. 50, no. 3, pp. 721–737. doi: 10.1109/22.989957

3. Ustinov A. B., Srinivasan G., Fetisov Y. K. Microwave Resonators based on Single-crystal YttriumIron Garnet and Single-crystal Lead Magnesium Niobate-lead Titanate Layered Structures. J. Appl. Phys. 2008, vol. 103, no. 6, art. 063901, 6 p.

4. Semenov A. A., Beljavski P. Yu., Nikitin A. A., Karmanenko S. F., Kalinikos B. A., Srinivasan G. Dual Tunable Thin-film Ferrite-ferroelectric Slotline Resonator. Electronics Lett. 2008, vol. 44, no. 24, pp. 1406–1407. doi: 10.1049/el:20082122

5. Fetisov Y. K., Patton C. E. Thermal Microwave Foldover and Bistability in Ferromagnetic Resonance. IEEE Trans. on Magnetics. 2004, vol. 40, no. 2, pp. 473–482. doi:10.1109/TMAG.2004.824132

6. Vitko V. V., Nikitin A. A., Ustinov A. B., Kalinikos B. A. Microwave Bistability in Active Ring Resonators with Dual Spin-wave and Optical Nonlinearities. IEEE Magnetics Lett. 2018, vol. 9, art. 3506304. doi: 10.1109/LMAG.2018.2870060

7. Fetisov Y. K., Patton C. E., Synogach V. T. Nonlinear Ferromagnetic Resonance and Foldover in Yttrium Iron Garnet Thin Films-inadequacy of the Classical Model. IEEE Trans. on Magnetics. 1999, vol. 35, no. 6, pp. 4511–4521. doi: 10.1109/20.809144

8. Gurevich A. G., Melkov G. A. Magnetic vibrations and waves. M.: Fizmatlit, 1994, 464 p. (In Russ.)

9. Zhang Y. T., Patton C. E., Kogekar M. Ferromagnetic Resonance Foldover in Single Crystal YIG Films – Sample Heating or Suhl Instability. IEEE Trans. on Magnetics. 1986, no. 5, pp. 993–995. doi: 10.1109/TMAG.1986.1064446

10. Gui Y. S., Wirthmann A., Hu C.-M. Foldover Ferromagnetic Resonance and Damping in Permalloy Microstrips. Physical Review В. 2009, vol. 80, art. 184422, 13 p. doi: 10.1103/PhysRevB.80.184422

11. Zhang Y. T., Patton C. E., Srinivasan G. Spinwave Instability and "true" Foldover in Singlecrustal YIG Films. J. Appl. Phys. 1988, vol. 63, pp. 13–18.

12. Praveen-Janantha P. A., Kalinikos B. A., Wu M. Foldover of Nonlinear Elgenmodes in Magnetic Thin Film based Feedback Rings. Physical Review В. 2017, no. 95, no. 6, art. 064422, 5 p. doi: 10.1103/PhysRevB.95.064422

13. Hyde P., Yao B. M., Gui Y. S., Zhang G.-Q., Hu C.-M., You J. Q., Hu C.-M. Direct Measurement of Foldover in Cavity Magnon-polariton Systems. Physical Review В. 2018, no. 95, art. 174423, 9 p. doi:10.1103/PhysRevB.98.174423

14. Chen M., Patton C. E., Srinivasan G., Zhang Y. T. Ferromagnetic Resonance Foldover and Spin-wave Instability in Single-crystal YIG Films. IEEE Trans. on Magnetics. 1989, vol. 25, no. 5, pp. 3485–3487. doi: 10.1109/20.42343

15. Seagle D. J., Charap S. H., Artman J. O. Foldover in YIG. J. Appl. Phys. 1985, vol. 57, no. 8, pp. 3706–3708.

16. Drozdovsky A. V., Ustinov A. B. Nonlinear response of a film ferromagnetic resonator under conditions of non-linear attenuation of magnetization oscillations. Lett. in ZhTF. 2010, vol. 36, no. 18, pp. 10-18. (In Russ.)

17. Yan H., Wang Q., Awai I. Resonant frequency shift in a MSSW-SER with excitation power. Electronics Lett. 1996, vol. 32, no. 19, pp. 1787–1789.

18. Lviv V. S. nonlinear spin waves. M.: Nauka, 1987, 270 p. (In Russ.)

19. Scott M. M., Patton C. E., Kostylev M. P., Kalinikos B. A. Nonlinear Damping of High-power Magneto-static Waves in Yttrium-Iron-Garnet Films. J. Appl. Phys. 2004, vol. 95, no. 11, pp. 6294–6301.

20. Kalinikos B. A., Kovshikov N. G., Ospanov E. A. Parametric regeneration of spin vibrations of a film ferromagnetic resonator by ultrahigh-frequency pumping. Lett. in ZhTF. 1997, vol. 23, no. 16, pp. 82-84. (In Russ.)

21. Migulin V. V., Medvedev V. I., Mustel E. R., Parygin V. N. Fundamentals of the theory of vibrations. M.: Nauka, 1988, 392 p. (In Russ.)