The cross-integration of spin-wave and superconducting technologies is a promising method for creating novel hybrid devices for future information processing technologies to store, manipulate, or convert data in both classical and quantum regimes. Such hybrid devices can exhibit interesting properties such as new resonance spectra features induced by the interchange between superconducting microwave lines and ferromagnetic resonance dynamics of yttrium iron garnet (Y3Fe5O12, YIG) films [1]. On the other hand, hybrid magnon-polariton systems have been typically studied using bulk YIG and three-dimensional microwave photon cavities [2,3]. Limitations in YIG growth have thus far inhibited its incorporation into CMOS compatible technology such as high quality factor superconducting quantum technology. To overcome this impediment, we have used Plasma Focused Ion Beam (PFIB) technology—taking advantage of precision placement down to the micron-scale—to integrate YIG with NbN superconducting microwave devices. Example hybrid devices are shown in Fig.1. Ferromagnetic resonance has been measured at milliKelvin temperatures on PFIB-processed YIG samples using planar microwave circuits. Furthermore, we demonstrate strong coupling between superconducting resonator and YIG ferromagnetic resonance modes by maintaining reasonably low loss while reducing the system down to the micron scale. This achievement of strong coupling on-chip is a crucial step toward fabrication of functional hybrid quantum devices that advantage from spin-wave and superconducting components. For more information, please see our recent publication [4]. This work was supported by the European Research Council under the Grant Agreements 648011 and 648604, the EPSRC through grant EP/M024423/1, the Leverhulme Trust, and the University of Glasgow.

![](https://assets.underline.io/uploads/markdown_image/1/image/2c0c030f03b19b6b02146d7b7ace69cf.jpg)

Strong magnon-photon coupling with chip-integrated YIG in the zero-temperature limit

Strong magnon-photon coupling with chip-integrated YIG in the zero-temperature limit

Recently ferromagnets with antisymmetric exchange (e.g. DMI) interactions have been actively investigated, in part because of the nonreciprocal propagation of spin waves where the frequency for positive and negative wavevectors, i.e. +k or -k, is not the same. This occurs because the DMI interaction leads to an effective field which is proportional to the wavevector k. In contrast, we study a system without DMI, but where the exchange interaction varies linearly as a function of position as shown in Fig. 1. Such a structure could be created by nonuniform lateral doping of Cu into Permalloy for example. [1] We also find an effective field which is linear in k, but the directions of the effective field are different from those found in the DMI systems. Using a simple one-dimensional model and a set of coupled Landau-Lifshitz equations, we set the exchange on the right side to be the value for iron, and it is decreased linearly by a factor of three at the left side. A field of 100 mT is applied perpendicular to the chain. The length of the system is 1 micron, but larger lengths give similar results. We demonstrate a number of interesting features: (1) The eigenstates are strongly asymmetric and can be localized on one side of the sample or the other [2]; (2) Depending on the frequency of excitation, there can be a huge asymmetry in propagation amplitudes for waves going in opposite directions as seen in Fig. 2, and (3) If a wave is excited at the center of a sample, there is a large asymmetry in propagation speed for waves travelling in different directions, where waves travelling in the region where the exchange is larger propagate at a higher speed than waves travelling where the exchange is smaller. We compare our results with analytic calculations, with reasonable agreement. We discuss the potential for applications such as isolators at the end.References: [1] N. Sorensen, R. E. Camley, and Z. Celinski, J. Magn and Magn. Mat. Vol. 477, p 344 (2019) [2] K L Livesey, D C Crew, R L Stamps, Phys. Rev. B Vol. 73, p. 184432 (2006)

Nonreciprocal Behavior in Ferromagnets with Spatially Varying Exchange

**Session chair:** Jaroslaw Klos, Uniwersytet im Adama Mickiewicza w Poznaniu


HOK - Spin Waves and Magnetization Dynamics I

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E4: Spin Wave I: Spatial and Nonlinear Behavior

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Strong magnon-photon coupling with chip-integrated YIG in the zero-temperature limit

Nonreciprocal Behavior in Ferromagnets with Spatially Varying Exchange

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