Over the last decade, quantum systems offering new computational and sensing capabilities have emerged [1]. One of these promising hybrid systems involves the
interaction between photons and magnons. This interaction is quantitatively known by the strength coupling g and furthermore by its ratio with the cavity frequency g/ω. It exists three
different domains of this ratio: the Strong Coupling (SC) for g/ω < 0.1; the Ultra-Strong Coupling (USC) for 0.1 < g/ω < 1; and the Deep-Strong Coupling (DSC) for g/ω > 1. One of the
objectives of this last decade is to achieve the USC, and to approach the DSC [2]. A few experimental works already exist on the USC regime [3] and it is still complicated to understand
the different Hamiltonian approximations used to fit experimental data [2]. Here, we present a tuneable hybrid system which makes possible experimental observation of a coupling regime
from strong to ultra-strong at room temperature (RT).
The hybrid system presented here is made of a double re-entrant cavity and a commercial single crystal of YIG (see Fig. 1). It is possible to tune the ratio g/ω with decreasing the gap
between the top of pillars and cavity which will decrease ω without changing g. We optimized two different cavities considering two YIG shapes (sphere and slab). These two cavities work in the USC regime, from the SC/USC limit to g/ω = 0.6. One of these measures
is presented in Fig. 2 where is shown the S21 parameter according to a sweep on RF frequencies and the static H-field. With the use of Finite Element Modelling, we were able to follow the
coupling strength from the SC to the USC domains and were in a good agreement with measurements. We observed that the standard Hamiltonians (Dicke and Hopfield) do not describe
our system. With modifying the Dicke model with adding a frequency shift ωΔ on the FMR, we were able to fit measures and simulations. It should be noted that this added term is
proportional to g2/ω.
We demonstrated the capability of a 3D magnonic cavity to work in the USC regime and its tuneability
with playing with the gap. To reach the DSC, it will be interesting to work on other cavity shapes to have a bigger ratio g/ω.
**References** [1] D. Lachance-Quirion, Y. Tabuchi, A. Gloppe, Appl. Phys. Exp., vol. 12, p. 070101 (2019)
[2] I.A. Golovchanskiy, N.N. Abramov, V.S. Stolyarov, Phys. Rev. Applied., vol. 16, p. 034029 (2021)
[3] A.F. Kockum, A. Miranowicz, S. De Liberato, Nat. Rev. Phys., vol. 1, p. 19-40 (2019)

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/2bebaf6c860d0278cb8854b56f601370.png) 
Fig. 1: Machined cavity 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8a647d4399590dfbaff83ff0e4148d48.png) 

Fig. 2: Spectral transmission S21

Spin Cavitronics System: from Strong to Ultra Strong Coupling

The direct interference of short wavelength spin waves in continuous layers is bringing new opportunities for efficient signal processing [1-2]. Several pionneer works established the possibility to shape the propagation of spin waves in ferromagnetic thin films using concepts borrowed from optics [3-5]. Along these ideas, we demonstrated that the focused emission of spin waves beams in ferromagnetic thin films from constricted coplanar waveguide follows directly the near-field interference pattern of the constriction geometry [6]. In this communication, we investigate the interference patterns of spin waves excited by curvilinear shaped antennas, which produce either a concentrating or a diffusing effect. Namely, we focused our study on two different types of demonstrators: (i) a spin wave â€œconcentratorâ€ as shown in Fig. 1, and (ii) the equivalent of a â€œYoung double-slitâ€ experiment for spin waves shown in Fig. 2. Firstly, we will present a near-field interference model that can be readily implemented for all spin wave modes and any arbitrary shape of antenna [7]. We show the validity and efficiency of our approach by comparing the near-field diffraction patterns obtained with our model and the corresponding MuMax3 micromagnetic simulations for a wide scope of geometries. Secondly, we present series of propagating spin wave spectroscopy done on 30nm YIG films and a 20nm Ni80Fe20 film magnetized out-of-plane, allowing for a discrete mapping of the spin wave intensity with a spatial resolution of about 1Âµm. We show that the transmission signals S21 measured at different locations follow very closely the simulated interference patterns for all the demonstrators, thus paving the way for future prototypes of magnon interferometric devices. This work was supported by the French ANR project â€œMagFuncâ€, and the DÃ©partement du FinistÃ¨re through the project â€œSOSMAGâ€.

Spin Wave Diffraction in Curvilinear Antennas

Non-reciprocal microwave components such as circulators, isolators, and phase shifters are indispensable tools in both today’s communication systems and future quantum
computers [1-2]. However, these components rely almost entirely on field-based bulky ferrimagnet, which tend to be relatively large, off-chip, and costly to assemble. In this context,
different fields of research are investigating solutions to miniaturize these non-reciprocal devices compatible with integrated circuit technology. Among them, the field of magnonic plays a
key role in this search benefiting from a wide range of non-reciprocal properties in the propagation of spin waves [3]. Recently, unidirectional transmission of spin waves was achieved by
taking advantage of the chiral coupling between the uniform resonance of Co nanowires and exchange spin waves in a thin YIG film [4, 5]. Here, we further miniaturized this method and
demonstrate the possibility of shaping non-reciprocal spin wave beams in a continuous thin YIG film. We performed spin wave spectroscopy on a series of devices made of arrays of Co
bars of dimensions: L=10µm in length, w=200 nm in width, 40nm in thickness, and laterally spaced by a=400nm (see Fig. 1). The transmission spectra done with the external field applied
along the length of the Co bars show perfect non-reciprocity for several peaks located around the resonance frequency of the Co bars, e.g. 8.4 to 10.4 GHz range as shown in Fig. 2. These
peaks correspond to integer values of the lateral spacing between Co bars, e.g. kn=nπ/a ranging up to 80rad/µm. Additional non-reciprocal peaks occurring at lower frequencies ranging
between 2 and 6 GHz correspond to the satellite peaks of the antenna directly coupled to the YIG film. Surprisingly, some of the peaks display a reversed non-reciprocity. Finally, we make
use of this multitude of transmission peaks to characterize the k-dependence of the relaxation time and the group velocity of dipole-exchange spin waves. 
**References** 87.png)[1] W. Palmer, et al., IEEE Micr. Magazine 20, 36 (2019) 
[2] M. Devoret, et al., Superconducting circuits for quantum information,Science 339, 1169 (2013) 
[3] J. Chen, et al., J. Phys. D. Appl. Phys. 55, 123001 (2022) 
[4] H. Wang, et al., Nano Res. 14, 2133–2138 (2021) 
[5] J. Chen, et al., Phys. Rev. B 100, 104427 (2019) 
 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/94e4cd227f20528c8226450f05b99d7c.png) 

SEM image of Co nanowires with length L=10μm, width w=200nm, and period a=400nm lithographed on a 50nm YIG film with thickness, and located under 2 µm wavelength Au coplanar waveguides (CPW)

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/0d51030b4d6ea35e8b9bbc51296dd09e.png) 
Transmission spectrum ΔL21
(blue) and ΔL12
(red) at 24mT applied field.

High Wave Vector Non reciprocal spin Wave Beams

GOC: Magnetization Dynamics III

technical paper

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GOB: Magnetization Dynamics II

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**Session Co-Chairs:** Joseph Sklenar, *Wayne State University* and Shuyuan Shi, *Beihang University*

Vincent Vlaminck

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Spin Cavitronics System: from Strong to Ultra Strong Coupling

Spin Wave Diffraction in Curvilinear Antennas

High Wave Vector Non reciprocal spin Wave Beams

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