🔬 mesoscale physics

Strong coupling between propagating spin wave and microwave photons in a superconducting resonator

This paper demonstrates strong coupling between propagating spin wave modes and microwave photons in a superconducting resonator-magnetic thin film hybrid circuit, achieving coupling strengths that exceed damping rates and revealing nonreciprocal spin wave radiation to advance the integration of spin-wave magnonics with quantum information science.

Original authors: Yi Li, Jinho Lim, Xingzhi Wang, Tomas Polakovic, Carissa Kiehl, Moojune Song, Phuoc Cao Van, Ralu Divan, Ulrich Welp, Charudatta Phatak, Jong-Ryul Jeong, Kab-Jin Kim, Jian-Min Zuo, Axel Hoffmann, Vale

Published 2026-06-26

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Yi Li, Jinho Lim, Xingzhi Wang, Tomas Polakovic, Carissa Kiehl, Moojune Song, Phuoc Cao Van, Ralu Divan, Ulrich Welp, Charudatta Phatak, Jong-Ryul Jeong, Kab-Jin Kim, Jian-Min Zuo, Axel Hoffmann, Valentine Novosad

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have two very different kinds of messengers trying to talk to each other: one is a microwave photon (a tiny packet of radio energy zipping through a superconducting wire), and the other is a spin wave (a ripple of magnetic energy moving through a special crystal).

Usually, these two messengers speak different languages and move at different speeds, making it hard for them to have a meaningful conversation. This paper describes how the researchers built a special "meeting room" where they forced these two to talk so loudly and clearly that they became a single, hybrid entity. This is called "strong coupling."

Here is a breakdown of how they did it and what they found, using simple analogies:

1. The Meeting Room: A Superconducting Resonator on a Crystal

Think of the YIG film (Yttrium Iron Garnet) as a very smooth, quiet dance floor where magnetic ripples (spin waves) can travel without tripping or losing energy. Usually, this dance floor is built on a substrate (a base layer) that gets noisy and absorbs energy when it gets very cold.

The researchers solved this by building the dance floor on a new, quiet base called YSGG (which doesn't contain rare-earth elements that cause trouble at low temperatures). On top of this, they built a superconducting resonator.

The Analogy: Imagine a violin string (the resonator) stretched directly over the dance floor. When the string vibrates, it doesn't just make sound; it creates a magnetic "wind" that pushes the dancers (the spin waves) on the floor. Because the string is made of superconducting material (which has zero electrical resistance), it vibrates very efficiently, even at freezing temperatures.

2. The Conversation: Catching the Ripples

The researchers wanted to catch specific types of magnetic ripples.

The Problem: The microwave photons in the wire are like a long, slow ocean wave. The spin waves in the crystal are like tiny, fast ripples. It's hard to match them up.
The Solution: They designed the "violin string" (the resonator) to be very narrow and short. This allowed it to vibrate at a frequency that matched the tiny, fast ripples on the dance floor.
The Result: When they turned on the magnetic field, the microwave photon and the spin wave started dancing together. They didn't just bump into each other; they merged. The energy swapped back and forth between the photon and the spin wave faster than either one could lose energy to the environment. This is what the paper calls "strong coupling."

3. Two Different Dance Styles

The paper shows they could make the dancers perform two different styles:

Damon-Eshbach (DE) Mode: The ripples move sideways across the magnetic field.
Backward-Volume (BV) Mode: The ripples move differently, almost like a compression wave.
The researchers found that the "violin string" could talk to both styles, but it was slightly louder (stronger coupling) with the sideways (DE) style because the magnetic "wind" from the wire pushed on the dancers more effectively in that direction.

4. The One-Way Street: Nonreciprocity

One of the coolest discoveries was about direction.

The Analogy: Imagine a hallway where you can walk from left to right easily, but if you try to walk from right to left, you hit a wall or get pushed back.
The Finding: When the spin waves moved in the "Damon-Eshbach" style, they acted like a one-way street. The researchers could send a signal from the resonator to a detector, and it would be loud. But if they tried to send the signal the other way, it was much quieter.
Why it matters: This proves that the hybrid system inherits a special "one-way" trait from the spin waves themselves. This is a natural feature of these magnetic ripples, and the researchers successfully integrated it into their circuit.

5. Why This Matters (According to the Paper)

The paper concludes that they have successfully built a bridge between two worlds:

Cavity Magnonics: The study of magnetic waves in a box.
Propagating Spin Waves: Magnetic waves that travel from point A to point B.

By proving these two can talk to each other strongly at very cold temperatures, they have opened a door for future technologies that might use these traveling magnetic waves to process information. The paper specifically mentions this could help build on-chip isolators (devices that let signals flow one way but not the other) and microwave-to-optical transducers (devices that convert radio waves to light), which are useful for quantum information science.

In short: The researchers built a super-efficient, super-cold bridge where radio waves and magnetic ripples can merge into a single, powerful hybrid, and they discovered that this hybrid naturally acts like a one-way street for information.

Technical Summary: Strong Coupling Between Propagating Spin Waves and Microwave Photons in a Superconducting Resonator

Problem Statement
While hybrid magnonics offers a versatile platform for quantum information processing by coupling solid-state magnetic excitations (magnons) with microwave photons, experimental demonstrations have predominantly focused on uniform collective spin excitations known as Kittel modes. The unique material properties required for advanced quantum functionalities—such as intrinsic magnon non-reciprocity for on-chip isolators and spin-wave-mediated entanglement—rely on propagating spin waves. However, exploring propagating spin waves in cavity magnonics, particularly at cryogenic temperatures, remains challenging. Metallic ferromagnets suffer from enhanced conductivity-like damping at low temperatures. Furthermore, the standard low-damping magnetic insulator, yttrium iron garnet (YIG), is typically grown on gadolinium gallium garnet (GGG) substrates, which exhibit complex magnetic ordering and strong microwave absorption at cryogenic temperatures, hindering integration with superconducting circuits.

Methodology
To address these challenges, the authors developed superconducting hybrid magnonic circuits integrating propagating spin waves with microwave photons. The experimental approach involved the following key steps:

Substrate and Film Growth: YIG thin films were grown via sputtering on rare-earth-free Y3Sc2Ga3O12 (YSGG) substrates. This choice avoids the magnetic complications of GGG at low temperatures. The films were annealed at 850 °C and confirmed to have high epitaxial quality via transmission electron microscopy (TEM).
Device Fabrication: Superconducting coplanar waveguide (CPW) resonators were fabricated directly on the YIG films using a NbN superconducting layer. To minimize magnetic proximity effects, a 10 nm SiN buffer layer was deposited between the YIG and NbN. Two resonator geometries were designed: a straight quarter-wavelength ( $\lambda/4$ ) resonator and a meandered resonator. Both featured micrometer-scale signal line widths (ranging from 0.5 to 2 $\mu$ m) to match short-wavelength spin wave modes, while maintaining millimeter-scale lengths to resonate with microwave photons.
Measurement: Vector Network Analyzer (VNA) spectroscopy was employed to measure transmission spectra under in-plane magnetic fields. The study examined both Damon-Eshbach (DE) and backward-volume (BV) spin wave configurations. To investigate non-reciprocity, a parallel CPW coupler was fabricated adjacent to the meander resonator to detect radiated spin waves.

Key Contributions and Results

Strong Coupling Achievement: The study demonstrates strong coupling between propagating spin wave modes and microwave photons, with coupling strengths ( $g$ $g$ ) exceeding both magnon ( $\kappa_m$ $κ_{m}$ ) and photon ( $\kappa_c$ $κ_{c}$ ) damping rates.
- For the $\lambda/4$ resonator ( $w=2$ $\mu$ m), a coupling strength of $g/2\pi = 115$ MHz was extracted, with a magnon damping rate of $\kappa_m/2\pi = 70$ MHz.
- For the meander resonator ( $w=1$ $\mu$ m), utilizing films with improved lattice matching, the coupling strength reached $g/2\pi = 150$ MHz for DE modes, with a reduced magnon damping rate of $\kappa_m/2\pi = 34$ MHz.
Mode Identification and Dispersion: The researchers observed avoided crossings between the resonator mode and specific spin wave modes. The spin wave modes exhibited frequency offsets relative to the quasi-Kittel mode consistent with theoretical dispersions: a positive offset for DE modes and a negative offset for BV modes. Additionally, perpendicular standing spin wave (PSSW) modes were observed, with the meander geometry enhancing coupling to these modes due to increased microwave field inhomogeneity.
Non-Reciprocity: By modifying the detection coupler, the authors demonstrated non-reciprocal transmission in the hybrid magnonic mode under the DE configuration. A power isolation of 4 dB was measured between forward ( $S_{21}$ ) and reverse ( $S_{12}$ ) transmission, which reversed upon flipping the magnetic field. This confirms the integration of intrinsic spin-wave non-reciprocity into the hybrid system.
Quantitative Analysis: The extracted coupling strengths and linewidths were analyzed against theoretical models. The cooperativity ( $C = g^2/\kappa_c\kappa_m$ ) was calculated to be 662 for the DE mode and 294 for the BV mode in the meander resonator, firmly placing the system in the strong-coupling regime. The study also estimated spin-wave radiation damping, finding it to be smaller than intrinsic magnon relaxation, indicating that intrinsic damping dominates in the current devices.

Significance
The paper claims that these results open new avenues for integrating spin-wave magnonics with cavity magnonics. By successfully achieving strong coupling with propagating spin waves at cryogenic temperatures using YIG/YSGG hybrid circuits, the work extends the scope of cavity magnonics beyond uniform Kittel modes. The demonstration of intrinsic non-reciprocity highlights the potential for incorporating such properties into hybrid systems for applications like on-chip isolators. Furthermore, the ability to achieve strong coupling without lateral spin wave confinement suggests a pathway toward building cryogenic hybrid magnonic circuits for quantum information science, including potential applications in quantum magnonic operations and sensing.

1. The Meeting Room: A Superconducting Resonator on a Crystal

2. The Conversation: Catching the Ripples

3. Two Different Dance Styles

4. The One-Way Street: Nonreciprocity

5. Why This Matters (According to the Paper)

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