Strong coupling between quantized magnon modes in a YIG microstucture and microwaves in a superconducting resonator

This paper reports the first realization of strong coupling between quantized magnon modes in a sub-10-micron YIG microplatelet and microwave photons in a superconducting resonator, achieved through focused ion beam fabrication and enabling efficient on-chip studies at ultra-low input powers.

The Gist

Imagine you have a tiny, super-efficient drum made of a special magnetic material called YIG (Yttrium Iron Garnet). In the world of physics, when you "hit" this drum with a magnetic field, it doesn't just vibrate like a normal drum; it creates ripples of magnetism called magnons. Think of these magnons as tiny, invisible waves of energy dancing across the surface of the drum.

For a long time, scientists could only make these magnetic drums large enough to hear the music clearly if they were the size of a grain of sand or larger (macroscopic). They wanted to shrink these drums down to the size of a speck of dust (microscopic) to fit them onto computer chips, but there was a problem: when you make the drum too small, it becomes too quiet to hear, and the connection to the "microphone" (the device reading the signal) becomes too weak.

The Big Breakthrough
This paper describes how a team of scientists finally managed to shrink this magnetic drum down to a microscopic size (about 7 micrometers wide, which is roughly the width of a human hair) and make it "sing" loudly enough to be heard clearly.

Here is how they did it, using some creative analogies:

1. The "Spotlight" Trick
Usually, to hear a tiny drum, you need a huge microphone right next to it. But in this experiment, the scientists used a special superconducting wire (a wire that conducts electricity with zero resistance) that acts like a spotlight.

• They took a tiny piece of the YIG crystal and placed it directly on top of a narrow "bottleneck" in this wire.
• Just like a spotlight concentrates light into a tiny, intense beam, this wire concentrates the magnetic "light" (microwaves) into a tiny, intense spot right where the YIG piece sits.
• This intense concentration allowed the tiny magnetic drum to interact strongly with the wire, even though the drum itself is microscopic.

2. The "Dance" of Strong Coupling
The goal was to achieve what physicists call "strong coupling."

• Imagine two dancers: one is the magnetic wave (magnon) and the other is the microwave signal (photon).
• In a weak connection, they might just wave at each other from across the room.
• In strong coupling, they grab hands and start dancing together so tightly that they become a single, new entity. They exchange energy back and forth so fast that they can't be told apart anymore.
• The scientists proved that their tiny YIG drum and the superconducting wire were dancing this tight dance. They saw this in their data as "avoided crossings"—a visual signature on a graph where the two dancers' paths get close but then veer away from each other, proving they are interacting.

3. The "Tiny Orchestra"
One of the coolest parts of this discovery is that the tiny drum didn't just play one note. Because the drum is so small and confined, it can only vibrate in specific, quantized patterns (like a guitar string that can only vibrate in whole numbers of loops).

• The scientists found that their setup could excite many different notes (magnon modes) at once.
• They used computer simulations (like a virtual reality model of the drum) to predict exactly which notes the drum should play, and the real-world experiment matched the prediction perfectly.

4. Whispering Loudly
Perhaps the most impressive feat is the volume. Usually, to get a signal this strong, you need to blast the system with a lot of power.

• However, because their "spotlight" (the wire) was so efficient, they could make these tiny magnetic waves dance with an input power as low as 10 femtowatts.
• To put that in perspective: 10 femtowatts is to a standard lightbulb what a single drop of water is to the entire ocean. They achieved a strong, clear signal with almost zero energy input.

Why This Matters (According to the Paper)
The paper states that this success is a foundational step. It proves that we can now take these high-quality magnetic materials, shrink them down to the size of a speck of dust, and integrate them onto computer chips without losing their special properties. This opens the door for building future devices that use these magnetic waves to process information, potentially leading to faster and more energy-efficient technologies, specifically targeting the field of quantum information science.

In short: They built a microscopic magnetic drum, shined a super-focused magnetic spotlight on it, and proved it can dance in perfect sync with a superconducting wire using almost no energy at all.

Technical Summary

1. Problem Statement

The field of magnonics aims to utilize spin waves (magnons) for low-power, high-frequency information processing and quantum information science (QISE). A critical requirement for these applications is strong coupling between magnons and other quantum systems (e.g., superconducting resonators), where the coupling rate exceeds the decay rates of the individual modes.

While strong coupling has been demonstrated in macroscopic Yttrium Iron Garnet (YIG) devices (mm to cm scale), achieving this in truly sub-10 micron structures has remained a significant challenge. The primary obstacles are:

• Volume Constraints: Strong coupling scales with the square root of the number of spins ($\sqrt{N}$). Reducing lateral dimensions drastically reduces the magnetic volume, weakening the interaction.
• Fabrication Limitations: Producing thick YIG films with low damping via standard deposition (sputtering, PLD) is difficult. Conversely, thick films grown via Liquid Phase Epitaxy (LPE) on Gadolinium Gallium Garnet (GGG) substrates introduce surface roughness and paramagnetic impurities that degrade superconducting resonators.
• Mode Overlap: Miniaturizing the magnetic element and the resonator simultaneously while maintaining sufficient mode overlap (spatial confinement of the RF field) is technically demanding.

2. Methodology

The authors developed a novel device architecture and fabrication workflow to overcome these limitations:

• Device Architecture:
  • Resonator: An optimized on-chip superconducting lumped-element LC resonator made of a Nb/NbN/Nb trilayer on a sapphire substrate. The design features a constricted inductive line (width $w = 4$ µm) to locally enhance the RF magnetic field and confine the photon mode volume.
  • Magnonic Element: A YIG micro-platelet with dimensions 7 µm × 8.6 µm × 790 nm.
• Fabrication Technique:
  • Instead of growing YIG directly on the resonator, the team used Focused Ion Beam (FIB) milling to cut a platelet from a high-quality, commercially available LPE-grown YIG film (790 nm thick) on a GGG substrate.
  • The platelet was transferred and placed directly onto the constricted inductive line of the resonator, fixed with Platinum (Pt) welds. This approach avoids the roughness and paramagnetic issues of direct integration while preserving the high quality of the YIG crystal.
• Experimental Setup:
  • Measurements were conducted at cryogenic temperatures ($T \approx 1.4$ K) in a 3D vector magnet.
  • Microwave transmission ($S_{21}$) was measured using a Vector Network Analyzer (VNA) with input powers ranging from 10 nW down to 10 fW (using a low-noise amplifier for the lowest power).
  • The external magnetic field ($H_{ext}$) was varied in strength and orientation ($\theta = 0^\circ$ and $90^\circ$ relative to the inductive line).
• Simulation & Theory:
  • Micromagnetic Simulations: Performed using MuMax3 to simulate spin wave dynamics and identify quantized modes.
  • Analytical Modeling: Used the Kalinikos-Slavin formalism and a coupled Hamiltonian approach to calculate mode frequencies and coupling strengths ($g$).
  • RF Simulations: CST Studio Suite was used to model the resonator's electromagnetic modes and field confinement.

3. Key Contributions

• First Sub-10µm Strong Coupling: Demonstrated strong coupling between a superconducting LC resonator and quantized magnon modes in a YIG structure with lateral dimensions of only ~7–8 µm.
• Novel Integration Strategy: Successfully integrated high-quality LPE-YIG with superconducting circuits by physically transferring a FIB-milled platelet, bypassing the limitations of direct substrate growth.
• Ultra-Low Power Operation: Achieved observable anti-crossings at input powers as low as 10 fW, demonstrating the potential for quantum-limited operation.
• Mode Identification: Identified and mapped multiple confined magnon modes (Damon-Eshbach and Backward Volume Magnetostatic Spin Waves) with specific quantization indices $(m_w, m_l)$ in both magnetic field orientations.

4. Results

• Observation of Anti-Crossings: The $S_{21}$ transmission spectra revealed numerous avoided crossings (anti-crossings) between the resonator mode (~3.6 GHz) and various magnon modes as the magnetic field was swept.
  • At $\theta = 0^\circ$, a large anti-crossing was observed at ~50 mT (Kittel/quasi-uniform mode), along with additional features at lower and higher fields corresponding to quantized modes.
  • At $\theta = 90^\circ$, anti-crossings were observed at higher fields, consistent with the selection rules for Backward Volume Magnetostatic Spin Waves (BVMSW).
• Coupling Strength:
  • Analytical calculations estimated the coupling constant for the quasi-uniform mode to be $g_{00} \approx 60$ MHz.
  • Even with conservative linewidth estimates (up to 20 MHz), the system operates firmly in the strong coupling regime ($g > \kappa, \gamma$).
  • Coupling strengths for higher-order modes ranged from ~1 MHz to 30 MHz.
• Mode Selection Rules: The experiments confirmed theoretical selection rules. For instance, the inductive line's geometry (smaller than the platelet) allowed the excitation of antisymmetric modes (even $m_w$) via the $z$-component of the RF field, which would not be excited in a uniform field.
• Power Efficiency: The anti-crossing signatures remained distinct even at 10 fW input power, proving that the enhanced field confinement in the constricted line compensates for the reduced magnetic volume.

5. Significance

This work represents a foundational step toward on-chip quantum magnonics. By successfully miniaturizing the magnetic element to the micron scale while maintaining strong coupling, the authors have:

1. Enabled Scalability: Demonstrated a pathway to integrate multiple magnonic elements on a single chip, a prerequisite for complex quantum circuits.
2. Reduced Power Requirements: Proved that strong coupling can be achieved at extremely low power levels (fW), which is essential for minimizing heating and decoherence in quantum systems.
3. Validated Hybrid Architectures: Established a robust method for integrating high-quality magnetic materials with superconducting circuits without compromising material quality or resonator performance.

The results pave the way for future devices utilizing confined magnon modes for quantum transduction, memory, and logic operations in the microwave regime.