Local temperature control of magnon frequency and direction of supercurrents in a magnon Bose-Einstein condensate

This study demonstrates that local laser heating in magnetic films induces both magnetization and demagnetizing field variations, which collectively create a local magnon frequency minimum that drives the formation of a magnon supercurrent directed away from the heated region.

The Gist

The Big Picture: A Crowd of Invisible Waves

Imagine a magnetic film (like a very thin, special type of plastic) filled with invisible, tiny waves called magnons. You can think of these magnons as a crowd of energetic dancers.

Usually, these dancers move randomly. But under the right conditions, they can all suddenly start dancing in perfect unison, moving together as one giant, coordinated wave. In physics, this synchronized state is called a Bose–Einstein Condensate (BEC). It's like the dancers forming a single, super-fluid entity that can flow without friction.

The researchers in this paper wanted to figure out how to control where this "super-dance" goes and how fast the dancers move, specifically by using heat.

The Experiment: Heating a Spot

The team took a magnetic film and used a laser to heat up a tiny, specific spot on it, creating a "hot spot."

The Expectation (The Intuitive Guess):
Usually, when you heat something up, it expands or changes in a way that makes things move toward the heat. You might expect the dancers (magnons) to gather in the warm spot because it feels "cozy" or because the heat creates a low point in the energy landscape where they want to settle.

The Reality (The Surprise):
The researchers found the exact opposite happened. When they heated the spot, the magnons didn't gather there; they fled. A "supercurrent" (a frictionless flow) formed that pushed the magnons away from the hot spot and toward the cooler areas.

Why Did This Happen? The "Magnetic Bubble" Analogy

Why did the dancers run away from the heat? The paper explains that it's not just about the temperature changing the material; it's about how the magnetic field changes shape.

1. The Magnetization Drop: When the laser heats the spot, the magnetic strength (magnetization) in that tiny area drops. Imagine the dancers in that spot suddenly becoming less "magnetic" or less connected to the group.
2. The Deformation: Because that spot is now weaker, it creates a distortion in the surrounding magnetic field, similar to how a deflated balloon creates a dip in a stretched rubber sheet.
3. The Frequency Hill: In the world of these waves, "frequency" is like the height of a hill. The researchers discovered that this specific combination of heat and magnetic distortion actually raised the hill in the hot spot.
   • Think of the magnons as water. Water naturally flows from high ground to low ground.
   • Because the heat created a "high frequency hill" in the center, the water (magnons) naturally flowed down the hill, away from the hot center and into the cooler surroundings.

The "Shape" Matters

The paper also noted that the size of the hot spot matters. If the hot spot is very small compared to the thickness of the film, the "hill" gets steeper, and the flow away from the center becomes stronger. It's like the shape of the terrain dictates how fast the water runs off.

How They Proved It

The team didn't just guess; they did three things to confirm this:

1. Math: They wrote equations to predict that heating would raise the frequency hill.
2. Computer Simulation: They built a digital model of the magnetic film and watched the virtual magnons flow away from the heat.
3. Real-Life Test: They used a laser to heat a real magnetic film and a special camera (Brillouin light scattering) to "see" the magnons. They watched the magnons pile up around the hot spot (because they were flowing out of it) and then leave a "dip" or empty space right in the center of the heat.

The Conclusion

The main takeaway is that by simply heating a tiny spot on a magnetic film, you can create a magnetic "hill" that forces these quantum waves to flow away from the heat. This gives scientists a new way to act like a traffic cop for these invisible waves, steering them around without needing to move any physical parts, just by changing the temperature.

Technical Summary

Technical Summary: Local Temperature Control of Magnon Frequency and Direction of Supercurrents in a Magnon Bose–Einstein Condensate

Problem Statement
The Bose–Einstein condensation (BEC) of magnons in magnetic insulators, such as yttrium iron garnet (YIG), and the resulting magnon supercurrents are phenomena of significant physical interest and potential application. While spatial control of magnon transport via external magnetic fields or magnetization gradients is established, the specific influence of local thermal modifications on the magnon spectrum requires deeper understanding. Previous studies have noted that local heating alters magnetization ($M$), thereby affecting magnon frequencies. However, the interplay between the temperature-induced reduction in saturation magnetization ($M_s$) and the consequent variations in the demagnetizing field ($H_{demag}$) has not been fully analytically or experimentally characterized in the context of BEC frequency shifts and supercurrent direction. The central problem addressed is whether local optical heating creates a potential landscape that traps magnons or repels them, and how the demagnetizing field contributes to this effect.

Methodology
The study employs a tripartite approach combining analytical theory, numerical simulation, and experimental verification:

1. Analytical Theory: The authors model a tangentially magnetized magnetic film containing a localized spheroidal region of reduced magnetization (simulating a heated spot). Using magnetostatic continuity conditions, they derive the intrinsic magnetic field ($H_{int}$) inside the spheroid, accounting for the demagnetizing factor ($N_x$) and the magnetization difference ($\Delta M$) between the spot and the surrounding film. They calculate the resulting shifts in the magnon dispersion frequencies for both parallel ($k \parallel M$) and perpendicular ($k \perp M$) wave vectors.
2. Numerical Simulation:
   • Micromagnetics: The internal magnetic field profile ($H_{int}$) for a realistic cylindrical magnetization well with a Gaussian profile was simulated using MuMax3. This allowed for the calculation of effective demagnetization factors ($N_x^{eff}$) as a function of the spot diameter-to-film thickness ratio.
   • Gross–Pitaevskii Equation: The dynamics of the magnon supercurrent were modeled by solving the one-dimensional Gross–Pitaevskii equation. The frequency shift induced by heating was treated as an external potential $P(Y)$, and the evolution of the BEC wave function $\Psi(Y, \tau)$ was tracked to observe supercurrent propagation.
3. Experimental Setup: Experiments were conducted on a YIG film (2.1 $\mu$m thick) tangentially magnetized by an external field ($H_{ext} \approx 1510$ Oe).
   • Thermal Patterning: A 457 nm heating laser, modulated by a spatial light modulator (SLM) and Fourier optics, created localized thermal spots with diameters adjustable between 2 $\mu$m and 9 $\mu$m.
   • Magnon Generation: A microstrip resonator provided parallel parametric pumping (12.705 GHz) to generate a dense magnon gas, driving the system toward BEC formation at the spectrum's bottom frequency ($\omega_{\parallel}$).
   • Detection: Brillouin Light Scattering (BLS) spectroscopy (532 nm probe) measured the magnon density spectrum $N(\omega)$ and spatial distribution with high temporal resolution.

Key Contributions and Results

• Demagnetizing Field Effect: The study demonstrates that local heating does not merely lower the magnetization; it induces a local increase in the minimum magnon frequency ($\omega_{\parallel}$) at the hot spot. Analytical and numerical results confirm that the combination of reduced $M_s$ and the associated demagnetizing field creates a local potential barrier. Specifically, for a prolate spheroid geometry (representing the heated spot), the frequency shift $\Delta \omega_{\parallel}$ is positive and proportional to the effective demagnetization factor $N_x^{eff}$ and $\Delta M$.
• Frequency Shifts: Both simulations and experiments verify that heating causes an upward shift in the bottom magnon frequency ($\omega_{\parallel}$) and a downward shift in the upper frequency ($\omega_{\perp}$). Experimental data showed a shift of approximately 80 MHz in $\omega_{\parallel}$, corresponding to a localized temperature increase exceeding 120 °C.
• Supercurrent Direction: The Gross–Pitaevskii simulations predicted that a local increase in the BEC frequency acts as a repulsive potential. Consequently, magnon supercurrents are directed away from the hot region.
• Experimental Observation of Supercurrents: Time-resolved BLS measurements confirmed the theoretical prediction. During and immediately after the pumping pulse, the hot spot was surrounded by areas of increased magnon density, indicating a flow of magnons out of the heated region. Once pumping ceased, the depletion of the condensate in the hot spot led to a deep density dip, while the density outside remained elevated compared to the unheated state.
• Geometric Dependence: The magnitude of the frequency shift and the effective demagnetization factor were shown to depend critically on the ratio of the hot-spot diameter ($w$) to the film thickness ($d$). The experimental data aligned well with the analytical dependence of $N_x$ on the aspect ratio of the spheroid.

Significance
The paper establishes that local temperature control in magnetic films is a viable method for manipulating magnon Bose–Einstein condensates, but it emphasizes that the demagnetizing field is a critical, non-negligible component of this mechanism. The primary significance lies in the demonstration that local heating creates a repulsive potential for magnons, driving supercurrents away from the heat source rather than trapping them. This finding provides a new degree of freedom for controlling magnon transport in thermal landscapes. The authors suggest that in thinner films where the dipole-exchange spectrum is more sensitive to magnetization changes, this mechanism could potentially lead to an inversion of the supercurrent direction, offering new possibilities for magnonic device design. The work bridges the gap between thermal management and quantum-like transport phenomena in magnonics.