Enhancement of magnon flux toward a Bose-Einstein condensate

TL;DR

This work addresses how the geometry of parametric pumping controls the transfer of pumped magnons toward the spectral minimum to enable magnon Bose–Einstein condensation in YIG. It combines a classical Hamiltonian formalism for parallel, transverse, and oblique pumping with kinetic-epoch analysis of four-magnon scattering, including Kolmogorov–Zakharov cascades and a kinetic-instability channel that can directly populate the bottom states. Experiments employing microfocused Brillouin light scattering with a vector magnet reveal that perpendicular pumping, though associated with a higher instability threshold, drastically enhances bottom-state magnon population via KI, outperforming parallel pumping by up to 20–25× at comparable supercriticalities. The results demonstrate that pumping geometry can selectively activate distinct nonlinear scattering pathways, providing practical guidelines to optimize magnon flux into the condensate and advance controlled magnon Bose–Einstein condensation in magnetic insulators.

Abstract

We present a combined theoretical and experimental study of angle-dependent parametric pumping of magnons in Yttrium Iron Garnet films, with a focus on the mechanisms that transfer parametrically injected magnons toward the spectral minimum where Bose-Einstein condensation occurs. Using a classical Hamiltonian formalism, we analyze the threshold conditions for parametric instability as a function of the angle between the microwave pumping field and the external magnetic field, continuously tracing the transition between parallel and transverse pumping. We also describe two competing four-magnon scattering mechanisms that transfer parametric magnons toward the bottom of their frequency spectrum: The step-by-step Kolmogorov-Zakharov cascade, which is allowed for all magnetic field values, and the kinetic instability mechanisms that provide a much more efficient single-step channel in transferring magnons directly to the lowest-energy states, but occurs within specific regions of the pumping angle and the external magnetic field where the conservation laws permit it. In the experimental part, we employ microfocused Brillouin light scattering spectroscopy in combination with a vector magnet, allowing for angle-resolved mapping of the magnon population spectrum under controlled pumping angle. We observe that transverse pumping, although characterized by a higher instability threshold, yields a markedly stronger population at the spectral minimum compared to parallel pumping. These observations demonstrate that the kinetic instability channel plays a dominant role in transferring magnons to the spectral minimum under such conditions. These results reveal the crucial role of pumping geometry in shaping the magnon distribution and provide guidelines for optimizing the flux of magnons into the condensate, thereby advancing the control of magnon Bose-Einstein condensation in magnetic insulators.

Figures (6)

• Figure 1: Calculated dispersion relation for a 6.7-thick in-plane--magnetized YIG film at room temperature in external fields (a) $H_\mathrm{ext} = \qty{1600}{\Oe} < H_\mathrm{crit}$ and (b) $H_\mathrm{ext} = \qty{1900}{\Oe} > H_\mathrm{crit}$, where $H_\mathrm{crit}\!\approx\!\qty{1750}{\Oe}$. At $H_\mathrm{ext}=H_\mathrm{crit}$, the frequency of uniform precession $\omega_0$ (the minimum of the transverse branch with $\theta_{\bm k}=\pi/2$ at $k=0$) coincides with the frequency $\omega_\mathrm{p}/2$. Blue dots denote magnons excited by parallel pumping, where the minimal threshold is reached at $\theta_{\bm k}=\pi/2$ for $H_\mathrm{ext} < H_\mathrm{crit}$ in (a) and shifts to $\theta_{\bm k}<\pi/2$ for $H_\mathrm{ext} >H_\mathrm{crit}$ in (b). Red dots denote magnons excited by transverse pumping, with the minimal threshold at $\theta_{\bm k}\!\approx\!\pi/4$. The corresponding parametric processes are illustrated by blue and red arrows, representing the decay of a microwave photon and a magnon into two magnons, respectively. The cyan dots indicate two global minima of the magnon spectrum, which are located on the longitudinal dispersion branches with $\theta_{\bm k}=0$.
• Figure 2: Isofrequency contours of magnons in the $(k_x,k_y)$ plane for $H_\mathrm{ext} = \qty{1750}{\Oe}$ and $\omega_{\rm p}/(2\pi) = \qty{14.094}{\giga\hertz}$. Red dots indicate magnons parametrically excited by perpendicular pumping ($\alpha_\mathrm{p}=\qty{90}{\degree}$) with $\omega(\bm{k}_\mathrm{p}) = \omega_\mathrm{p}/2$, while blue dots correspond to magnons excited by parallel pumping ($\alpha_\mathrm{p}=\qty{0}{\degree}$). The red-to-blue segments of the magnon isofrequency contour $\omega_\mathrm{p}/2$ schematically indicate the spectral positions of parametrically excited magnons for different oblique-pumping angles (see the color scale for the pumping angle $\alpha_\mathrm{p}$). The dashed and solid green arrows represent the wavevector and the group velocity of parametrically excited magnons, respectively. In this schematic example ($\alpha_\mathrm{p}=\qty{30}{\degree}$), the latter is directed along the axis of the pumping resonator (depicted as the yellow stripe), while the wavevector is shown qualitatively to indicate the alignment of the group velocity with the resonator axis. The double-headed cyan--magenta arrow illustrates the scattering of two pumped magnons into one at the spectral minima and an upper state with frequency $\omega_\mathrm{p}-\omega_\mathrm{min}$. Such processes of four-magnon scattering underlie the phenomenon of kinetic instability.
• Figure 3: A schematic picture of the experimental setup utilized for the measurements. The magnon spectrum is measured with the micro-focused Brillouin light scattering technique, marked by the green beam path. The inset presents the sample configuration with regard to the external magnetic field $H_{\rm ext}$ and the pumping field $h_{\rm p}$.
• Figure 4: Threshold power as a function of the external magnetic field for various pumping geometries. The characteristic jump observed for parallel pumping ($\alpha_\mathrm{p}=\qty{0}{\degree}$) at the critical field, originating from the leakage of magnons out of the parametric interaction region Neumann2009_2, gradually disappears as $\alpha_\mathrm{p}$ approaches the perpendicular pumping geometry ($\alpha_\mathrm{p}=\qty{90}{\degree}$).
• Figure 5: Frequency-resolved BLS intensity as a function of the external magnetic field $H_\mathrm{ext}$ for three pumping geometries: parallel ($\alpha_\mathrm{p} = \qty{0}{\degree}$), oblique ($\alpha_\mathrm{p} = \qty{45}{\degree}$), and perpendicular ($\alpha_\mathrm{p} = \qty{90}{\degree}$). The magnetic field was incremented in steps of 50. Red and blue dots denote the calculated frequencies of the uniform precession mode ($\omega_0$) and the spectral minimum ($\omega_\mathrm{min}$), respectively, while the dashed orange line marks the frequency of parametrically injected magnons ($\omega_\mathrm{p}/2$). The BLS intensity was normalized across all three panels to illustrate the intensity difference between the geometries.