Enhancement of magnon flux toward a Bose-Einstein condensate

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>α</a:mi> <a:mi>p</a:mi> </a:msub> </a:math> between the microwave pumping field <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mi mathvariant="bold-italic">h</b:mi> <b:mi>p</b:mi> </b:msub> <b:mrow> <b:mo>(</b:mo> <b:mi>t</b:mi> <b:mo>)</b:mo> </b:mrow> </b:mrow> </b:math> and the external magnetic field <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi mathvariant="bold-italic">H</d:mi> <d:mi>ext</d:mi> </d:msub> </d:math> , continuously tracing the transition between parallel (for <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msub> <f:mi>α</f:mi> <f:mi>p</f:mi> </f:msub> <f:mo>=</f:mo> <f:mn>0</f:mn> </f:mrow> </f:math> ) and transverse pumping (for <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:msub> <g:mi>α</g:mi> <g:mi>p</g:mi> </g:msub> <g:mo>=</g:mo> <g:mi>π</g:mi> <g:mo>/</g:mo> <g:mn>2</g:mn> </g:mrow> </g:math> ). 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 values of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msub> <h:mi>H</h:mi> <h:mi>ext</h:mi> </h:msub> </h:math> , 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 <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:msub> <i:mi>α</i:mi> <i:mi>p</i:mi> </i:msub> </i:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:msub> <j:mi>H</j:mi> <j:mi>ext</j:mi> </j:msub> </j:math> 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 <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:msub> <k:mi>α</k:mi> <k:mi>p</k:mi> </k:msub> </k:math> . 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.