Parallel-Pumped Spin-Wave Instability Threshold Characteristics in Polycrystalline Yttrium Iron Garnet Excited by the Varied Rising-Edge Microwave Pulses (2022)

The parallel-pumped spin-wave instability (SWI) threshold power, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{\mathrm {th}}$ </tex-math></inline-formula> , of polycrystalline yttrium iron garnet (YIG) excited by microwave pulses with the varied rising-edge time was investigated theoretically and experimentally. The SWI threshold model associated with the rising-edge time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r}$ </tex-math></inline-formula> is developed in terms of the attributes of half-frequency spin waves in the applied static fields <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\mathrm {ext}}$ </tex-math></inline-formula> . The results manifest a significant increase in microwave-excited SWI threshold power level when the rising-edge time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r}$ </tex-math></inline-formula> is shortened from 600 to 100 ns at the X-band. In addition, the rising-edge microwave pulses with different time scale distinctly present different threshold responses under the left-wing field region of the butterfly curves. The SWI thresholds associated with the spin-wave initial amplitude grow with increasing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\mathrm {ext}}$ </tex-math></inline-formula> when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r}$ </tex-math></inline-formula> is smaller than the spin-wave relaxation time ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r}~ \boldsymbol {\le }~200$ </tex-math></inline-formula> ns), while SWI thresholds are more sensitive to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -dependent spin-wave linewidth, which decreases with the increasing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\mathrm {ext}}$ </tex-math></inline-formula> as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r}$ </tex-math></inline-formula> exceeds the spin-wave relaxation time ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{r} ~ \boldsymbol {\ge }~400$ </tex-math></inline-formula> ns). The calculated responses of the SWI threshold are in close agreement with the measurements.