Magnons and Phonons Optically Driven out of Local Equilibrium in a Magnetic Insulator

The coupling and possible nonequilibrium between magnons and other energy carriers have been used to explain several recently discovered thermally driven spin transport and energy conversion phenomena. Here, we report experiments in which local nonequilibrium between magnons and phonons in a single crystalline bulk magnetic insulator, ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$, has been created optically within a focused laser spot and probed directly via micro-Brillouin light scattering. Through analyzing the deviation in the magnon number density from the local equilibrium value, we obtain the diffusion length of thermal magnons. By explicitly establishing and observing local nonequilibrium between magnons and phonons, our studies represent an important step toward a quantitative understanding of various spin-heat coupling phenomena.

Figure 1

Schematic of micro-BLS setup for measuring magnon and phonon BLS spectra in YIG under stage heating or focused laser heating.

Figure 2

Temperature-dependent BLS spectra for (a) magnons and (b) phonons, obtained with the YIG sample heated uniformly on a heater stage. Solid lines are fits using (a) symmetric and (b) asymmetric squared Lorentzian functions (see the Supplemental Material [23]). The arrow in (b) is drawn to show the small downward frequency shift of the phonon signal. The numbers inside the figure represent the stage temperature rise from room temperature.

Figure 3

(a) Peak frequency changes of magnons and phonons as a function of the sample stage temperature rise. The red line is a linear fitting of the phonon data while the blue line is a quadratic fitting of the magnon data. (b) Peak frequency changes for magnons and phonons as a function of the red heating laser power when the stage is kept at room temperature. The lines are polynomial fitting of the data. (c) Equivalent stage temperature rise in the stage heating measurement yielding the same strain-corrected phonon frequency downshifts in the laser heating measurement is plotted as a function of the heating laser power. (d) Magnon peak frequency changes ($\mathrm{\Delta }{f}_m$) as a function of phonon peak frequency changes ($\mathrm{\Delta }{f}_p$) in the two different heating configurations after the strain effects are accounted for. The arrow shows the difference ($\delta f_m^R>0$) in the magnon frequency between the 13.2 mW red laser heating and the corresponding stage heating that yields the same strain-corrected $\mathrm{\Delta }{f}_p$. Raw BLS spectra of (e) phonon and (f) magnon under 30 K stage temperature rise (blue) and 13.2 mW laser heating (red). Solid lines are fittings. The spectra are normalized to their maximum counts.

Figure 4

Simulated spatial profiles of (a) the difference in the local phonon temperature rise in two simulations caused by the red laser heating and (b) magnon frequency deviation between the two heating conditions calculated with $l_r=3.1\mu \mathrm{m}$. The displayed volume is $50\mu \mathrm{m}$ in both the radial and axial directions in both spatial profiles. (c) Weighted averages of $\delta f_m^R$ over the probe laser spot as a function of $l_r$. The red line shows the relation between each $l_r$ used in the simulations and the calculated $⟨\delta f_m^R⟩$. The gray area represents the uncertainty of measured $\delta f_m^R$, while the black solid line is the mean of measurements. $\mathrm{\Delta }{l}_r$ is the possible range of $l_r$ for the calculated values due to the uncertainty of the measurement. (d) Simulated profiles of the magnon population rise relative to the room temperature value at the surface of the YIG. The red and blue lines represent the magnon population rises for the red laser heating experiment ($\mathrm{\Delta }{n}_R$) and the stage heating condition ($\mathrm{\Delta }{n}_S$), respectively, as a function of position including the effect of the green probe laser. The magnon population rises are normalized by the room temperature value.