a) Thermal effect caused by illumination of a pump pulseThe photon energy of the pump pulses (0.89 eV) was below the lowest d-d transition in Fe 3+ ions (1.4 eV) 29 , leading to a virtual excitation. The pump fluence was 200 mJ/cm 2 .In our sample, the refractive index was 2.4, and the absorption coefficient was 0.3 cm -1 for the pump wavelength. Therefore, the absorbed pump fluence was less than 1 mJ/cm 2 , which enabled almost uniform excitation across the entire thickness of 110 μm.Considering that the specific heat is 0.4 J/g K and the density is 7 g/cm 3 , the instantaneous temperature increase caused by a pump pulse is calculated to be ~ 0.05 K.From the thermal conductivity (0.05 W/cm K), the heat diffusion length from a Gaussian spot with r 0 = 25 μm is calculated to be ~ 0.2 nm after 3 ns. Therefore, the thermal effect does not play a major role in our experiment with a spatial resolution of 20 μm. Indeed, the incoherent signal was not experimentally observed outside the pump spot.
b) Theoretical modelLet us start with the Landau-Lifshitz equation for the unit magnetization vector ( ) ,t = m m r , where 2 1 = m . If the effective magnetic pulse field, ( , ) t h r , generated via the inverse Faraday effect is perpendicular to the sample surface, that is, ( , ) ( , , ) t h x y t = h r z , the Landau-Lifshitz equation takes the form effˆ[ ] ( ) ( , ) x y d m m h t dt γ γ = − × + − m m H y x r ,where eff H is the effective field, determined through the variation of the magnetic energy of the system with respect to magnetization; x , ŷ , and ẑ are unit vectors along the x, y, and z axes, respectively; and B g = /h γ μ ( 0 > ) is the gyromagnetic constant, where B μ is SUPPLEMENTARY INFORMATION