Resolving photon-shortage mystery in femtosecond magnetism

For nearly a decade, it has been a mystery why the small average number of photons absorbed per atom from an ultrashort laser pulse is able to induce a strong magnetization within a few hundred femtoseconds. Here we resolve this mystery by directly computing the number of photons per atom layer by layer as the light wave propagates inside the sample. We find that for all the 24 experiments considered here, each atom has more than one photon. The so-called photon shortage does not exist. By plotting the relative demagnetization change versus the number of photons absorbed per atom, we show that, depending on the experimental condition, 0.1 photon can induce about 4%-72% spin moment change. Our perturbation theory reveals that the demagnetization depends linearly on the amplitude of the laser field. In addition, we find that the transition frequency of a sample may also play a role in magnetization processes. As long as the intensity is not zero, the intensity of the laser field only affects the matching range of the transition frequencies, but not whether the demagnetization can happen or not.