To the editor:
Following excitation by a femtosecond laser pulse, ultrafast quenching of the magnetization of ferromagnetic metals is probed using the magneto-optical Kerr effect (MOKE)1. It has been argued2 that the MOKE signal is modified through non-equilibrium electron distributions created during the femtosecond pulse, and that under these conditions the MOKE signal can no longer be linked directly to the magnetization. Zhang et al.3 recently claimed to have found conditions leading to a correlation between the measurable change of the MOKE spectrum, called the optical response, and the unknown change of the magnetic moment, called the magnetic response. The authors3 report that they have solved this long-standing dispute and laid a solid theoretical foundation for femtomagnetism.
In this correspondence we present arguments against such a conclusion. We address the following issues: first, the presented model3 does not treat a pump-probe set-up; second, it only considers how the magnetization is modified due to optical transitions of band electrons; and third, the studied3 first-order magnetic response can be shown to be zero.
First: a meaningful treatment of the optical response of the system to a pump must include perturbations due to the pump and the probe laser. A method for such a problem has already been developed within linear-response theory4. Alternatively, the impact of the pump pulse can be included in calculations using non-equilibrium distributions of electrons; this was used to reveal5,6 a modification of the MOKE and X-ray magnetic circular dichroism7 of nickel. An approach based on a density matrix that evolves according to the Liouville equation as performed in ref. 3 should also be applicable, but the probe pulse should be included correctly.
The optical response is represented3 by a quantity Im[Pxy(1)], called off-diagonal first-order polarization. It follows from inserting the first-order density into the formula 〈P(t)〉=ΣkTr[ρk (t)Dk]. Notably, the only perturbation present in the first-order density is the pump pulse. In other words, the probe signal is identical to that of the pump, and the change to the situation with no pump is being simulated, not the standard experimental situation that has a time delay between these two laser signals. Considering then the presented results for Im[Pxy(1)] (see Fig. 2a of ref. 3), it is not surprising that the simulated magneto-optical response decays immediately when the pump signal diminishes, which is in striking contrast to experiments, where it is seen for picoseconds.
Second: the paper3 considers only the change of the magnetization induced directly by laser excitation of electrons in nickel. Spin flips during optical transitions can occur only because of spin-orbit coupling. Such a demagnetizing influence of light was previously estimated to be very small8, and insufficient to explain the observed large demagnetization. Also, all arguments in ref. 3 are based on a first-order magnetization Mx, induced by a pulse with Ey linear-polarization, and denoted Im[Mxy(1)]. However, Mx is not the transient magnetization probed in usual pump-probe experiments, where the Mz -projected response is traced with Ey- polarized light.
Third: the employed3 linear-response expression for Im[Mxy(1)] (using the unperturbed electron density, Supplementary equation 7) defines a magneto-electric susceptibility , which connects a pseudovector M with a polar vector E. This magneto-electric susceptibility vanishes in crystals with inversion symmetry9, such as face-centred cubic (fcc) nickel. The question remains as to why it doesn't disappear in the reported3 calculations.
Although Zhang et al. conclude that the long-standing dispute is finally solved, a careful examination of the presented evidence reveals that the simulation does not realistically address what is actually measured in femtosecond pump-probe experiments. Therefore, this paper3 does not solve the question of whether the MOKE signal in ultrafast pump-probe experiments really probes the magnetization.
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Carva, K., Battiato, M. & Oppeneer, P. Is the controversy over femtosecond magneto-optics really solved?. Nature Phys 7, 665 (2011). https://doi.org/10.1038/nphys2067
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