Angular Momentum Conservation for Coherently Manipulated Spin Polarization in Photoexcited NiO: An Ab Initio Calculation

In an ultrafast laser-induced magnetization-dynamics scenario we demonstrate for the first time an exact microscopic spin-switch mechanism. Combining ab initio electronic many-body theory and quantum optics analysis we show in detail how the coherently induced material polarization for every elementary process leads to angular-momentum exchange between the light and the irradiated antiferromagnetic NiO. Thus we answer the long-standing question where the angular momentum goes. The calculation also predicts a dynamic Kerr effect, which provides a signature for monitoring spin dynamics, by simply measuring the transient rotation and ellipticity of the reflected light.

Figure 1

Time-dependent polarization. Panel (a) shows the $\mathrm{Ni}{\mathrm{O}}_5^{-8}$ cluster and panel  (e) its induced polarization throughout the whole $\Lambda$ process. In panels (c) and (d) two time windows are magnified and one can see that the phase difference between $⟨P_x(t)⟩$ and $⟨P_y(t)⟩$ changes sign, which corresponds to different helicities of the participating light. Panel (f) shows the envelope of the laser pulse. Panel (b) is a schematic view of the angular-momentum flow during absorption and emission; the cluster has always a net change of $\Delta J=+1$ and the reflected light a net total helicity of ${\sigma }_{-}$.

Figure 2

Fourier transform of the laser-induced polarization in the material (compare also with Fig. 1).

Figure 3

Upper panel: Expectation value of the energy of the cluster. Middle panel: Expectation values of the spin, orbital angular momentum, and total angular momentum. Lower panel: Contour plot of the polarization of the emitted light at frequencies around that of the incident light as a function of energy and time. Blue [black in phase (i)] means ${\sigma }_{+}$ and red [gray in phase (iii)] ${\sigma }_{-}$ light (color code in atomic units). The horizontal dashed line indicates the energy (0.443 eV) of the incident ${\sigma }_0$ light. One can clearly distinguish the change of the polarization when going from absorption to emission (compare upper and lower panel). The four vertical dashed lines roughly indicate phases (i), (ii), and (iii) (see text).

Figure 4

Dynamical magneto-optical Kerr effect. The height of the peaks signifies the amplitude of the ${\sigma }_0$ light emitted or absorbed by the material. The color code indicates polarization angle in degrees (physically meaningful only in the presence of a peak). The peak is centered at the maximum of the pulse [phase (ii)] and is surrounded by two smaller peaks. The Kerr angle can become both negative and positive.