Ultrafast Spin-State Dynamics in Transition-Metal Complexes Triggered by Soft-X-Ray Light

Recent advances in attosecond physics provide access to the correlated motion of valence and core electrons on their intrinsic timescales. For valence excitations, processes related to the electron spin are usually driven by nuclear motion. For core-excited states, where the core hole has a nonzero angular momentum, spin-orbit coupling is strong enough to drive spin flips on a much shorter time scale. Here, unprecedented short spin crossover is demonstrated for $L$-edge ($2p\to 3d$) excited states of a prototypical Fe(II) complex. It occurs on a time scale, which is faster than the core-hole lifetime of about 4 fs and can be manipulated by the excitation conditions. A detailed analysis of such phenomena will help to gain a fundamental understanding of spin-crossover processes and establish the basis for their control by light.

Figure 1

(a) X-ray absorption spectrum of $[\mathrm{Fe}({\mathrm{H}}_2\mathrm{O}{)}_6{]}^{2+}$; arrows denote the excitation energies considered in case II, see text. (b) Collective contributions of the quintet (red bars) SF states to the stationary SOC eigenstates ($\sum _{j,M_S}|c_j^{(S=2,M_S)}{|}^2$, see Eq. (1); the grey areas correspond to the triplet SF states ($\sum _{j,M_S}|c_j^{(S=1,M_S)}{|}^2$), which together with quintet ones, sum up to unity. The particular contributions of valence SF states (${\mathrm{SF}}_{\text{val}}$, green bars) and core SF states (${\mathrm{SF}}_{\text{core}}$, blue bars) to the different SOC states are also shown. Numbered ranges reflect the bandwidths of 0.5 eV (1 and 3) and 5.0 eV (1’, 2’, and 3’) pulses, with carrier frequencies denoted in panel (a), in terms of the involved SOC states. (c) Evolution of spin-density difference, ${\rho }_{\uparrow }-{\rho }_{\downarrow }$ (red—positive, blue—negative, contour value 0.001), obtained in case I for an initial state, which corresponds to the ${\mathrm{SF}}_{\text{core}}$, with $M_S=+2$. (d) Evolution of the total population of the quintet and triplet electronic states after instantaneous excitation to the ${\mathrm{SF}}_{\text{core}}$ state (case I). (e) Evolution of the total population of the quintet and triplet electronic states after explicit field excitation (case II), with the pulse centered at $\hslash \mathrm{\Omega }=708.4\mathrm{eV}$, having a bandwidth of $\hslash /\sigma =5.0\mathrm{eV}$ and $E_0=2.5E_h{\mathrm{e}}^{-1}\mathrm{b}\mathrm{o}\mathrm{h}{\mathrm{r}}^{-1}$. The envelope of the excitation pulse is shown in grey. The population of $M_S$ components of the ground state is shown by the blue line.

Figure 2

Spin dynamics initiated by the explicit field excitation with different carrier frequencies and bandwidths corresponding to: (a) 706.9 eV and 5.0 eV, (b) 711.5 eV and 5.0 eV, (c) 706.9 eV and 0.5 eV, (d) 711.5 eV and 0.5 eV, respectively [for the spectral overlap with the SOC states, cf. Fig. (1)]. The field amplitude is $E_0=2.5E_h{\mathrm{e}}^{-1}\mathrm{b}\mathrm{o}\mathrm{h}{\mathrm{r}}^{-1}$ for panels (a) and (b), and $E_0=1.5E_h{\mathrm{e}}^{-1}\mathrm{boh}{\mathrm{r}}^{-1}$ for (c) and (d).