Applicability and breakdown of transient magnetic linear dichroism

In highly out-of-equilibrium states of matter, such as those induced by a pump laser, the applicability of well-established spectroscopic probes of magnetic order are called into question. Here we address the validity of x-ray absorption techniques in pump laser conditions, focusing on magnetic linear dichroism (MLD), a crucial probe of antiferromagnetic (AFM) order. We directly compute the dynamics of the square of the spin moment and compare the results to those obtained via the MLD response. For AFM FePd the agreement between these distinct routes to the magnetic moment severely degrades at pulse fluences greater than $\sim 1\mathrm{mJ}/{\mathrm{cm}}^2$, indicating a breakdown of the MLD response as an accurate probe of the transient moment. This contrasts with the MLD for ferromagnetic FePt, which reliably tracks the moment for fluences (and absorbed energies) up to an order of magnitude greater than the breakdown threshold for AFM FePd. We find the underlying microscopic reason for this to be increased laser induced excitations out of the $d$ band in AFM FePd, where this increase is made possible by the AFM pseudogap.

Figure 1

Transient moments obtained (i) directly via the spin density and (ii) via the $L_3$ edge response functions in laser-pumped FePt and FePd. The pump laser electric field is shown in (a), with, for all results, the frequency (1.55 eV) and duration (24 fs) held fixed, and fluence was modified by changing the amplitude. The transient normalized moment is shown for laser-pumped ferromagnetic FePt in (b), with the transient normalized moment squared shown for ferromagnetic FePt in (c) and antiferromagnetic FePd in (d). In each case the solid lines denote the moment obtained from spin density, and the open circles show that obtained via the $L_3$ edge response. Evidently, while magnetic circular dichroism (MCD) and linear dichroism (MLD) capture well the transient moment in ferromagnetic FePt, in antiferromagnetic FePd the failure of MLD becomes significant at a fluence of $2.3\mathrm{mJ}/{\mathrm{cm}}^2$.

Figure 2

Response function methods fail for the total transient moment but capture well the $d$-band moment. Shown is the square of the transient magnetic moment (normalized as indicated on the axis) for the total Fe moment (purple solid line), the $d$-band moment (light blue dashed line), and the MLD at the $L_3$-edge-derived moment (orange rings) in laser-pumped (a) antiferromagnetic FePd [matching the red data in Fig. 1] and 1 ferromagnetic FePt. Note the dramatically increased fluence ($34.0\mathrm{mJ}/{\mathrm{cm}}^2$ as opposed to $2.3\mathrm{mJ}/{\mathrm{cm}}^2$) and also the excellent agreement of MLD with the $d$-band moment even when it grossly fails to capture the total transient moment. The pulse frequency and duration employed are, in each case, those presented in Fig. 1.

Figure 3

Primary role of magnetic structure in the accuracy of MLD as a probe of demagnetization. Shown is the square of the transient moment (normalized as indicated on the axis), calculated both from the spin density and from the MLD response of the $L_3$ edge in laser-pumped ferromagnetic FePt (red), antiferromagnetic FePd (blue), and antiferromagnetic FePt (yellow). Evidently, enforcing an antiferromagnetic order in FePt results in a failure of the MLD probe very similar to that found in FePd. The pump pulse is that presented in Fig. 1 with the fluence set to $2.3\mathrm{mJ}/{\mathrm{cm}}^2$.

Figure 4

Influence of magnetic ordering on $sp\text{−}d$ hybridization. The equilibrium density of states (DOS) for ferromagnetic FePt (red solid line), antiferromagnetic FePt (orange dashed line), and antiferromagnetic FePd (blue solid line), with, in each case, the Fermi energy set to zero. The species and angular momentum resolved DOS, as indicated by the labels on the separate panels, reveal an increase in $sp$ states close to the Fermi energy that, along with the peak in minority $d$ states, allows increased pump laser excitation of minority electrons away from $d$ states. As described in the text, this results in significant underestimation of demagnetization as recorded in a MLD pump-probe setup. Note that for the case of antiferromagnetic FePd and FePt the available spin up ($\uparrow$) and down ($\downarrow$) states are reversed on the second Fe atom (not shown).