Nonlinear optical quantum theory of demagnetization in L1$_0$ FePt and FePd

TL;DR

This work develops a nonlinear optical quantum theory for laser-induced demagnetization by focusing on the spin moment and showing that, in centrosymmetric materials, the leading response is second order and consists of four SFG and four DFG terms, with DFG (optical rectification) dominating. It introduces a Hermitian second-order density matrix and a second-order density of states, $oldsymbol{\sigma^{(2)}_{ab}}(E; u_p, u_q)$, to compute the light-induced spin moment $m^{(2)}$ from first principles. Applying the framework to FePt and FePd, the authors find a larger negative spin moment change and stronger demagnetization in FePt than FePd, consistent with real-time simulations and experiments. The approach provides a quantitative, time-efficient means to compare demagnetization across materials, laying a solid foundation for femtomagnetism studies in all-optical spintronics.

Abstract

It is now well established that a laser pulse can demagnetize a ferromagnet. However, for a long time, it has not had an analytic theory because it falls into neither nonlinear optics (NLO) nor magnetism. Here we attempt to fill this gap by developing a nonlinear optical theory centered on the spin moment, instead of the more popular susceptibility. We first employ group theory to pin down the lowest order of the nonzero spin moment in a centrosymmetric system to be the second order, where the second-order density matrix contains four terms of sum frequency generation (SFG) and four terms of difference frequency generation (DFG). By tracing over the product of the density matrix and the spin matrix, we are now able to compute the light-induced spin moment. We apply our theory to FePt and FePd, two most popular magnetic recording materials with identical crystal and electronic structures. We find that the theory can clearly distinguish the difference between those two similar systems. Specifically, we show that FePt has a stronger light-induced spin moment than FePd, in agreement with our real-time ultrafast demagnetization simulation and the experimental results. Among all the possible NLO processes, DFGs produce the largest spin moment change, a manifestation of optical rectification. Our research lays a solid theoretical foundation for femtomagnetism, so the light-induced spin moment reduction can now be computed and compared among different systems, without time-consuming real-time calculations, representing a significant step forward.

Figures (6)

• Figure 1: (a) FePt/FePd crystal structures. The filled circles are Fe atoms, while the unfilled ones are Pt/Pd. (b) Symmetry difference between the polarization ${\bf P}$ and magnetization ${\bf M}$ determines how the $n$th-order polarization and magnetization depend on the external electric field ${\bf E}$ differently.
• Figure 2: (a) Band structure of FePt. (b) Density of states of the ground state in FePt, where the solid line denotes the spin majority states and the dashed line the spin minority states plotted on the negative axis. (c) Band structure of FePd. (d) Density of states of the ground state in FePd.
• Figure 3: (a) Second-order density of states in FePt. The solid line denotes $\sigma{^{(2)}_{xx}}$ with both laser polarizations along the $x$ axis, while the dotted line denotes $\sigma{^{(2)}_{xy}}$ with cross-polarizations along the $x$ and $y$ axes. Here the photon energy is $h\nu_a=h\nu_b=1.6$ eV. The long-dashed line is $\sigma{^{(2)}_{xx}}$ with $h\nu_a=h\nu_b=2.0$ eV. (b) Second-order magnetic moment $m{^{(2)}}$ in FePt as a function of photon energy $h\nu$. The key feature is that except $m{^{(2)}_{xx}}$ with a different broadening of $\Gamma=0.03$ Ry (empty diamonds), the convergences with the ${\bf k}$ points and functionals are reached within 1-3% as estimated from their overlaps. Here the filled circles denote $m{^{(2)}_{xx}}$ and the filled boxes denote $m{^{(2)}_{xy}}$ components, both with $\Gamma=0.05$ Ry. The empty circles are $m{^{(2)}_{xx}}$ with a larger ${\bf k}$ mesh of $34\times 34\times 25$. The thin star line and empty boxes are $m{^{(2)}_{xx}}$ and $m{^{(2)}_{xy}}$ computed with LDA instead of GGA. All the calculations are done with one parameter changed, while the rest are fixed. (c) Same as (a) but for FePd. (d) Same as (c) but for FePd. (e) and (f) are $m{^{(2)}_{xx}}$ and $m{^{(2)}_{xy}}$ for bcc Fe and fcc Ni, respectively.
• Figure 4: (a) Contribution of the sum frequency [SFG$_1$ (dashed line), SFG$_2$ (long-dashed line)] and difference frequency generations [DFG$_1$ (solid line), DFG$_2$ (dotted line)] to $m{^{(2)}}$ as a function of time $t$. Here the photon energy is $h\nu_a=\hbar\nu_b=1.6$ eV. (b) Total $m{^{(2)}_{xx}}$ as a function of time $t$ for FePt (solid line), FePd (dotted line), bcc Fe (dashed line) and fcc Ni (long-dashed line).
• Figure 5: Laser-parameter and intraband-bracket energy dependence of ultrafast demagnetization in FePt (black solid line) and FePd (red dashed line). (a) The laser photon energy is $h\nu=1.6$ eV, vector field potential is $A_0=0.015\ \rm Vfs/\AA,$ and pulse duration $\tau=60$ fs. (b) Same as (a) but with the pulse duration $\tau=120$ fs. (c) Same as (a) but with $h\nu=2.0$ eV. (d) $A_0$ is increased to 0.03 $\rm Vfs/\AA$. (e) The spin moment reduction in FePt as a function of the bracket energy $\delta$ which controls the contribution of the intraband transitions. (f) The spin moment reduction in FePt as a function of vector potential amplitude.