Correlation Between Spin and Orbital Dynamics During Laser-Induced Femtosecond Demagnetization

Spin and orbital angular momenta are two intrinsic properties of an electron and are responsible for the physics of a solid. How the spin and orbital evolve with respect to each other on several hundred femtoseconds is largely unknown, but it is at the center of laser-induced ultrafast demagnetization. In this paper, we introduce a concept of the spin-orbital correlation diagram, where spin angular momentum is plotted against orbital angular momentum, much like the position-velocity phase diagram in classical mechanics. We use four sets of highly accurate time-resolved x-ray magnetic circular dichroism (TR-XMCD) data to construct four correlation diagrams for iron and cobalt. To our surprise, a pattern emerges. The trace on the correlation diagram for iron is an arc, and at the end of demagnetization, it has a pronounced cusp. The correlation diagram for cobalt is different and appears more linear, but with kinks. We carry out first-principles calculations with two different methods: time-dependent density functional theory (TDDFT) and time-dependent Liouville density functional theory (TDLDFT). These two methods agree that the experimental findings for both Fe and Co are not due t experimental errors. It is the spin-orbit coupling that correlates the spin dynamics to the orbital dynamics.Microscopically, Fe and Co have different orbital occupations, which leads to distinctive correlation diagrams. We believe that this correlation diagram presents a useful tool to better understand spin and orbital dynamics on an ultrafast time scale. A brief discussion on the magnetic anisotropy energy is also provided.

Spin Berry points as crucial for ultrafast demagnetization

Laser-induced ultrafast demagnetization has puzzled researchers around the world for over two decades. Intrinsic complexity in electronic, magnetic, and phononic subsystems is difficult to understand microscopically. So far it is not possible to explain demagnetization using a single mechanism, which suggests a crucial piece of information still missing. In this paper, we return to a fundamental aspect of physics: spin and its change within each band in the entire Brillouin zone. We employ fcc Ni as an example and use an extremely dense {bf k} mesh to map out spin changes for every band close to the Fermi level along all the high symmetry lines. To our surprise, spin angular momentum at some special {bf k} points abruptly changes from $pm hbar/2$ to $mp hbar/2$ simply by moving from one crystal momentum point to the next. This explains why intraband transitions, which the spin superdiffusion model is based upon, can induce a sharp spin moment reduction, and why electric current can change spin orientation in spintronics. These special {bf k} points, which are called spin Berry points, are not random and appear when several bands are close to each other, so the Berry potential of spin majority states is different from that of spin minority states. Although within a single band, spin Berry points jump, when we group several neighboring bands together, they form distinctive smooth spin Berry lines. It is the band structure that disrupts those lines. Spin Berry points are crucial to laser-induced ultrafast demagnetization and spintronics.

Harmonic generation predominantly from a single spin channel in a half metal

Harmonic generation in atoms and molecules has reshaped our understanding of ultrafast phenomena beyond the traditional nonlinear optics and has launched attosecond physics. Harmonics from solids represent a new frontier, where both majority and minority spin channels contribute to harmonics.} This is true even in a ferromagnet whose electronic states are equally available to optical excitation. Here, we demonstrate that harmonics can be generated {mostly} from a single spin channel in half metallic chromium dioxide. {An energy gap in the minority channel greatly reduces the harmonic generation}, so harmonics predominantly emit from the majority channel, with a small contribution from the minority channel. However, this is only possible when the incident photon energy is well below the energy gap in the minority channel, so all the transitions in the minority channel are virtual. The onset of the photon energy is determined by the transition energy between the dipole-allowed transition between the O-$2p$ and Cr-$3d$ states. Harmonics {mainly} from a single spin channel can be detected, regardless of laser field strength, as far as the photon energy is below the minority band energy gap. This prediction should be tested experimentally.

High-order harmonic generation in solid $rm bf C_{60}$

High harmonic generation (HHG) has unleashed the power of strong laser physics in solids. Here we investigate HHG from a large system, solid C$_{60}$, with 240 valence electrons engaging harmonic generation at each crystal momentum, the first of this kind. We employ the density functional theory and the time-dependent Liouville equation of the density matrix to compute HHG signals. We find that under a moderately strong laser pulse, HHG signals reach 15th order, consistent with the experimental results from C$_{60}$ plasma. The helicity dependence in solid C$_{60}$ is weak, due to the high symmetry. In contrast to the general belief, HHG is unsuitable for band structure mapping in C$_{60}$. However, we find a window of opportunity using a long wavelength, where harmonics are generated through multiple-photon excitation. In particular, the 5th order harmonic energies closely follow the transition energy dispersion between the valence and conduction bands. This finding is expected to motivate future experimental investigations.

An attempt to simulate laser-induced all-optical spin switching in a crystalline ferrimagnet

Interest in all-optical spin switching (AOS) is growing rapidly. The recent discovery of AOS in Mn$_2$RuGa provides a much needed clean case of crystalline ferrimagnets for theoretical simulations. Here, we attempt to simulate it using the state-of-the-art first-principles method combined with the Heisenberg exchange model. We first compute the spin moments at two inequivalent manganese sites and then feed them into our model Hamiltonian. We employ an ultrafast laser pulse to switch the spins. We find that there is a similar optimal laser field amplitude to switch spins. However, we find that the exchange interaction has a significant effect on the system switchability. Weakening the exchange interaction could make the system unswitchable. This provides a crucial insight into the switching mechanism in ferrimagnets.

All-optical spin switching under different spin configurations

We employ an atomic spin model and present a systematic investigation from a single spin to a large system of over a million spins. To have an efficient spin switching, the electron initial momentum direction must closely follow the spins orientation, so the orbital angular momentum is transverse to the spin and consequently the spin-orbit torque lies in the same direction as the spin. The module of the spin-orbit torque is $lambda |{bf S}||{bf r}||{bf P}| sqrt{cos^2alpha+cos^2beta-2cosalpha cosbeta cosgamma} $, where $alpha(beta)$ is the angle between spin {bf S} and position {bf r}(momentum { bf P}) and $gamma$ is the angle between {bf r} and {bf P}. These findings are manifested in a much larger system. The spin response depends on underlying spin structures. A linearly polarized laser pulse creates a dip in a uniform inplane-magnetized thin film, but has little effects on eel and Bloch walls. Both right- and left- circularly polarized light ($sigma^+$ and $sigma^-$) have stronger but different effects in both uniform spin domains and Neel walls. While $sigma^+$ light creates a basin of spins pointing down, $sigma^-$ light creates a mound of spins pointing up. In the vicinity of the structure spins are reversed, similar to the experimental observation. $sigma^+$ light has a dramatic effect, disrupting spins in Bloch walls. By contrast, $sigma^-$ light has a small effect on Bloch walls because $sigma^-$ only switches down spins up and once the spins already point up, there is no major effect.

Laser-induced ultrafast transport and demagnetization at the earliest time: First-principles and real-time investigation

Here we carry out a first-principles time-dependent calculation to investigate how fast electrons actually move under laser excitation and how large the electron transport affects demagnetization on the shortest time scale. To take into account the transport effect, we implement the intraband transition in our theory. In the bulk fcc Ni, we find the effect of the spin transport on the demagnetization is extremely small, no more than 1%. The collective electron velocity in Ni is 0.4 $rm AA/fs$, much smaller than the Fermi velocity, and the collective displacement is no more than 0.1 $rm AA$. But this does not mean that electrons do not travel fast; instead we find that electron velocities at two opposite crystal momenta cancel each other. We follow the $Gamma$-X line and find a huge dispersion in the velocities in the crystal momentum space. In the Fe/W(110) thin film, the overall demagnetization is larger than Ni, and the Fermi velocity is higher than Ni. However, the effect of the spin transport is still small in the Fe/W(110) thin film. Based on our numerical results and existing experimental findings, we propose a different mechanism that can explain two latest experimental results. Our finding sheds new light on the effect of ballistic transport on demagnetization.

Understanding all-optical spin switching: Comparison between experiment and theory

Information technology depends on how one can control and manipulate signals accurately and quickly. Transistors are at the core of modern technology and are based on electron charges. But as the device dimension shrinks, heating becomes a major problem. The spintronics explores the spin degree of electrons and thus bypasses the heat, at least in principle. For this reason, spin-based technology offers a possible solution. In this review, we survey some of latest developments in all-optical switching (AOS), where ultrafast laser pulses are able to reverse spins from one direction to the other deterministically. But AOS only occurs in a special group of magnetic samples and within a narrow window of laser parameters. Some samples need multiple pulses to switch spins, while others need a single-shot pulse. To this end, there are several models available, but the underlying mechanism is still under debate. This review is different from other prior reviews in two aspects. First, we sacrifice the completeness of reviewing existing studies, while focusing on a limited set of experimental results that are highly reproducible in different labs and provide actual switched magnetic domain images. Second, we extract the common features from existing experiments that are critical to AOS, without favoring a particular switching mechanism. We emphasize that given the limited experimental data, it is really premature to identify a unified mechanism. We compare these features with our own model prediction, without resorting to a phenomenological scheme. We hope that this review serves the broad readership well.

First-principles and model simulation of all-optical spin reversal

All-optical spin switching is a potential trailblazer for information storage and communication at an unprecedented fast rate and free of magnetic fields. However, the current wisdom is largely based on semiempirical models of effective magnetic fields and heat pulses, so it is difficult to provide high-speed design protocols for actual devices. Here, we carry out a massively parallel first-principles and model calculation for thirteen spin systems and magnetic layers, free of any effective field, to establish a simpler and alternative paradigm of laser-induced ultrafast spin reversal and to point out a path to a full-integrated photospintronic device. It is the interplay of the optical selection rule and sublattice spin orderings that underlines seemingly irreconcilable helicity-dependent/independent switchings. Using realistic experimental parameters, we predict that strong ferrimagnets, in particular, Laves phase C15 rare-earth alloys, meet the telecommunication energy requirement of 10 fJ, thus allowing a cost-effective subpicosecond laser to switch spin in the GHz region.

Is perpendicular magnetic anisotropy essential to all-optical ultrafast spin reversal in ferromagnets?

All-optical spin reversal presents a new opportunity for spin manipulations, free of a magnetic field. Most of all-optical-spin-reversal ferromagnets are found to have a perpendicular magnetic anisotropy (PMA), but it has been unknown whether PMA is necessary for the spin reversal. Here we theoretically investigate magnetic thin films with either PMA or in-plane magnetic anisotropy (IMA). Our results show that the spin reversal in IMA systems is possible, but only with a longer laser pulse and within a narrow laser parameter region. The spin reversal does not show a strong helicity dependence where the left- and right-circularly polarized light lead to the identical results. By contrast, the spin reversal in PMA systems is robust, provided both the spin angular momentum and laser field are strong enough while the magnetic anisotropy itself is not too strong. This explains why experimentally the majority of all-optical spin-reversal samples are found to have strong PMA and why spins in Fe nanoparticles only cant out of plane. It is the laser-induced spin-orbit torque that plays a key role in the spin reversal. Surprisingly, the same spin-orbit torque results in laser-induced spin rectification in spin-mixed configuration, a prediction that can be tested experimentally. Our results clearly point out that PMA is essential to the spin reversal, though there is an opportunity for in-plane spin reversal.