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Lei Lei,1 Yihua Bai,1 Yang Fan,1 Yaling Li,1 Hongying Jiang,1 Jiaping Wang2 1Department of Nephrology, The Second Hospital Affiliated to Kunming Medical University, Kunming, Yunnan, People’s Republic of China; 2Department of Radiology, The Second Hospital Affiliated to Kunming Medical University, Kunming, Yunnan, People’s Republic of ChinaCorrespondence: Yihua Bai, Department of Nephrology, The Second Hospital Affiliated to Kunming Medical University, Kunming, Yunnan, People’s Republic of China, Email baiyihua@kmmu.edu.cnBackground: Diabetic nephropathy (DN) is a primary driver of end-stage renal disease. Given the heterogeneity of renal lesions and the complex mechanisms of DN, the present-day diagnostic approach remains highly controversial. We aimed to design a diagnostic model by bioinformatics methods for discriminating DN patients from normal subjects.Methods: In this study, transcriptome sequencing was performed on 6 clinical samples (3 from DN patients and 3 from healthy volunteers) from the Second Affiliated Hospital of Kunming Medical University. Construction of a competing endogenous RNA (ceRNA) network based on differentially expressed (DE)-mRNAs and -long noncoding RNAs (lncRNAs). Subsequently, the CytoHubba plugin was used to identify hub genes from DE-mRNAs in the ceRNA network and to perform functional enrichment analysis on them. The least absolute shrinkage and selection operator (LASSO) regression analysis was responsible for screening the diagnostic biomarkers from hub genes and assessing their diagnostic power using ROC curves. The pathways involved in hub genes were revealed by single-gene Gene Set Enrichment Analysis (GSEA). Moreover, we verified the expression levels of diagnostic biomarkers by quantitative real-time polymerase chain reaction (qRT-PCR) and Western blot.Results: A total of 10 hub genes were screened from the ceRNA network, which appeared to be associated with the viral infection, kidney development, and regulation of immune and inflammatory responses. Subsequently, LASSO regression analysis established a diagnostic model consisting of DDX58, SAMD9L, and TLR6 with a robust diagnostic potency (AUC = 1). Similarly, single-gene GSEA showed a strong association of these diagnostic biomarkers with the viral infection. Furthermore, PCR and Western blot demonstrated showed that DDX58, SAMD9L, and TLR6 were upregulated in DN patients at both transcriptome and protein levels compared to healthy controls.Conclusion: We confirmed that differentially expressed hub genes may be novel diagnostic biomarkers in DN.Keywords: diabetic nephropathy, DN, diagnosis, ceRNA, biomarker

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.

Lattice vibration in solids may carry angular momentum. But unlike the intrinsic spin of electrons, the lattice vibration is rarely rotational. To induce angular momentum, one needs to find a material that can accommodate a twisted normal mode, two orthogonal modes or excitation of magnons. If excitation is too strong, one may exceed the Lindemann limit, so the material melts. Therefore these methods are not ideal. Here, we theoretically propose a new route to phonon angular momentum in a molecular crystal $\rm C_{60}$. We find that a single laser pulse is able to inject a significant amount of angular momentum to $\rm C_{60}$, and the momentum transfer is helicity-dependent. Changing from right-circularly polarized light to left-circularly polarized light switches the direction of phonon angular momentum. On the ultrafast time scale, the orbital angular momentum change closely resembles the displacive excitation of coherent phonons, with a cosine-function dependence on time, different from the spin counterpart. Atomic displacements, even under strong laser excitation, remain far below the Lindemann criterion. Under thermal excitation, spinning $\rm C_{60}$ even at room temperature generates a huge angular momentum close to several hundred $\hbar$. Our finding opens the door to a large group of fullerenes, from $\rm C_{60}$, C$_{70}$ to their endohedral derivatives, where angular momentum can be generated through light or temperature. This paves the way to the phononic control electronic spin and harvesting thermal energy through phonon angular momentum., 19 pages, Four figures

Polaritons in two-dimensional van der Waals (vdW) materials possess extreme light confinement, which have emerged as a potential platform for next-generation biosensing and infrared spectroscopy. Here, we propose an ultra-thin and electric tunable graphene/hexagonal boron nitride/graphene metasurface for detecting molecular fingerprints over a broad spectrum. The vdW metasurface supports hybrid plasmon–phonon polariton resonance with high-quality factor (Q > 120) and electrically controlled broadband spectra tunability from 6.5 to 7 μm. After coating a thin layer of bio-molecular (e.g., CBP) on top of the metasurface, the molecular absorption signatures can be readout at multiple spectral points and, thus, achieve broadband fingerprint retrieval of bio-molecules. Additionally, our electric tunable metasurface works as an integrated graphene-based field-effect transistor device, without the need of multiple resonance generators such as angle-resolved or pixelated dielectric metasurfaces for broadband spectra scanning, thereby paving the way for highly sensitive, miniaturized, and electrically addressed biosensing and infrared spectroscopy.

We introduce a method for detecting the topological charge of power-exponential-phase vortex beam(PEPVB) and its power-exponent parameter by using a Laguerre-Gaussian beam that interferes with a PEPVB. The intensity shows a unique flower pattern after interference. According to the number of petals l-l0 and the topological charge of LG light l0 , we can obtain the topological charge of the PEPVB 𝑙. One of the most significant characteristics of PEPVB is the petals in the interference pattern become narrower clockwise. Moreover, the angle of the largest petal Δφ gradually decreases with an increasing power-exponent parameter. By measuring the angle φ1, φ2, the value of the power-exponent parameter 𝑛 can be calculated.

Surface plasmon polaritons (SPPs), surface electromagnetic waves propagating along metal-dielectric interfaces, have found numerous applications in integrated photonic devices, optical storage, and optical sensing, etc. In recent years, there has been a surge of interest in the fundamental and applications of SPPs carrying orbital angular momentum, namely SPP vortices or plasmonic vortices. In this review, we summarize the fundamental concepts of plasmonic vortices, and highlight recent advances in the generation and applications of plasmonic vortices, from SPPs at lightwave frequencies to spoof SPPs at microwave and Terahertz frequencies.

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., Comment: 19 pages and nine figures, Invited paper to Modern Physics Letters B

Based on the ABCD matrix method and Collins diffraction integral formula, the general analytical expression for the partially coherent modified Bessel–Gauss beam propagating in a gradient-index medium is derived. The propagation trajectory, intensity, and phase distribution of such a beam are numerically investigated. The effects of the topological charge, the coherence parameter, and the coefficient of the gradient refractive index on propagation properties are considered. Results show that the propagation trajectory of such beam focuses and diverges periodically, which is different from free-space propagation. The period of intensity distribution is consistent with that of phase distribution under different cases. As propagation distance increases, the dark core always exists and the phase singularities remain stable and do not split. The dark core can be modulated by topological charge and coherence parameter, and the periodical distance can be modulated by the coefficient of the gradient refractive index. These results will help to explore such beams and find applications in optical communication and optical trapping.

High-order harmonic generation (HHG) has unleashed the power of strong laser physics in solids. Here we investigate HHG from a large system, solid ${\mathrm{C}}_{60}$, with 240 valence electrons engaging harmonic generation at each crystal momentum. 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 ${\mathrm{C}}_{60}$ plasma. The helicity dependence in solid ${\mathrm{C}}_{60}$ is weak, due to the high symmetry. In contrast to the general belief, HHG is unsuitable for band structure mapping in ${\mathrm{C}}_{60}$. However, we find a window of opportunity using a long wavelength, where harmonics are generated through multiple-photon excitation. In particular, the fifth-order harmonic energies closely follow the transition energy dispersion between the valence and conduction bands. This finding is expected to motivate future experimental investigations.

Recent advances in the research of vortex beams, structured beams carrying orbital angular momentum (OAM), have revolutionized the applications of light beams, such as advanced optical manipulations, high-capacity optical communications, and super-resolution imaging. Undoubtedly, the methods for generation of a vortex beam and detection of its OAM are of vital importance for the applications of vortex beams. In this review, we first introduce the fundamental concepts of vortex beams briefly and then summarize approaches to generating and detecting the vortex beams separately, from bulky diffractive elements to planar elements. Finally, we make a concise conclusion and outline that is yet to be explored.

Laser-induced femtosecond demagnetization, femtomagnetism, offers a potential route to develop faster magnetic storage devices. It is generally believed that the traditional spin-wave theory, which is developed for thermally driven slow demagnetization, can not explain this rapid demagnetization by design. Here we show that this traditional spin-wave theory, once augmented by laser-induced spin-orbit torque, provides a highly efficient paradigm for demagnetization, by capturing low-energy spin-wave excitation that is absent in existing mechanisms. Our paradigm is different from existing ones, but does not exclude them. Microscopically, we find that optical spin-orbit torque generates massive spin waves across several hundred lattice sites, collapsing the long-range spin-spin correlation within 20 fs. Our finding does not only explain new experiments, but also establishes an alternative paradigm for femtomagnetism. It is expected to have far-reaching impacts on future research., 21 pages, 5 figures, 2 tables

High-order harmonic generation (HHG) from atoms is a coherent light source that opens up attosecond physics, but it is the application of HHG to solids that brings much of excitement for the last decade. Here we report a completely new kind of harmonics in a quasi-one-dimensional and hexagonal barium titanium sulfide: Under circularly polarized laser excitation, harmonics are generated only at first, fifth, seventh and eleventh orders. These magic harmonics appear only with circularly polarized light, not with linearly polarized light. Neither cubic nor tetragonal cells have magic harmonics even with circularly polarized light. Through a careful group-theory analysis, we find that two subgroups of symmetry operations unique to the hexagonal symmetry cancel out third and ninth harmonics. This feature presents a rare opportunity to develop HHG into a crystal-structure characterization tool for phase transitions between hexagonal and nonhexagonal structures., 16 pages, Four figures, 2 Tables

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., Comment: 5 pages, and 2 figures

A multipoint interferometer (MI), uniformly distributed point-like pinholes in a circle, was proposed to measure the orbital angular momentum (OAM) of vortex beams [Phys. Rev. Lett. 101, 100801 (2008)PRLTAO0031-900710.1103/PhysRevLett.101.100801], which can be used for measuring OAM of light from astronomical sources. This is a simple and robust method; however, it is noted that this method is only available for low topological charge because the diffracted intensity patterns for vortex beams with higher OAM will repeat periodically. Here, we propose an improved multipoint interferometer (IMI) for measuring the OAM of an optical vortex with high topological charge. The structure of our IMI is almost the same as the MI, but the size of each pinhole is larger than a point in the MI. Such a small change enables each pinhole to get more phase information from the incident beams; accordingly, the IMI can distinguish any vortex beams with different OAM. We demonstrate its viability both theoretically and experimentally.

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., Comment: 32 pages, 6 figures, (accepted for publication in Journal of Physics: Condensed Matter (2018))

High-order harmonic generation (HHG) in solids has entered a new phase of intensive research, with envisioned band-structure mapping on an ultrashort time scale. This partly benefits from a flurry of new HHG materials discovered, but so far has missed an important group. HHG in magnetic materials should have profound impact on future magnetic storage technology advances. Here we introduce and demonstrate HHG in ferromagnetic monolayers. We find that HHG carries spin information and sensitively depends on the relativistic spin-orbit coupling; and if they are dispersed into the crystal momentum ${\bf k}$ space, harmonics originating from real transitions can be ${\bf k}$-resolved and carry the band structure information. Geometrically, the HHG signal is sensitive to spatial orientations of monolayers. Different from the optical counterpart, the spin HHG, though probably weak, only appears at even orders, a consequence of SU(2) symmetry. Our findings open an unexplored frontier -- magneto-high-order harmonic generation., 19 pages, 4 figures

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., Comment: Review article, 30 pages long, comments are welcome, Modern Physics Letters B. (2018)

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., 23 pages, 6 figures and one table

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., 20 pages, 4 figures and one table

In magneto-optics the spin angular momentum $S_z$ of a sample is indirectly probed by the rotation angle and ellipticity, which are mainly determined by the off-diagonal susceptibility $\chi^{(1)}_{xy}$. A direct and analytic relation between $S_z$ and $\chi^{(1)}_{xy}$ is necessary and of paramount importance to the success of magneto-optics, but is often difficult to acquire since quantum mechanically the relation is hidden in the sum-over-states. Here we propose a new and simple model to establish such a much needed relation. Our model is based on the Hookean model, but includes spin-orbit coupling. Under cw excitation, we show that $\chi^{(1)}_{xy}(\omega)$ is indeed directly proportional to $S_z$ for a fixed photon frequency $\omega$. Such an elegant relation is encouraging, and we wonder whether our model can describe spin dynamics as well. By allowing the spin to change dynamically, to our surprise, our model predicts that an ultrafast laser pulse can induce a spin precession; with appropriate parameters, the laser can even reverse spin from one direction to another. This works for both the circularly and linearly polarized light. The spin reversal window is narrow. These unexpected results closely resemble all-optical helicity-dependent magnetic switching found in much more complicated ferrimagnetic rare earth compounds. Therefore, we believe that our spin-orbit coupled model may find some important applications in spin switching processes, a hot topic in femtomagnetism., Comment: 6 pages, 2 figures

Using an ultrafast laser pulse to manipulate the spin degree of freedom has broad technological appeal. It allows one to control the spin dynamics on a femtosecond time scale. The discipline, commonly called femtomagnetism, started with the pioneering experiment by Beaurepaire and coworkers in 1996, who showed subpicosecond demagnetization occurs in magnetic Ni thin films. This finding has motivated extensive research worldwide. All-optical helicity-dependent spin switching (AOS) represents a new frontier in femtomagnetism, where a single ultrafast laser pulse can permanently switch spin without any assistance from a magnetic field. This review summarizes some of the crucial aspects of this new discipline: key experimental findings, leading mechanisms, controversial issues, and possible future directions. The emphasis is on our latest investigation. We first develop the all-optical spin switching rule that determines how the switchability depends on the light helicity. This rule allows one to understand microscopically how the spin is reversed and why the circularly polarized light appears more powerful than the linearly polarized light. Then we invoke our latest spin-orbit coupled harmonic oscillator model to simulate single spin reversal. We consider both cw excitation and pulsed laser excitation. The results are in a good agreement with the experimental result. We then extend the code to include the exchange interaction among different spin sites. We show where the "inverse Faraday field" comes from and how the laser affects the spin reversal nonlinearly. Our hope is that this review will motivate new experimental and theoretical investigations and discussions., Comment: Invited short review article, 33 pages. Another related paper on AOS can be found arXiv:1609.05855 Add a new reference and also revised a few sentences in the paper

Faster magnetic recording technology is indispensable to massive data storage and big data sciences. {All-optical spin switching offers a possible solution}, but at present it is limited to a handful of expensive and complex rare-earth ferrimagnets. The spin switching in more abundant ferromagnets may significantly expand the scope of all-optical spin switching. Here by studying 40,000 ferromagnetic spins, we show that it is the optical spin-orbit torque that determines the course of spin switching in both ferromagnets and ferrimagnets. Spin switching occurs only if the effective spin angular momentum of each constituent in an alloy exceeds a critical value. Because of the strong exchange coupling, the spin switches much faster in ferromagnets than weakly-coupled ferrimagnets. This establishes a paradigm for all-optical spin switching. The resultant magnetic field (65 T) is so big that it will significantly reduce high current in spintronics, thus representing the beginning of photospintronics., Comment: 12 page2, 6 figures. Accepted to Europhysics Letters (2016). Extended version with the supplementary information. Contribution from Indiana State University,Europhysics Letters (2016)

We investigate how electron correlation and band structure affect laser-induced demagnetization. Pure electron-electron scattering cannot explain the large spin moment reduction observed, and the band relaxation and exchange splitting are essential to the spin change.

Conventional understanding of the magneto-optical Kerr effect, in which changes in the magnetization of a material cause changes in the polarization of reflected light, assumes that this incident light is continuous. However, first-principles simulations of nickel show that this assumption breaks down for femtosecond pulses of light, and establishes a firm foundation for understanding the dynamics of femtomagnetism. The magneto-optical Kerr effect (MOKE) is a powerful tool for studying changes in the magnetization of ferromagnetic materials. It works by measuring changes in the polarization of reflected light. However, because the conventional theoretical basis for interpreting a MOKE signal assumes measurement with continuous-wave light1,2, its use for understanding high-speed magnetization dynamics of a material probed with femtosecond optical pulses3,4 has been controversial5,6,7,8,9,10. Here we establish a new paradigm for interpreting time-resolved MOKE measurements, through a first-principles investigation of ferromagnetic nickel. We show that the time-resolved optical and magnetic responses energetically follow their respective optical and magneto-optical susceptibilities. As a result, the one-to-one correspondence between them sensitively depends on the incident photon energy. In nickel, for photon energies below 2 eV the magnetic response is faithfully reflected in the optical response, but above 2 eV they decouple. By constructing a phase-sensitive polarization versus magnetization plot, we find that for short pulses the magnetic signals are delayed by 10 fs with respect to the optical signals. For longer pulses, the delay shortens and the behaviour approaches the continuous-wave response. This finally resolves the long-standing dispute over the interpretation in the time-resolved MOKE measurements and lays a solid foundation for understanding femtomagnetism3,4.

Two parallel block tridiagonalization algorithms and implementations for dense real symmetric matrices are presented. Block tridiagonalization is a critical pre-processing step for the block tridiagonal divide-and-conquer algorithm for computing eigensystems and is useful for many algorithms desiring the efficiencies of block structure in matrices. For an ''effectively'' sparse matrix, which frequently results from applications with strong locality properties, a heuristic parallel algorithm is used to transform it into a block tridiagonal matrix such that the eigenvalue errors remain bounded by some prescribed accuracy tolerance. For a dense matrix without any usable structure, orthogonal transformations are used to reduce it to block tridiagonal form using mostly level 3 BLAS operations. Numerical experiments show that block tridiagonal structure obtained from this algorithm directly affects the computational complexity of the parallel block tridiagonal divide-and-conquer eigensolver. Reduction to block tridiagonal form provides significantly lower execution times, as well as memory traffic and communication cost, over the traditional reduction to tridiagonal form for eigensystem computations.

The exchange interaction among electrons is one of the most fundamental quantum mechanical interactions in nature and underlies any magnetic phenomena from ferromagnetic ordering to magnetic storage. The current technology is built upon a thermal or magnetic field, but a frontier is emerging to directly control magnetism using ultrashort laser pulses. However, little is known about the fate of the exchange interaction. Here we report unambiguously that photoexcitation is capable of quenching the exchange interaction in all three $3d$ ferromagnetic metals. The entire process starts with a small number of photoexcited electrons which build up a new and self-destructive potential that collapses the system into a new state with a reduced exchange splitting. The spin moment reduction follows a Bloch-like law as $M_z(\Delta E)=M_z(0)(1-{\Delta E}/{\Delta E_0})^{\frac{1}{\beta}}$, where $\Delta E$ is the absorbed photon energy and $\beta$ is a scaling exponent. A good agreement is found between the experimental and our theoretical results. Our findings may have a broader implication for dynamic electron correlation effects in laser-excited iron-based superconductors, iron borate, rare-earth orthoferrites, hematites and rare-earth transition metal alloys., Comment: 16 pages, 3 figures, one supplementary material file

A block tridiagonalization algorithm is proposed for transforming a sparse (or "effectively" sparse) symmetric matrix into a related block tridiagonal matrix, such that the eigenvalue error remains bounded by some prescribed accuracy tolerance. It is based on a heuristic for imposing a block tridiagonal structure on matrices with a large percentage of zero or "effectively zero" (with respect to the given accuracy tolerance) elements. In the light of a recently developed block tridiagonal divide-and-conquer eigensolver [Gansterer, Ward, Muller, and Goddard, III, SIAM J. Sci. Comput. 25 (2003), pp. 65--85], for which block tridiagonalization may be needed as a preprocessing step, the algorithm also provides an option for attempting to produce at least a few very small diagonal blocks in the block tridiagonal matrix. This leads to low time complexity of the last merging operation in the block divide-and-conquer method. Numerical experiments are presented and various block tridiagonalization strategies are compared.

Our framework, computing approximate eigensystems (CApE), efficiently approximates symmetric linear eigenvalue problems occurring in the self-consistent field method used during electronic structure computations. CApE has several algorithmic tools that both detect matrix structure in application problems and compute solutions to prescribed accuracy.

A decade ago Rhie \et (Phys. Rev. Lett. {\bf 90}, 247201 (2003)) reported that when ferromagnetic nickel is subject to an intense ultrashort laser pulse, its exchange splitting is reduced quickly. But to simulate such reduction remains a big challenge. The popular rigid band approximation (RBA), where both the band structure and the exchange splitting are held fixed before and after laser excitation, is unsuitable for this purpose, while the time-dependent density functional theory could be time-consuming. To overcome these difficulties, we propose a time-dependent Liouville and density functional theory (TDLDFT) that integrates the time-dependent Liouville equation into the density functional theory. As a result, the excited charge density is reiterated back into the Kohn-Sham equation, and the band structure is allowed to change dynamically. Even with the ground-state density functional, a larger demagnetization than RBA is found; after we expand Ortenzi's spin scaling method into an excited-state (laser) density functional, we find that the exchange splitting is indeed strongly reduced, as seen in the experiment. Both the majority and minority bands are shifted toward the Fermi level, but the majority shifts a lot more. The ultrafast reduction in exchange splitting occurs concomitantly with demagnetization. While our current theory is still unable to yield the same percentage loss in the spin moment as observed in the experiment, it predicts a correct trend that agrees with the experiments. With a better functional, we believe that our results can be further improved., 18 pages, 3 figures

When a femtosecond (fs) laser pulse strikes a ferromagnet, it demagnetizes the sample within a few hundred fs but its underlying mechanism has remained elusive for over a decade. Here a possible microscopic picture is revealed through an energy- and crystal momentum-resolved first-principles investigation, first by locating the optimal excitation-energy window for the maximal magnetization change and then mapping out every magnetic contribution from each crystal momentum $\mathbf{k}$ point along the high-symmetry lines within the Brillouin zone. We find that not all the $\mathbf{k}$ points contribute evenly, where a few momentum $\mathbf{k}$ points show a much stronger magnetic-moment change than others. In ferromagnetic nickel, less than 50% of the $\mathbf{k}$ points contribute over 90% of the magnetization change. By closely examining the transition-matrix elements and spin-moment change associated with those $\mathbf{k}$ points, we further find the reduction in the dynamical magnetic moment is directly connected with these transition-moments and spin-moment changes between band states.

Superatomic molecular orbitals (SAMOs) in C 60 are ideal building blocks for functional nanostructures. However, imaging them spatially in the gas phase has been unsuccessful. It is found experimentally that if C 60 is excited by an 800-nm laser, the photoelectron casts an anisotropic velocity image, but the image becomes isotropic if excited at a 400-nm wavelength. This diffuse image difference has been attributed to electron thermal ionization, but more recent experiments (800 nm) reveal a clear nondiffuse image superimposed on the diffuse image, whose origin remains a mystery. Here we show that the nondiffuse anisotropic image is the precursor of the f SAMOs. We predict that four 800-nm photons can directly access the 1f SAMO, and with one more photon, can image the orbital, with the photoelectron angular distribution having two maxima at 0° and 180° and two humps separated by 56.5°. Since two 400-nm photons only resonantly excite the spherical 1s SAMO and four 800-nm photons excite the anisotropic 1f SAMO, our finding gives a natural explanation of the nondiffuse image difference, complementing the thermal scenario.

Laser chirp has found many applications in pulse shaping, high harmonic generation, and dynamical control of the vibrational excitation. Here, we show that the laser chirp can significantly affect the amount of the magnetic moment change in the laser-induced femtosecond magnetism. Under the same laser condition, an increase in the chirp from 0 to 0.04 rad/fs2 results in the magnetic moment change from 0.4% to 5% in ferromagnetic nickel. We find that the laser pulse duration has a direct effect on the effectiveness of the chirp. For a shorter pulse of duration 12 fs, the spin change with the chirp is small. We attribute this to a shorter interaction time and consequently a smaller instantaneous photon energy. We also investigate the effect of chirp on laser-induced local-spin-switching on molecular magnets consisting of two magnetic centers (Fe, Co, and Ni) bridged by Na atoms. We find that the effect of chirping differs depending on the original switching behavior of the atom. On Fe the chirp renders the process slightly less effective, on Ni it leads to a more dramatic loss of fidelity due to quantum interference, and for Co the effect lies in-between. Our study opens a new way to manipulate spin on femtosecond time scales.

Different from thermally and magnetically induced demagnetization, the laser-induced demagnetization relies on the laser photon field. However, what has been unknown is how the spin moment reduction correlates with the number of photons. Here, our first-principles calculation in ferromagnetic nickel and cobalt clusters shows that the number of photons is not the sole decisive factor for the magnetization change, contrary to earlier belief. For the same number of photons absorbed, the shorter the laser pulse, the larger the induced spin moment reduction. Besides a simple decrease in the magnetic moment, a short pulse also excites a strong coherent spin oscillation, which disappears when using a longer pulse. The longest pulse duration where we observed this oscillation is about 20 fs. Future experiments can directly test our prediction. We show that for our generic ultrafast spin-switching Λ-process on metallic nanoclusters the electronic correlations constitute a key ingredient, which allows for spin and ...

When an ultrafast laser impinges a magnetic material, it excites charge and then, via spin-orbit-coupling, spin. This holds great promise for the future magnetic storage. However, the coupling of the two dynamics is far from clear, which hampers the experimental effort in femtosecond magnetism. Since not every excitation induces the same spin excitation, a clear understanding of the correlation between charge and spin is crucial. In this paper we investigate in a complete first-principles manner the energy dispersion of the spin-moment change in ferromagnetic Ni and the effect of the distance between the magnetic centers upon the spin localization and local-spin-flip times in metallic chains. Thus we establish the missing link between the spin-momentum change and the density-of-states change, and derive rules-of-thumb for localized spin manipulation.

Ultrafast demagnetization in ferromagnets has attracted much attention both experimentally and theoretically for over a decade. This includes a lively debate as to whether the observed signal represents a true magnetization process. Here, a first-principles and time-dependent calculation is performed for ferromagnetic nickel under laser illumination to directly compute the magnetization and polarization changes. It is found that while the polarization exhibits both rapid and slow oscillations, the magnetization mainly shows a slow oscillation. The slow component of the polarization generally follows the magnetization evolution with a margin of 2–3fs deviation. The correlation between the magnetization and polarization tends to be better in the absence of laser radiation.

We present a parallel implementation of the block-tridiagonal divide-and-conquer algorithm that computes eigensolutions of symmetric block-tridiagonal matrices to reduced accuracy. In our implementation, we use mixed data/task parallelism to achieve data distribution and workload balance. Numerical tests show that our implementation is efficient, scalable and computes eigenpairs to prescribed accuracy. We compare the performance of our parallel eigensolver with that of the ScaLAPACK divide-and-conquer eigensolver on block-tridiagonal matrices.