Spin Dynamics Simulations Research Articles

Thermal Hall effect of chiral spin fluctuations

Using a two-dimensional square lattice Heisenberg model with a Rashba-type Dzyaloshinskii-Moriya interaction, we demonstrate that chiral spin fluctuations can give rise to a thermal Hall effect in the absence of any static spin texture or momentum space topology. It is shown by means of Monte Carlo and stochastic spin dynamics simulations that the thermal Hall response is finite at elevated temperature outside of the linear spin wave regime and consistent with the presence of thermal fluctuation-induced nontrivial topology. Our result suggests that the high-fluctuation phases outside of the conventional regime of magnonics may yet be a promising area of exploration for spin-based electronics.

Discovery and characterization of a new type of domain wall in a row-wise antiferromagnet

Antiferromagnets have recently moved into the focus of application-related research, with the perspective to use them in future spintronics devices. At the same time the experimental determination of the detailed spin texture remains challenging. Here we use spin-polarized scanning tunneling microscopy to investigate the spin structure of antiferromagnetic domain walls. Comparison with spin dynamics simulations allows the identification of a new type of domain wall, which is a superposition state of the adjacent domains. We determine the relevant magnetic interactions and derive analytical formulas. Our experiments show a pathway to control the number of domain walls by boundary effects, and demonstrate the possibility to change the position of domain walls by interaction with movable adsorbed atoms. The knowledge about the exact spin structure of the domain walls is crucial for an understanding and theoretical modelling of their properties regarding, for instance, dynamics, response in transport experiments, and manipulation.

Spin dynamics of the antiferromagnetic Heisenberg model on a kagome bilayer

We study the spin dynamics of classical Heisenberg antiferromagnet with nearest neighbor interactions on a quasi-two-dimensional kagome bilayer. This geometrically frustrated lattice consists of two kagome layers connected by a triangular-lattice linking layer. By combining Monte Carlo with precessional spin dynamics simulations, we compute the dynamical structure factor of the classical spin liquid in kagome bilayer and investigate the thermal and dilution effects. While the low frequency and long wavelength dynamics of the cooperative paramagnetic phase is dominated by spin diffusion, weak magnon excitations persist at higher energies, giving rise the half moon pattern in the dynamical structure factor. In the presence of spin vacancies, the dynamical properties of the diluted system can be understood within the two population picture. The spin diffusion of the "correlated" spin clusters is mainly driven by the zero-energy weather-van modes, giving rise to an autocorrelation function that decays exponentially with time. On the other hand, the diffusive dynamics of the quasi-free "orphan" spins leads to a distinctive longer time power-law tail in the autocorrelation function. We discuss the implications of our work for the glassy behaviors observed in the archetypal frustrated magnet SrCr$_{9p}$Ga$_{12-9p}$O$_{19}$ (SCGO).

Element‐Specific Magnetization Damping in Ferrimagnetic DyCo5 Alloys Revealed by Ultrafast X‐ray Measurements

The dynamic response of magnetically ordered materials to an ultrashort external stimulus depends on microscopic parameters, such as magnetic moment, exchange, and spin–orbit interactions. Whereas it is well established that, in multicomponent magnetic alloys and compounds, the speed of demagnetization and spin switching processes has an element‐specific character, the magnetization damping was assumed to be a universal parameter for all constituent magnetic elements irrespective of their different spin–orbit couplings and electronic structure. Herein, experimental and theoretical evidence for an element‐specific magnetic damping parameter is provided by investigating the ultrafast magnetization response of a high‐anisotropy ferrimagnetic DyCo5 alloy to femtosecond laser excitation. Strikingly different demagnetization and remagnetization dynamics of Dy and Co magnetic moments is revealed by employing femtosecond laser pump–X‐ray magnetic circular dichroism probe measurements combined with atomistic spin dynamics (ASD) simulations using ab initio calculated parameters. These observations, fully corroborated by the ASD simulations, are linked to the element‐specific spin–orbit coupling strengths of Dy and Co, which are incorporated in the phenomenological magnetization damping parameters. These findings can be used as a recipe for tuning the speed and magnitude of laser‐driven magnetic processes and consequently allow control over various dynamic functionalities in multicomponent magnetic materials.

Through-space 11 B-27 Al correlation: Influence of the recoupling channel.

Through-space heteronuclear correlation (D-HETCOR) experiments based on heteronuclear multiple-quantum correlation (D-HMQC) and refocused insensitive nuclei enhanced by polarization transfer (D-RINEPT) sequences have been proven to be useful approaches for the detection of the spatial proximity between half-integer quadrupolar nuclei in solids under magic-angle spinning (MAS) conditions. The corresponding pulse sequences employ coherence transfers mediated by heteronuclear dipolar interactions, which are reintroduced under MAS by radiofrequency irradiation of only one of the two correlated nuclei. We investigate herein using numerical simulations of spin dynamics and solid-state NMR experiments on magnesium aluminoborate glass how the choice of the channel to which the heteronuclear dipolar recoupling is applied affects the transfer efficiency of D-HMQC and D-RINEPT sequences between 11 B and 27 Al nuclei. Experimental results show that maximum transfer efficiency is achieved when the recoupling scheme is applied to the channel, for which the spin magnetization is parallel to the B0 axis in average.

The decay of the refocused Hahn echo in double electron-electron resonance (DEER) experiments.

Double electron-electron resonance (DEER) is a pulse electron paramagnetic resonance (EPR) technique that measures distances between paramagnetic centres. It utilizes a four-pulse sequence based on the refocused Hahn spin echo. The echo decays with increasing pulse sequence length , where and are the two time delays. In DEER, the value of is determined by the longest inter-spin distance that needs to be resolved, and is adjusted to maximize the echo amplitude and, thus, sensitivity. We show experimentally that, for typical spin centres (nitroxyl, trityl, and Gd(III)) diluted in frozen protonated solvents, the largest refocused echo amplitude for a given is obtained neither at very short (which minimizes the pulse sequence length) nor at (which maximizes dynamic decoupling for a given total sequence length) but rather at values smaller than . Large-scale spin dynamics simulations based on the coupled cluster expansion (CCE), including the electron spin and several hundred neighbouring protons, reproduce the experimentally observed behaviour almost quantitatively. They show that electron spin dephasing is driven by solvent protons via the flip-flop coupling among themselves and their hyperfine couplings to the electron spin.

Lattice dynamics and ultrafast energy flow between electrons, spins, and phonons in a 3d ferromagnet

The ultrafast dynamics of magnetic order in a ferromagnet are governed by the interplay between electronic, magnetic and lattice degrees of freedom. In order to obtain a microscopic understanding of ultrafast demagnetization, information on the response of all three subsystems is required. A consistent description of demagnetization and microscopic energy flow, however, is still missing. Here, we combine a femtosecond electron diffraction study of the ultrafast lattice response of nickel to laser excitation with ab initio calculations of the electron-phonon interaction and energy-conserving atomistic spin dynamics simulations. Our model is in agreement with the observed lattice dynamics and previously reported electron and magnetization dynamics. Our approach reveals that the spin system is the dominating heat sink in the initial few hundreds of femtoseconds and implies a transient non-thermal state of the spins. Our results provide a clear picture of the microscopic energy flow between electronic, magnetic and lattice degrees of freedom on ultrafast timescales and constitute a foundation for theoretical descriptions of demagnetization that are consistent with the dynamics of all three subsystems.

Analytical models of probe dynamics effects on NMR measurements

This paper provides a detailed analysis of three common NMR probe circuits (untuned, tuned, and impedance-matched) and studies their effects on multi-pulse experiments, such as those based on the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. The magnitude of probe dynamics effects on broadband refocusing pulses are studied as a function of normalized RF bandwidth. Finally, the probe circuit models are integrated with spin dynamics simulations to design hardware-specific RF excitation and refocusing pulses for optimizing user-specified metrics such as signal-to-noise ratio (SNR) in grossly inhomogeneous fields. Preliminary experimental results on untuned probes are also presented.

A giant spin molecule with ninety-six parallel unpaired electrons

SummaryUnpaired electrons which are essential for organic radicals and magnetic materials are hardly to align parallel, especially upon the increasing of spin numbers. Here, we show that the antiferromagnetic interaction in the largest Cr(III)-RE (rare earth) cluster {Cr10RE18} leads to 96 parallel electrons, forming a ground spin state ST of 48 for RE = Gd. This is so far the third largest ground spin state achieved in one molecule. Moreover, by using the classical Monte Carlo simulation, the exchange coupling constants can be determined. Spin dynamics simulation reveals that the strong Zeeman effects of 18 Gd(III) ions stabilize the ground ferrimagnetic state and hinder the magnetization reversals of these spins. In addition, the dysprosium(III) analog is an exchange-biasing single-molecule magnet. We believe that the ferrimagnetic approach and analytical protocol established in this work can be applied generally in constructing and analyzing giant spin molecules.

TB2J: A python package for computing magnetic interaction parameters

We present TB2J, a Python package for the automatic computation of magnetic interactions, including exchange and Dzyaloshinskii–Moriya, between atoms of magnetic crystals from the results of density functional calculations. The program is based on the Green’s function method with the local rigid spin rotation treated as a perturbation. As input, the package uses the output of either Wannier90, which is interfaced with many density functional theory packages, or of codes based on localized orbitals. One of the main interests of the code is that it requires only one first-principles electronic structure calculation in the non-relativistic case (or three in the relativistic case) and from the primitive cell only to obtain the magnetic interactions up to long distances, instead of first-principles calculations of many different magnetic configurations and large supercells. The output of TB2J can be used directly for the adiabatic magnon band structure and spin dynamics calculations. A minimal user input is needed, which allows for easy integration into high-throughput workflows. Program summaryProgram Title: TB2JCPC Library link to program files:https://doi.org/10.17632/dm45fcn69d.1Developer’s repository link:https://github.com/mailhexu/TB2JCode Ocean capsule:https://codeocean.com/capsule/6486145Licensing provisions: BSD 2-clauseProgramming language: PythonNature of problem: TB2J is a package for the computing of parameters in the extended Heisenberg model of the magnetic interaction, including the isotropic exchange, anisotropic exchange and Dzyaloshinskii–Moriya interactions from first principles result. It can make use of the Wannier function Hamiltonian, which can be constructed from many first principles codes, or localized orbital based codes.Solution method: It uses the magnetic force theorem and takes the rigid spin rotation as a perturbation to the electronic structure. The energy variation is calculated from the Green’s functions from tight-binding like Hamiltonian based on Wannier functions or localized orbitals.Additional comments including restrictions and unusual features: Isotropic exchange, anisotropic exchange, and Dzyaloshinskii–Moriya interactions can all be computed with the input of many DFT codes through the interface of Wannier90, or directly from localized orbital codes. The magnetic interaction parameters up to any distance can be computed from one DFT calculation. A minimum user-input is required which provides a black-box like experience. It generates output for several spin dynamics codes and thus bridges the first principles electronic structure simulation with the large scale spin dynamics simulation.

Role of element-specific damping in ultrafast, helicity-independent, all-optical switching dynamics in amorphous (Gd,Tb)Co thin films

Ultrafast control of the magnetization in ps timescales by fs laser pulses offers an attractive avenue for applications such as fast magnetic devices for logic and memory. However, ultrafast helicity-independent all-optical switching (HI-AOS) of the magnetization has thus far only been observed in Gd-based, ferrimagnetic amorphous (\textit{a}-) rare earth-transition metal (\textit{a}-RE-TM) systems, and a comprehensive understanding of the reversal mechanism remains elusive. Here, we report HI-AOS in ferrimagnetic \textit{a}-Gd$_{22-x}$Tb$_x$Co$_{78}$ thin films, from x = 0 to x = 18, and elucidate the role of Gd in HI-AOS in \textit{a}-RE-TM alloys and multilayers. Increasing Tb content results in increasing perpendicular magnetic anisotropy and coercivity, without modifying magnetization density, and slower remagnetization rates and higher critical fluences for switching but still shows picosecond HI-AOS. Simulations of the atomistic spin dynamics based on the two-temperature model reproduce these results qualitatively and predict that the lower damping on the RE sublattice arising from the small spin-orbit coupling of Gd (with $L = 0$) is instrumental for the faster dynamics and lower critical fluences of the Gd-rich alloys. Annealing \textit{a}-Gd$_{10}$Tb$_{12}$Co$_{78}$ leads to slower dynamics which we argue is due to an increase in damping. These simulations strongly indicate that acounting for element-specific damping is crucial in understanding HI-AOS phenomena. The results suggest that engineering the element specific damping of materials can open up new classes of materials that exhibit low-energy, ultrafast HI-AOS.

The decay of the refocused Hahn echo in DEER experiments

Abstract. Double electron–electron resonance (DEER) is a pulse electron paramagnetic resonance (EPR) technique that measures distances between paramagnetic centres. It utilizes a four-pulse sequence based on the refocused Hahn spin echo. The echo decays with increasing pulse sequence length 2(τ1 + τ2), where τ1 and τ2 are the two time delays. In DEER, the value of τ2 is determined by the longest inter-spin distance that needs to be resolved, and τ1 is adjusted to maximize the echo amplitude and thus sensitivity. We show experimentally that for typical spin centres (nitroxyl, trityl, Gd(III)) diluted in frozen protonated solvents, the largest refocused echo amplitude for a given τ2 is obtained neither at very short τ1 (which minimizes the pulse sequence length) nor at τ1 = τ2 (which maximizes dynamic decoupling for a given total sequence length), but rather at τ1 values smaller than τ2. Large-scale spin dynamics simulations including the electron spin and several hundred neighbouring protons reproduce the experimentally observed behaviour almost quantitatively. They show that electron spin dephasing is driven by solvent protons via the flip-flop coupling among themselves and their hyperfine couplings to the electron spin.

Nuclear polarization effects in cryptochrome-based magnetoreception.

The mechanism of the magnetic compass sense of migratory songbirds is thought to involve magnetically sensitive chemical reactions of light-induced radical pairs in cryptochrome proteins located in the birds' eyes. However, it is not yet clear whether this mechanism would be sensitive enough to form the basis of a viable compass. In the present work, we report spin dynamics simulations of models of cryptochrome-based radical pairs to assess whether accumulation of nuclear spin polarization in multiple photocycles could lead to significant enhancements in the sensitivity with which the proteins respond to the direction of the geomagnetic field. Although buildup of nuclear polarization appears to offer sensitivity advantages in the more idealized model systems studied, we find that these enhancements do not carry over to conditions that more closely resemble the situation thought to exist in vivo. On the basis of these simulations, we conclude that buildup of nuclear polarization seems unlikely to be a source of significant improvements in the performance of cryptochrome-based radical pair magnetoreceptors.

Signatures of a liquid-crystal transition in spin-wave excitations of skyrmions

Understanding the spin-wave excitations of chiral magnetic order, such as the skyrmion crystal (SkX), is of fundamental interest to confirm such exotic magnetic order. The SkX is realized by competing Dzyaloshinskii-Moriya and ferromagnetic-exchange interactions with a magnetic field or anisotropy. Here, we compute the dynamical spin structure factor, using Monte Carlo and spin dynamics simulations, extracting the spin-wave spectrum in the SkX, in the vicinity of the paramagnet to SkX transition. Inside the SkX, we find six spin-wave modes, which are supplemented by another mode originating from the ferromagnetic background. Above the critical temperature Ts for the skyrmion crystallization, we find a diffusive regime, reminiscent of the liquid-to-crystal transition, revealing that topological spin texture of skyrmionic character starts to develop above Ts as the precursor of the SkX. We discuss the opportunities for the detection of the spin waves of the SkX using inelastic-neutron-scattering experiments in manganite-iridate heterostructures.

Size- and temperature-dependent magnetization of iron nanoclusters

The magnetic behavior of bcc iron nanoclusters, with diameters between 2 and 8 nm, is investigated by means of spin dynamics (SD) simulations coupled to molecular dynamics (MD-SD), using a distance-dependent exchange interaction. Finite-size effects in the total magnetization as well as the influence of the free surface and the surface/core proportion of the nanoclusters are analyzed in detail for a wide temperature range, going beyond the cluster and bulk Curie temperatures. Comparison is made with experimental data and with theoretical models based on the mean-field Ising model adapted to small clusters, and taking into account the influence of low coordinated spins at free surfaces. Our results for the temperature dependence of the average magnetization per atom M(T), including the thermalization of the transnational lattice degrees of freedom, are in very good agreement with available experimental measurements on small Fe nanoclusters. In contrast, significant discrepancies with experiment are observed if the translational degrees of freedom are artificially frozen. The finite-size effects on M(T) are found to be particularly important near the cluster Curie temperature. Simulated magnetization above the Curie temperature scales with cluster size as predicted by models assuming short-range magnetic ordering (SRMO). Analytical approximations to the magnetization as a function of temperature and size are proposed.

Asymmetric skyrmion-antiskyrmion production in ultrathin ferromagnetic films

Ultrathin ferromagnets with frustrated exchange and the Dzyaloshinskii-Moriya interaction can support topological solitons such as skyrmions and antiskyrmions, which are metastable and can be considered particle-antiparticle counterparts. When spin-orbit torques are applied, the motion of an isolated antiskyrmion driven beyond its Walker limit can generate skyrmion-antiskyrmion pairs. Here, we use atomistic spin dynamics simulations to shed light on the scattering processes involved in this pair generation. Under certain conditions a proliferation of these particles and antiparticles can appear with a growth rate and production asymmetry that depend on the strength of the chiral interactions and the dissipative component of the spin-orbit torques. These features are largely determined by scattering processes between antiskyrmions, which can be elastic or result in bound states or annihilation.

Walker-like domain wall breakdown in layered antiferromagnets driven by staggered spin\u2013orbit fields

Within linear continuum theory, no magnetic texture can propagate faster than the maximum group velocity of the spin waves. Here, by atomistic spin dynamics simulations and supported by analytical theory, we report that a strongly non-linear transient regime due to the appearance of additional magnetic textures results in the breaking of the Lorentz translational invariance. This dynamical regime is akin to domain wall Walker-breakdown in ferromagnets and involves the nucleation of an antiferromagnetic domain wall pair. While one of the nucleated domain walls is accelerated beyond the magnonic limit, the remaining pair remains static. Under large spin–orbit fields, a cascade of multiple generation and recombination of domain walls are obtained. This result may clarify recent experiments on current pulse induced shattering of large domain structures into small fragmented domains and the subsequent slow recreation of large-scale domains.

A Giant Spin Molecule with Ninety-Six Parallel Unpaired Electrons

Unpaired electrons which are essential for organic radicals and magnetic materials are hardly to align parallel, especially upon the increasing of spin numbers. Here we show the antiferromagnetic interaction in the largest Cr(III)-RE (RE = rare earth) cluster {Cr10RE18} leads to 96 parallel electrons, forming a ground spins state ST of 48 for RE = Gd. This is so far the third largest ground spin state achieved in one molecule. Moreover, by using the classical Monte Calo simulation the exchange-coupling constants J_ij can be determined. Spin dynamics simulation reveals that the strong Zeeman effects of 18 Gd(III) ions stabilize the ground ferrimagnetic state and hinder the magnetization reversals of these spins. In addition, the dysprosium(III) analogue is an exchange-biasing single-molecule magnet. We believe the ferrimagnetic approach and analytical protocol established in this work can be applied generally in constructing and analysing giant spin molecules.

Ultrafast antiferromagnetic switching in NiO induced by spin transfer torques

NiO is a prototypical antiferromagnet with a characteristic resonance frequency in the THz range. From atomistic spin dynamics simulations that take into account the crystallographic structure of NiO, and in particular a magnetic anisotropy respecting its symmetry, we describe antiferromagnetic switching at THz frequency by a spin transfer torque mechanism. Sub-picosecond S-state switching between the six allowed stable spin directions is found for reasonably achievable spin currents, like those generated by laser induced ultrafast demagnetization. A simple procedure for picosecond writing of a six-state memory is described, thus opening the possibility to speed up current logic of electronic devices by several orders of magnitude.

The role of ultrafast magnon generation in the magnetization dynamics of rare-earth metals.

Ultrafast demagnetization of rare-earth metals is distinct from that of 3d ferromagnets, as rare-earth magnetism is dominated by localized 4f electrons that cannot be directly excited by an optical laser pulse. Their demagnetization must involve excitation of magnons, driven either through exchange coupling between the 5d6s-itinerant and 4f-localized electrons or by coupling of 4f spins to lattice excitations. Here, we disentangle the ultrafast dynamics of 5d6s and 4f magnetic moments in terbium metal by time-resolved photoemission spectroscopy. We show that the demagnetization time of the Tb 4f magnetic moments of 400 fs is set by 4f spin-lattice coupling. This is experimentally evidenced by a comparison to ferromagnetic gadolinium and supported by orbital-resolved spin dynamics simulations. Our findings establish coupling of the 4f spins to the lattice via the orbital momentum as an essential mechanism driving magnetization dynamics via ultrafast magnon generation in technically relevant materials with strong magnetic anisotropy.