Precessional Dynamics Research Articles

The heat and work of quantum thermodynamic processes with quantum coherence**Project supported by the National Natural Science Foundation of China (Grant Nos. 11421063, 11534002, and 51776178) and the National Key Basic Research Program of China (Grant Nos. 2012CB922104 and 2014CB921403).

Energy is often partitioned into heat and work by two independent paths corresponding to the change in the eigenenergies or the probability distributions of a quantum system. The discrepancies of the heat and work for various quantum thermodynamic processes have not been well characterized in literature. Here we show how the work in quantum machines is differentially related to the isochoric, isothermal, and adiabatic processes. We prove that the energy exchanges during the quantum isochoric and isothermal processes are simply depending on the change in the eigenenergies or the probability distributions. However, for a time-dependent system in a non-adiabatic quantum evolution, the transitions between the different quantum states representing the quantum coherence can affect the essential thermodynamic properties, and thus the general definitions of the heat and work should be clarified with respect to the microscopic generic time-dependent system. By integrating the coherence effects in the exactly-solvable dynamics of quantum-spin precession, the internal energy is rigorously transferred as the work in the thermodynamic adiabatic process. The present study demonstrates that the quantum adiabatic process is sufficient but not necessary for the thermodynamic adiabatic process.

Skyrmion-Mediated Voltage-Controlled Switching of Ferromagnets for Reliable and Energy-Efficient Two-Terminal Memory.

We propose a two-terminal nanomagnetic memory element based on magnetization reversal of a perpendicularly magnetized nanomagnet employing a unipolar voltage pulse that modifies the perpendicular anisotropy of the system. Our work demonstrates that the presence of Dzyaloshinskii-Moriya interaction can create an alternative route for magnetization reversal that obviates the need for utilizing precessional magnetization dynamics as well as a bias magnetic field that are employed in traditional voltage control of magnetic anisotropy (VCMA)-based switching of perpendicular magnetization. We show with extensive micromagnetic simulation, in the presence of thermal noise, that the proposed skyrmion-mediated VCMA switching mechanism is robust at room temperature leading to extremely low error switching while also being potentially 1-2 orders of magnitude more energy efficient than state-of-the-art spin transfer torque-based switching.

In-situ, In-Memory Stateful Vector Logic Operations based on Voltage Controlled Magnetic Anisotropy

Recently, the exponential increase in compute requirements demanded by emerging applications like artificial intelligence, Internet of things, etc. have rendered the state-of-art von-Neumann machines inefficient in terms of energy and throughput owing to the well-known von-Neumann bottleneck. A promising approach to mitigate the bottleneck is to do computations as close to the memory units as possible. One extreme possibility is to do in-situ Boolean logic computations by using stateful devices. Stateful devices are those that can act both as a compute engine and storage device, simultaneously. We propose such stateful, vector, in-memory operations using voltage controlled magnetic anisotropy (VCMA) effect in magnetic tunnel junctions (MTJ). Our proposal is based on the well known manufacturable 1-transistor - 1-MTJ bit-cell and does not require any modifications in the bit-cell circuit or the magnetic device. Instead, we leverage the very physics of the VCMA effect to enable stateful computations. Specifically, we exploit the voltage asymmetry of the VCMA effect to construct stateful IMP (implication) gate and use the precessional switching dynamics of the VCMA devices to propose a massively parallel NOT operation. Further, we show that other gates like AND, OR, NAND, NOR, NIMP (complement of implication) can be implemented using multi-cycle operations.

Effect of synchrotron radiation on the dynamics of electron spin precession in the process of laser-plasma acceleration

A model was developed and tested for studying the dynamics of spin precession and trajectories of charged particles in the wake fields generated in a laser-plasma accelerator. The model takes into account the radiation reaction force in the Landau – Lifshits form. An investigation is made of the effect of synchrotron radiation on the dynamics of energy gaining and spin precession of electrons accelerated in model constant fields as well as on the particle beam polarisation in the acceleration at a separate acceleration stage in the case of self-consistent description of the nonlinear dynamics of a laser pulse and its generated accelerating and focusing plasma wake fields. It is shown that synchrotron radiation hardly affects the energy gain rate and polarisation of the electrons that are accelerated in the fields characteristic for a moderately nonlinear mode of laser-plasma acceleration up to an energy of 3.8 TeV.

Tuning of Microwave Frequency and Power Enhancement Using Spin Torque Nano-Oscillator With Tilted Polarizer

In this paper, we theoretically devised a spin torque nano-oscillator (STNO) with tilted polarizer (TP) with the help of two independent variables (β and θ). The spin torque induced magnetization precession dynamics is studied numerically by solving the governing Landau-Lifshitz-Gilbert-Slonczewski equation. The TP STNO free layer precession frequency is determined by varying TP angle (β) from 0° to 90°. For a particular value of β, we can vary (θ) the angle between the free layer magnetization and easy axis of magnetization from 0° to 90°. It is found that the frequency range is accessible at all tilt angles and highly tunable in the order of GHz. Also, the maximum operating frequency 124.5 GHz and corresponding power of 1.478 μW/GHz/mA <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is obtained for β = 60° and 8 = 90° with the applied current density of 10 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sup> Am <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . Moreover, our results allow great freedom in choosing the detailed layer structure of the TP STNO and these findings pave a new route for the implementation of nanoscale microwave sources for future generation integrated electronics.

Influence of anisotropic dipolar interaction on the spin dynamics of Ni80Fe20 nanodot arrays arranged in honeycomb and octagonal lattices

Ultrafast spin dynamics in ferromagnetic nanodot arrays with dot diameter 100 nm and thickness 20 nm arranged in honeycomb and octagonal lattice symmetries are studied to explore the tunability of the collective magnetization dynamics. By varying the inter-dot separation between 30 nm and 300 nm drastic variation in the precessional dynamics from strongly collective to completely isolated regime has been observed by using all-optical time-resolved magneto-optical Kerr microscope. Micromagnetic simulation is exploited to gain insights about the resonant mode profiles and magnetic coupling between the nanodots. A significant spectral and spatial variation in the resonant mode with increasing dipolar interaction is demonstrated with increasing inter-dot separation. The spins driven by effective field inside single nanodots are prone to precess independently, generating two self-standing centre and edge modes in the array that are influenced by the relative orientation between the inter-dot coupling direction and bias magnetic field. The anisotropic behavior of dipolar field is rigorously investigated here. Splitting of the centre mode in case of octagonal lattice is experimentally observed here as a consequence of the anisotropic dipolar field between the nanodot pairs coupled horizontally and vertically, which is not found in the honeycomb lattice. In addition, proper understanding of the modification of dynamic mode profile by neighboring dipolar interaction built up here, is imperative for further control of the dynamic dipolar interaction and the corresponding collective excitation in magnonic crystals. The usage of nanodot lattices with complex basis structures can be advantageous for the designing of high density magnetic recording media, spin-wave filter and logic devices.

Numerical relativity simulations of precessing binary neutron star mergers

We present the first set of numerical relativity simulations of binary neutron mergers that include spin precession effects and are evolved with multiple resolutions. Our simulations employ consistent initial data in general relativity with different spin configurations and dimensionless spin magnitudes $\sim 0.1$. They start at a gravitational-wave frequency of $\sim392$~Hz and cover more than $1$ precession period and about 15 orbits up to merger. We discuss the spin precession dynamics by analyzing coordinate trajectories, quasi-local spin measurements, and energetics, by comparing spin aligned, antialigned, and irrotational configurations. Gravitational waveforms from different spin configuration are compared by calculating the mismatch between pairs of waveforms in the late inspiral. We find that precession effects are not distinguishable from nonprecessing configurations with aligned spins for approximately face-on binaries, while the latter are distinguishable from a nonspinning configurations. Spin precession effects are instead clearly visible for approximately edge-on binaries. For the parameters considered here, precession does not significantly affect the characteristic postmerger gravitational-wave frequencies nor the mass ejection. Our results pave the way for the modeling of spin precession effects in the gravitational waveform from binary neutron star events.

Trapped particle precession and sub-bounce zonal flow dynamics in tokamaks

A drift-kinetic calculation in an axisymmetric tokamak, with super-diamagnetic flows, is presented to elucidate the relation between the radial electric field, $E_{r}$, zonal flows and the rapid precession of the trapped particle (TP) population. It has been shown earlier (Rosenbluth &amp; Hinton, Phys. Rev. Lett., vol. 80(4), 1998, p. 724, hereafter RH) that an initial radial electric field results in geodesic acoustic mode oscillations which subsequently Landau damp, resulting in a much smaller final residual electric field, and accompanying parallel zonal flows. We observe an apparent paradox: the final angular momentum in the RH parallel zonal flow is much smaller than the angular momentum expected from the well-known rapid precession of the trapped particle population in the RH residual electric field. We reconcile this paradox by illuminating the presence of a population of reverse circulating particle flows that, dominantly, are equal and opposite to the rapid TP precession. Mathematically, the calculation is facilitated by transforming to an energy coordinate shifted from conventional by an amount proportional to $E_{r}$. We also discuss the well-known RH coefficient in the context of effective mass and show how the TP precession and the opposite circulating flows contribute to this mass. Finally, we show that in the long wavelength limit, the RH flows and RH coefficient arise as a natural consequence of conservation of toroidal angular momentum and the second adiabatic invariant.

Ultrafast control of coherent spin precession in ferromagnetic thin films via thermal spin excitation processes induced by two-pulse laser excitation

We investigate the laser-induced spin precession dynamics in ferromagnetic $\mathrm{N}{\mathrm{i}}_{0.8}\mathrm{F}{\mathrm{e}}_{0.2}$ thin films by using a time-resolved magneto-optical Kerr effect (TR-MOKE) measurement with two pump pulses. By changing the time interval between the pump pulses, the amplitude of the TR-MOKE signal is strongly modulated according to the phase of the TR-MOKE signal at the time when the second pulse arrives. The change in the oscillation amplitude can be explained with the temporal evolution of the spin precession induced by laser heating, as shown with a numerical simulation. We conclude that the ultrafast control of coherent spin precession dynamics is possible by multiple pump pulses via thermal excitation.

Relativistic dynamics of point magnetic moment

The covariant motion of a classical point particle with magnetic moment in the presence of (external) electromagnetic fields is revisited. We are interested in understanding extensions to the Lorentz force involving point particle magnetic moment (Stern–Gerlach force) and how the spin precession dynamics is modified for consistency. We introduce spin as a classical particle property inherent to Poincaré symmetry of space-time. We propose a covariant formulation of the magnetic force based on a ‘magnetic’ 4-potential and show how the point particle magnetic moment relates to the Amperian (current loop) and Gilbertian (magnetic monopole) descriptions. We show that covariant spin precession lacks a unique form and discuss the connection to g-2 anomaly. We consider the variational action principle and find that a consistent extension of the Lorentz force to include magnetic spin force is not straightforward. We look at non-covariant particle dynamics, and present a short introduction to the dynamics of (neutral) particles hit by a laser pulse of arbitrary shape.

Efficient adaptive pseudo-symplectic numerical integration techniques for Landau-Lifshitz dynamics

Numerical time integration schemes for Landau-Lifshitz magnetization dynamics are considered. Such dynamics preserves the magnetization amplitude and, in the absence of dissipation, also implies the conservation of the free energy. This property is generally lost when time discretization is performed for the numerical solution. In this work, explicit numerical schemes based on Runge-Kutta methods are introduced. The schemes are termed pseudo-symplectic in that they are accurate to order p, but preserve magnetization amplitude and free energy to order q &amp;gt; p. An effective strategy for adaptive time-stepping control is discussed for schemes of this class. Numerical tests against analytical solutions for the simulation of fast precessional dynamics are performed in order to point out the effectiveness of the proposed methods.

Strain-mediated magnetoelectric effect for the electric-field control of magnetic states in nanomagnets

Electric-field control of magnetism without electric currents potentially revolutionizes spintronics toward ultralow power. Here, by using mechanically coupled phase field simulations, we computationally demonstrate the application of the strain-mediated magnetoelectric effect for the electric-field control of magnetic states in a heterostructure. In the model heterostructure constituted of the soft nanomagnet Co and the piezoelectric substrate PMN–PT, both the volatility of magnetic states and the magnetization switching dynamics excited by the electric field are explored. It is found that an electric field can drive the single-domain nanomagnet into an equilibrium vortex state. The nanomagnet remains in the vortex state even after removing the electric field or applying a reverse electric field, i.e., the vortex state is extremely stable and nonvolatile. Only by utilizing the precessional magnetization dynamics, the 180 $$^\circ $$ magnetization switching is possible in small-sized nanomagnets which are free of the stable vortex state. Electric-field pulses can realize the deterministic 180 $$^\circ $$ switching if the electric-field magnitude, pulse width, and ramp time are carefully designed. The minimum switching time is found to be less than 10 ns. These results provide useful information for the design of low-power, reliable, and fast electric-field-controlled spintronics.

Precessional one-dimensional solitons in antiferromagnets with low dynamic symmetry

The nonlinear internal dynamics of one-dimensional topological magnetic solitons in antiferromagnets were studied theoretically, taking into consideration their real magnetic symmetry. The presence of the Dzyaloshinskii–Moriya interaction, which can lead to the appearance of weak non-collinearity of the antiferromagnet sublattices, results in a lowering in the dynamic symmetry of the magnet. As a consequence, there appear the effects of lowering the symmetry of the soliton with internal precession dynamics: precession of the spins becomes inhomogeneous in time and it is accompanied by oscillations of the soliton center. In a certain frequency range, the effects of short-wave magnon radiation are also possible.

Thermally induced magnetization dynamics of optically excited YIG/Cu/Ni81Fe19 trilayers

The response of ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}\text{/}\mathrm{Cu}\text{/}{\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ trilayer structures to excitation by a femtosecond laser pulse has been studied in optical pump-probe experiments and compared with the response of ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$ (YIG) and ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ reference samples. The optical pump induces a partial demagnetization of the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$, a large thermal gradient within the YIG, and temperature differences across the interfaces within the sample stack. When a moderate magnetic field is applied close to normal to the sample plane, so as to quasialign the YIG magnetization with the field and cant the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ magnetization from the plane, ultrafast demagnetization initiates precession of the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ magnetization. The transient temperature profile within the samples has been modeled using a one-dimensional finite-element computational model of heat conduction, while the magnetization dynamics are well described by a macrospin solution of the Landau-Lifshitz-Gilbert equation. The precessional response of the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ layers within the trilayers and the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ reference sample are very similar for pump fluences of up to $1.5\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^{2}$, beyond which irreversible changes to the magnetic properties of the films are observed. These results suggest that the spin Seebeck effect is ineffective in modifying the precessional dynamics of the present $\mathrm{YIG}\text{/}\mathrm{Cu}\text{/}{\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ samples when subject to ultrafast optical excitation.

Pseudo-symplectic numerical schemes for Landau-Lifshitz dynamics

Numerical techniques for the time integration of Landau-Lifshitz magnetization dynamics are considered. In the continuous model, such dynamics implies the conservation of magnetization amplitude and, when dissipation is neglected, even the conservation of free energy, a property which is generally corrupted by the time-discretization method. In this work, two classes of explicit schemes, based on Runge-Kutta and midpoint methods respectively, are introduced. The schemes are termed pseudo-symplectic in that they are accurate to order p, but preserve magnetization amplitude and free energy to order q>p. Numerical tests are performed on the simulation of fast precessional switching dynamics for which an analytical solution is available.

Vortex precession dynamics in general radially symmetric potential traps in two-dimensional atomic Bose-Einstein condensates

We consider the motion of individual two-dimensional vortices in general radially symmetric potentials in Bose-Einstein condensates. We find that although in the special case of the parabolic trap there is a logarithmic correction in the dependence of the precession frequency $\omega$ on the chemical potential $\mu$, this is no longer true for a general potential $V(r) \propto r^p$. Our calculations suggest that for $p>2$, the precession frequency scales with $\mu$ as $\omega \sim \mu^{-2/p}$. This theoretical prediction is corroborated by numerical computations, both at the level of spectral (Bogolyubov-de Gennes) stability analysis by identifying the relevant precession mode dependence on $\mu$, but also through direct numerical computations of the vortex evolution in the large $\mu$, so-called Thomas-Fermi, limit. Additionally, the dependence of the precession frequency on the radius of an initially displaced from the center vortex is examined and the corresponding predictions are tested against numerical results.

Micromagnetic simulation of electric field-modulation on precession dynamics of spin torque nano-oscillator

Understanding electric field effects on precession dynamics is crucial to the design of spin transfer torque devices for improving the performance in nano-oscillator. In this letter, the precession dynamics of a CoFeB/MgO multi-layer structured nano-oscillator under externally applied electric field is predicted using a micromagnetic simulation. It is revealed that the electric field can modify the range of oscillation spectra in single frequency mode. With the increase in electric field, there is a red-shift of the resonant frequency. When a positive electric field pulse is applied, a phase lag of the spin precession is induced, which is proportional to the pulse amplitude and duration. The present work is expected to stimulate future experimental efforts on designing devices with electric-field modulated spin transfer torque nano-oscillators.

Efficient Modulation of Spin Waves in Two-Dimensional Octagonal Magnonic Crystal.

Efficient tunability of magnonic spectra is demonstrated in two-dimensional ferromagnetic antidot lattices with different lattice constants arranged in the octagonal lattice which can be considered as quasi-periodic magnonic crystals due to the presence of broken translational symmetry. The precessional dynamics of these samples are investigated in the frequency domain with the help of broadband ferromagnetic resonance spectrometer. A rich variation in the spin wave spectra is observed with the variation of lattice constant as well as the strength and orientation of the bias magnetic field. A broad band of spin wave modes are observed for the denser array, which finally converges to two spin wave modes for the sparsest one. In addition to this, the most intense spin wave frequency shows an 8-fold anisotropy with a superposition of weak 4- and 2-fold anisotropy, which arises due to the angular variation of the magnetostatic field distribution at different regions of the octagonal lattice. Micromagnetic simulations qualitatively reproduce the experimentally observed modes, and the simulated mode profiles reveal the presence of different types of extended and quantized standing spin wave modes in these samples. The observations are important for the tunable and anisotropic propagation of spin waves in magnonic crystal based devices.

Homogeneous microwave field emitted propagating spin waves: Direct imaging and modeling

We explore the generation of propagating dipolar spin waves by homogeneous magnetic field excitation in the proximity of the boundaries of magnetic microstructures. Domain wall motion, precessional dynamics, and propagating spin waves are directly imaged by time-resolved wide-field magneto-optical Kerr effect microscopy. The aspects of spin wave generation are clarified by micromagnetic calculations matching the experimental results. The region of dipolar spin wave formation is confined to the local resonant excitation due to non-uniform internal demagnetization fields at the edges of the patterned sample. Magnetic domain walls act as a border for the propagation of plane and low damped spin waves, thus restraining the spin waves within the individual magnetic domains. The findings are of significance for the general understanding of structural and configurational magnetic boundaries for the creation, the propagation, and elimination of spin waves.

Dynamics of the magnetic moment of small dipole lattices in an alternating field

Dynamic modes of the total magnetic moment of the square dipole 2 × 2 and 3 × 3 lattices have been investigated in alternating magnetic field with the linear and circular polarization, the static magnetic field being perpendiculat to it. A way to observe the dynamics of regular, quasiperiodic, or chaotic precession of the magnetic moments of lattices with different mode attractors has been shown. The effect of static field orientation and the type of anisotropy on the resonance dynamics has been studied.