scholarly journals Hamiltonian and Lagrangian Dynamical Matrix Approaches Applied to Magnetic Nanostructures

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Roberto Zivieri ◽  
Giancarlo Consolo
Keyword(s):  
Magnetic Nanoparticles ◽  
Matrix Method ◽  
Spin Dynamics ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Spin Current ◽  
Magnetic Nanostructures ◽  
Spin Transfer Torque ◽  
Dynamical Matrix ◽  
Dissipative Effects

Two micromagnetic tools to study the spin dynamics are reviewed. Both approaches are based upon the so-called dynamical matrix method, a hybrid micromagnetic framework used to investigate the spin-wave normal modes of confined magnetic systems. The approach which was formulated first is the Hamiltonian-based dynamical matrix method. This method, used to investigate dynamic magnetic properties of conservative systems, was originally developed for studying spin excitations in isolated magnetic nanoparticles and it has been recently generalized to study the dynamics of periodic magnetic nanoparticles. The other one, the Lagrangian-based dynamical matrix method, was formulated as an extension of the previous one in order to include also dissipative effects. Such dissipative phenomena are associated not only to intrinsic but also to extrinsic damping caused by injection of a spin current in the form of spin-transfer torque. This method is very accurate in identifying spin modes that become unstable under the action of a spin current. The analytical development of the system of the linearized equations of motion leads to a complex generalized Hermitian eigenvalue problem in the Hamiltonian dynamical matrix method and to a non-Hermitian one in the Lagrangian approach. In both cases, such systems have to be solved numerically.

scholarly journals Interpretation of the Spin Torque Sign Change in F/N/F Structures in Terms of a Mechanical Analogy

2020 ◽  
Vol 65 (10) ◽  
pp. 889
Author(s):  
Ya. B. Bazaliy
Keyword(s):  
Mechanical System ◽  
Spin Current ◽  
Magnetic Nanostructures ◽  
Spin Transfer Torque ◽  
Spin Transfer ◽  
Spin Torque ◽  
Spin Accumulation ◽  
Clear Explanation ◽  
Sign Change ◽  
Torque Values

A useful interpretation of the spin-accumulation and spin-current distributions in magnetic nanostructures with diffusive transfer has been discussed. A mathematically equivalent mechanical system was proposed that provides an intuitive understanding of the dependence of the spin-transfer torque values on various parameters. In particular, it gives a clear explanation for the sign change of the spin-transfer torque in asymmetric F/N/F structures.

scholarly journals Horizon radiation reaction forces

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Walter D. Goldberger ◽  
Ira Z. Rothstein
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Finite Size ◽  
Radiation Reaction ◽  
Effective Field ◽  
Compact Objects ◽  
Finite Size Effect ◽  
Binary Black Holes ◽  
Dissipative Effects ◽  
Reaction Forces

Abstract Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

scholarly journals Magnetic Normal Mode Calculations in Big Systems: A Highly Scalable Dynamical Matrix Approach Applied to a Fibonacci-Distorted Artificial Spin Ice

2021 ◽  
Vol 7 (3) ◽  
pp. 34
Author(s):  
Loris Giovannini ◽  
Barry W. Farmer ◽  
Justin S. Woods ◽  
Ali Frotanpour ◽  
Lance E. De Long ◽  
...  
Keyword(s):  
Normal Modes ◽  
Low Frequency ◽  
Fibonacci Sequence ◽  
Exchange Interactions ◽  
Geometric Distortion ◽  
Dynamical Matrix ◽  
Spin Ice ◽  
Magnetization Dynamics ◽  
Distortion Parameter ◽  
Artificial Spin Ice

We present a new formulation of the dynamical matrix method for computing the magnetic normal modes of a large system, resulting in a highly scalable approach. The motion equation, which takes into account external field, dipolar and ferromagnetic exchange interactions, is rewritten in the form of a generalized eigenvalue problem without any additional approximation. For its numerical implementation several solvers have been explored, along with preconditioning methods. This reformulation was conceived to extend the study of magnetization dynamics to a broader class of finer-mesh systems, such as three-dimensional, irregular or defective structures, which in recent times raised the interest among researchers. To test its effectiveness, we applied the method to investigate the magnetization dynamics of a hexagonal artificial spin-ice as a function of a geometric distortion parameter following the Fibonacci sequence. We found several important features characterizing the low frequency spin modes as the geometric distortion is gradually increased.

Magnetic normal modes in ferromagnetic nanoparticles: A dynamical matrix approach

2004 ◽  
Vol 70 (5) ◽  
Author(s):  
M. Grimsditch ◽  
L. Giovannini ◽  
F. Montoncello ◽  
F. Nizzoli ◽  
Gary K. Leaf ◽  
...  
Keyword(s):  
Normal Modes ◽  
Dynamical Matrix ◽  
Ferromagnetic Nanoparticles ◽  
Matrix Approach

SPINMOTIVE FORCE IN MAGNETIC NANOSTRUCTURES

SPIN ◽  
2013 ◽  
Vol 03 (02) ◽  
pp. 1330004 ◽  
Author(s):  
JUN'ICHI IEDA ◽  
YUTA YAMANE ◽  
SADAMICHI MAEKAWA
Keyword(s):  
Energy Transfer ◽  
Spin Current ◽  
Magnetic Nanostructures ◽  
Mutual Interaction ◽  
Conduction Electrons ◽  
Recent Developments ◽  
Basic Concepts

The mutual interaction between spin current and magnetization is a key phenomenon in spintronics. This interaction leads to a spinmotive force, a mechanism of energy-transfer from magnetization into conduction electrons. In this paper, the basic concepts and recent developments of the spinmotive force are introduced.

Calculating Fundamental Vibrational Frequencies of Rutile by Combining Ab Initio Method with GF Matrix Method

1994 ◽  
Vol 05 (02) ◽  
pp. 299-301
Author(s):  
Lin Libin ◽  
Zheng Xiangyin
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Matrix Method ◽  
Cluster Model ◽  
Normal Modes ◽  
Vibrational Frequencies ◽  
Ab Initio Method ◽  
Environment Factor ◽  
Factor Α ◽  
Good Agreement

Based on cluster model, we have calculated the fundamental vibrational frequencies of rutile by combining ab initio method and Wilson’s GF-matrix method. In the calculation, we have introduced the concept of environment factor α to correct the force field of the cluster model. The results of calculation are in good agreement to the experimental data and the normal modes give us clear physical picture of the crystal vibration.

scholarly journals Probing nanoscale behavior of magnetic materials with soft X-ray spectromicroscopy

2012 ◽  
Vol 1 (1) ◽  
pp. 5-15 ◽  
Author(s):  
Peter Fischer ◽  
Charles S. Fadley
Keyword(s):  
Magnetic Properties ◽  
Magnetic Materials ◽  
Spin Dynamics ◽  
Magnetic Nanostructures ◽  
Magnetic Behavior ◽  
Research Area ◽  
X Ray ◽  
Spatially Resolved ◽  
Buried Interfaces ◽  
Analytical Tools

AbstractThe magnetic properties of matter continue to be a vibrant research area driven both by scientific curiosity to unravel the basic physical processes which govern magnetism and the vast and diverse utilization of magnetic materials in current and future devices, e.g., in information and sensor technologies. Relevant length and time scales approach fundamental limits of magnetism and with state-of-the-art synthesis approaches we are able to create and tailor unprecedented properties. Novel analytical tools are required to match these advances and soft X-ray probes are among the most promising ones. Strong and element-specific magnetic X-ray dichroism effects as well as the nanometer wavelength of photons and the availability of fsec short and intense X-ray pulses at upcoming X-ray sources enable unique experimental opportunities for the study of magnetic behavior. This article provides an overview of recent achievements and future perspectives in magnetic soft X-ray spectromicroscopies which permit us to gain spatially resolved insight into the ultrafast spin dynamics and the magnetic properties of buried interfaces of advanced magnetic nanostructures.

scholarly journals Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

2006 ◽  
Author(s):  
M. Amabili ◽  
C. Touze´ ◽  
O. Thomas
Keyword(s):  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Nonlinear Responses ◽  
Nonlinear Normal ◽  
The Galerkin Method ◽  
Proper Orthogonal

The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.

scholarly journals Spin transport and spin dynamics in antiferromagnets

2021 ◽  
Author(s):  
◽  
Geert Hoogeboom
Keyword(s):  
Magnetic Field ◽  
Heavy Metal ◽  
Spin Transport ◽  
Spin Dynamics ◽  
Magnetic Moments ◽  
Spin Current ◽  
Active Role ◽  
Metal Films ◽  
Alternating Direction ◽  
High Processing

Ferromagnets (FMs) have been a key ingredient in information technology because it is easy to manipulate and read out the magnetization. Antiferromagnets (AFMs) have magnetic moments with alternating direction resulting in negligible magnetization. This gives them high processing and device downscaling features, but this also makes it challenging to manipulate and interact with the AFM order. This thesis studies this interaction with antiferromagnets. NiO AFM order has been read out by electrically injecting spin current via the spin Hall effect in thin heavy metal films. In DyFeO3, both Dy and Fe magnetic moments, their excitation and interaction have been probed. A magnetic field lifts the degeneracy of magnetic excitations with opposite magnon spin, allowing a spin current to be detected nonlocally. The AFM order and the generation of spin current can easily be controlled by an adjacent FM. Thereby, we show that AFMs have the potential to play an active role in spintronics.

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