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

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.

Phonon Dynamics in Anisotropic Dilute CuAl1–xFexO2 Delafossite Alloys by a Weighted Dynamical Matrix Approach

2019 ◽  
Vol 123 (50) ◽  
pp. 30604-30612
Author(s):  
M. Aziziha ◽  
S. Akbarshahi ◽  
S. Ghosh ◽  
P. Pramanik ◽  
J. P. Lewis ◽  
...  
Keyword(s):  
Dynamical Matrix ◽  
Matrix Approach ◽  
Phonon Dynamics

Symmetry properties of the normal modes of vibration of calcite and α-corundum

1969 ◽  
Vol 47 (13) ◽  
pp. 1381-1391 ◽  
Author(s):  
E. R. Cowley
Keyword(s):  
Theoretical Analysis ◽  
Normal Modes ◽  
Dispersion Curves ◽  
Dynamical Matrix ◽  
Space Group ◽  
Symmetry Properties ◽  
Modes Of Vibration ◽  
Symmetry Species ◽  
Group Theoretical Analysis

A group theoretical analysis is carried out on the symmetry properties of the normal modes of vibration of crystals with the calcite and α-corundum structures. Both of these structures have the space group [Formula: see text]. The symmetry species present in the dispersion curves are determined for important wave vectors, and a transformation to block-diagonalize the dynamical matrix at the zone center is given.

Dynamical Structure Factor and Vibrational Normal Modes of SiO2 Glass

1992 ◽  
Vol 291 ◽  
Author(s):  
Wei Jin ◽  
Rajiv K. Kalia ◽  
Priya Vashishta
Keyword(s):  
Molecular Dynamics ◽  
Structure Factor ◽  
Interatomic Potential ◽  
Inelastic Neutron Scattering ◽  
Normal Modes ◽  
Dynamic Structure ◽  
Md Simulations ◽  
Inelastic Neutron ◽  
Dynamical Structure ◽  
Dynamical Matrix

ABSTRACTWe study the atomic vibrational dynamics in silica glass (a-SiO2) using molecular-dynamics (MD) simulations and classical lattice dynamics method. The SiO2 glasses were generated by molecular-dynamics and steepest-descent quench (SDQ) using an effective interatomic potential consisting of two-body and three-body interactions. The frequency and eigenvectors of vibrational normal modes are obtained by diagonalization of the dynamical matrix. The partial and total vibrational density of states (DOS), bond-projected DOS, participation ratio (PR), and neutron-weighted dynamic structure factor are calculated. The results are compared with inelastic neutron scattering experiments on SiO2 glass.

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.

The dynamics of a honeycomb array of domain walls as a network of interconnected strings

1990 ◽  
Vol 68 (7-8) ◽  
pp. 587-598 ◽  
Author(s):  
Neil D. Shrimpton ◽  
Béla Joós
Keyword(s):  
Domain Wall ◽  
Boundary Conditions ◽  
Domain Walls ◽  
Normal Modes ◽  
Rare Gas ◽  
Dynamical Matrix ◽  
Vibrational Modes ◽  
Interconnected Network ◽  
Energy Mode ◽  
Incommensurate Phases

A honeycomb array of domain walls such as is found in incommensurate phases of rare-gas monolayers on graphite is shown to vibrate as an interconnected network of strings. The vibrational modes of the network are determined by the vertices, which provide the boundary conditions for the domain-wall segments. The dynamical matrix is constructed and solved for the normal modes. The krypton on graphite system is used as a test to the theory. A Hamiltonian is constructed for the domain-wall network and the amplitude of the lowest energy mode, the breathing mode, is discussed.

Collective effects in artificial two-dimensional lattices of ferromagnetic nanoparticles

2000 ◽  
Vol 170 (3) ◽  
pp. 331 ◽  
Author(s):  
S.A. Gusev ◽  
Yu.N. Nozdrin ◽  
M.V. Sapozhnikov ◽  
A.A. Fraerman
Keyword(s):  
Collective Effects ◽  
Ferromagnetic Nanoparticles ◽  
Two Dimensional
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