Construction of basis functions for the spin-cluster expansion of the magnetic energy on the atomic scale in rotationally invariant systems

2006 ◽  
Vol 47 (11) ◽  
pp. 113503 ◽  
Author(s):  
R. Singer ◽  
M. Fähnle
Keyword(s):  
Cluster Expansion ◽  
Magnetic Energy ◽  
Basis Functions ◽  
Atomic Scale ◽  
Spin Cluster ◽  
Rotationally Invariant

scholarly journals Probing atomic-scale symmetry breaking by rotationally invariant machine learning of multidimensional electron scattering

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Mark P. Oxley ◽  
Maxim Ziatdinov ◽  
Ondrej Dyck ◽  
Andrew R. Lupini ◽  
Rama Vasudevan ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Center Of Mass ◽  
Simulated Data ◽  
Atomic Scale ◽  
Data Sets ◽  
Scanning Transmission ◽  
Scale Yielding ◽  
Latent Representations ◽  
Rich Data ◽  
Rotationally Invariant

AbstractThe 4D scanning transmission electron microscopy (STEM) method maps the structure and functionality of solids on the atomic scale, yielding information-rich data sets describing the interatomic electric and magnetic fields, structural and electronic order parameters, and other symmetry breaking distortions. A critical bottleneck is the dearth of analytical tools that can reduce complex 4D-STEM data to physically relevant descriptors. We propose an approach for the systematic exploration of 4D-STEM data using rotationally invariant variational autoencoders (rrVAE), which disentangle the general rotation of the object from other latent representations. The implementation of purely rotational rrVAE is discussed as are applications to simulated data for graphene and zincblende structures. The rrVAE analysis of experimental 4D-STEM data of defects in graphene is illustrated and compared to the classical center-of-mass analysis. This approach is universal for probing symmetry-breaking phenomena in complex systems and can be implemented for a broad range of diffraction methods.

scholarly journals Probing atomic-scale symmetry breaking by rotationally invariant machine learning of 4D-STEM Data.

2021 ◽  
Vol 27 (S1) ◽  
pp. 2200-2201
Author(s):  
Mark Oxley ◽  
Maxim Ziatdinov ◽  
Ondrej Dyck ◽  
Andrew R. Lupini ◽  
Rama Vasudevan ◽  
...  
Keyword(s):  
Machine Learning ◽  
Symmetry Breaking ◽  
Atomic Scale ◽  
Rotationally Invariant

scholarly journals Atomistic spin model based on a spin-cluster expansion technique: Application to the IrMn3/Co interface

2011 ◽  
Vol 83 (2) ◽  
Author(s):  
L. Szunyogh ◽  
L. Udvardi ◽  
J. Jackson ◽  
U. Nowak ◽  
R. Chantrell
Keyword(s):  
Cluster Expansion ◽  
Spin Model ◽  
Spin Cluster ◽  
Model Based ◽  
Expansion Technique

scholarly journals Atomic-scale imaging of a 27-nuclear-spin cluster using a quantum sensor

Nature ◽  
2019 ◽  
Vol 576 (7787) ◽  
pp. 411-415 ◽  
Author(s):  
M. H. Abobeih ◽  
J. Randall ◽  
C. E. Bradley ◽  
H. P. Bartling ◽  
M. A. Bakker ◽  
...  
Keyword(s):  
Nuclear Spin ◽  
Atomic Scale ◽  
Spin Cluster

scholarly journals Performant implementation of the atomic cluster expansion (PACE) and application to copper and silicon

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Yury Lysogorskiy ◽  
Cas van der Oord ◽  
Anton Bochkarev ◽  
Sarath Menon ◽  
Matteo Rinaldi ◽  
...  
Keyword(s):  
Machine Learning ◽  
Cluster Expansion ◽  
Large Scale ◽  
Pareto Front ◽  
General Purpose ◽  
Basis Functions ◽  
Atomic Energy ◽  
Atomistic Simulations ◽  
Interatomic Potentials ◽  
Atomic Cluster

AbstractThe atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code that is suitable for use in large-scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in shifts a previously established Pareto front for machine learning interatomic potentials toward faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.

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