A feedforward unitary equivariant neural network.

We devise a new type of feedforward neural network. It is equivariant with respect to the unitary group U(n). The input and output can be vectors in ℂn with arbitrary dimension n. No convolution layer is required in our implementation. We avoid errors due to truncated higher order terms in Fourier-like transformation. The implementation of each layer can be done efficiently using simple calculations. As a proof of concept, we have given empirical results on the prediction of the dynamics of atomic motion to demonstrate the practicality of our approach.

A machine-learned spin-lattice potential for dynamic simulations of defective magnetic iron.

A machine-learned spin-lattice interatomic potential (MSLP) for magnetic iron is developed and applied to mesoscopic scale defects. It is achieved by augmenting a spin-lattice Hamiltonian with a neural network term trained to descriptors representing a mix of local atomic configuration and magnetic environments. It reproduces the cohesive energy of BCC and FCC phases with various magnetic states. It predicts the formation energy and complex magnetic structure of point defects in quantitative agreement with density functional theory (DFT) including the reversal and quenching of magnetic moments near the core of defects. The Curie temperature is calculated through spin-lattice dynamics showing good computational stability at high temperature. The potential is applied to study magnetic fluctuations near sizable dislocation loops. The MSLP transcends current treatments using DFT and molecular dynamics, and surpasses other spin-lattice potentials that only treat near-perfect crystal cases.

Quantum de-trapping and transport of heavy defects in tungsten.

The diffusion of defects in crystalline materials1 controls macroscopic behaviour of a wide range of processes, including alloying, precipitation, phase transformation and creep2. In real materials, intrinsic defects are unavoidably bound to static trapping centres such as impurity atoms, meaning that their diffusion is dominated by de-trapping processes. It is generally believed that de-trapping occurs only by thermal activation. Here, we report the direct observation of the quantum de-trapping of defects below around one-third of the Debye temperature. We successfully monitored the de-trapping and migration of self-interstitial atom clusters, strongly trapped by impurity atoms in tungsten, by triggering de-trapping out of equilibrium at cryogenic temperatures, using high-energy electron irradiation and in situ transmission electron microscopy. The quantum-assisted de-trapping leads to low-temperature diffusion rates orders of magnitude higher than a naive classical estimate suggests. Our analysis shows that this phenomenon is generic to any crystalline material.

3D lattice distortions and defect structures in ion-implanted nano-crystals.

Focussed Ion Beam (FIB) milling is a mainstay of nano-scale machining. By manipulating a tightly focussed beam of energetic ions, often gallium (Ga+), FIB can sculpt nanostructures via localised sputtering. This ability to cut solid matter on the nano-scale revolutionised sample preparation across the life, earth and materials sciences. Despite its widespread usage, detailed understanding of the FIB-induced structural damage, intrinsic to the technique, remains elusive. Here we examine the defects caused by FIB in initially pristine objects. Using Bragg Coherent X-ray Diffraction Imaging (BCDI), we are able to spatially-resolve the full lattice strain tensor in FIB-milled gold nano-crystals. We find that every use of FIB causes large lattice distortions. Even very low ion doses, typical of FIB imaging and previously thought negligible, have a dramatic effect. Our results are consistent with a damage microstructure dominated by vacancies, highlighting the importance of free-surfaces in determining which defects are retained. At larger ion fluences, used during FIB-milling, we observe an extended dislocation network that causes stresses far beyond the bulk tensile strength of gold. These observations provide new fundamental insight into the nature of the damage created and the defects that lead to a surprisingly inhomogeneous morphology.

Impact of magnetic fluctuations on lattice excitations in fcc nickel.

The spin-space averaging formalism is applied to compute atomic forces and phonon spectra for magnetically excited states of fcc nickel. Transverse and longitudinal magnetic fluctuations are taken into account by a combination of magnetic special quasi random structures and constrained spin-density-functional theory. It turns out that for fcc Ni interatomic force constants and phonon spectra are almost unaffected by both kinds of spin fluctuations. Given the computational expense to simulate coupled magnetic and atomic fluctuations, this insight facilitates computational modeling of magnetic alloys such as Ni-based superalloys.

Temperature for a dynamic spin ensemble.

In molecular dynamics simulations, temperature is evaluated, via the equipartition principle, by computing the mean kinetic energy of atoms. There is no similar recipe yet for evaluating temperature of a dynamic system of interacting spins. By solving semiclassical Langevin spin-dynamics equations, and applying the fluctuation-dissipation theorem, we derive an equation for the temperature of a spin ensemble, expressed in terms of dynamic spin variables. The fact that definitions for the kinetic and spin temperatures are fully consistent is illustrated using large-scale spin dynamics and spin-lattice dynamics simulations.

Parallel algorithm for spin and spin-lattice dynamics simulations.

To control numerical errors accumulated over tens of millions of time steps during the integration of a set of highly coupled equations of motion is not a trivial task. In this paper, we propose a parallel algorithm for spin dynamics and the newly developed spin-lattice dynamics simulation [P. W. Ma, Phys. Rev. B 78, 024434 (2008)]. The algorithm is successfully tested in both types of dynamic calculations involving a million spins. It shows good stability and numerical accuracy over millions of time steps (approximately 1 ns) . The scheme is based on the second-order Suzuki-Trotter decomposition (STD). The usage can avoid numerical energy dissipation despite the trajectory and machine errors. The mathematical base of the symplecticity, for properly decomposed evolution operators, is presented. Due to the noncommutative nature of the spin in the present STD scheme, a unique parallel algorithm is needed. The efficiency and stability are tested. It can attain six to seven times speed up when eight threads are used. The run time per time step is linearly proportional to the system size.