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 ℂ with arbitrary dimension n.

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.

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

The diffusion of defects in crystalline materials controls macroscopic behaviour of a wide range of processes, including alloying, precipitation, phase transformation and creep. 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.

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.

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.

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.

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.