No abstract

A parallel implementation of coupled spin-lattice dynamics in the LAMMPS molecular dynamics package is presented. The equations of motion for both spin only and coupled spin-lattice dynamics are first reviewed, including a detailed account of how magneto-mechanical potentials can be used to perform a proper coupling between spin and lattice degrees of freedom. A symplectic numerical integration algorithm is then presented which combines the Suzuki-Trotter decomposition for non-commuting variables and conserves the geometric properties of the equations of motion. The numerical accuracy of the serial implementation was assessed by verifying that it conserves the total energy and the norm of the total magnetization up to second order in the timestep size. Finally, a very general parallel algorithm is proposed that allows large spin-lattice systems to be efficiently simulated on large numbers of processors without degrading its mathematical accuracy. Its correctness as well as scaling efficiency were tested for realistic coupled spin-lattice systems, confirming that the new parallel algorithm is both accurate and efficient.

Chirality, a foundational concept throughout science, may arise at ferromagnetic domain walls 1 and in related objects such as skyrmions 2. However, chiral textures should also exist in other types of ferroics such as antiferromagnets for which theory predicts that they should move faster for lower power 3 , and ferroelectrics where they should be extremely small and possess unusual topologies 4,5. Here we report the concomitant observation of antiferromagnetic and electric chiral textures at domain walls in the room-temperature ferroelectric antiferromagnet BiFeO 3. Combining reciprocal and real-space characterization techniques, we reveal the presence of periodic chiral antiferromagnetic objects along the domain walls as well as a priori energetically unfavorable chiral ferroelectric domain walls. We discuss the mechanisms underlying their formation and their relevance for electrically controlled topological oxide electronics and spintronics. Metallic ferromagnets have been the elemental bricks of spintronics for the last three decades and continue to hold promises on the basis of non-collinear chiral spin textures such as skyrmions. These topologically protected objects are envisioned to be the future of magnetic data storage thanks to their specific stability, dynamics, and scalability 2. In parallel, antiferromagnets (AFs) are emerging as a new paradigm for spintronics 6. They are intrinsically stable (being insensitive to spurious magnetic fields), scalable (no cross talk between neighbouring memory cells), and fast (switching frequencies in the THz regime). The opportunity of gathering the best of these two worlds and realize "antiferromagnetic skyrmions" is then tremendously appealing but faces at least two major challenges. The first one is to achieve antiferromagnetic chirality and the second one is to identify appropriate control stimuli to create, annihilate and move these chiral objects. On one hand, chirality may naturally emerge at domain walls. The antiferromagnetic domain wall structure is a virtually uncharted territory but this is where translational symmetry is broken and spin rotation favoured. On the other hand, AF manipulation is hampered by the intrinsic lack of net magnetization, which prevents a straightforward magnetic actuation. This fundamental issue may be