Nanoscopic time crystal obtained by non-ergodic spin dynamics

We study the far-from-equilibrium properties of quenched magnetic nanoscopic classical spin systems. In particular, we focus on the interplay between lattice vibrations and magnetic frustrations induced by surface effects typical of an antiferromagnet. We use a combination of Monte Carlo simulations and explore the dynamical behaviours by solving the stochastic Landau-Lifshitz-Gilbert equation at finite temperature. The Monte Carlo approach treats both the ionic degrees of freedom and spin variables on the same footing, via an extended Lennard-Jones Hamiltonian with a spin-lattice coupling. The zero temperature phase diagram of the finite size nanoscopic systems with respect to the range of the Heisenberg interaction and the Lennard-Jones coupling constant shows two main structures with non-trivial magnetisation triggered by antiferromagnetism: a simple cubic and a body-centred cubic. At non zero temperature, the competition between spins and the ionic vibrations considerably affects the magnetization of the system. Exploring the dynamics reveals a non-trivial structural induced behaviour in the spin relaxation with a concomitant memory of the initially applied ferromagnetic quench. We report the observation of a non-trivial dynamical scenario, obtained after a ferromagnetic magnetic quench at low temperature. Furthermore, we observe long-lived non-thermal states which could open new avenues for nano-technology.