We study the thermal relaxation of artificial spin ice with photoemission electron microscopy, and are able to directly observe how such a system finds its way from an energetically excited state to the ground state. On plotting vertex-type populations as a function of time, we can characterize the relaxation, which occurs in two stages, namely a string and a domain regime. Kinetic Monte Carlo simulations agree well with the temporal evolution of the magnetic state when including disorder, and the experimental results can be explained by considering the effective interaction energy associated with the separation of pairs of vertex excitations.

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Artificial spin ice systems have been proposed as a playground for the study of monopole-like magnetic excitations, similar to those observed in pyrochlore spin ice materials. Currents of magnetic monopole excitations have been observed, demonstrating the possibility for the realization of magnetic-charge-based circuitry. Artificial spin ice systems that support thermal fluctuations can serve as an ideal setting for observing dynamical effects such as monopole propagation and as a potential medium for magnetricity investigations. Here, we report on the transition from a frozen to a dynamic state in artificial spin ice with a square lattice. Magnetic imaging is used to determine the magnetic state of the islands in thermal equilibrium. The temperature-induced onset of magnetic fluctuations and excitation populations are shown to depend on the lattice spacing and related interaction strength between islands. The excitations are described by Boltzmann distributions with their factors in the frozen state relating to the blocking temperatures of the array. Our results provide insight into the design of thermal artificial spin ice arrays where the magnetic charge density and response to external fields can be studied in thermal equilibrium.

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X-ray photoemission electron microscopy combined with x-ray magnetic circular dichroism is used to study the magnetic properties of individual iron nanoparticles with sizes ranging from 20 down to 8 nm. While the magnetocrystalline anisotropy of bulk iron suggests superparamagnetic behavior in this size range, ferromagnetically blocked particles are also found at all sizes. Spontaneous transitions from the blocked state to the superparamagnetic state are observed in single particles and suggest that the enhanced magnetic energy barriers in the ferromagnetic particles are due to metastable, structurally excited states with unexpected life times. DOI: 10.1103/PhysRevLett.112.107201 PACS numbers: 75.30.Gw, 68.37.Yz, 75.50.Bb Metastability is a well-known phenomenon in condensed matter, where energy barriers prevent a system to relax from a higher-energy state to the ground state. Since the barrier heights usually scale with the system size, the preparation of metastable, higher-energy states becomes possible at the nanoscale [1,2]. Such states can be of profound interest when searching for materials with novel properties. For instance, much effort is currently undertaken to find magnetic nanostructures with properties that enable us to overcome the so-called "superparamagnetic limit," which will occur when further reducing the magnetic bit size for future high-density magnetic data storage devices [3][4][5]. Such applications require a magnetic energy barrier E m that is sufficiently high to prevent thermally driven switching of the magnetization at relevant temperatures (superparamagnetism). The barriers are usually provided by the magnetic anisotropy energy (MAE), which to first order scales with the particle volume. The magnetic relaxation rate v of a small magnet at a given temperature T is given by an Arrhenius law according to v ¼ v 0 expð−E m = k B TÞ with the thermal energy k B T. The attempt frequency v 0 depends on temperature, saturation magnetization, and the MAE [6][7][8]. The corresponding relaxation time is τ r ¼ 1=v.A direct experimental access to structural higher-energy states and their impact on the magnetic properties is, however, not trivial, particularly when ensemble measurements are considered. Even monodisperse nanomagnet ensembles can show considerable particle-to-particle variations in their properties either due to size effects, interparticle interactions, their individual interfaces with the environment, or surface effects [9]. Experiments with single particle sensitivity enable us to disentangle the different contributions, and thus to distinguish lower or ground state properties from higher-energy states [10,11]. Here, we study the magnetization of individual iron (Fe) nanoparticles by magnetic spectromicroscopy. The magnetocrystalline anisotropy of bulk Fe suggests superparamagnetic (SPM) behavior at room temperature (RT). Indeed, such particles have been found experimentally [12]. However, other authors reported enhanced magnetic energy barriers from ensemble measurements, which...