Universal scaling of the magnetic anisotropy in two-dimensional rare-earth layers

Abstract

Unraveling the influence that low dimensionality has upon the spin's stability in two-dimensional (2D) systems is instrumental for the efficient engineering of energy barriers in ultrathin magnetic layers. Taking rare-earth-based ultrathin multilayered nanostructures as a model system, we have investigated the dissimilar impact that low dimensionality and finite-size effects have upon the magnetic anisotropy energy (MAE) at the nanoscale. We conclusively show that the reduced dimensionality of the spin's system in 2D ferromagnetic layers imprints on the MAE constants a universal temperature decay as a quadratic power law of the reduced magnetization. This result is in agreement with predictions, although in marked contrast to the rank-dependent, thereby faster, decay of the MAE constants observed in three-dimensional nanostructures. [7], and plays an essential part in spin dynamics [8], has gathered huge interest [9,10], being in the spotlight of countless studies aiming to explore and gain control over the MAE of nanometersized matter [11].The relentless trend for miniaturization imposes the shrinking of the device size down to the nanoscale, which entails the arising of dominating surface/interface [12] contributions into MAE. In this way, the symmetry breaking of the lattice potential at the nanosystem boundaries gives rise to huge energy barriers [13,14], which are predominantly contributed by perimeter-edge ions [15]. On the contrary, as layer thickness becomes comparable to the spin-spin exchange range, the magnetic ordering temperatures [16][17][18] are shifted towards lower ones and the spin polarization [19] diminishes faster than in bulk systems as temperature increases. These two facts reflect in the enhancing efficacy of thermally activated spin waves [20] to annihilate long-range magnetic order [21] at the nanoscale.Newly engineered magnetic two-dimensional (2D) hybrid systems [22] have opened up an exciting new route for faster, more power-efficient spintronics [23], albeit they are not exempt from fundamental challenges. Thus, the reduced dimensionality of the crystal field in transition-metal-based nanosystems is well known to revive orbital moments, which contributes to stabilize the magnetic order in nanometer-sized matter [13,24]. However, the impact that the spin's low dimensionality has upon their thermal stability and, therefore, its crucial role in determining their magnetic response, is still poorly understood. The thermal stability of 2D magnets could be elucidated by measuring the temperature scaling of the model-independent MAE in ultrathin layers; nevertheless, such an experimental test has remained elusive upon until now. Here we report on the distinctive way in which finite-size and the spin's dimensionality effects determine the MAE in ultrathin layers. Taking RE superlattices (SLs) as a model system [33], which is featured by the precise modeling of their MAE [29,30], we demonstrate that the two dimensionality of the spin system in ultrathin RE layers imprints a universal, rank-i...