# Multimodal mechanisms of coherent magnetization reversal in transition-metal clusters

The magnetic anisotropy is one of the main characteristics of a magnetic material. This fundamental relativistic effect determines the low-temperature orientation of the magnetization with respect to the structure of the system, as well as its stability against temperature-induced fluctuations or external fields. Controlling the orientation and stability of the magnetization direction * M* in transition-metal (TM) nanostructures is crucial for the development of new magnetic materials for high-density recording, spintronic devices and medical treatments.

The magnetic properties of nanoscale TM particles are known to be very sensitive to system size, dimensionality and structure. This general tendency is particularly noticeable regarding magnetic anisotropy, since the latter is closely related to the local point group symmetry. In particular, the magnetic anisotropy energy (MAE) of small 3*d* TM clusters deserves special attention. The aim of this work is to investigate the mechanisms underlying the magnetization reversal in magnetic nanostructures. In particular, we intend to identify any possible deviations from the often assumed uniaxial behaviour. First, we search for TM nanoclusters (Fe_{n} , Co_{n} and Ni_{n} ) with high structural stability using density functional theory calculations (VASP). Using these structures, We explore the complete MAE surface as a function of the magnetization direction, by performing full-vectorial calculations in the framework of a self-consistent tight-binding theory without imposing any restrictions to the orientation of magnetization ** M**, which allow us to explore

*E*(

**) as an energy landscape. The easy magnetization axes, transition states and hard axes have been identified. Representative examples for different low-lying cluster geometries illustrate the role of different point-group symmetries on the MAE landscapes.**

*M*##### (Left) Contour plot of the MAE surface of the uniformly relaxed Co_{4}. The colour scale on the right gives the corresponding energy differences in meV with respect to the easy axis. Easy axes – C_{2} axes – are shown by blue, hard axes – C_{3} axes – by red and bonds by green dots. Notice that green dots have lower energy relative to the hard axes. Symmetry planes are presented by dashed lines. MEP has been shown by black solid line. Starting from an easy (C_{2}) axis, e.g., **e** which lies within *xy* plane, the reversal does not occur within the plane but it goes out of plane up to the saddle point (*t*) and then goes back to the plane, landing on the next C_{2} which is π/2 away from **e**. This procedure repeats once again until the spin moments are along the **e'**. (Right) Illustration of the high symmetry Co_{4} cluster (belonging to the T_{d} point group). Among all symmetry elements, only C_{2} axes by yellow lines and a rotoreflection plane (*xy* plane) by transparent pink plane have been shown. Blue arrows represent **e** and **e'** while grey arrows show **t**. MEP is illustrated by the orange curve.

**e**

*t*

**e**

**e'**

**e**

**e'**

**t**

Reference: F. Z. Sheikh-Abbasi, David Gallina, G. M. Pastor and J. Dorantes-Dávila, unpublished.