## 3 Results
### Helicity-Dependent All Optical Switching (HD-AOS)
#### 3.1.1 Helicity-Dependent All Optical Switching with Inverse Faraday Effect
Each pulse is applied every \(\Delta t_{L}~{}=~{}1\) ns. The last snapshot shows the final relaxed state after 25 laser pulses. A video of these HD-AOS is provided as Supplementary Material (video S1). Four different final states can be obtained depending on \(F\) and \(B^{0}_{MO}\) (see Figure 3). For low fluences, i.e., \(F<0.5\,\mathrm{J/m^{2}}\), electron temperature remains always below \(T_{C}\). For those fluences, the magnetization dynamics only depicts thermal noise fluctuations, and random domains which have transitorily inverted its initial magnetization finally collapse under the action of very low moderate magneto-optical field \(\overset{\rightarrow}{B}_{MO}\) (\(B^{0}_{MO}<1\) T). These combinations of \((F,B^{0}_{MO})\) result in a non-inverted state (black squares in Figure 3a,b). The local switching is achieved if \(B^{0}_{MO}\) is high enough for \(F<0.5\,\mathrm{J/m^{2}}\) (red circles in Figure 3a,c). Thermal agitation along with \(\overset{\rightarrow}{B}_{MO}\) produce the inversion of the magnetic state in the central part of the sample, as indicated by red dots in Figure 3a. An example of the final inverted state is shown in Figure 3c. Note that the critical value of the \(B^{0}_{MO}\) decreases gradually as \(F\) increases. For \(F\geq 0.5\,\mathrm{J/m^{2}}\), the electron temperature overcomes \(T_{C}\) in an extended region of the sample, and the ferromagnetic order is lost in the central part of the sample during every laser pulse. After a few fs, the electron temperature decreases under \(T_{C}\) (see Figure 1 as an example of the electron temperature evolution) and magnetic moments are remagnetized under the presence of \(\overset{\rightarrow}{B}_{MO}\), that may last longer than the laser pulse or maintain a high enough value when the sample is below \(T_{C}\). Therefore, the sample reverses its initial state even for moderate \(\overset{\rightarrow}{B}_{MO}\). If the fluence is further increased, the electron temperature also increases, and it takes longer to cool down to \(T_{C}\). In this situation two cases are possible: if the \(B^{0}_{MO}\) is relatively low, the sample ends in a random multi-domain configuration consisting on up and down domains under the laser spot (Figure 3e). For higher \(B^{0}_{MO}\) values, there is a region around the center of the laser spot which presents moderate values of \(T_{e}\) and \(B^{0}_{MO}\). These combinations lead to magnetic inversion in a surrounding ring around the center of the laser spot. However, \(T_{e}\) is still over \(T_{C}\) in the central part when the \(\overset{\rightarrow}{B}_{MO}\) disappears, which promotes the multi-domain central pattern. Consequently, the final state depicts an inverted external ring around the central multi-domain core (Figure 3d). Figure 3: (**a**) Phase diagram of final states as a function of the fluence (\(F\)) and the maximum amplitude of the magneto-optical field (\(B^{0}_{MO}\)) starting from a uniform up magnetization (\(\overset{\rightarrow}{m}\uparrow\) ). The results were obtained by applying a train of laser pulses with left-handed helicity (\(\sigma^{-}\)). Snapshots (**b**–**e**) represent typical final possible states. The black squares correspond to no-inversion combinations (**b**). The red dots correspond to cases where the local magnetization under the laser beam reverses its initial state (**c**). The green triangles correspond to a multi-domain final state (**d**), and the blue stars depict combinations of where the central area below the laser beam becomes demagnetized with an inverted ring around a multi-domain pattern (**e**). Real experiments depict similar four final magnetization patterns when the laser fluence is varied [10]. Although \(F\) can somehow be experimentally estimated, the local magnitude of \(\overset{\rightarrow}{B}_{MO}\), which is time and space dependent, remains essentially unknown.