Supplementary Figure S1 The magneto-optical images of Gd24Fe66.5Co9.5

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1 Supplementary Figure S1 The magneto-optical images of Gd24Fe66.5Co9.5 continuous film obtained after the action of a sequence of the N right-handed (σ+ σ+) σ+ and left-handed (σ σ ) σ circularly-polarized 100 fs laser pulses. Initial homogeneously magnetized state with magnetization up (a,b). Panel (c) shows the film after an excitation with N (N=1, 2..5) circularly polarized pulse with a fluence of 2.30 mj/cm2. Panel (d) shows the film after excitation with N (N=1, 2..5) circularly polarized pulses with a fluence of 2.25mJ/cm2. The scale bar represents a length of 20µm. 1

2 Supplementary Figure S2 The magneto-optical images of GdFeCo continuous films with different compensation temperatures: (a) Gd 22 Fe 68.2 Co 9.8 (T M =100 K), (b) Gd 24 Fe 66.5 Co 9.5 (T M =280K), and (c) Gd 26 Fe 64.7 Co 9.3 (T M =390 K). Each image is obtained after the action of N=1 or N=2 100 fs laser pulses. All experiments were performed at room temperature. The scale bar represents a length of 20µm. 2

3 Supplementary Figure S3 Time resolved magnetization dynamics of the z- component of the two sublattices (upper panels). Dashed blue lines are the Fe sublattices and the solid red lines are the Gd. Lower panels show the temperature profile during the simulation with (a) having T start =82K (lower than the compensation temperature) and (b) T start =300K (above the compensation temperature). The dashed grey line shows the compensation temperature for the simulated system. The result clearly shows switching for both of the sublattices, independent on whether the temperature of the electronic system goes through the compensation point. 3

4 Supplementary Figure S4 Numerical simulations showing the demagnetization of the two sublattice model with each one having equal local moments. Panel a) shows the response of the sublattice A (blue dashed lines) and sublattice B (solid red lines) moments to a laser pulse when the local moments of each species are equal to the Fe moment. Panel b) shows the same as a) but with the moments equal to that of Gd. Panel c) shows the evolution of the electronic temperature. 4

5 Supplementary Methods Dependence on Polarization and Fluence of the Laser Pulse In order to demonstrate clearly the irrelevance of the inverse Faraday effect, H IFE ~ E E * for the observed reversal in thin films we studied the switching with right- (σ+) and left-handed (σ ) circularly polarized pulses experimentally. Depending on the sense of the laser pulse helicity, the effective light-induced field H IFE is directed either parallel or antiparallel to the light wavevector. Supplementary Figure S1(a,c) shows the effect of N, σ+ and σ pulses on a continuous film of Gd 24 Fe 66.5 Co 9.5. As one can see the sequence of the switching events occurs independently of pulse polarization, proving that the direction of the magnetization reversal is not dictated by the direction of H IFE. This mechanism of reversal occurs in a relatively wide range of laser pulse fluencies. Interestingly, by reducing the laser fluence one can realize the transition from this reversal driven by generation of an excited state to the reported previously alloptical helicity-dependent reversal 7. The latter is observed in a narrow (up to 10%) laser fluence range 13. Supplementary Figure S1(b,d) shows the magneto-optical images of the same continuous film after the action of N circularly polarized pulses of fluence corresponding to the helicity-dependent reversal. In contrast to the results in panels (a) and (c), a single pulse of only one helicity can reverse the magnetization. All the following pulses of the same helicity cannot reverse the magnetization back. No reversal at all is observed for the pulses of opposite helicity. This clearly demonstrates that in this case the direction of the reversal is defined by the sign of the field H IFE. We 5

6 note that this is the all-optical dependent reversal responsible for the rim opposite to the initial state apparent for each even pulse in Supplementary Figure S1 (c). Role of the Magnetization Compensation Point Several explanations of the process of reversal in these types of ferrimagnetic materials have included a discussion of the magnetization and angular momentum compensation temperatures 7,9. These explanations involve a discussion of the change in magnetization dynamics at or around these temperatures. However, experimental observations presented here show that the magnetization and compensation temperatures play no role in this reversal mechanism if we preclude increasing the temperature across these points. In order to confirm experimentally that the observed reversal does not rely on crossing the compensation point, we studied the reversal in several GdFeCo alloys which have different compensation points. Supplementary Figure S2 shows the result of the action of a single or sequence of 2 pulses on the films with T M below (Supplementary Figure S2 (a,b)) and above (Supplementary Figure S2 (c)) room temperature. The results in Supplementary Figure S2 clearly demonstrate that the all-optical reversal happens in all three samples. This confirms that crossing the compensation point is not required for the observed reversal process, in agreement with the results of the atomistic calculations. To support this experimental observation we also performed numerical simulations beginning at T start =82K and T start =300K. In the numerical model, T M =250K so 6

7 for the first starting temperature (T start =82K), the laser increases the temperature of the electron system (to which the spins are coupled) through the compensation temperature and for T start =300K, the system is equilibrated to a temperature above T M. The result is shown on Supplementary Figure S3. Supplementary Figures S2 and S3 clearly show that the position of the compensation temperature and whether the temperature is increased through this point or not has no bearing on whether the system switches or not. Importance of Non-Equivalent Sublattices It was shown in Ref. 9 that Fe and Gd demagnetize at different rates. The demagnetization time (longitudinal relaxation) of independent sublattices is dependent on the correlator (equation (4)) and the exchange field acting on the spins and thus Gd metal is intrinsically slower than Fe 27. The individual atomic spins forming a coupled system are, however, equivalent (at least for the short time) in terms of the longitudinal relaxation associated with each sublattice (the eigenvalues corresponding to the normal mode of a two sub-lattice system). This means that the initial demagnetization rate should be the same for both sublattices at least for a linear response. However, the actual demagnetization value should depend on the value of the magnetic moment through the correlator (equation (4)). Because of the different species having different moments, the two sublattices of ferrimagnet are non-equivalent. 7

8 The importance of this non-equivalence between the sublattices was tested by repeating the simulations while setting the local magnetic moments to be equal on both sublattices. We tested both instances of the equivalent moments having, in the first instance, the moments equal to the experimental Fe moment and for the second equal to the Gd moment. This means that we have in each case an artificial ferrimagnet without a compensation point. Now the individual atomic spins are equivalent in terms of the correlator associated with each site. This means that the demagnetization rate will be the same for both sub-lattices. We leave the exchange values the same, thus two magnetic sub-lattices are formed because of the presence of the anti-ferromagnetic exchange. The results of these simulations are shown in Supplementary Figure S4. In spite of the fact that the two sublattices have different intra-sublattice exchange, they are practically equivalent in their longitudinal response, at least for the short time. The exchange is kept the same as for the switching simulations, so no exchange scaling is carried out so that only the effect of the magnitude of the correlator is observed. It can be clearly seen from Supplementary Figure S4 that no reversal occurs, thus the nonequivalence of the sublattices plays an essential role in this mechanism of thermal energy load driven magnetization reversal. 8

9 Supplementary References: 27. Chubykalo-Fesenko, O., Nowak, U., Chantrell, R. W. and Garanin, D. Dynamic approach for micromagnetics close to the Curie temperature. Physical Review B, 74, (2006). 9