SUPPLEMENTARY INFORMATION

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1 do: /nature09901 Supplementary Informaton: Sample propertes The nvestgated sample was a 30 nm Gd 25 Fe 65.6 Co 9.4 thn flm deposted by magnetron sputterng on a free-standng Al fol of 500 nm thckness. To avod oxdaton of the GdFeCo layer, S 3 N 4 flms of 100 nm and 60 nm thckness were used as buffer and cappng layers, respectvely. The presence of Co n the GdFeCo alloy leads to stronger out-of-plane magnetc ansotropy and to larger coercve felds. The latter ones are necessary to have a well defned ntal and fnal magnetc state durng the pump-probe cycles n the tme-resolved XMCD measurements. The out-of-plane magnetc ansotropy of GdFeCo samples has been deduced from the measured element-specfc hysteress curves. The measured hysteress curves show a ferromagnetc algnment of Co and Fe and an antferromagnetc algnment of Fe and Gd magnetc moments (see also Fg. 1 of the man paper). Smlar coercve felds are measured at the Co edge compared to both Fe and Gd as the sample s thermally drven through the magnetzaton compensaton pont. Below the magnetzaton compensaton temperature T M =250 K, the magnetzaton of the Gd sublattce s larger than that of Fe and n an external magnetc feld the Gd-sublattce s algned along the feld (see drawngs at the bottom of Fg. 1 n the man paper). Above T M =250 K, the magnetzaton of Gd s smaller than that of Fe and the spn system favours ant-parallel orentaton of Gd wth respect to the external magnetc feld. The angular momentum compensaton temperature T A occurs at a temperature of about 50 K above T [1] M. The exchange nteracton between the sublattces s so strong that both sublattces have the same Cure temperature of ~550 K. 1. Expermental procedure for the element-specfc study of laser-nduced spn dynamcs In order to probe ndependently the magnetzatons of the two sublattces we employed the element-specfc X-ray Magnetc Crcular Dchrosm technque. Statc and dynamc XMCD measurements have been performed n transmsson geometry for a fxed X-ray lght helcty and opposte orentatons of the external magnetc feld of ±0.5 T. Soft X-ray lght coverng the L 3,2 absorpton edges of Fe and Co and the M 5,4 edges of Gd has been employed to measure the magnetc response of the elements n the composte alloy. A typcal data set of XMCD spectra measured at Fe and Gd edges as the sample s thermally drven through the compensaton temperature (here T M =300 K) s shown n Supplementary Fg. 1. We observe clearly the 1

2 do: /nature09901 ferrmagnetc algnment of Fe and Gd and the sgn change of XMCD upon crossng the compensaton pont. Supplementary Fgure 1: XMCD spectra of Fe and Gd upon crossng the magnetzaton compensaton pont. XMCD spectra measured at Fe and Gd edges as a functon of temperature for a sample wth magnetzaton compensaton pont at 300 K. The XMCD polarty change appears upon crossng the magnetzaton compensaton temperature. In the tme-resolved experment we photo-excte electrons of the hybrdzed Fe 3d - Gd 5d6s bands wth 60 fs laser pulses at a photon energy of 1.55 ev (see Supplementary Fg. 2). The bndng energy of the occuped spn-up 4f state s around 9 ev.e. much larger than the energy of the photons n the pump. Subsequent laser-nduced dynamcs s probed by measurng the magnetzaton-dependent absorpton of crcularly polarzed 100 fs X-ray pulses at the Fe L 3 absorpton edge (photon energy 707 ev) and at the Gd M 5 edge (photon energy 1189 ev). At these energes we probe the dynamcs of the 3d magnetc moment of Fe and the 4f moment of Gd. Varyng the delay between the pump and probe pulses we were able to perform an element specfc study of the laser-nduced magnetc changes wth sub-pcosecond temporal resoluton. The measurements were performed at the femto-slcng faclty 2,3 at BESSY II, whch provdes femtosecond soft X-ray pulses wth varable polarzaton. The laser-nduced changes of X-ray transmsson were measured for opposte orentatons of the magnetc feld usng an avalanche photodode and a gated boxcar detecton 2. Thereby, we were able to measure the tme evoluton of the pumped (n the presence of laser exctaton) and un-pumped (n absence of laser exctaton) sgnals. From the transmsson changes measured 2

3 do: /nature09901 for opposte magnetc felds we obtaned the absorpton changes and from the dfference of the latter ones the dynamc XMCD curves. In the man paper we show the rato of the pumped and un-pumped XMCD curves. The typcal sze of the laser beam n focus was 0.8 x 0.4 mm 2 that led to an ncdent laser fluence of 4.4 mj/cm 2. The X-ray beam sze was 0.3 x 0.1 mm 2. The XMCD measurements shown n the man paper were performed at a sample temperature of 83 K.e. below the compensaton temperature of 250 K. The energy resoluton of the tme-resolved XMCD experment s ~5 ev, whch means that the measured transent XMCD sgnal s essentally ntegrated over the entre absorpton edge.e. over all avalable fnal states for the X-ray transtons. The moderate laser fluence used n the experment together wth the above argument lead us to conclude that optcal bleachng effects are hghly unlkely. Supplementary Fgure 2: Pumpng and probng mechansm n the schematc electronc structure of GdFeCo alloy. 3

4 do: /nature Fluence Dependence of Magnetzaton Swtchng for Fe and Gd Supplementary Fgure 3: Fluence dependence of Fe and Gd swtchng dynamcs. The change of the magnetzaton swtchng tmes for Fe and Gd moments upon varyng the ncdence laser fluence as labeled n the fgure. The lnes are fts to the data accordng to a bexponental ft functon (see 3. Data Fttng Procedure) The transent XMCD sgnal measured at the Fe and Gd absorpton edges as a functon of the ncdent laser fluence s shown n Supplementary Fgure 3. Upon decreasng the fluence we observe a slower swtchng process for both Fe and Gd magnetc moments wth ther dstnct transent dynamcs beng preserved. Consequently, the transent ferromagnetc-lke algnment lves longer. For nstance, gong from 4.4 to 4 mj/cm 2 the lfetme of the transent ferromagnetclke state ncreases from 1.2 ps to ~3 ps. Further decreasng the fluence the transent sgnal approaches ncreasngly slower the zero sgnal level and for a fluence of 2.6 mj/cm 2 (not shown) no swtchng occurs. These results suggest the exstence of a narrow laser fluence - sample temperature parameter space n whch magnetzaton swtchng and the transent ferromagnetc-lke state occur. 4

5 do: /nature Data Fttng Procedure For fttng the transent XMCD data we have used a double exponental ft functon convoluted wth the tme resoluton of the experment: Here G(t) stands for the Gaussan functon denotng the tme resoluton of the measurements of 100 fs full wdth half maxmum, A s the value of the transent sgnal at negatve delays, and are the tme constants characterzng the two processes - the ntal rapd drop and the slower remagnetzaton n the opposte magnetzaton drecton - descrbng the temporal evoluton of the data, and B and C are exponental ampltudes. In Supplementary Fgure 4 we show an exemplary ft for the case of Gd dynamcs wth the fnal ft functon (the sold lne) and two exponentals plotted separately (the dashed and dashed-dotted lne). As one can see the resultng ft descrbes very well the expermental data. The tme constants deduced for Gd are = 430±100 fs and = 28.4±1.28 ps whereas for the case of Fe = 100±25 fs and = 0.9±0.092 ps. The error bars deduced from the fttng procedure are standard devatons. Supplementary Fgure 4: Exemplary fttng procedure shown for Gd transent XMCD sgnal usng the b-exponental ft functon. 5

6 do: /nature The Localzed Atomstc Spn Model The localzed atomstc spn model uses a Hesenberg exchange, the Hamltonan s gven by E z JjS S j KS B nn S z Where J s the exchange ntegral, whch we lmt to nearest neghbour nteractons, K s the j ansotropy energy constant, whch we assume to be unaxal and s J/spn, whch s large enough to support a perpendcular magnetzaton. The B s the appled magnetc feld and S s reduced atomc localzed spn, whch s normalzed to one on the atomc stes. Each atomc ste has an assocated magnetc moment, gven by. The on-ste effectve feld s then H E S The spn dynamcs are then descrbed by the Landau-Lfshtz-Glbert (LLG) equaton for localsed atomstc spns S t S H S H (1 ) 2 Here s a mcroscopc dampng parameter, whch couples the spn system to a heat bath. The dampng term n the LLG equaton allows for dsspaton of energy away from the spn system. We augment the effectve feld usng a stochastc term ncluded nto the effectve feld to mmc thermal fluctuatons. Ths allows for heat to flow nto the spn system. The correlator s gven by a b k BT ( t) j ( t) 2 j ab ( t t) t In the model we assume that GdFeCo s a two sub-lattce system, wth FeCo beng descrbed by a generc transton metal (TM) and the Gd we descrbe by the term rare earth (RE). Expermentally GdFeCo s amorphous, whch s extremely dffcult to characterze fully, however we can make a smplfcaton n the model by assumng that we have a fxed face centered cubc (fcc) lattce. The fcc lattce s then populated randomly wth TM speces and RE speces to mmc the amorphous nature of the system. The exchange constants were obtaned by fttng 6

7 do: /nature09901 statc XMCD data for the Fe and Gd sublattces, the values are stated per lnk and do not take nto account the number of neghbors of each speces. They were J Fe-Fe =2.835x10-21 J/lnk, J Gd- Gd=1.26x10-21 J/lnk (correspondng to the Cure temperature of bulk Gd) and J Fe-Gd =-1.09x10-21 J/lnk. Takng nto account the number and type of neghbors, the effectve Fe-Fe exchange s 1.96x10-20 J per spn (~35 fs), the Gd-Gd effectve exchange s 8.72x10-22 J per spn (~760 fs) and the Fe-Gd effectve exchange s 4.77x10-20 J per spn(~140 fs). The gyromagnetc ratos of each speces were set to adjust the angular momentum compensaton pont (T A =283 K) above the magnetzaton compensaton pont (T M =250 K), γ TM =1.05γ and γ RE =1.00γ, wth γ=1.76x10 11 T -1 s -1. The number of spns n the smulatons s 500,000 n a cubc structure wth perodc boundary condtons on all sdes as the samples used are much larger than that smulated. The tmestep we use s 0.1fs, usng the Heun scheme. The spns are equlbrated before the applcaton of any temperature to ensure that the magnetzaton s at equlbrum. Followng ref. 4 we couple the spn system to the electron temperature that s calculated usng the so-called two-temperature model 5. To focus on the magnetc propertes, the model assumes the same electron temperature and the same dampng constants for Gd and Fe (λ TM =λ RE =0.05). 5. Magnetzaton dynamcs as a functon of RE-RE exchange nteracton Supplementary Fgure 5: The varaton of the reversal tme for the RE and TM sub-lattces wth the exchange nteracton. Numercal calculatons of reversal tme n the FeCo (TM) and 7

8 do: /nature09901 Gd (RE) systems (tme for each sublattce to cross zero axs) as a functon of the Gd-Gd exchange parameter. The effectve Fe-Fe exchange s 1.96x10-20 J per spn. The dstance between the red and the blue curves gves the tme for whch the system s n the transent ferromagnetc-lke state. We see very lttle dfference n fundamental behavour on changng ths parameter. Supplementary Fg. 5 shows numercal results of the effect of changng the Gd-Gd exchange parameter, up to the strength of the (FeCo)-(FeCo) exchange. The dstance between ponts on the red and blue lnes show the tme durng whch the system s n ths transent ferromagnetclke state. We see lttle dfference n the behavour upon ncrease of the exchange nteracton. 6. μ/λ dependence on the longtudnal relaxaton tme The dfferent tmescales for the collapse of the magnetzatons, can be explaned n terms of the characterstc tme of longtudnal relaxaton of the magnetzaton 6. We test the assumpton of longtudnal relaxaton tme dependng on the rato of the magnetc moment and the nput (ntrnsc) dampng parameter numercally. By smulatng a Heavsde type step n the temperature pulse from 0 to 300K and measurng the response of the system and fttng an exponentally decayng functon of the form tme. We calculate for each sublattce, m ( t) m (0) e z z t / where s the ntal relaxaton keepng the magnetc moment of the TM stes constant and varyng the moment on the RE stes and measurng the ntal relaxaton tme. We show results for two dampng values =0.02 and =0.05, plottng the tme multpled by the dampng parameter. The used theory predcts that these lnes should agree. We can see from Supplementary Fg. 6 that the relaxaton tme for the RE s much longer than that of the TM n the hgh RE regon (correspondng to the expermental stuaton). The two curves agree very well. It should be noted that wth lower dampng there s more scatter n the data as the relaxaton tme s much longer leadng to larger errors n the fttng procedure. Also at the hgh RE end of the curve there s a large devaton from the expected value, ths agan s due to the long relaxaton tme assocated wth the hgher Gd moment, whch means that we are no longer just observng the ntal slope, other effects become mportant and the theory breaks down. 8

9 do: /nature09901 Supplementary Fgure 6: The longtudnal relaxaton tme as a functon of the RE magnetc moment. Longtudnal relaxaton tme multpled by the nput dampng, whch descrbes the ntrnsc longtudnal relaxaton process. We show data for changng the magnetc moment on the RE stes and two values of the dampng parameter. As we can see we have a lnear ncrease n relaxaton tme wth ncreasng RE magnetc moment. Wth larger RE moment the error n the approxmaton ncreases, though the two sets of data show excellent agreement. References: 1. Stancu, C.D. et al. Ultrafast spn dynamcs across compensaton ponts n ferrmagnetc GdFeCo: The role of angular momentum compensaton. Phys. Rev. B. 73, (R) (2006). 2. Stamm, C. et al., Femtosecond modfcaton of electron localzaton and transfer of angular momentum n nckel. Nature Mater. 6, (2007). 3. Khan, S. et al., Femtosecond undulator radaton from slced electron bunches. Phys. Rev. Lett. 97, (2006). 4. Kazantseva, N. et al. Slow recovery of the magnetzaton after a sub-pcosecond heat pulse EPL 81, (2008). 5. Ansmov, S.I., Kapelovch, B.L., Perelman, T.L., Electron emsson from metal surfaces exposed to ultrashort laser pulses, Sov. Phys. JETP, 39, 375 (1974). 6. Akhezer, A. I., Bar yakhtar, V.G. & Peletmnsk, S.V. Spn Waves (North-Holland, Amsterdam, 1968). 9