Distinguishing the ultrafast dynamics of spin and orbital moments in solids
(27 May 2010)
09 October 2009
06 April 2010
For an isolated quantum particle, such as an electron, the orbital (
L) and spin ( S) magnetic moments can change provided that the total angular momentum of the particle is conserved. In condensed matter, an efficient transfer between L and S can occur owing to the spin–orbit interaction, which originates in the relativistic motion of electrons . Disentangling the absolute contributions of the orbital and spin angular momenta is challenging, however, as any transfer between the two occurs on femtosecond timescales. Here we investigate such phenomena by using ultrashort optical laser pulses to change the magnetization of a ferromagnetic film 1 and then probe its dynamics with circularly polarized femtosecond X-ray pulses 2 , 3 , 4 , 5 , 6 , 7 . Our measurements enable us to disentangle the spin and orbital components of the magnetic moment, revealing different dynamics for 8 L and S. We highlight the important role played by the spin–orbit interaction in the ultrafast laser-induced demagnetization of ferromagnetic films, and show also that the magneto-crystalline anisotropy energy is an important quantity to consider in such processes. Our study provides insights into the dynamics in magnetic systems as well as perspectives for the ultrafast control of information in magnetic recording media 9 . 10
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Figures at a glance
Figure 1: Geometry of the pump–probe experiment.
Sketch of the geometry of the pump–probe experiment at the femtoslicing synchrotron beam line at BESSY. Time-resolved XMCD allows measurement of the ultrafast dynamics of spin and orbital momenta along the quantification axis
z parallel to the applied magnetic field. Optical pulses with a central wavelength of λ pump = 790 nm and a duration of τ pump = 60 ± 20 fs excite the ferromagnetic films perpendicularly, aligning the electric vector E in the film plane. The density of absorbed laser energy is E abs = 12 mJ cm −2. The ellipsoidal shape of - E PMA illustrates the perpendicular anisotropy of the film. The easy magnetization direction is defined by the largest value of the z-axis projected value of L, ( L). On applying the external magnetic field z H ext, the spin magnetic moment S aligns parallel to the orbital magnetic moment L along the z axis. A variable delay can be set between the near-infrared pulse and the X-ray probe pulse.
Figure 2: Static energy resolved X-ray absorption spectra of CoPd film using circularly polarized light.
Two XAS spectra (red and black) and the normalized difference spectrum XMCD (line in blue) at the Co L
2,3 edges are displayed for the 15-nm Co 0.5 Pd 0.5 film in normal incidence geometry with a magnetic field of ±4 kOe, collinear with the incident circularly polarized X-rays. The two XAS spectra are obtained by extracting the logarithm of the transmitted X-ray signals recorded by the photodiode. This avoids any saturation effects in the XAS signal ( Supplementary Information). Integration of the energy resolved XMCD spectrum (green curve) allows a quantitative determination of the static values (without pump) of the spin and orbital magnetic moments at t < 0: ( S) z stat = 0.78 ± 0.01 per atom and ( L) z stat = 0.24 ± 0.01 per atom. A large number of pairs of XAS spectra allow such an accurate determination. a.u., arbitrary units.
Figure 3: Femtosecond evolution of the magnetic and electronic states.
a, b, Time-resolved XMCD at the Co L 3 and Co L 2 edges measured on a 15-nm Co 0.5Pd 0.5 alloy film using femtoslicing. The film has an out-of-plane anisotropy. A linear relation connects the two Co L 3 and Co L 2 XMCD signals with the two magnetic moments 19, 20 L and z S . The dashed lines for Co L z 3( t) and Co L 2( t) are calculated from the fitted time evolutions of L( z t) and S( z t), for which the resolution broadened double exponential function were used (see Fig. 4a continuous lines and Supplementary Information). c, Time dependence of the electronic Co L 3 XAS intensity recorded at energy E = 780.8 eV. The measured electronic XAS difference (for pumped and non-pumped sample) is related to the electronic changes observed in the valence band of the Co 3 d bands when excited with the laser pulse. The pump conditions are identical to those used for the magnetic data (density of absorbed laser energy: E abs = 12 mJ cm −2). The continuous line is a time dependent simulation using the resolution broadened double exponential given in Supplementary Information. The initial rise time τ e-e = 220 ± 20 fs corresponds to the thermalization of the electrons at the Fermi level following the laser excitation. The subsequent decay time of 360 ± 20 fs is related to the relaxation time of the electrons to the lattice. Error bars of experimental data show standard deviation.
Figure 4: Femtosecond evolution of the magnetic spin and orbital moments.
a, Sum rule extracted effective spin and orbital magnetic moments S( z t) and L( z t) as a function of the delay time between the laser pump and the X-ray probe. The continuous lines are fits obtained by using a 130-fs FWHM Gaussian function accounting for the time resolution of the experiment (including the X-ray probe and the femtosecond laser pump). The blue dashed line represents the fit to L( z t) scaled to the value of S( z t) before laser excitation. The characteristic thermalization times of both spin and orbital magnetic moments are: τ th( L) = 220 z ± 20 fs and τ th( S) = 280 z ± 20 fs. The fitting procedure and error bars providing the thermalization times are explained in Supplementary Information. The difference between both thermalization times is 60 ± 30 fs, showing a faster decrease of the orbital moment. The maximum relative variation for S( z t) is –55 ± 3%, whereas for L( z t) it is –67 ± 6.5%. b, The ratio ( L/ z S)( z t) obtained as a function of the delay time shows that the orbital magnetic moment reduces more than the effective spin magnetic moment during the ultrafast demagnetization process. The black continuous line is the ratio between the two simulations of L( z t) and S( z t), showing a relative variation of –29 ± 5%. The red line is the ratio obtained when we take two identical values τ th( L) = z τ th( S) = 260 z fs. The error bars for L( z t), S( z t) and ( L/ z S)( z t) are obtained from the error bars of the time resolved XMCD at the Co L 2 and Co L 3 edges.