the frequency of the scattered light obeys the Doppler shift equal to the spin-wave frequency[22]. The quantum and classical scattering processes are shown in Fig. 3.2. Both surface and volume modes can be measured with this tech-nique. The surface mode is characterized by the different heights of the Stokes and Anti-Stokes peaks, due to limited propagation of magnons at the sample surface.
Figure 3.2: Schematical representation of Brillouin light scattering. a) scattering process of phonons at magnons. Inelastic scattering of the light at spin waves: b) magnon and incoming light propagate in the same direction, c) magnon and incoming light propagate in the opposite direction. Both cases are parallel to the sample plane. Figure taken from [22].
To measure the small shift in frequency, the conventional Fabry-Perot-Inter-ferometer has to be improved to achieve the contrast needed to resolve the weak Brillouin doublets. Multipassing was first experimentally realized by Sandercock[23]. This is done by coupling the two synchronized Fabry-Perot-Interferometers, which significantly increases the contrast and thereby pre-vents overlapping of different orders of interference. The Tandem-Fabry-Perot-Interferometer has a frequency resolution in the sub-GHz range and a contrast better than 1 : 1010[24].
Magnetostatic modes have been investigatedin situ using BLS and are reported in detail in [25]. Due to the focused laser light, spatially resolved measurements can also be made with BLS. This technique is also used to investigate dipolar Damon-Eschbach modes and spatially localized spin waves on structured ferro-magnetic films[26, 27].
3.2 All-optical pump-probe experiments
As mentioned in the previous section, the pump-probe technique uses a pump pulse to excite the sample, and a probe pulse to detect the sample relaxation.
By varying the time delay relative to the pump pulse, time resolved measure-ments are possible. In an all-optical pump-probe scheme both the sample ex-citation and the detection of the relaxation process is done using laser pulses.
Depending on the probe scheme, both the electron dynamics and magnetization dynamics can be recorded. To follow electron relaxation upon laser excitation, time resolved reflectivity is measured. The reflectivity measurements are not
explicitly included in this thesis. The details are published in [28, 29]. The time resolved Kerr effect is measured to follow the magnetization relaxation upon laser excitation.
The intense pump-laser pulse strongly perturbs the ferromagnetic sample. The energy of the pump-laser pulse is transferred to the sample within the pulse duration of ∆τ =80fs. This causes an ultrafast demagnetization of the sample on timescales of<1ps and triggers the coherent precession of the magnetization on the 100ps timescale. The excitation mechanisms and relevant time scales for both regimes are given in the following sections.
3.2.1 Ultrafast demagnetization
Demagnetization upon laser excitation can be attributed to the increased spin temperature from absorption of the pump-laser pulse. Nevertheless, on timescales of <1ps, the highly non-equilibrium state is a playground of various intensive interactions which challenges both experimentalists and theorists. The demag-netization of the nickel samples was first observed in the all-optical pump-probe experiments by Beaurepaire in [30].
Figure 3.3: Schematical representation of the optical excitation by the pump pulse.
The energy of the pump-laser pulse is first deposited to the electron system, and the further distributed to the phonon and spin system. The excitation process is shown in Fig. 3.3. Before excitation by the intensive pump-laser pulse, the electrons satisfy the Fermi Dirac distribution at temperatureT. Ex-posure to the intensive pump pulse causes optical transitions and induces the inversion of the population of allowed states with the hot electrons. Due to electron-electron scattering, the electron system thermalizes to the Fermi-Dirac distribution at the higher temperatureT+ ∆T. The energy is then transferred from the thermalized electron system to the lattice and spin system by the electron-phonon and electron-spin scattering processes. The increased sample temperature causes the loss of the ferromagnetic order as shown in Fig. 3.4.
The ultrafast demagnetization and restoration of the ferromagnetic order on the ps timescale upon laser excitation can be described using the Three
Tem-3.2 All-optical pump-probe experiments
Figure 3.4: Schematical view of the demagnetization, caused by an increase of the sample temperature.
perature model [30, 31]. This model assumes independent electron, lattice and spin baths temperatures of Te, Tp and Ts, in which the interactions between them are described by the coupling constantsgep,gesandgsp, shown in Fig. 3.5.
Figure 3.5: Schematical presentation of the three Temperature model. Figure adapted from [32].
The temporal evolution of these temperatures is given by the following system of coupled differential equations:
Ce(Te)dTe
dt = −gep(Te−Tp)−ges(Te−Ts) +P(t) Cs(Ts)dTs
dt = −ges(Ts−Te)−gsp(Ts−Tp) Cp(Tp)dTp
dt = −gep(Tp−Te)−gsp(Ts−Tp) ,
in whichCe,CsandCprepresent the heat capacities of the electron, the spin and
phonon system respectively andP(t) denotes the laser field of the pump pulse.
A closed-form expression can be given for the differential equation system[28, 32].
3.2.2 Induced magnetization precession
The absorption of the intensive pump-laser pulse not only induces the reduction of the magnetization amplitude, but also changes the easy axis of the system and triggers a precession of the magnetization. This effect was first observed in [32, 33]. The Anisotropy field pulse describes the ps pulse from the sudden tem-perature rise which starts the precession of the magnetization. The anisotropy field pulse is shown in Fig. 3.6.
Figure 3.6: Anisotropy field pulse in all-optical pump-probe experiments.
The absorption of the intensive laser pulse will briefly increase the temperature of the sample under the pump-laser spot. This temperature rise changes the anisotropy of the sample and thereby the easy axis of the magnetization, for a couple of ps. The magnetization then starts to precess around the new easy axis with a tendency to align with the new effective field. Nevertheless, the thermally induced anisotropy change takes only a couple of ps, after which the easy axis is returned to the orientation from before the pump laser illuminated the sample. The magnetization, already out of equilibrium, is not aligned with the effective magnetic field and begins to precess around it. The magnetic damping determines the timescale on which the magnetization aligns with the effective field. Therefore, the magnetization precession is determined by the constant effective magnetic field and not by the anisotropy field pulse, which only triggers the magnetization precession and determines the opening angle of the magnetization torque.