The vivid field of ultrafast magnetization dynamics shows that the mechanisms responsible for demagnetization are not entirely disentangled yet. Both, the thermal LLB and the m3TM approaches, based on exchange interaction and spin disorder, show a wide agreement with experimental data for thin films.
The super-diffusive mechanism is worth consideration, because at first view it provides an explanation to the discrepancy between the measured high electron temperatures and the relatively low and saturating demagnetization of the thin d= 2 nm,5 nm nickel films at high fluences.
1.5.1 Summary
The objective of the experiments discussed in the first part of this thesis has been to investigate, how distinct the features of the thermal model described by the LLB equation, which is derived starting with single spins in fluctuating Langevin fields, show in the experimental data. The analysis, fitting the analytical solution of the three temperature model extended by a second relaxation time τM,re to the experi-mental data proves the validity of the thermal model. All the features predicted by this model namely, the critical slowing down of the demagnetization and the slow relaxation at high temperatures are exhibited in the experimental data. They can be quantified by the extracted relaxation times.
The analysis of the reflectivity data shows that the two temperature model is a suitable approach to experimentally determine the electron temperatures required as input parameters to model magnetization dynamics via the LLB equation. The temperatures extracted from reflectivity data for nickel film thicknesses around the penetration depth lead to excellent agreement between experimental and simulated magnetization dynamics data. For the magnetization dynamics of nickel films thin-ner than the penetration depth, the experimentally obtained electron temperatures do not provide reliable values to be used as input data into the simulations. Further work on this particular subject is necessary. Using more transparent substrates, e.g. MgO, instead of Si might reduce the contribution of the substrate to the re-flectivity signal, delivering more reliable electron temperature values. Applying shorter probe pulse wavelengths (λ ≈400 nm) would reduce the penetration depth to Λopt ≈13 nm. This is not enough to discard the signal contribution from the Si substrate for the thin nickel films. In addition to that, also Ni films thicker than Λopt do not provide information about the electron temperature from reflectivity experiments. There, a different method needs to be implemented in order to gain insight in these processes. In that case, the change of the probe pulse wave length might help avoiding the sign change, exhibited in the data shown in figure B.12.
Figure 1.24: Demagnetization curves, measured applying pump pulses temporarily stretched to approximately 2.6 ps, on the 15 nm Ni film, and fluences up to 50 mJ/cm2. Inset: Maximum demagnetization from saturation mag-netization at 300 K, applying the stretched, and the 80 fs pump pulse for comparison. Adapted from [44].
1.5.2 Outlook
Future experiments will help to disentangle the underlying mechanisms responsi-ble for demagnetization as well as their relevance, which is currently under a vivid discussion. In a next step the magnetization dynamics can be triggered applying temporally stretched pump pulses around 1−4 ps. This will avoid the generation of hot electrons during excitation even at high pump fluences. The first results obtained in such experiments are plotted in figure 1.24. The graphs show magneti-zation dynamics spectra of a 15 nm Ni film, triggered by pump pulses temporarily stretched to approximately 2.6 ps. In those experiments the same fluences were applied as in the previously presented experiments, where the magnetization dy-namics was triggered by short excitation pulses [44]. The dydy-namics for the two lowest fluences (10 mJ/cm2 and 15 mJ/cm2) have not been measured, because the demagnetization is hardly detectable in this range. In those experiments, the max-imum electron temperatures barely exceed TC at high fluences, making sure that there are no relevant contributions from hot electrons. At the same time, the max-imum demagnetization is around 10% higher than in the experiments using short excitation pulses (see inset of figure 1.24). This outcome is supported by the findings
1 Ultrafast Spin Dynamics in [38], stating that non-thermal electrons are not decisive for ultrafast demagneti-zation. However, these results are controversial to the latest ab-initio calculations presented in [15]. There the spin-flip probabilities were calculated using the energy-and spin dependent Eliashberg function energy-and for comparison the same probabilities were calculated using the Elliott approximation. This comparison is important, be-cause the Elliott-Yafet electron-phonon spin-flip scattering so far is considered the main mechanism for ultrafast spin dissipation. Further, in [15] they argue that not the spin-flip probability is decisive for demagnetization, but the imbalance between the majority and minority subband occupation and that in the non-thermal state this imbalance leads to a higher spin-flip probability for majority spin electrons than the minority spin electrons, thus leading to a higher demagnetization rate than in the thermalized state, where the imbalance is smaller. They conclude that in the El-liott approximation the ElEl-liott-Yafet phonon-mediated demagnetization is not high enough to explain ultrafast demagnetization in the thermalized state, but rather in the non-thermalized.
With this discussion just opened, the field leaves a lot of open questions to be clarified in further research. A further verification of the LLB model, in which now the quantum mechanic spins have been implemented [3], will follow shortly. So far, the spins have been treated semi-classically [6]. The comparison to experiments carried out using variable pump pulse lengths will show, which mechanisms are underlying the ultrafast spin-flips. Further experimental verification of the super-diffusive model is necessary, as well as the estimation of the Kerr rotation stemming from the electrons super-diffusing into the Si substrate, which is a very interesting mechanism for thermal spin injection by itself.
2 Magneto-Seebeck Effect in Tunnel Junctions
2.1 Thermoelectric Effects
In 1821 Thomas Johann Seebeck, when working on galvanic chains discovered that heating one end of a metallic plate, which is connected in a closed loop with a copper coil induces a current. At that time, the current was measured by a compass needle placed along the coil. An electric current through the coil induces a magnetic field and forces the compass needle to turn from its original direction. The force on the needle is proportional to the current through the coil. This phenomenon was only shortly discovered by Hans Christian Oersted in 1819.
By holding one end of a metallic plate (bismuth, antimony) at a constant tem-perature in iced water and heating the other, he was also able to discover that the current through the coil was increasing with the temperature difference between both ends of the plate. The electric current measured using the copper coil stemmed from the voltage generated by the temperature gradient through the metallic plates [55].
The Seebeck effect is the first thermoelectric effect, which has been discovered.
Several others followed. Recently, a lot of new interest emerged from these effects in combination with magnetism. The development of conventional electronics seems to have reached an end and is threatened by a breakdown of Moore’s law, as with smaller device sizes current densities increase. Therefore, combining magnetism with thermoelectric effects seems to be inevitable to build an expandable foundation for new control systems of logic and memory devices.
In this chapter, thermoelectric effects are introduced, starting with the derivation of a completed concept to describe the thermoelectric and thermomagnetic effects.
These phenomena of simultaneous heat flow and electric current in one system re-quire the formalism of irreversible thermodynamics as a tool. The derivation for the description of the thermoelectric effects follows the steps in [14, Chapter 16,17]. A supplementary inclusion of magnetic currents into this description is given, accord-ing to [36]. Followaccord-ing that, the effects are explained from a phenomenological point of view for a clearer understanding of the presented experiments.
The construction and features of the experimental setup to measure the magneto-Seebeck effect in magnetic tunnel junctions by generating the temperature gradient optically are presented. The experimental data is discussed in the view of ab-initio calculations of the magneto-Seebeck effect in MgO-based magnetic tunnel junctions.