# Verification of the atomic stacking by transmission electron microscopy (TEM)

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## Anisotropic magnetoresistance (AMR)

One can see from experiments, that the resistivity ρ of magnetic materials depends on the angle between magnetization and the direction of the current (see fig(1.9). This eﬀect is called anisotropic magnetoresistance (AMR). The angular dependence of the resistance can be expressed by: ρ(θ) = ρk + (ρ⊥ − ρk) · sin2(θ) (1.29) with θ the angle between magnetization and current. For further explications on AMR one should consider [43].

Giant magnetoresistance (GMR)

The eﬀect of giant magnetoresistance was discovered in 1988 ([2] and [1]), and honored with the Nobel Prize in 2007. It can be observed in samples with nanometric length scales. These length scales are given, depending on the geometric configuration, by the electron mean free path or the spin diﬀusion length. A simple phenomenological approach is the following:
The resistivity of a magnetic layer diﬀers for spins with a magnetic moment parallel to the magnetization r↑, from spins with a magnetic moment antiparallel to the magne-tization r↓. In other words the resistivity is spin-dependent (see fig.(1.10)). Considering a configuration, where two magnetic layers are separated by a nonmagnetic conducting layer ( a so-called spin valve), we discuss a parallel and an antiparallel orientation of the magnetic layers. Electrons with a spin parallel to the layer magnetization pass more easily through the trilayer(resistivity r↑), than spins, that are antiparallel to the magnetization (resistivity r↓). The total resistivity of this configuration is called rP . In the case of antiparallel magnetic layers, the resistivity is the same for both spin directions. The total resistivity for the antiparallel configuration is called rAP . One can then define the GMR as: GMR = rAP − rP = r↑ − r↓ (1.30) rP 4r↑r↓.

Propagation of a DW in a nanowire considering pinning sites

Pinning and depinning eﬀects play an important role for the dynamics of a DW in a nanowire. In the following we are going to discuss pinning sites and then in a second part, the stochastic behavior of pinning and depinning events.

### DW pinning sites in nanowires

Due to the geometrical confinement in a nanowire, we do not only have intrinsic pinning sites due to structural defects, but also geometrical pinning sites (see fig.(1.17). The geometrical pinning is explained the following way: The total energy of a DW EDW is given by: EDW = σ · t · l (1.41). where σ is the DW energy per surface, t the thickness of the magnetic layer and l the length of the DW. A DW can be pinned on a site where it is short. For real samples geometrical pinning comes for example from the roughness of the wire due to the lithography process, or it can be imposed by so-called notches (a constriction in the wire) or Hall crosses. The depinning from a geometrical pinning site under field is governed by a competition between the DW energy EDW and the Zeeman energy EZ . Etot = EDW + EZ (1.42) A small displacement of the DW leads to an increase of EDW given by: ∂L dEDW = σt dy (1.43).

#### Current-induced magnetization reversal and steady states precession in nanopillars

Nanopillars with a spin valve structure consist of two magnetic layers separated by a nonmagnetic metallic layer. The magnetic properties are generally chosen in a way, that one layer, the soft layer (SL), is much easier to reverse than the other layer, called the hard layer (HL) or reference layer. The current flows perpendicular to the layers. The idea is, that the current is spin-polarized when passing through the HL. This current then applies a torque on the magnetization of the SL depending on the relative orientation of current, polarization and magnetizations. This torque can lead either to magnetization reversal or to steady state precessions (e.g. [8]) (see fig.(1.20)). The dimensions of nanopillars are in general inferior to the exchange length lex (compare sec.(1.1.6)). Accordingly the application of a macrospin model is appropriate. Such a model is developed for example by [58]. They find for the spin torque: ST = −βIη(Θ)ˆem × (ˆem × eˆp) (1.53).

1 Basics of magnetism and spin transfer torque
1.1 Magnetic moment and magnetic interactions
1.1.1 Magnetic moment
1.1.2 Itinerant vs localized magnetism
1.1.2.1 Transition metals (TM)- model of itinerant magnetism
1.1.2.2 Magnetism of rare earth elements(RE) – model of localized electrons
1.1.3 Magnetic interactions
1.1.3.1 Zeeman energy
1.1.3.2 Exchange interaction
1.1.3.3 Dipolar energy and shape anisotropy
1.1.3.4 Magnetocrystalline anisotropy (MCA)
1.1.4 MCA of rare earth elements and MCA of transition metals .
1.1.5 Anisotropy of thin films
1.1.6 Magnetic domains and domain walls (DW)
1.2 Magnetoresistance
1.2.1 Anisotropic magnetoresistance (AMR)
1.2.2 Giant magnetoresistance (GMR)
1.2.3 Extraordinary Hall effect (EHE)
1.3 Magnetization reversal
1.3.1 Stoner Wohlfarth model
1.3.2 Magnetization reversal in thin films
1.3.2.1 Nucleation process
1.3.2.2 Propagation process
1.3.3 Domain wall propagation in a nanowires under field
1.3.4 Propagation of a DW in a nanowire without pinning sites
1.3.5 Propagation of a DW in a nanowire considering pinning sites .
1.3.5.1 DW pinning sites in nanowires
1.3.5.2 The depinning process in nanowires
1.3.6 Conclusion for the choice of a material as a model system
1.4 Magnetization reversal induced by a spin-polarized current
1.4.1 Dynamic of a magnetic moment : LLGS equation
1.4.2 Current-induced magnetization reversal and steady states precession in nanopillars
1.4.3 Current-induced DW propagation
1.5 Materials for spin torque experiments
1.5.1 In-plane vs out-of-plane materials
1.5.2 Materials used for experiments on spin transfer torque switching in nanopillars
1.5.3 Materials used for experiments on spin current driven domain wall propagation
1.6 Outline for the following manuscript
2 Les alliages de Co1−xTbx 51
2 CoTb-based alloys
2.1 Growth and Structure
2.1.1 Sample preparation by DC magnetron sputtering
2.1.2 Structural analysis by transmission electron microscopy (TEM)
2.2 Magnetic properties
2.2.1 Magnetic structure of rare earth(RE) – transition metal(TM) alloys
2.2.2 Magnetization of the CoTb system
2.2.3 Perpendicular anisotropy in CoTb alloys
2.2.4 Magnetism of CoTb alloys as a function of layer thickness
2.2.5 Further data
2.2.5.1 Soft-magnetic contribution to hysteresis loops
2.2.5.2 Effects of annealing
2.2.6 Models describing the origin of PMA in RE-TM alloys
2.2.7 Conclusion on the magnetic properties of CoTb alloys
2.3 Magnetization reversal in Co1−xTbx alloys and Co1−xTbx-based spin valves
2.3.1 Reversal process of CoTb films
2.3.1.1 Domain pattern of CoTb films during reversal
2.3.1.2 Barkhausen length lB of the reversal process
2.3.1.3 Conclusion on the reversal process
2.3.2 Dipolar coupling in CoTb-based spin valves
2.3.2.1 Magnetometry results
2.3.2.2 Analysis by MFM imaging
2.3.2.3 Modelization of the dipolar field
2.3.2.4 Modification of the nucleation field
2.3.2.5 Conclusion
2.3.3 Conclusion on magnetization reversal in Co1−xTbx alloys and Co1−xTbx-based spin valves
2.4 Transport properties of CoTb alloys
2.4.1 Magnetoresistance of a Co88Tb12 layer
2.4.2 Magnetoresistance of CoTb-based spin valves
2.4.3 Temperature dependence of magnetoresistance
2.4.4 Angular dependence of magnetoresistance in CoTb alloys
2.4.5 Conclusion on the magnetoresistance of CoTb alloys
2.5 All-Optical magnetization switching in Co1−xTbx alloys
2.5.1 Mechanisms of all-optical magnetization switching
2.5.2 First results obtained for Co1−xTbx alloys
2.5.3 Conclusion and new perspectives
2.6 Conclusion and perspectives for CoTb alloys
3 Les super-r´eseaux [Co/Ni](111) ´epitaxi´es
3 Epitaxial [Co/Ni](111) superlattices 101
3.1 Growth and structure of epitaxial [Co/Ni] films
3.1.1 Growth of [Co/Ni](111) superlattices
3.1.1.1 Al2O3 (1120) substrate
3.1.1.2 Growth of V(110)on Al2O3 (1120)
3.1.1.3 Growth of Au(111) on V(110)
3.1.1.4 Growth of [Co/Ni](111) superlattices on Au(111)
3.1.1.5 Conclusion on the growth of [Co/Ni](111) superlattices by molecular beam epitaxy
3.1.2 Ex-situ analysis of the sample structure
3.1.2.1 Verification of the atomic stacking by transmission electron microscopy (TEM)
3.1.2.2 Exact determination of lattice parameters
3.1.3 Conclusion on growth and structure of epitaxial [Co/Ni] films .
3.2 Magnetic properties of epitaxial [Co/Ni] superlattices
3.2.1 Part 1: Macroscopic magnetic properties
3.2.1.1 Hysteresis loops
3.2.1.2 Magnetization
3.2.1.3 Coercivity and saturation fields 3.2.1.4 Simple model explaining the perpendicular anisotropy
of [Co/Ni] superlattices
3.2.1.5 In-plane anisotropy of [Co/Ni] superlattices
3.2.2 Part 2: Microscopic magnetic properties
3.2.2.1 Details on the experiment and the treatment of XMCD data
3.2.2.2 XAS results
3.2.2.3 Determination of the magnetic moment by XMCD .
3.2.2.4 Conclusion on XMCD
3.2.3 Part 3: Dynamic magnetic properties
3.2.4 Conclusion on the magnetic properties of [Co/Ni] superlattices
3.3 Fully epitaxial spin valves based on [Co/Ni](111) superlattices
3.3.1 Growth and magnetic properties
3.3.2 Spin-resolved photoemission
3.3.2.1 Basics of spin-resolved photoemission
3.3.2.2 Experimental results for [Co/Ni] superlattices
3.3.3 Transport properties of [Co/Ni]/Au/[Co/Ni] spin valves
3.3.4 Conclusion on [Co/Ni]-based spin valve systems
3.4 Magnetization reversal of [Co/Ni] nanowires
3.4.1 Magnetization reversal in patterned [Co/Ni] layers
3.4.2 Propagation of domain walls in [Co/Ni] nanowires
3.4.3 Conclusion on the DW propagation in [Co/Ni] nanowires
3.5 Conclusions and perspectives for epitaxial [Co/Ni] superlattices
4 Conclusion
References