This work presents a detailed investigation of magnetization dynamics in synthetic antiferromagnets (SAFs), which has been studied both experimentally, using electrically-detected ferromagnetic resonance (ED-FMR) and vector-network analyzer-based ferromagnetic resonance (VNA-FMR), and theoretically. Two modes, one with in-phase and one with 180° out-of-phase precessing magnetizations of the layers, are identified in all applied field regimes, namely, a low-field antiferromagnetically coupled regime (when magnetizations of the layers have opposite directions), a spin-flop regime at intermediate field values (when magnetizations are non-collinear) and a high-field saturation regime (when both magnetazations are collinear to each other and the external magnetic field direction). The qualitative theoretical description, found to be in good agreement with the experimental data, is given using a system of coupled Landau-Lifshitz equations. In this work, for the first time to our knowledge, it is shown that for SAFs with different magnetic moments of the individual layers, dynamic, and not static, Zeeman and interlayer exchange coupling energies are solely resposible for the frequency-field dependence in the antiferromagnetically coupled regime. The changes in the dynamical energy terms lead to the changes in the dynamical components of the precessing magnetizations. As the external magnetic field is varied, the amplitude of the components vary continiously in different ways for different modes, dropping to zero in the spin-flop regime, which is reflected in the amplitudes of ED-FMR and VNA-FMR. This effect appears only in SAFs with different magnetic moments of the layers and is related to the different increase in the Zeeman energy of the layers as the externally applied field increases.
The variation of the dynamical components leads to the modulation of an exchange of spin-angular momentum between the layers (so called spin-pumping effect).This is directly reflected in the measured linewidths for the modes in both ED-FMR and VNA-FMR. As was shown before in the literature and is also confirmed here, spin-pumping leads to a constant difference in linewidths between two modes for SAFs in the saturated case. Here, we extend the previous findings to non-saturated regimes. We show that in non-saturated states, the linewidth difference does not remain constant and varries with the external magnetic field. This linewidth difference changes can be qualitatively explained using the modulation of the dynamical magnetization components. In order to directly model the spin-pumping effects, additional terms are introduced in the coupled Landau-Lifshitz equations, related to the intrinsic damping in the magnetic layers and spin-pumping induced effects. The calculations of linewidth dependences using the extended model are not in full agreement with the experiments, suggesting that additional effects must be added to the model (for example, potential domain formations).
Additionly, due to the dependence of the effect on the Zeeman energy asymmetry between the layers of the SAF, SAFs with different ratio of thicknesses are studied. Although the trends described above are common to all the samples, no significant enhancement of spin-pumping effects are observed. Modeling shows that, although the evolution of the dynamical magnetization components does depend on the magnetic moment ratio between the layers, the difference between maximum and minimum values remains almost constant and does not alter the observed linewidth-field dependence.:1 Fundamentals 1
1.1 Magnetic moment 1
1.2 Magnetic energy contributions 6
1.2.1 Zeeman energy 6
1.2.2 Demagnetization energy 7
1.2.3 Magnetic anisotropy 9
1.2.4 Direct Exchange Energy 13
1.2.5 Indirect Exchange. Interlayer Exchange Coupling Energy 15
1.3 Magnetoresistance 17
1.3.1 Ordinary Magnetoresistance 17
1.3.2 Anisotropic Magnetoresistance 20
1.3.3 Giant Magnetoresistance 22
1.4 Magnetization dynamics 25
1.4.1 Classical motivation 25
1.4.2 Quantum mechanical justification 27
1.5 Spin-currents and Spin-pumping 29
2 Experimental methods 33
2.1 Vibrating Sample Magnetometry 33
2.2 Ferromagnetic resonance 34
2.2.1 Cavity-FMR 35
2.2.2 VNA-FMR 36
2.3 Electrically detected ferromagnetic resonance 39
3 Synthetic antiferromagnets. Theoretical model 47
3.1 Static model 47
3.2 Dynamical model 54
4 Sample fabrication and characterization 58
4.1 Fabrication 58
4.2 Static characterization 62
5 Magnetization dynamics in asymmetric SAFs 68
5.1 Dynamical measurements on Py(3nm)/ Ru(0.85 nm)/Py(9 nm) 68
5.2 Theoretical explanation 71
5.3 Dynamics in SAFs with varying asymmetry of the layers 80
6 High-frequency spin-pumping in SAFs 86
6.1 Spin-pumping in magnetic trilayers 86
6.2 Spin-pumping in SAFs 88
6.3 Dependence on the asymmetry between the layers 94
7 Conclusions and outlook 99
A General description of the trilayer system without damping and spin-pumping contributions 102
A.1 Effective fields 103
A.2 Final equations 107
B Mathematica program used for the theoretical modeling 108
B.1 Matrix Elements 108
B.2 Frequency-Modes 109
B.3 Dynamical components and corresponding dynamical energies 112
B.4 Equilibrium condition 114
B.5 Dynamical Energies 118
B.6 Dynamical Trajectories 121
Bibliography 125
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:76055 |
| Date | 23 September 2021 |
| Creators | Sorokin, Serhii |
| Contributors | Faßbender, Jürgen, Arias, Rodrigo, Technische Universität Dresden, Helmholtz-Zentrum Dresden-Rossendorf |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/acceptedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | info:eu-repo/grantAgreement/European Commission/Horizon 2020/737038//Terahertz RAdio communication using high ANistropy SPIn torque REsonators/TRANSPIRE |
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