Part I Magnonic Modes in Nanomagnets, Chaotic and Coherent Magnonic States 1 Spin-Wave Eigen-Modes in a Normally Magnetized Nano-Pillar

Contents

Part I Magnonic Modes in Nanomagnets, Chaotic and Coherent Magnonic States 1 Spin-Wave Eigen-modes in a Normally Magnetized Nano-pillar ... 3 V.V. Naletov, G. de Loubens, S. Borlenghi, and O. Klein 1.1 Introduction ...... 3 1.2 Identiﬁcation of the Spin-Wave Modes ...... 5 1.2.1 Single Magnetic Disk ...... 6 1.2.2 Double Magnetic Disks ...... 7 1.2.3 Micromagnetic Simulations vs. Mechanical-FMR Experiments ...... 9 1.3 Conclusion ...... 14 References ...... 14 2 Bottom up Magnonics: Magnetization Dynamics of Individual Nanomagnets ...... 17 P.S. Keatley, P. Gangmei, M. Dvornik, R.J. Hicken, J. Grollier, C. Ulysse, J.R. Childress, and J.A. Katine 2.1 Introduction ...... 17 2.2 Experimental Methods and Sample Details ...... 18 2.3ResultsandDiscussion...... 20 2.4Summary...... 27 References ...... 27 3 Features of Chaotic Spin Waves in Magnetic Film Feedback Rings .29 Aaron M. Hagerstrom and Mingzhong Wu 3.1 Introduction ...... 29 3.2 Experiments ...... 30 3.3 Frequency- and Time-Domain Signals ...... 32 3.4 Ambiguity Functions ...... 32 3.5 Tuning of Ambiguity Function Properties via Ring Gain ...... 33 3.6 Effects of Signal Duration on Ambiguity Function ...... 35

xi xii Contents

3.7 Cross Ambiguity Function ...... 35 3.8 Conclusion ...... 37 References ...... 38

4 Magnon Coherent States and Condensates ...... 39 Sergio M. Rezende 4.1 Introduction ...... 39 4.2 Coherent Magnon States ...... 41 4.3 Linear Excitation of Magnons by a Microwave Field ...... 43 4.4 Microwave Excitation of Parametric Magnons in Thin Films .... 44 4.5 BoseÐEinstein Condensation of a Microwave Driven Interacting Magnon Gas ...... 46 4.5.1 Dynamics of the Microwave Driven Magnon Gas in k Space 46 4.5.2 Coherence of the Magnon Condensate ...... 49 4.5.3 Wavefunction of the Magnon Condensate ...... 51 4.6Summary...... 53 References ...... 54

Part II Probing and Manipulation of Magnons with Femtosecond Light and Polarized Electrons: Experiment and Simulations

5 The Role of Angular Momentum in Ultrafast Magnetization Dynamics ...... 59 Andrei Kirilyuk, Alexey V. Kimel, and Theo Rasing 5.1 Introduction ...... 59 5.2 Precession in Ferrimagnetic Materials ...... 60 5.3 Laser-Induced Magnetization Reversal ...... 63 5.4 Transient Ferromagnetic State ...... 64 5.5 Conclusions ...... 68 References ...... 69

6 Photo-Magnonics ...... 71 Benjamin Lenk, Fabian Garbs, Henning Ulrichs, Nils Abeling, and Markus Münzenberg 6.1 Introduction ...... 71 6.1.1 Spin-Wave Modes in a Thin Ferromagnetic Film ...... 72 6.2 Samples and Experiments ...... 73 6.2.1 Thin-Film Magnetization Dynamics ...... 73 6.3 Bloch-Like Modes in CoFeB Antidot Lattices ...... 74 6.3.1 Effects of Antidot-Lattice Symmetry ...... 76 6.4 Spin-Wave Spectra from Plane-Wave Calculations ...... 77 6.5 Localized Modes in Nickel Antidot Lattices ...... 78 6.6 Outlook: Magnonic Control over Spin Waves ...... 79 References ...... 80 Contents xiii

7 Probing Magnons by Spin-Polarized Electrons ...... 83 K. Zakeri and J. Kirschner 7.1 Introduction ...... 83 7.2 Basic Concepts ...... 84 7.2.1SpinWaves...... 85 7.2.2 Stoner Excitations ...... 86 7.2.3 Heisenberg Description of Magnons ...... 88 7.2.4 Spin Dependence of Electron Scattering ...... 89 7.3 Spin-Polarized Electron Energy Loss Spectroscopy ...... 92 7.4 Recent Experimental Achievements ...... 94 7.4.1 Magnon Excitations in Ferromagnetic Thin Films ..... 94 7.4.2 Distinguishing Between Magnons and Phonons ...... 95 7.5 Conclusion ...... 97 References ...... 97 8 Micromagnetic Simulations in Magnonics ...... 101 M. Dvornik, Y. Au, and V.V. Kruglyak 8.1 Introduction ...... 101 8.2 Real-SpaceÐTime Domain Analysis: Magnonic Devices ...... 102 8.3 Real-SpaceÐFrequency Domain Analysis: Magnonic Normal Modes ...... 105 8.4 Reciprocal-SpaceÐFrequency Domain: Magnonic Dispersion and ScatteringParameters...... 108 8.5Semargl...... 112 8.6 Conclusions and Outlook ...... 113 References ...... 114

Part III Magnon Spintronics: Spin Currents, Spin Pumping and Magnonic Spin-Torque Devices 9 Spin Waves, Spin Currents and Spin Seebeck Effect ...... 119 Hiroto Adachi and Sadamichi Maekawa 9.1 Introduction ...... 119 9.2 Local Picture of Thermal Spin Injection ...... 120 9.3 Magnon-Driven Spin Seebeck Effect ...... 123 9.4 Phonon-Drag Spin Seebeck Effect ...... 125 9.5 Conclusion ...... 127 References ...... 127 10 Spin Pumping at Ytrium Iron Garnet Interfaces ...... 129 Capucine Burrowes and Bretislav Heinrich 10.1 Introduction ...... 129 10.2 Theory of Spin Pumping ...... 130 10.2.1SpinTransportbySpinDiffusioninaNM...... 132 10.2.2 Spin Transport in the Presence of Paramagnons ...... 134 10.3 Experimental Results and Discussion ...... 134 10.3.1FMR...... 134 xiv Contents

10.3.2YIG/Au...... 135 10.3.3YIG/Pd...... 139 References ...... 140 11 Spin-Torque Microwave Detectors ...... 143 Oleksandr V. Prokopenko, Ilya N. Krivorotov, Thomas J. Meitzler, Elena Bankowski, Vasil S. Tiberkevich, and Andrei N. Slavin 11.1 Introduction ...... 144 11.2BasicPhysicsofSTTandTMR...... 145 11.3 Small-Angle In-Plane Dynamical Regime of STMD Operation . . 146 11.3.1 Analytical Theory of Noise Properties of a STMD in IP-Regime...... 147 11.3.2 The Performance of a STMD in the Presence of Thermal Noise...... 153 11.4 Large-Angle Out-of-Plane Dynamical Regime of STMD Operation 155 11.4.1AnalyticalDescriptionofOOP-Regime...... 155 11.4.2 Performance of a STMD in OOP-Regime ...... 158 11.5Summary...... 160 References ...... 161 12 Spin-Wave Emission from Spin-Torque Nano-Oscillators and Its Control by Microwave Pumping ...... 163 Vladislav E. Demidov, Sergei Urazhdin, and Sergej O. Demokritov 12.1 Introduction ...... 163 12.2StudiedSamplesandTheirElectronicCharacterization...... 164 12.3 BLS Characterization of the Emitted Spin Waves ...... 166 12.4 Relationship Between the Emission Characteristics and the Spin-Wave Spectrum ...... 168 12.5 Nonlinear Frequency Conversion in STNO ...... 170 12.6 Effect of the Microwave Pumping on the Spin-Wave Emission Characteristics...... 172 12.7Summary...... 173 References ...... 174 13 Nano-Contact Spin-Torque Oscillators as Magnonic Building Blocks 177 Stefano Bonetti and Johan Åkerman 13.1 Introduction ...... 177 13.1.1 Magnonics and Magnonic Devices ...... 177 13.1.2Spin-TransferTorque...... 178 13.1.3 Scope ...... 178 13.2 Fabrication of Nano-Contact STOs ...... 179 13.3 Spin Wave Dynamics in Nano-Contact STOs ...... 180 13.3.1 Fundamentals ...... 180 13.3.2 Propagating Waves as Magnonic Signals ...... 181 13.4 Nano-Contact-Based Magnonic Building Blocks ...... 183 13.4.1SpinWaveInjectors...... 183 Contents xv

13.4.2SpinWaveManipulators...... 184 13.4.3SpinWaveDetectors...... 184 13.5 Conclusions ...... 185 References ...... 185

Part IV Static and Dynamic Magnonic Crystals 14 Spin Waves in Artiﬁcial Crystals and Metamaterials Created from Nanopatterned Ni80Fe20 Antidot Lattices ...... 191 Sebastian Neusser, Georg Duerr, Rupert Huber, and Dirk Grundler 14.1 Introduction ...... 191 14.2 Nanofabrication and All-Electrical Spin-Wave Spectroscopy ....192 14.3 Antidot Lattices in the Short Wavelength Limit: Bandgap Materials 193 14.3.1 Large-Period Antidot Lattice: Forbidden Frequency Gaps due to Bragg Reﬂection ...... 193 14.3.2 Short-Period Antidot Lattice: Miniband Formation due to Coherent Coupling of Edge Modes ...... 196 14.4 Antidot Lattice in the Long Wavelength Limit: Effective-Media Concept ...... 198 14.4.1 Effective Magnetization of a Nanopatterned Antidot Lattice 198 14.4.2 Transmission of Spin Waves Across the Boundary of an Antidot Lattice ...... 199 14.5 Conclusions ...... 201 References ...... 201 15 Spin Wave Band Structure in Two-Dimensional Magnonic Crystals . 205 G. Gubbiotti, S. Tacchi, M. Madami, G. Carlotti, R. Zivieri, F. Montoncello, F. Nizzoli, and L. Giovannini 15.1 Introduction ...... 206 15.2 Sample Details and Experiment ...... 207 15.3 Theoretical Description: Dynamical Matrix Method Applied to 2DMCs...... 208 15.4ResultsandDiscussion...... 210 15.4.1 Sample #1: Bidimensional Array of Disks ...... 210 15.4.2 Sample #2: Bidimensional Array of Circular Holes .....213 15.5Summary...... 219 References ...... 219 16 Normal Mode Theory for Magnonic Crystal Waveguide ...... 223 N.Y. Grigoryeva and B.A. Kalinikos 16.1 Introduction ...... 223 16.2 LandauÐLifshitz Equation of Motion for Space Harmonics in Magnonic Crystal Waveguide ...... 227 16.3 General Dispersion Relation for DipoleÐExchange Spin Waves in Magnonic Crystal Waveguide ...... 232 16.4 Example of Theory Application ...... 237 16.5 Conclusion ...... 239 References ...... 239 xvi Contents

17 The Dynamic Magnonic Crystal: New Horizons in Artiﬁcial Crystal Based Signal Processing ...... 243 Andrii V. Chumak, Alexy D. Karenowska, Alexander A. Serga, and Burkard Hillebrands 17.1 Introduction ...... 243 17.2 The State-of-the-Art in Magnonic Crystal Science ...... 244 17.3 The Design of Dynamic Magnonic Crystals ...... 245 17.4 The Engineering of Dynamic Magnonic Crystal Characteristics . . 247 17.5 A Signal See-Saw: Oscillatory Inter-modal Energy Exchange in the Dynamic Magnonic Crystal ...... 249 17.6 Frequency Conversion and Time Reversal in the Dynamic Magnonic Crystal ...... 252 17.7 Concluding Comments ...... 255 References ...... 255 Index ...... 259