Dynamical measurements of the Spin Hall angle Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften (Dr.rer.nat) der Fakultät für Physik der Universität Regensburg vorgelegt von Oleksandr Talalaevskyy aus Kiew März 2017 3 Contents Introduction 5 1. Magnetization Dynamics 9 1.1 Ferromagnetism…………………………………………………………………………………… 9 1.2 Landau-Lifshitz equation….…………………………………………………………..…………. 11 1.3 Consideration of the damping mechanism. Energy dissipation mechanisms…………………….. 13 1.4 FMR in thin films……………………………………………………………………………...…. 19 1.5 Magnetic properties of YIG……………………………………………………………………..... 21 2. Magnetostatic spin waves 23 2.1 Maxwell equations………………………………………………………………………………... 23 2.2 Magnetostatic approach and Walkers equation…………………………………………………... 24 2.3 Magnetostatic volume and surface waves………………………………………………………… 24 3. Spin pumping and spin Hall effect 29 3.1 Phenomenological explanation of spin pumping………………………………………………… 29 3.2 Theory of the spin pumping……………………………………………………………………… 29 3.3 Spin Hall effect phenomena……………………………………………………………………… 33 3.4 Skew scattering contribution……………………………………………………………………... 34 3.5 Side-jump contribution………………………………………………………………………….... 36 3.6 Intrinsic contribution………………………………………………………………………......…. 37 3.7 Experimental approach to SHE measurements…………………..……………………………….. 39 4 4. Experimental setups and sample preparation 41 4.1 FMR setup with coplanar waveguide……………………………………………………..……… 41 4.2 FMR setup with cavity………………….………………………………………………………... 43 4.3 Magneto-optical Kerr effect (MOKE)……………………………………………………………. 47 4.4 Experimental setup for MOKE measurements…………………………………………………… 48 4.5 Time resolved measurements…………………………………………………………………….. 50 4.6 Sample preparation…………….…………………………………………………………………. 51 5. Experimental results 55 5.1 Sample characterization………….……………………………………………………………….. 55 5.2 Spin wave measurements…………….…………………………………………………………... 60 5.3 Spin pumping at YIG/Ti interfaces………………………………………………………………. 74 5.4 Spin Hall effect measurements in thin sputtered YIG films……………………………………… 77 5.5 Spin Hall effect measurements in pulsed current mode…………..……………………………… 81 5.6 Spin Hall effect measurements of thick LPE YIG, using a cavity method………………………. 82 Conclusions 85 Appendix 88 Acknowledgement 95 Bibliography 98 5 Introduction Spintronics is a relatively new research field emerged in last two decades. This field emphasizes on the spin degree of freedom of the electron and its interaction with electrical and magnetic fields. The historical backgrounds of the field started in year 1924, when Ellet and Wood1 studied the degree of polarization of mercury vapor fluorescence. They discovered that the degree of polarization depends strongly on the orientation of the experimental setup with respect to magnetic field of the Earth. The observed effect was the Hanle effect. The fluorescence was depolarized by the Earth´s transverse magnetic field. Later these results were explained by Hanle. This was followed by the work of Brossel and Kastler2 who created a non-equilibrium distribution of angular magnetic moments by optical excitation, manipulated it by applying a magnetic field and measured the intensity of the luminescence polarization. In 1936 Nevill Mott built his two current model, that explained the high resistivity of ferromagnetic metals. The conductivity was expressed as a superposition of two different contributions each of them corresponded to an opposite spin direction. With this, Mott showed a possibility to manipulate the transport properties with magnetism. Despite the concept was already known for a long time, the new era of this field started only recently. Significant progress in technology of nanofabrication allowed producing structures where all “spin based” effects become much easier to observe. Here we refer to the 2-D (thin films) and 1-D (nanodots) structures. The first big “jump“ in this research area was triggered by discovery of Giant magnetoresistance(GMR) in 1988. Albert Fert and Peter Grünberg found out that the electrical resistance of a trilayer (Ferromagnet\Normal metal\Ferromagnet) strongly depends on the magnetization orientation. If both layers are magnetized parallel to each other, the resistance of the trilayer is much smaller than in case when they are magnetized antiparallel. This effect found the application in computer hard drives and magnetic random access memory (MRAM). The efficiency of the magneto resistance is defined as difference between maximum and minimum resistance of the trilayer divided by the maximum resistance. Another effect- tunnel magnetoresistance (TMR) was found by Moodera3 and simultaneously by Miyazaki4 in 1995. The structure for TMR elements looks very similar to the structure of GMR. TMR requires a trilayer (Ferromagnet\Insulator\Ferromagnet). These trilayers are called magnetic tunnel junctions (MTJ) and have a magnetoresistance efficiency much higher than GMR structures. In TMR there is no direct current flow through the structure because of the insulating layer. However, there is a tunneling effect and the probability of tunneling of the electron strongly depends on 6 its spin. So if the current is injected into a first magnetic layer of the trilayer we can get almost 100 percent spin polarized current (spin current) in the second magnetic layer. Nowadays the most effective „spin polarizes“ are MTJs with MgO insulating layers. Another interesting concept is that of a “pure” spin current. One way to create a pure spin current is the Spin Hall (SHE) effect which was observed first by Kato5 and Wunderlich6 in 2004. The physics of the SHE is the following: If we pass an electrical current through a metal with large spin-orbit coupling, the electrons with opposite spins deflect in opposite directions. Thus, a transverse spin current is created. The most remarkable feature for further applications is the fact that SHE creates a spin current without a charge current (pure spin current). The carrier of the spin is an electron, but if the electrons are moving in opposite directions the resulting charge current is zero. The Onsager relations show that there should be an effect reciprocal to SHE. Indeed, the Inverse spin Hall effect (ISHE) was observed in 2006 separately by Saitoh7, Zhao8 and Valenzuela9. In the ISHE a spin current creates a transverse charge current. In order to detect both effects a ferromagnetic (FM) layer should be brought in contact with a metal where the current flows. In case of SHE the spin current flows into the FM providing an extra torque on the magnetization vector. Depending on the electrical current polarity the provided torque can either increase or decrease the amplitude of the magnetization precession which means it can vary the Gilbert damping parameter. A lot of experiments showed successful manipulation of the damping parameter10 11. In most cases platinum (Pt) was used as NM layer due to its large spin-orbit coupling. One of the materials that is used as a ferrimagnetic layer is Yttrium-iron-garnet (Y Fe O ) (YIG). YIG is one of the most widely used 3 5 12 materials for studying high frequency magnetization dynamics due to its extremely low Gilbert damping parameter, which can reach values as low as 5·10-5 for YIG spheres12. Its high Curie temperature and high chemical stability13 makes the material attractive in addition to its interesting magnetic properties. Consequently the material is used for building delay lines, RF filters, attenuators, resonators, Y-junctions and other high frequency devices. The spin wave (SW) propagation in YIG allows transporting the information without transport of the electrical current. Kajiwara et al14 demonstrated successful transport of the signal for a distance of 1 mm via the SWs and successful conversion of this signal into a voltage via spin pumping. This can be potentially interesting for the computer applications. Studying SW propagation in YIG films and in ultra-thin YIG layers has become interesting lately since high quality ultra-thin YIG films have only become available recently using standard deposition techniques such as pulsed layer deposition (PLD)15 16 17 18 19 20 or sputter deposition21 22 23. In this PhD thesis we perform a broad study of magnetic properties of thin sputtered YIG films. The first chapter is dedicated to the physical principles of ferromagnetism, magnetization dynamics and ferromagnetic resonance (FMR). From postulation of the Landau-Lifshitz equation we derive the 7 equilibrium condition for the magnetization vector, the expression for the magnetic susceptibility tensor and equations for the eigenfrequencies of a magnetic ellipsoid. A phenomenological explanation of relaxation mechanisms in a ferromagnetic body is provided. The second chapter is dedicated to SW propagation in thin magnetic films. The dispersion relation for Damon-Eschbach (DE) and other modes is derived from Maxwell´s equations. The third chapter is dedicated to the theory of SHE, ISHE, and spin pumping. The physical principles of these effects are described. We derive relations for the spin currents through the ferromagnetic/normal metal interface and describe its influence on the Gilbert damping parameter. In the fourth chapter we give a detailed description of the experimental setups and methods that were used for sample preparation and characterization. Chapter five is dedicated to the experimental results. The characterization of thin sputtered YIG films starts with structural analysis. X- ray reflectivity and atom force microscopy (AFM) measurements are performed to characterize the thickness and the surface roughness of the grown films. Thereafter, we perform the magnetic characterization of our samples. We determine the Gilbert damping, saturation magnetization and magnetic anisotropy of the YIG films. Further we study the propagation of the SWs and their mode structure in microstructured YIG stripes. The SW attenuation length is extracted from these measurements. SW attenuation length characterizes efficiency of magnetic material as a media for the SW transport. Furthermore, we investigate the spin pumping at the interface between YIG and different metals. The milestone of the experimental part is the measurement of the SHE in YIG/Platinum interfaces and calculation of the spin Hall angle. The thesis is summarized with the conclusion. 1. Magnetization Dynamics 9 1. Magnetization Dynamics 1.1 Ferromagnetism All ferromagnetic materials possess a magnetic moment even without magnetic bias field. This is called spontaneous magnetization. Spontaneous magnetization distinguishes ferromagnets from paramagnets that could be magnetized by external magnetic field. This happens when magnetic moments of the electrons are ordered in one direction. The magnetic moment of the electron consists of the electrons moment (spin) and orbital moment. According to Pauli principle all the internal electron orbitals have two electrons with opposite spin in each energy state. That means that these electrons can not contribute to ferromagnetism. Only the electrons from the internal partially filled shells can contribute to the ferromagnetism. The reason for spontaneous magnetization is the exchange energy. As we know from quantum mechanics the wave functions of two electrons depends on the relative orientation of their spins. For the electron system it can also be defined as the energy released when two or more electrons exchange their positions. If two electrons with parallel spins are placed in the same state, this state will be forbidden by the Pauli principle. One can imagine an “extra force” acting on the electrons and trying to push the electrons away from each other. The operator of the exchange energy of two particles with spins S and S can be written as follows: 1 2 ( ) ⃗ ⃗ (1.1) The value of the exchange integral ( ) decreases rapidly with the increase of distance between the two particles. We should note that the ferromagnet order can be easily destroyed by the temperature. For ferromagnets the critical temperature is called Curie temperature. For yttrium iron garnet (Yig) the Curie temperature is 560 K. Let us consider a fully magnetized ferromagnetic at the temperature below the Curie temperature. In this case instead of every single magnetic moment one can derive the magnetization ⃗⃗⃗⃗ as follows: ⃗⃗⃗⃗ ∑ ⃗⃗⃗ (1.2) Here ∑ ⃗⃗⃗ is the sum of all moments of the small volume . The magnetic induction ⃗⃗ can be expressed as follows: ⃗⃗ ( ⃗⃗⃗ ⃗⃗⃗⃗) (1.3) 1.1 Ferromagnetism 10 The magnetic induction defined in eq. (1.3) enters the Maxwell equations and is a fundamental quantity in electrodynamics. One of the most important tasks in magnetism is describing the motion of the magnetization vector ⃗⃗⃗⃗ and its equilibrium position. The equilibrium position corresponds to the direction of the magnetization vector such that the free energy of the system is minimal. For most magnetic systems it can be described as sum of 4 components: exchange, demagnetization, anisotropy and Zeeman energy. In this case the equilibrium condition is written as follows: ∫ = 0 (1.4) (1.5) where is the total free energy. We briefly discuss all the components in the eq. (1.5). The first term is the exchange energy. It consists of uniform and non-uniform parts. The non-uniform part has spatial derivatives of magnetization. ⃗⃗⃗ ⃗⃗⃗ (1.6) The values of the constants and depend on the exchange integral from eq. (1.1) The second term in eq. (1.5) is the anisotropy energy. In ferromagnets there are often directions, which are energetically preferred for the magnetization vector. The reason for this is the spin-orbit interaction. The most energetically favorable directions are called anisotropy axes. The rotation of the spins with respect to the lattice changes the shape of the electron clouds of the atom. As the consequence the exchange energy of the system also changes. Such anisotropy is also called magneto-crystalline. So if demagnetization and Zeeman energy contributions are excluded, the magnetization vector points along the anisotropy axis. Depending on the crystal system there can be one or more anisotropy axes. For the cubic lattice (iron) the anisotropy can be expressed as ( ) (1.7) where - first order anisotropy constant, α ,α ,α are the direction cosines α = ⃗⃗⃗ / M. x y z ijk ijk Another case is the uniaxial anisotropy. In many systems there is only one energetically favored axis.