As features on integrated circuits continue to shrink, currently at 22 nm and predicted to approach 10 nm by 2020, the semiconductor industry is rapidly brushing up against the fundamental limits of electric charge and current based devices. These limits are due to the fact that charges are being pushed around in tiny areas and they repel one another with significant force. Fortunately, there are many other degrees of freedom in solids that do not suffer from these limitations and are just waiting to be harnessed in useful devices. This idea is behind all of the fields that have lately been proliferating ending in -onics, photonics, plasmonics, phononics, and of most relevance to this dissertation spintronics. Spintronics refers to a field of research wherein ways are sought to utilize the spin property of the electron in devices. One of the most attractive aspects of electron spin is that it can be used to store (transiently or permanently), process, and transmit information. The main challenge in spintronics is accessing the spin degree of freedom. Until the discovery of the giant magnetoresistance effect in the late 1980's, the only way to manipulate the electron spin was through a magnetic field. Recent developments have shown that electron spins can be controlled with direct currents of both heat and electrons, which have the benefit of being easy to generate and direct without interfering over a large area. The purpose of this dissertation is to study methods of controlling the dynamics of magnetization in thin films for spintronic applications by imaging the spin wave intensity in devices. To this end we have constructed a micro-focus Brillouin Light Scattering system to map the intensity of spin waves propagating in thin ferromagnetic films on the sub-micron scale. We have studied issues relating to fundamental issues of spin wave propagation in thin films. We have investigated the possibility of spin wave amplification with direct charge currents and spin currents generated by the spin Hall effect. Furthermore, we have demonstrated the ability to measure the magnon and phonon temperatures, which is important for studies of thermal transport. / text

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This thesis describes a diversity of scattering experiments on a number of different systems. Using time-of-flight neutron scattering, a study of polycrystalline sodium in the highmomentum limit known as the impulse approximation has been performed. The purpose of this study was to look for anharmonic effects in the neutron recoil scattering of sodium as the temperature was increased from 30K to 300K. No such effects were detected and the results agreed with an isotropic harmonic solid to an accuracy of about 4%. Two experiments were carried out on antiferromagnetic systems using triple-axis neutron scattering techniques to measure the spin-wave dispersion relations. The first was on CuO to verify its description as a spin 1/2 one-dimensional antiferromagnet. The dispersion relation was measured along the chain direction up to an energy transfer of 8OmeV. This was done above and below the Néel temperature (T_N =240K). However, no evidence was seen to justify the description of CuO as a one-dimensional antiferromagnet, with the spin waves behaving like those in a classical three-dimensional system. The other spin-wave study examined the two-dimensional antiferromagnet KFeF₄ . The measurement of the spin-wave dispersion relation at two temperatures (50K and 100K) below the Néel temperature (T_N =136.75±0.25K), confirmed the description of KFeF₄ as a two-dimensional Heisenberg antiferromagnet with small Ising anisotropy. Studies of the magnetic phase transition in KFeF₄ revealed that below the Néel temperature, the critical behaviour is described by two-dimensional Ising models, and above a crossover to Heisenberg behaviour is seen. This crossover was detected by measuring the order parameter below T_N, and the static and dynamic susceptibilities above T_N using neutron scattering techniques. The results were compared to power-law behaviour and also to theories for the classical Heisenberg antiferromagnet and the more recent quantum Heisenberg antiferromagnetic model. The final study of KFeF₄ involved an x-ray experiment on the structural phase transition around 400K. It has been suggested that there is a second-order transition at 410K to an incommensurate phase, which then undergoes a first-order lock-in transition at 400K to the low-temperature structure. This single crystal x-ray scattering study confirms the existence of the first-order phase transition, but shows no evidence for a higher temperature second-order transition or for the incommensurate phase.

Abstract Helium is the second most abundant element in the Universe. It is the only known substance that can exist in liquid state at absolute zero. There are two stable isotopes of helium, fermionic ³He and bosonic ⁴He. At sufficiently low temperatures, both isotopes undergo a phase transition into a superfluid state. These superfluids are usually characterised by their ability to flow without resistance, but this is by no means their only remarkable property. In this thesis, we study theoretically superfluid ³He. The work consists of two separate projects. First, we study the effect of a quantised vortex line to spin dynamics of the superfluid. We find that the interplay between the vortex and the magnetisation of the liquid generates spin waves, dissipating energy. We find that the theoretically predicted energy dissipation is in agreement with experimental data, implying that spin-wave radiation can be an important mechanism of magnetic relaxation in superfluid ³He. Second, we study the drag force acting on an object moving through zero-temperature superfluid at a constant velocity. The drag arises if momentum is transferred from the object to the fluid. At low velocities, no such mechanism exist and thus the drag vanishes. If the velocity exceeds the Landau velocity \(v_L\), it becomes possible for the object to create quasiparticle excitations that could, in principle, transfer momentum away from the object. Thus, \(v_L\) has been generally assumed to be the critical velocity, that is, the velocity above which the drag force starts to increase rapidly towards the normal-state value. We find that this is not necessarily the case. Objects much larger than the superfluid coherence length modify the superfluid flow field around them. The spatial variation of the flow field can shield the object, preventing quasiparticles from transferring momentum away from the object. This leads to a critical velocity greater than \(v_L\). / Original papers The original publications are not included in the electronic version of the dissertation. Laine, S. M., & Thuneberg, E. V. (2016). Calculation of Leggett–Takagi Relaxation in Vortices of Superfluid ³He-B. Journal of Low Temperature Physics, 183(3–4), 222–229. https://doi.org/10.1007/s10909-016-1516-x Kuorelahti, J. A., Laine, S. M., & Thuneberg, E. V. (2018). Models for supercritical motion in a superfluid Fermi liquid. Physical Review B, 98(14). https://doi.org/10.1103/physrevb.98.144512 http://jultika.oulu.fi/Record/nbnfi-fe2018112148794 Laine, S. M., & Thuneberg, E. V. (2018). Spin-wave radiation from vortices in ³He−B. Physical Review B, 98(17). https://doi.org/10.1103/PhysRevB.98.174516 http://jultika.oulu.fi/Record/nbnfi-fe2019092630083

No description available.

<p> A theory of spin waves for the spin structures found in the rare earth metals of hcp crystal structure is described. The theory is developed for the conical spiral spin structure which contains the planar spiral, the nonplanar ferromagnet and the planar ferromagnet as special cases. Included in the Hamiltonian are isotropic and anisotropic exchange interactions, single-ion crystal field terms, and magnetoelastic terms, both of the single-ion type and the two-ion type. Equations of motion for the spin operators are linearized with the help of the random phase approximation which makes it possible to express some spin-wave interaction effects in terms of powers of the reduced magnetization. Expressions for the spin-wave energies are given for the four structures under consideration.</p> / Thesis / Master of Science (MSc)

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This dissertation presents our theoretical study of fundamental topological properties of ferromagnetic and antiferromagnetic systems, including topological magnetic excitations and topological magnetic textures. In the first part, we explored the topological magnonic phases in various systems with Dzyaloshinskii-Moriya interaction using a linear spin-wave theory. We have calculated the magnonic Chern number, topological phase diagram, and magnon thermal Hall conductivity at low temperature with tunable interactions due to the lattice deformation. In particular, we have investigated the topological phase transitions between distinct topological magnonic phases characterized by magnonic Chern numbers. We have also studied the magnon band topology and magnonic edge states in each topological phase. We found a sign reversal of the thermal Hall conductivity during topological phase transitions. We explicitly demonstrated the correspondence of thermal Hall conductivity with the topological edge states and their propagation directions. In the second part, a magnonic metamaterial in the presence of spatially modulated Dzyaloshinskii-Moriya interaction was theoretically proposed and demonstrated by micromagnetic simulations. By analogy to the fields of photonics, we first established magnonic Snell’s law for spin waves passing through an interface between two media with different dispersion relations due to different Dzyaloshinskii-Moriya interactions. Based on magnonic Snell’s law, we found that spin waves can experience total internal reflection. The critical angle of total internal reflection was strongly dependent on the sign and strength of Dzyaloshinskii-Moriya interaction. Furthermore, spin-wave beam fiber and spin-wave lens were designed by utilizing the artificial magnonic metamaterials with inhomogeneous Dzyaloshinskii-Moriya interactions. In the last part, we studied the impact of spin Hall torque, spin transfer torque, and topological torque on the velocity-current relation of antiferromagnetic skyrmions with the aim of reducing the deformation. Using a combination of micromagnetic simulations and analytical derivations, we demonstrated that the lateral expansion of the antiferromagnetic skyrmion is reminiscent of the well-known Lorentz contraction identified in one-dimensional antiferromagnetic domain walls. We also showed that in the flow regime the lateral expansion is accompanied by a progressive saturation of the skyrmion velocity when driven by spin Hall and topological torques. This saturation occurs at much smaller velocities when driven by the topological torque, while the lateral expansion is reduced, preventing the skyrmion size from diverging at large current densities. Our findings suggested that a compromise must be made between skyrmion velocity and lateral expansion during the device design. In this respect, exploiting the topological torque could lead to better control of the skyrmion velocity in antiferromagnetic racetracks.

In this thesis results of x-ray scattering and neutron scattering experiments on several strongly correlated transition metal oxides are presented. The prototypical charge ordered cuprate La1.48Nd0.4Sr0.12CuO4 was investigated using polarised neutron scattering. The results show that several proposed schemes for the magnetic order in this class of materials may be ruled out, however the data are consistent with one-dimensional stripe-like magnetic order. X-ray diffraction was used to show that the charge order is insensitive to an applied magnetic field, but might be affected by the existence of superconductivity. The magnetic excitations were also studied, and at low energies a gap in the magnetic fluctuations was observed and there is tentative evidence that this is related to magnetic anisotropy. The spin state transition in LaCoO3 was investigated using neutron inelastic scattering, and excitations reminiscent of those observed in ferromagnets above their critical temperatures were observed. The debate surrounding the nature of the excited spin state, S=1 or S=2, could not be resolved, however. The nature of the spin excitations in La0.82Sr0.18CoO3 was investigated using polarised neutrons and it was found that at low energies the excitations take the form of spin-waves. At higher energies this mode becomes heavily damped, and several possible damping mechanisms for this are discussed. Finally, the multiferroic material DyMn2O5 was studied using x-ray resonant scattering. A complex, temperature dependent, magnetic structure was found using a Dy resonance, which reflects an underlying order of the Mn ions. The measurements were in agreement with a theory of multiferroics based on acentric spin-density waves.

This thesis contains results of numerical investigations of magnetisation dynamics in nanostructed ferromagnetic materials. Magnetic systems have been simulated using the open source micromagnetic solver: Object Oriented Micromagnetic Framework (OOMMF), and thoroughly analysed using my own software: semargl. A systematic study of collective magnonic modes confined in 2D and 3D systems of rectangular ferromagnetic nano-elements is presented. The collective character of the excitations results from the dynamic magnetic dipole field. The magnetization dynamics of isolated rectangular elements is found to be spatially non-uniform which means that the dynamic dipolar coupling is highly anisotropic. A semi-analytical theory of collective magnonic modes has been developed to evaluate the properties of the dynamic magnetic dipole field. It was found that the theory is only valid for certain eigenmodes of the isolated element. In particular the modes where the magnetic dipole coupling between the elements is much lower than the internal energy of the corresponding eigenmodes of the isolated element. It is then demonstrated that the confinement of spin waves is strongly affected by the ground state of the system. In particular it has been found that symmetry properties of the topology of 2D arrays affect the dynamics of the strongly localised modes. The effect is found to be significant for arrays of any number of elements. At the same time the relative contribution of the localized modes to the uniform response decreases with the number of elements in the array. The dispersion relation of spin waves in 2D arrays of rectangular nano-elements has been calculated for the first time using micromagnetic simulations. The form of the dispersion is used to estimate the spatial anisotropy of the dynamic dipolar coupling. Simulations of the 3D confinement of spin waves in stacks of magnetic nano-elements have been performed. The calculation of both the dispersion and spatial profiles of the corresponding magnonic modes facilitates the investigation of the localisation of collective spin waves. Furthermore the dispersion of collective magnonic modes has been calculated for stacks of rectangular nano-elements for a range of in-plane aspect ratios. Finally, a numerical method has been developed to extract the scattering parameters of magnonic logic devices. This method has been demonstrated by applying it to the simplest possible magnonic device so that the results could be compared to an analytical expression of the scattering parameters.