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Curved magnets attract considerable interest for their unusually rich phase diagram, often encompassing exotic (e.g., topological or chiral) spin states. Micromagnetic simulations are playing a central role in the theoretical understanding of such phenomena; their predictive power, however, rests on the availability of reliable model parameters to describe a given material or nanostructure. Here we demonstrate how noncollinear-spin polarized density-functional theory can be used to determine the flexomagnetic coupling coefficients in real systems. By focusing on monolayer CrI_{3}, we find a crossover as a function of curvature between a magnetization normal to the surface to a cycloidal state, which we rationalize in terms of effective anisotropy and Dzyaloshinskii-Moriya contributions to the magnetic energy. Our results reveal an unexpectedly large impact of spin-orbit interactions on the curvature-induced anisotropy, which we discuss in the context of existing phenomenological models., We acknowledge financial support from the Swedish Research Council (VR—2018-06807). M. S. acknowledges the support of Ministerio de Ciencia e Innovación (MICINN-Spain) through Grant No. PID2019–108573GBC22, and Severo Ochoa FUNFUTURE center of excellence (CEX2019-000917-S); of Generalitat de Catalunya (Grant No. 2017 SGR1506); and of the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 724529). P. B. and S. P. acknowledge financial support from Italian MIUR under the PRIN project “Tuning and Understanding Quantum Phases in 2D Materials— Quantum2D,” Grant No. 2017Z8TS5B and “TWEET: Towards Ferroelectricity in Two Dimensions,” Grant No. 2017YCTB59, respectively. D. A. and S. P. acknowledge financial support by the Nanoscience Foundries and Fine Analysis (NFFA-MIUR Italy) project. The authors thankfully acknowledge the computer resources at Pirineus and the technical support provided by CSUC (RES-FI- 2021-1-0034). Additionally, computational work was done on resources at PDC, Stockholm, via the Swedish National Infrastructure for Computing (SNIC)., With funding from the Spanish government through the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2019-000917-S).

In absence of external fields, vibrational modes of periodic systems are usually considered as linearly polarized and, as such, they do not carry angular momentum. Our work proves that non-adiabatic effects due to the electron-phonon coupling are time-reversal symmetry breaking interactions for the vibrational field in systems with non-collinear magnetism and large spin-orbit coupling. Since in these systems the deformation potential matrix elements are necessarily complex, a nonzero synthetic gauge field (Berry curvature) arises in the dynamic equations of the ionic motion. As a result, phonon modes are elliptically polarized in the non-adiabatic framework and intrinsic vibrational angular momenta occur even for non-degenerate modes and without external probes. These results are validated by performing fully relativistic ab-initio calculations on two insulating platinum clusters and a metallic manganese compound, with non-collinear magnetism. In both cases, non-adiabatic vibrational modes carry sizeable angular momenta comparable to the orbital electronic ones in itinerant ferromagnets.

Due to their magnetic and physical properties, rare earth magnetic borides have been applied to a variety of critical technologies. In particular, rare earth tetraborides are more abundant as frustrated antiferromagnets. Here, the atomic structures, magnetic structures, and electronic structures of NdB4 have been studied by first-principle calculations. The ground state magnetic structure of NdB4 is determined. Moreover, the small energy difference between different magnetic structures means that there may be more than one magnetic structure that coexist. One can glean from the electronic structure of the magnetic ground state that the d orbital of Nd is strongly hybridized with the p orbital of B, and the f electron of Nd is highly localized. The computational results reveal the complexity of the magnetic structure and provide a theoretical basis for studying the magnetic ground state of NdB4.

Magnetic materials offer an opportunity to overcome the scalability and energy consumption limits affecting the semiconductor industry. New computational device architectures, such as low-power solid state magnetic logic and memory-in-logic devices, have been proposed which rely on the unique properties of magnetic materials. Magnetic skyrmions, topologically protected quasi-particles, are at the core of many of the newly proposed spintronic devices. Many different materials systems have been shown hosting ferromagnetic skyrmions at room temperature. However, a magnetic field is a key ingredient to stabilize skyrmions, and this is not desirable for applications, due to the poor scalability of active components generating magnetic fields. Here we report the observation of ferromagnetic skyrmions at room temperature and zero magnetic field, stabilized through interlayer exchange coupling (IEC) between a reference magnet and a free magnet. Most importantly, by tuning the strength of the IEC, we are able to tune the skyrmion size and areal density. Our findings are relevant to the development of skyrmion-based spintronic devices suitable for general-use applications which go beyond modern nanoelectronics.

In this thesis, complex spin structures driven by frustration of magnetic interactions are studied in ultrathin Co and Mn films. Therefore, density functional theory (DFT) calculations using the full potential linearized augmented planewave method are mapped onto an atomistic spin model. On this basis, spindynamics simulations are performed to analyse the properties of non-collinear spin structures such as domain walls (DWs), skyrmions and antiskyrmions. The obtained results are compared to spin-polarized scanning tunnelling microscopy (SP-STM) measurements performed by experimental collaborators. For the prominent Pt/Co/Ir interface, additive effects have been proposed in magnetic multilayer systems to enhance the Dzyaloshinskii-Moriya interaction (DMI); however, here it is shown that this phenomenon does not occur in atomic Pt/Co bilayers (BLs) on Ir(111). Even though an enhancement of the DMI from Co/Ir(111) to Pt/Co/Ir(111) is observed, the interfacial DMI appears more complex and a frustration of DMI is predicted – an effect which has been neglected so far. It results in a dependence of the rotational sense on the period of spin spirals and demonstrates that DMI calculations can give wrong results when unsuitable non-collinear spin structures are considered. Furthermore, the exchange interaction of Co/Ir(111) is tuned with 4d top layers from weakly to strongly ferromagnetic. Replacing Ir(111) by its 4d equivalent Rh(111), the spin-orbit coupling dependent interactions can be controlled. Exceptionally large frustration is found for Rh/Co/Ir(111). This stabilizes atomic-scale non-collinear spin structures such as DWs and skyrmions without an external magnetic field. SP-STM measurements confirm this prediction and reveal a large non-collinear magnetoresistance at the Fermi energy. This effect is explained by a spin mixing of a majority dxz and a minority pz state in the Rh/Co BL and allows for the detection of skyrmions and DWs with non-magnetic tips. Antiferromagnetic (AFM) materials are promising for spintronic applications and the prototypical AFM Mn holds a wide spectrum of magnetic and structural properties. Although a seemingly simple c(2 × 2) AFM ground state in a Mn double layer on W(001) has been suggested by SP-STM measurements, the presented DFT calculations highlight a dead magnetic layer in the Mn subsurface driven by strong frustration effects. This is confirmed by excellent agreement of theory and experiment. In Mn/Re(0001), experimental collaborators have discovered the row-wise antiferromagnetic (RW-AFM) and the 3Q state in STM measurements. Calculations point out strong frustration of exchange and DMI, but also of higher order exchange interactions due to hybridization of Mn and Re(0001). The coupling of the RW-AFM state to the lattice in Mn-fcc is explained by the interplay of dipolar and pseudo-dipolar interactions, whereas a distortion of the 3Q state in Mn-hcp towards the RW-AFM is predicted by DFT.

The large-scale Density Functional Theory (DFT) code KKRnano allows one to perform ab initio simulations for thousands of atoms. In this thesis an extension of KKRnano is presented and utilized which facilitates the investigation of exotic non-collinear magnetic textures in bulk materials on huge length scales. Such an undertaking inevitably involves the utilization of High Performance Computing (HPC), which is itself a scientific field. The work in this context includes the adaptation of new coding paradigms and the optimization of codes on constantly changing hardware architectures. In KKRnano, the runtime of a simulation scales linearly with the number of atoms due to an advanced Korringa-Kohn-Rostoker (KKR) scheme that is applied, in which the sparsity of the matrices in the multiple-scattering equations is exploited. This enables us to investigate phenomena that occur on a length scale of nanometers involving thousands of atoms. The main purpose of this thesis was to generalize the KKR formalism in KKRnano in such a way that a non-collinear alignment of the atomic spins can be treated. In addition to this, the relativistic coupling of spin and orbital degrees of freedom, which arises from the Dirac equation, was introduced to the code. This coupling gives rise to the Dzyaloshinskii-Moriya interaction (DMI) from which the formation of non-collinear magnetic textures usually originates. Other methodological features that were added to KKRnano or were re-established in the context of this thesis are the Generalized Gradient Approximation (GGA), Lloyd’s formula and a semi-core energy contour integration. GGA is known to be a better approximation to the exchange-correlation energy in DFT than the still very popular Local Density Approximation (LDA), Lloyd’s formula allows to determine the charge density exactly, despite the angular momentum expansion of all quantities, and the semi-core energy contour integration facilitates the treatment of high-lying electronic core states. Furthermore, an experimental port of the multiple-scattering solver routine to Graphics Processing Unit (GPU) architectures is discussed and the large-scale capabilities of KKRnano are demonstrated by benchmark calculations on the supercomputer JUQUEEN that include more than 200.000 atoms. The new version of KKRnano is used to investigate the magnetic B20 compounds B20-MnGe and B20-FeGe as well as alloys of B20-Mn1−xFexGe type with varied proportions of Mn and Ge. These compounds are well known for their exhibition of helical states. Recently reported observations of topologically protected magnetic particles, also known as skyrmions, make them a promising candidate for future spintronic devices. Initially, the known pressure-induced transition from a high-spin to a low-spin state in B20-MnGe is reproduced with KKRnano and an examination of the magnetocrystalline anisotropy yields unexpected results. Different non-collinear magnetic states are then analyzed with both an extended Heisenberg model Hamiltonian and KKRnano. The parameters for the model Hamiltonian are extracted with the KKR method. The advantage of such a model is that micromagnetic quantities can be derived from it, which provide information on the helical wavelength of a magnetic texture, and that the Curie temperature can be estimated from the isotropic model parameters. Furthermore, the model parameters can be fed into an Atomistic Spin Dynamics (ASD) simulation package. The subsequent simulations show that skyrmions and anti-vortices are metastable in B20-MnGe. The calculations with KKRnano lead to the conclusion that helical states are stable in B20-MnGe, if the chosen lattice parameter is larger than the experimentally reported one.

The ground--state magnetic phase diagram is investigated for the two-- and three--dimensional $t$--$t'$ Hubbard model. We take into account commensurate ferro--, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often missed in previous investigations. We trace the influence of correlation effects on the stability of both spiral and collinear magnetic order by comparing the results of employing both the generalized non-correlated mean--field (Hartree--Fock) approximation and generalized slave boson approach by Kotliar and Ruckenstein with correlation effects included. We found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistic large Hubbard $U$, if the correlation effects are taken into account. The electronic phase separation plays an important role in the formation of magnetic states and corresponding regions are wide, especially in the vicinity of half--filling. The details of magnetic ordering for different cubic lattices are discussed., Invited Report on the Moscow International Symposium on Magnetism MISM-2014, 6 pages, final version

Ground state magnetic phase diagrams of the square and simple cubic lattices are investigated for the narrow band Hubbard model within the slave-boson approach by Kotliar and Ruckenstein. The transitions between saturated (half-metallic) and non-saturated ferromagnetic phases as well as similar transition in antiferromagnetic (AFM) state are considered in the three-dimensional case. Two types of saturated antiferromagnetic state with different concentration dependences of sublattice magnetization are found in the two-dimensional case in the vicinity of half-filling: the state with a gap between AFM subbands and AFM state with large electron mass. The latter state is hidden by the phase separation in the finite-U case., Comment: Invited Report on the Moscow International Symposium on Magnetism MISM-2017, 7 pages, J. Magn. Magn. Mater., in press

The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistically large Hubbard $U$ by the correlation effects if nesting is absent and van Hove singularities are well away from the paramagnetic phase Fermi level. The magnetic phase separation plays an important role in the formation of magnetic states, the corresponding phase regions being especially wide in the vicinity of half-filling. The details of non-collinear and collinear magnetic ordering for different cubic lattices are discussed., 18 pages, final published version

In this thesis, the structural, electronic, and magnetic properties of nanostructures at surfaces, such as ultra-thin films and single adatoms, are explored based on density functional theory as implemented within the full-potential linearized plane wave (FLAPW) method. The focus of this work are complex non-collinear spin structures due to competing magnetic interactions and the effect of spin-orbit coupling. First, the origin of non-collinear magnetic structures is examined, i.e., structures in which the spins of neighboring atoms are aligned neither parallel nor antiparallel to each other but can take arbitrary angles. Such a non-collinear spin texture is found in a monolayer of Cr on Pd(111), which exhibits a Néel state with angles of 120° between adjacent magnetic moments. It is demonstrated that this magnetic ground state arises due to topological frustration of the antiferromagnetic nearest-neighbor exchange coupling. Spin-polarized scanning tunneling microscopy (STM) images are simulated and allow for a direct comparison with experimental results leading to the first theoretically predicted and experimentally confirmed observation of a Néel state. An even more intriguing non-collinear magnetic state occurs in the double layer of Mn on W(110), where the magnetic moments of an antiparallel spin arrangement are canted with respect to the surface plane and rotate on a cone with an opening angle of about 30°. It is shown that this transverse conical spin-spiral state is induced by higher-order spin interactions. The first finding of such a complex magnetic structure at a surface demonstrates the relevance of spin interactions beyond pair-wise Heisenberg exchange. Furthermore, this thesis contains a study of the tunneling anisotropic magnetoresistance (TAMR) of single atoms adsorbed on magnetic thin films on W(110). Due to the exchange coupling of the magnetic moment of the adatom to the underlying sample’s spin structure, it is feasible to rotate the spin without an external magnetic field and allow a direct comparison of the calculated TAMR with STM experiments. It is demonstrated that the TAMR stems from the mixing of d states with different orbital symmetry due to the spin-orbit interaction. This mixing induces magnetization-direction dependent changes in the vacuum density of states that are on the order of 20% for a single Co adatom on the double layer Fe on W(110). By replacing the Co atom with an Ir atom, which exhibits a stronger spin-orbit coupling, the TAMR can be enhanced by a factor of up to four. For Co adatoms adsorbed on the Mn monolayer on W(110), which shows an atomic-scale spin spiral state, the TAMR is found to be in the range of −25% to +25%. In dieser Arbeit werden die strukturellen, elektronischen und magnetischen Eigenschaften von Nanostrukturen an Oberflächen, insbesondere für ultradünne Filme und einzelne Adatome, untersucht. Hierzu wird die Dichtefunktionaltheorie mittels der implementierten ’Full-Potential Linearized Augmented Plane Wave’ (FLAPW) Methode verwendet. Im Schwerpunkt dieser Arbeit liegen komplexe nichtkollineare Spinstrukturen, die aufgrund von konkurrierenden Wechselwirkungen und dem Effekt der Spin-Bahn-Kopplung auftreten können. Zunächst wird die Herkunft von solchen Strukturen untersucht. In nichtkollinearen magnetischen Ordnungen sind die Spins benachbarter Atome weder parallel noch antiparallel zueinander ausgerichtet, sondern können jeden beliebigen Winkel einschließen. Solch eine Spinkonfiguration findet sich z. B. in einer Monolage von Cr auf Pd(111). Diese weist einen Néel-Zustand auf, welcher sich durch einen Winkel von 120° zwischen den magnetischen Momenten benachbarter Atome auszeichnet. Es wird gezeigt, dass dieser magnetische Grundzustand durch die topologische Frustration der antiferromagnetischen Austauschkopplung zwischen nächsten Nachbarn hervorgerufen wird. Die Simulation von Bildern der spinpolarisierten Rastertunnelmikroskopie (RTM) erlaubt den direkten Vergleich mit dem Experiment und ermöglicht so die erste Beobachtung eines theoretisch vorhergesagten sowie experimentell nachgewiesenen Néel-Zustandes. Ein noch interessanterer nichtkollinearer Grundzustand tritt in der Doppellage Mn auf W(110) auf. Hier sind die magnetischen Momente einer antiparallelen Spinanordnung senkrecht zur Oberfläche verkippt und rotieren auf einem Kegel mit einem Öffnungswinkel von 30°. Es wird demonstriert, dass dieser transversale konische Spinspiralenzustand von Spinwechselwirkungen höherer Ordnung verursacht wird. Der erste Fund einer solchen komplexen magnetischen Struktur an einer Oberfläche verdeutlicht die Relevanz der Spinwechselwirkungen über den paarweisen Heisenberg-Austausch hinaus. Weiterhin enthält diese Arbeit eine Studie des Tunnel-Anisotropie-Magnetowiderstandes (TAMR) von einzelnen Atomen, die auf magnetischen dünnen Filmen auf W(110) adsorbiert sind. Aufgrund der Austauschwechselwirkung zwischen dem magnetischen Moment des Adatoms und der darunter befindlichen Spinstruktur der Probe, ist es möglich, den Spin zu rotieren ohne ein externes Magnetfeld anzulegen. Somit kann ein direkter Vergleich zwischen dem berechneten TAMR und den RTM Experimenten stattfinden. Es wird gezeigt, dass der TAMR vom Mischen von d-Zuständen mit unterschiedlicher Orbitalsymmetrie aufgrund der Spin-Bahn-Kopplung herrührt. Dieses Mischen verursacht magnetisierungsrichtungsabhängige Änderungen in der Vakuumzustandsdichte, die für ein einzelnes Co-Adatom auf einer Doppellage Fe auf W(110) in etwa 20% betragen. Tauscht man dieses Co-Atom durch ein Ir-Atom mit stärkerer Spin-Bahn-Kopplung aus, so kann der TAMR um einen Faktor von bis zu vier erhöht werden. Für Co-Atome, die auf einem Film adsorbieren, welcher wie die Mn-Monolage auf W(110) einen Spinspiralenzustand auf atomarer Skala besitzt, rangiert der TAMR im Bereich von −25% bis +25%.

Density-Functional Theory (DFT) is presently the most widely used approach to determine the electronic structure of atoms, molecules and solids. Its applicability depends crucially on physically sound and numerically accessible approximations to the exchange-correlation-energy functional. Despite the fact that the original Hohenberg-Kohn theorem was generalized to explicitly include the spin degrees of freedom by von Barth and Hedin more than 30 years ago, recent applications are mostly based on approximations to the exchange- correlation energy devised to describe collinear spin magnetizations. In this thesis we present a novel functional for Spin-Density-Functional Theory (SDFT) that is explicitly constructed for non-collinear spin magnetizations, i.e. , it appreciates the possibility for the spin magnetization to change its orientation and not only its magnitude. The functional is constructed in close analogy to the well-known Local-Spin-Density Approximation (LSDA) which uses the uniform electron gas with a constant spin magnetization as reference system. We define a semi-local approximation for the exchange-correlation energy by generalizing the reference system to the uniform electron gas in the spin-spiral-wave (SSW) state. The SSW state, discovered by Overhauser, is investigated using various many-body techniques in order to obtain the required reference data. We demonstrate that it is possible to extend the idea of the LSDA by the inclusion of a Spin-Gradient Extension (SGE), derived from the aforementioned SSW state. By construction the SGE yields exchange- correlation-magnetic fields that are non-collinear w.r.t. the spin magnetization. This indicates that the new functional will improve the description of spin dynamics, by means of Time-Dependent Spin-Density- Functional Theory (TD-SDFT), because it takes into account that the Kohn-Sham spin-current density does not reproduce the physical spin-current density. This is of importance for the ab-initio description of spintronics, i.e. , the manipulation and control of the spin degrees of freedom from first principles, which in recent years emerged as an important field of research due to its potential application for data storage and information processing., Dichtefunktionaltheorie (DFT) ist eine der am weitesten verbreiteten Methoden zur Bestimmung der elektronischen Struktur von Atomen, Molekülen und Festkörpern. Die Anwendbarkeit von DFT hängt von der Verfügbarkeit von physikalisch sinnvollen und numerisch stabilen Näherungen des Austausch- Korrelations-Energiefunktionals ab. Obwohl das Hohenberg-Kohn Theorem vor mehr als 30 Jahren durch von Barth und Hedin um die explizite Miteinbeziehung des Spin-Freiheitsgrades erweitert wurde, basieren die meisten Anwendungen heutzutage auf Austausch-Korrelations-Energiefunktionalen, die für kollineare Spinmagnetisierungen entwickelt wurden. In der vorliegenden Arbeit präsentieren wir ein neues Funktional für Spindichtefunktionaltheorie (SDFT), welches explizit für die Beschreibung von nicht-kollinearem Spinmagnetismus konzipiert wurde. Das Funktional berücksichtig die Möglichkeit der Spinmagnetisierung, seine Richtung räumlich zu verändern. Die Konstruktion des Funktionals erfolgt in Analogie zur Herleitung der bekannten lokalen Spinmagnetisierungsnäherung (LSDA), welche das homogene Elektronengas (HEG) mit einer konstanten Spinmagnetisierung als Referenzsystem heranzieht. Wir definieren eine semi-lokale Näherung für das Austausch-Korrelations- Energiefunktional, indem wir das HEG mit einer spiralförmigen Spinmagnetisierung als Referenzsystem benutzen, welches in den 60er Jahren von Overhauser qualitativ beschrieben wurde. Als Vorbereitung zur Konstruktion des Funktionals untersuchen wir das HEG mit einer spiralförmigen Magnetisierung quantitativ unter Anwendung verschiedener Vielteilchen Methoden. Wir zeigen, dass das Funktional die LSDA um die Abhängigkeit von Gradienten der Spinmagnetisierung erweitert. Die sogenannte Spingradientenerweiterung erzeugt Austausch-Korrelations-Magnetfelder, welche nicht parallel zur Spinmagnetisierung sind, was die Tatsache berücksichtigt, dass die Spinstromdichten des physikalischen Systems und des Kohn-Sham Systems nicht identisch sind. Dies ist wichtig für die dynamische Beschreibung von Spinsystemen im Rahmen der zeitabhängigen SDFT. Zeitabhängigen SDFT ist von enormer Bedeutung für die ab-initio Behandlung von Spintronik, welche sich in jüngster Zeit als wichtiges Forschungsgebiet etabliert, da die Manipulation und Kontrolle des Spin-Freiheitsgrades der Elektronen vielversprechende Anwendungen auf dem Gebiet der Datenspeicherung und Informationsverarbeitung bietet.

The results of the investigation of the magnetic structure of the Cr3 cluster are shown. The calculations were performed for free standing cluster using the linear combination of atomic orbitals formalism based on density functional theory. We show that the cluster has non-collinear magnetic structure in the ground state, where the canting angle between nearest magnetic moments is 120º. Also we find the parameters for the model Hamiltonian which describe different magnetic states of the cluster., Представлены результаты исследования магнитной структуры кластера Cr3 в рамках теории функционала плотности. Показано, что неколлинеарная магнитная конфигурация соответствует основному состоянию кластера при отклонении одного магнитного момента от другого на угол 120º. Описание системы с помощью модели классических спинов позволило утверждать, что для исследования магнитных возбуждений необходимо учитывать ориентационные состояния, находящиеся вблизи основного состояния кластера., Представлено результати дослідження магнітної структури кластера Cr3 у рамках теорії функціоналу густини. Показано, що неколінеарна магнітна конфігурація відповідає основному стану кластера при відхиленні одного магнітного моменту від іншого на кут 120º. Опис системи за допомогою моделі класичних спінів дозволив стверджувати, що для дослідження магнітних збуджень необхідно враховувати орієнтаційні стани, що знаходяться поблизу основного стану кластера

In this thesis, non-collinear magnetism has been studied by using density functional theory and the augmented plane wave method with local orbitals (APW+lo). Two conditions for non-collinear instabilities have been identified in this thesis. First, the Fermi energy should cut through both spin up and down states. Secondly, strong nesting between the spin up and spin down Fermi surfaces is needed. The two criteria described here can be fulfilled by tuning the exchange-splitting and/or by modifying the volume. Calculations on several elements; bcc V, bcc and fcc Mn, bcc Fe, bcc and fcc Co, and bcc and fcc Ni show that a non-collinear state can be stabilized provided that the criteria discussed above are met. More complex materials have also been analyzed in terms of these two criteria. The substitutional alloys TlCo2Se2-xSx are found in experiments to possess spin spiral structures for x = {0-1.5} and at a concentration x = 1.75 the alloys become ferromagnetic. As S takes the place of Se in the crystal structure the distance between the Co layers is reduced and the turn angle of the spin spiral becomes smaller until it totally vanishes at x = 1.75. This thesis show that the evolution of the magnetic structure in these alloys is the consequence of a modification of the distance between Co layers, which induces a change in the interlayer exchange coupling. Fermi surfaces have been analyzed in TbNi5 in order to determine nesting features which would be responsible for the magnetic spin spiral observed in this material. The electronic structure of CeRhIn5 is also reported in this thesis. Furthermore, the 3-k magnetic structure of UO2 was investigated and the crystal field levels were calculated. Transition metal systems such as Fe in the superconducting high-pressure hcp phase and in the fcc crystal structure were also studied. The results obtained for fcc Fe are in accordance with previous reports. However the paramagnetic state in hcp Fe is found to be more stable than the antiferromagnetic configurations discussed earlier in the literature as being favored in the volume range where the hcp phase is stable and superconductivity appears (~ 15 GPa). The complex non-collinear magnetic structure in Mn3IrSi was calculated and the results are found to be in good agreement with experiments.

The present thesis concerns method development and applications in the field of first principles electronic structure calculations. Augmented planewaves combine the simple planewaves with exact solutions of the Schrödinger equation for a spherical potential. This combination yields a very good set of basis functions for describing the electronic structure everywhere in a crystal potential. In the present work, developments of the original augmented planewave (APW) method are presented. It is shown that the exact APW eigenvalues can be found using information from the eigenvalues of the APW secular matrix. This provides a more efficient scheme to solve the APW eigenvalue problem, than the traditional evaluation of the secular determinant. Further, a new way of linearizing the APW method is presented and compared to the traditional linearized APW method (LAPW). Using a combination of the original APW basis functions and the so called local orbitals (lo), the APW+lo linearization is found to reproduce the results of the LAPW method, but already at a smaller basis set size. Another advantage of the new linearization is a faster convergence of forces, with respect to the basis set size, as compared to the LAPW method. The applications include studies of the non-collinear magnetic configuration in the fcc-based high-temperature phase of iron, γ-Fe. The system is found to be extremely sensitive to volume changes, as well as to a tetragonal distortion of the cubic unit cell. A continuum of degenerate spin spiral configurations, including the global energy minimum, are found for the undistorted crystal. The in-plane anisotropy of the ideal interface between a ferromagnetic layer of bcc Fe and the semiconducting ZnSe crystal is also investigated. In contrast to the four-fold symmetric arrangement of the atoms at the interface, the in-plane magnetic anisotropy displays a large uniaxiality. The calculated easy axes are in agreement with experiments for both Se and Zn terminated interfaces. In addition, calculations of the hyperfine parameters were performed for Li intercalated battery materials.