The modeling of magnetic materials at finite temperatures is an ongoing challenge in the field of theoretical physics. This field has strongly benefited from the development of computational methods, which allow to predict material’s properties and explain physical effects on the atomic scale, and are now employed to direct the design of new materials. However, simulations need to be as accurate as possible to give reliable insights into solid-state phenomena, which means that, most desirably, all competing effects occurring in a system at realistic conditions should be included. This task is particularly difficult in the modeling of magnetic materials from first principles, due to the quantum nature of magnetism and its interplay with other phenomena related to the atomic degrees of freedom. The aim of this thesis is therefore to develop methods that enable the inclusion of magnetic effects in finite temperature simulations based on density functional theory (DFT), while considering on the same footing vibrational and structural degrees of freedom,with a particular focus on the high-temperature paramagnetic phase. The type of couplings investigated in this thesis can be separated in two big categories: interplay between magnetism and structure, and between magnetism and vibrations.

Regarding the former category, I have tried to shine some light on the effect of the paramagnetic state on atomic positions in a crystal in the presence of defects or for complicated systems, as opposed to the ordered magnetic state. To model the high-temperature paramagnetic phase of magnetic materials, the disordered local moment (DLM) approach is employed in the whole work. In this framework, I have developed a method to perform local lattice relaxations in the disordered magnetic state, which consists of a step-wise partial relaxation of the atomic positions, while changing the configuration of the magnetic moments at each step of the procedure. This method has been tested on point defects in paramagnetic bcc Fe, namely the single vacancy and, separately, the C interstitial in octahedral position, and on Fe_1-xCr_x alloys, finding non-negligible effects on formation energies. In addition, the feasibility of investigating extended defects like dislocations in the paramagnetic state with this method has also been proven by studying the screw dislocation in bcc Fe. The DLM-relaxation method has then been used to investigate intrinsic and extrinsic defects in CrN, an antiferromagnetic semiconductor studied for thermoelectric applications, found in the paramagnetic state at operating temperature, and a newly synthesized compound, Fe₃CO₇, which features a complicated crystal structure and unusual electronic properties, with possible important implications for the chemistry of Earth’s mantle.

The other focus of this thesis is the coupling between magnetism and lattice vibrations. As a pre-step to perform fully coupled atomistic spin dynamics-ab initio molecular dynamics (ASD-AIMD) simulations, I have first investigated the effect of vibrations on the so called longitudinal spin fluctuations, a mechanism occurring at finite temperatures and important for itinerant electron magnetic systems. I have developed a framework to investigate the dependence of the local moment’s energy landscapes on the instantaneous positions of the atoms, testing it on Fe at different temperature and pressure conditions. This study has laid the foundation to apply machine learning techniques to the prediction of the energy landscapes during an ASD-AIMD simulation. Finally, I have investigated the phase stability of Fe at ambient pressure from the theoretical Curie temperature up to its melting point with ASD-AIMD. This task is carried out by applying a pool of thermodynamic techniques to calculate free energy differences, and therefore I have defined a strategy to discern the thermodynamic equilibrium structure in magnetic materials in the high temperature paramagnetic phase based on first principles dynamical simulations. The methodologies developed and applied in this work constitute an improvement towards the simulation of magnetic materials accounting for the coupling of all effects, and the hope is to bridge a gap between theory and experiments.

Chromium-nitride based materials have shown unexpected promise as thermo-electric materials for, e.g., wasteheat harvesting. Here, CrN and (Cr,V)N thin films were deposited by reactive magnetron sputtering. Thermoelectric measurements of pure CrN thin films show a low electrical resistivity between 1.2 and 1.5 x 10(-3) Omega cm and very high values of the Seebeck coefficient and thermoelectric power factor, in the range between 370-430 mu V/K and 9-11 x 10(-3) W/mK(2), respectively. Alloying of CrN films with small amounts (less than 15 %) of vanadium results in cubic (Cr,V)N thin films. Vanadium decreases the electrical resistivity and yields powerfactor values in the same range as pure CrN. Density functional theory calculations of sub-stoichiometric CrN1-delta and (Cr,V)N1-delta show that nitrogen vacancies and vanadium substitution both cause n-type conductivity and features in the band structure typically correlated with a high Seebeck coefficient. The results suggest that slight variations in nitrogen and vanadium content affect the power factor and offers a means of tailoring the power factor and thermoelectric figure of merit.

Investigating magnetic materials at realistic conditions with first-principles methods is a challenging task due to the interplay of vibrational and magnetic degrees of freedom. The most difficult contribution to include in simulations is represented by the longitudinal magnetic degrees of freedom [longitudinal spin fluctuation (LSF)] due to their inherent many-body nature; nonetheless, schemes that enable to take into account this effect on a semiclassical level have been proposed and employed in the investigation of magnetic systems. However, assessment of the effect of vibrations on LSF is lacking in the literature. For this reason, in this work we develop a supercell approach within the framework of constrained density functional theory to calculate self-consistently the size of local-environment-dependent magnetic moments in the paramagnetic, high-temperature state in the presence of lattice vibrations and for liquid Fe in different conditions. First, we consider the case of bcc Fe at the Curie temperature and ambient pressure. Then, we perform a similar analysis on bcc Fe at Earths inner-core conditions, and we find that LSFs stabilize nonzero moments which affect atomic forces and the electronic density of states of the system. Finally, we employ the present scheme on liquid Fe at the melting point at ambient pressure and at Earths outer-core conditions (p approximate to 200 GPa, T approximate to 6000 K). In both cases, we obtain local magnetic moments of sizes comparable to the solid-state counterparts.

Disorder in crystalline materials can take different forms and originate from different sources. In particular, temperature introduces disorder in any kind of material. This can be observed as the appearance of vacant lattice sites in an otherwise perfect crystal, or as a random distribution of different elements on the same lattice in an alloy; at the same time, if the material is magnetic, temperature induces disorder also on the magnetic degrees of freedom. In this thesis, different levels of disorder associated to structure and magnetism are investigated by means of density functional theory and thermodynamic models.

I start with diffusion of Ti vacancies in TiN, which is studied by means of nonequilibrium ab initio molecular dynamics using the color diffusion algorithm at different temperatures. The result is an Arrhenius behavior of Ti vacancy jump rates.

A method to perform structural relaxations in magnetic materials in their hightemperature paramagnetic phase is then developed based on the disordered local moments approach in order to study vacancies, interstitial atoms, and combinations of defects in paramagnetic bcc Fe and B1 CrN, as well as the mixing enthalpy of bcc Fe1−xCrx random alloys. A correction to the energetics of every system due to the relaxation in the disordered magnetic state is observed in all cases.

Not related to temperature and disorder, but very important for an accurate description of magnetic materials, is the choice of the exchange and correlation functional to be employed in the first principles calculations. We have investigated the performance of a recently developed meta-GGA functional, the strongly constrained and appropriately normed (SCAN) functional, in comparison with the more commonly used LDA and PBE on the ferromagnetic elemental solids bcc Fe, fcc Ni, and hcp Co, and SCAN it is found to give negligible improvements, if not a worsening, in the description of these materials.

Finally, the coupling between vibrational and magnetic degrees of freedom is discussed by reviewing the literature and proposing an investigation of the influence of vibrations on longitudinal spin fluctuations. These excitations are here studied by means of thermodynamic models based on Landau expansion of the energy in even powers of the magnitude of the local magnetic moments. We find that vibrational and magnetic disorder alter the energy landscapes as a function of moment size also in bcc Fe, which is often considered a Heisenberg system, inducing a more itinerant electron behavior.

The first-principles calculation of many material properties, in particular related to defects and disorder, starts with the relaxation of the atomic positions of the system under investigation. This procedure is routine for nonmagnetic and magnetically ordered materials. However, when it comes to magnetically disordered systems, in particular the paramagnetic phase of magnetic materials, it is not clear how the relaxation procedure should be performed or which geometry should be used. Here we propose a method for the structural relaxation of magnetic materials in the paramagnetic regime, in an adiabatic fast-magnetism approximation within the disordered local moment (DLM) picture in the framework of density functional theory. The method is straightforward to implement using any ab initio code that allows for structural relaxations. We illustrate the importance of considering the disordered magnetic state during lattice relaxations by calculating formation energies and geometries for an Fe vacancy and C insterstitial atom in body-centered cubic (bcc) Fe as well as bcc Fe1-xCrx random alloys in the paramagnetic state. In the vacancy case, the nearest neighbors to the vacancy relax toward the vacancy of 0.14 angstrom (-5% of the ideal bcc nearest-neighbor distance), which is twice as large as the relaxation in the ferromagnetic case. The vacancy formation energy calculated in the DLM state on these positions is 1.60 eV, which corresponds to a reduction of about 0.1 eV compared to the formation energy calculated using DLM but on ferromagnetic-relaxed positions. The carbon interstitial formation energy is found to be 0.41 eV when the DLM relaxed positions are used, as compared to 0.59 eV when the FM-relaxed positions are employed. For bcc Fe0.5Cr0.5 alloys, the mixing enthalpy is reduced by 5 meV/atom, or about 10%, when the DLM state relaxation is considered, as compared to positions relaxed in the ferromagnetic state.