Extreme pressure is a powerful tool for finding new complex functional materials, altering material properties, and inducing correlation effects and magnetic phenomena. While atmospheric pressure is of the order 1 bar, the pressure in the Earth’s inner core can reach million times higher pressures, which experimental methods like diamond anvil cells can today even surpass. Especially the latter opens a wide configurational space to find previously unknown materials or even new chemistry that leads to sought after properties or possibilities to gain fundamental understanding of underlying physics. However, high pressure strongly limits the available experimental techniques, and thus theoretical investigations are crucial, using first-principles modeling of the materials.

This thesis concerns theoretical investigations of complex materials under extreme pressures: understanding magnetic phenomena in solid and liquid Fe and the fcc FeNi system as well as characterizing the dynamical stability, electronic and magnetic properties of newly synthesized nitrogen- and carbo-nitride containing materials under high pressure. The majority of results in this thesis concerns materials that have been synthesized at extreme pressures with a focus on understanding their dynamical stability and electronic properties, both at synthesis pressure but also at ambient conditions. The main methodology throughout the thesis is first-principles calculations based on density functional theory.

Understanding the behavior of magnetic materials under extreme conditions requires accounting for the interplay between atomic vibrations, structural disorder, and magnetic fluctuations. The evolution of the local magnetic moments in solid and liquid iron is investigated at extreme conditions relevant to Earth’s inner and outer core. Longitudinal spin fluctuations are shown to stabilize local magnetic moments even in highly disordered and liquid environments, and these may influence the forces and electronic properties of the material. It highlights the importance of including magnetic fluctuations when describing iron under realistic, finite temperature, conditions.

The fcc Fe-Ni system is particularly interesting due to the Invar alloy which exhibits an anomalously low thermal expansion at room temperature. Changing the Fe-Ni composition only by a narrow range leads to a loss of this low thermal expansion at ambient conditions, while for a higher Ni concentration the effect can be observed at elevated pressure. It is shown that this effect is related to a magnetic transition from a ferromagnetic to a complex noncollinear magnetic state. The transition is shown to be present in the typical Invar composition and is induced by pressure in the FeNi system with higher Ni concentration, explaining the different Ni-concentration dependence as a function of pressure. The transition is related to an anomaly in the equation of state, where the ferromagnetic and noncollinear states correspond to two different branches.

Recently, experimental collaborators have synthesized a PN₂ compound hosting PN₆ octahedra at high pressure conditions, where first computations found unusual nitrogen-nitrogen distances that do not reflect a nitrogen single bond but are too close to be non-interacting. In order to shed light on this unusual behavior, electronically related high-pressure synthesized as well as predicted AN₂ compounds (where A = Si, P, S) were investigated. It is shown that the N-N dimer as observed in experiments is unstable in static calculations in the P-N system, but in molecular dynamics simulations the system is stabilized by a dynamical switching between forming and breaking N-N dimers. The electronic structures of Si, S, and P containing compounds are compared, and a quantitative explanation of the underlying mechanism of the peculiar dynamic bonding is formulated.

Lastly, carbo-nitrogen containing ternary compounds are considered. The stability and electronic properties are investigated of newly synthesized La, Ce, and Tb containing carbo-nitride compounds featuring previously only theorized CN₃ and CN₅ units. This initial investigation led to a detailed study of the electronic structure of CeCN₅ and TbCN₅ at high pressure conditions. Surprisingly the compounds show different electronic properties while being isostructural. This leads in particular to a different oxidation state of the lanthanide atoms. It is shown that this charge difference is compensated by the extended C-N network that accommodates for the additional electron. Motivated by the flexibility of the CN-network, and particularly the XCN5 prototype, a wide range of element substitutions for the ternary atom was investigated. These predicted compounds show quasi-layered structures dynamically stable at ambient conditions, nearly fully agnostic to the X-type element. The layered phases show promising electronic structures for further investigation of possible applications and might open a new road toward lanthanide and rare-earth containing layered materials.