Quantum Magnetism in π-electron Molecular Systems

In this Thesis, we study quantum magnetism in molecular systems of $\pi$-orbital electrons. We use spectroscopic methods such as electron paramagnetic resonance (EPR), nuclear magnetic resonance (NMR) and muon spin rotation/relaxation ($\mu$SR) to probe the static and dynamic properties of the magnetic state in selected compounds at the local scale. The studied systems include alkali superoxides and sesquioxides (AO$_2$ and A$_4$O$_6$, where A = Cs, Rb, Na), with the O$_2^-$ superoxide ion as the source of the principal magnetic moment, and the aromatic crystal systems, where the unpaired electrons occupying their $\pi$ molecular orbitals form quasi one-dimensional structures. Orbital ordering leading to strong antiferromagnetic interactions along $b$ crystal axis was suggested for the CsO$_2$ system. With the use of theoretical models based on quantum field theory and bosonization technique, the CsO$_2$ EPR data analysis shows good agreement with one-dimensional spin chain and the underlying Tomonaga-Luttinger liquid framework. Additionally, we discuss the presence of Ising-type anisotropy. The Cs$_4$O$_6$ and Rb$_4$O$_6$ systems' oxygen units are at room temperature in an average charge state O$_2^{-4/3}$. Extensive EPR, NMR and $\mu$SR measurements on both samples lead us to the discovery of a Verwey-type structural and charge ordering transition from high-temperature cubic to low-temperature tetragonal phase. Additionally, another subtle structural transition is discovered in Rb$_4$O$_6$ that further breaks the symmetry, and together with orbital ordering enables the formation of low-temperature quantum ground state of weakly coupled spin dimers. The coupling between lattice, charge, orbital and spin degrees of freedom is discussed. Geometric frustrations of nearest-neighbour exchange interactions are the most probable cause for the absence of long-range magnetic order in the Rb$_4$O$_6$ system. Finally, as the representative of low-dimensional organic compounds, we study the alkali-metal-doped triphenylene family. The three compounds with intercalated K, Rb or Cs alkali metals exhibit low-dimensional magnetism with a spin gap in the excitation spectrum. By the use of $\mu$SR, slowing down of collective spin fluctuations is observed. These quantum spin fluctuations prevent the formation of long-range magnetic order and are proposed to be a signature of a quantum spin liquid.