A deep understanding of magnetism is essential for its application in magnetic semiconductors, spintronic devices and unconventional superconductors. In this work, we study magnetic structures and their corresponding excitations in several strongly correlated electron systems, where exotic orderings can be induced as a result of magnetic frustration and quantum fluctuations. We show that emergent spin textures can arise close to a magnetic field-induced quantum critical point, when the single magnon excitations have several degenerate non-coplanar minima. In this case, quantum fluctuations can lift such degeneracy and lead to the crystallization of the magnetic vortex strings.;Magnetic frustration also plays an important role in Fe-based superconductors. We analyze the spin excitations in the ordered as well as paramagnetic phase of these materials, and find that higher order spin exchanges are essential for understanding the inelastic neutron scattering experiments (INS). The presence of such higher order spin interactions has far-reaching consequences, potentially resulting in more exotic phases, such as the multipolar orders. In particular, we find propensity to ferro-quadrupolar order, which we propose as a candidate for the ground state of the iron selenide FeSe. We find that the calculated spin excitations in this quadrupolar state closely resemble the results of recent INS measurements.;In addition to electron spins, orbital physics also plays a prominent role in Fe-based superconductors. We study the interplay between spin and orbital degrees of freedom and show that the so-called nematic order can be naturally understood as the decoupling of the two transitions, when orbital ordering preempts long-range magnetic spin order. Our results reveal that magnetic frustration plays an important role in several strongly correlated electron systems, and elucidating its consequences is crucial for the understanding and potential application of these materials.
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