Chiral Magnetism in 2D Crystals from First Principles

The realm of magnetic materials are expanding more than ever, and our ability to manipulate the magnetic texture is expanding with it. Objects in the magnetic texture such as domain walls and magnetic quasiparticles called skyrmions present an intriguing method for moving data without moving the electrons. In parallel, the field of magnetism has been expanding into the realm of 2D materials, where several types of magnetic orders have now been realized. The possibility of creating skyrmions in 2D materials creates new avenues for spintronics applications. Theory already predicts skyrmion lattices in Janus monolayers [1, 2], but in practice van der Waals structures still require a finite thickness [3, 4]. The gap between theoretical and experimental structures warrants thorough investigation into the intrinsic magnetic order of the vast possible theoretical 2D magnets.
In this thesis we delve into numerical discoveries of ground state properties of 2D materials. We have conducted three high throughput studies of different exotic ground states. The largest one being our study into non-collinear magnetic order. We present the studies in order from high symmetry to low symmetry.
First we study non-magnetic topological crystalline insulators, which exhibit a non-trivial fractional polarization despite having no polar axis. Our high throughput study reveals them to be very common in 2D materials with three-fold rotational symmetry. We find non-trivial examples in several commonly known experimental structures such as the transition metal dichalcogenides AB₂ where A ∈ {Mo, W} and B ∈ {S, Se, Te}.
Then we turn to altermagnets, which have collinear antiferromagnetic order, but lacking certain symmetries which results in strong spin splitting in the band structure. These are found to be uncommon, yet we find experimentally relevant compounds RuF₄ VF₄ and AgF₂ which are likely to be exfoliable. However, we also highlight the conflicting notion that altermagnets are most interesting in crystals with small spin-orbit coupling, but magnetism in 2D materials requires large spin-orbit coupling.
Finally, we perform spin spiral calculations using the Generalized Bloch Theorem to predict the magnetic ground state of 2D materials with one magnetic moment. We find that non-collinear ground states comprise the majority, which call attention to the prevalence of magnetic frustration in 2D materials. We include the effects of spin-orbit coupling and find several ferromagnets, which destabilize to chiral spin spirals. As an example, we find chiral magnetoelectric coupling in ferroelectric AgVP₂Se₆. Additionally, the type II multiferroic coupling is generally expected in 2D materials with spin spiral magnetic order.