Frustrated magnetism

While unfrustrated magnetic materials will order magnetically at relatively high temperatures, geometric or other frustration can suppress the magnetic ordering and reveal novel topological orders known as spin liquids. Spin liquids are the simplest correlated electronic phases that exhibit fractionalization and topological order, and provide a great playground to study these phenomena. Unfortunately, these phases are difficult to realize in materials, which requires exploring novel ways to stablize spin liquid phases.

Stuffed honeycomb lattice

We have studied the stuffed honeycomb lattice in detail, both the classical and quantum limits. This lattice couples together two frustated lattices that host spin liquids: the honeycomb and the triangular lattices, leading to a rich classical phase diagram, and revealing a multi-critical point on for J₂/J₁ = 1/8 in the triangular lattice limit.

Classical phase diagram of the stuffed honeycomb lattice

We have examined the quantum phase diagram as well, both the S = 1/2 limit using exact diagonalization (with Prof. Clark at UIUC, coming soon) and by examining all possible spin liquids on this lattice to look for connections between potential spin liquids on the triangular and honeycomb axes.

Symmetric spin liquids on the stuffed honeycomb lattice

Different kinds of polarization on the Poincare sphere

Floquet engineering in frustrated magnetism

Spin liquids can be difficult to access experimentally, as they occupy narrow regions of model phase diagrams that may not be realized in any particular compound. Floquet engineering is a way to use periodic laser light to drive these systems into new regions of phase space. Traditionally, the light is monochromatic, with amplitude, frequency, and polarization varied. We introduced Floquet engineering via unpolarized light built from quasimonochromatic light. Unpolarized light can modify strongly correlated systems, while preserving the original symmetries. As an example, we treated insulating magnetic materials on a triangular lattice Modification of J3/J1 and J2/J1 and showed how unpolarized light can induce a Dirac spin liquid.

Floquet Engineering Correlated Materials with Unpolarized Light

Polarization as a tuning parameter for Floquet engineering: Magnetism in the honeycomb, square, and triangular Mott insulators

A cartoon of the effect of lattice vibrations on a honeycomb lattice of magnetic moments, where the lattice vibrations shift the spins out of position, leading to changes in the effective first and second nearest neighbor interactions. — Cartoon of how nonequilibrium phonons can tune magnetic interactions. Optical phonons (ω₀) are pumped by IR light leading to a non-equilibrium q = 0 phonon distribution, n_ph(ω₀). This affects the interatomic distances, inducing spin-phonon mediated changes to the magnetic interactions, δJ. Strong pumping without significant heating is possible if the IR light is below the Mott gap scale, ω₀ ≪ U.

Driving exotic magnetism using spin-phonon pumping

Theoretical models of quantum magnets can host unusual spin liquids where local magnetic moments form exotic topological phases of matter whose neutral fractional excitations (spin ½) are fundamentally different from the spin-flip excitations (spin 1) of conventional orders. Unfortunately, real materials rarely intrinsically fit into these relatively narrow model regimes. Recent experimental advances allow non-equilbirium control of quantum materials by coupling light to lattice vibrations (phonons), where large, out of equilibrium phonon populations can be induced. Here, we address how this phenomena can be used to tune quantum magnets by developing a theoretical treatment of how large, driven phonon populations can modify the underlying model parameters and potentially drive materials into realizing these exotic spin liquids.

Exploiting the new experimental capabilities to drive non-equilibrium phonon populations in insulating magnetic materials requires generic, easy to interpret theories describing what types of tuning are possible, and how to optimize the protocol for specific materials. We developed a leading order quantum treatment that captures the changes in magnetic interactions when lattice vibrations are fast compared to the spin motion, which means the spins feel averaged effective interactions. We show several intriguing applications that induce spin liquids: increased magnetic frustration by generating further neighbor interactions; increased magnetic anisotropy; and reduced undesirable interactions.

Tuning magnetic interactions with non-equilibrium optical phonon populations

NSF logo Much of this research was supported by my NSF CAREER grant (NSF DMR-1555163).