Condensed Matter Theory

Abstract:

We analyze the effect of quenched disorder on spin-1/2 quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2D valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1/2 moments. This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations. Similarly, when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1/2 magnetic moments, and whose residual interactions decide the ultimate low-energy fate. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin 1/2 per statistical unit cell. These conjectures are supported by an argument for 1D spin chains. We apply insights from this study to the phenomenology of YbMgGaO4, a recently discovered triangular lattice spin-1/2 insulator which was proposed to be a quantum spin liquid. We instead explore a description based on the present theory. Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO4 and related materials.

Abstract:

We report a method to control the positions of ellipsoidal magnets in flowing channels of rectangular or circular cross section at low Reynolds number. A static uniform magnetic field is used to pin the particle orientation and the particles move with translational drift velocities resulting from hydrodynamic interactions with the channel walls which can be described using Blake’s image tensor. Building on his insights, we are able to present a far-field theory predicting the particle motion in rectangular channels and validate the accuracy of the theory by comparing to numerical solutions using the boundary element method. We find that, by changing the direction of the applied magnetic field, the motion can be controlled so that particles move either to a curved focusing region or to the channel walls. We also use simulations to show that the particles are focused to a single line in a circular channel. Our results suggest ways to focus and segregate magnetic particles in lab-on-a-chip devices.