Graphene is the most two-dimensional platform currently available as a host for an electron gas, and offers promise to make observable a variety of effects in a perpendicular magnetic field. For example, recent advances in aligning graphene on a boron-nitride substrate have led to the creation of high-quality Moire patterns with large unit cells. Similar large-cell superlattices can also be created in twisted bilayers. In a perpendicular magnetic field, near zero energy the periodicity has little effect on the spectrum, but with increasing energy the spectrum evolves into the much-anticipated Hofstadter butterfly. The crossover between these behaviors is controlled by a saddle point in the zero-field spectrum. We demonstrate through a semiclassical analysis how the quantization of orbits changes as the saddle point is crossed, allowing the richness of the Hofstadter spectrum to emerge above it, and discuss some possible experimental consequences. We then consider graphene systems in much higher magnetic fields -- the quantum Hall regime -- where transport is controlled by edge states. For undoped graphene these edge states may have a helical nature. We discuss what happens when an "internal edge" is created in bilayer graphene using a split gate geometry, where a surprisingly rich internal structure emerges with a number of possible states. Such a geometry admits transport probes which potentially reveal different aspects of the internal structure, and we discuss our expectations for how the state of this internal edge can be reflected in such measurements.

A knowledge of the spin-wave excitations in magnetic materials allows a robust determination of exchange parameters in suitable model Hamiltonians. We have used time-of-flight inelastic neutron scattering to measure the excitation spectra from field-polarized states of exotic frustrated magnets. We have taken this approach with two pyrochlores, Er2Ti2O7 and Yb2Ti2O7, whose magnetic properties have until this point been somewhat puzzling. Our strategy is to apply a magnetic field to push the systems to be in as classical a phase as possible, and then extract the exchange parameters using linear spin wave theory. Then, ramping the field down in the model, we reveal new information about the zero-field states of these magnets. The ground states of the frustrated spin-1/2 XY pyrochlores Er2Ti2O7 and Yb2Ti2O7 are thus revealed to be realizations of "quantum order by disorder" and "quantum spin ice", respectively. I will explain what these terms mean and show how the models lead to predictions, one of which we have confirmed (a small spin wave gap in Er2Ti2O7 opened by quantum fluctuations) and another which is still debated (does Yb2Ti2O7 support emergent electrodynamics?).

Usually, when considering Mott transitions, one treats the system as homogeneous – either with localized, or with itinerant electrons. However, such localized – itinerant crossover can occur not nesessarily homogeneously in the whole sample, but there may appear in a solid small clusters –“molecules” (dimers, trimers, heptamers etc) in which electrons already can be treated as weakly-correlated, whereas the hopping between such clusters may still be small, so that the whole material may still be insulating. In this talk I will discuss the conditions for such phenomenon (in particular, low-dimensionality and magnetic frustrations usually facilitate creation of such clusters), present several examples, and consider some special properties of such molecular clusters, such as e.g. the orbital-selective Peierls transition with partial quenching of magnetic moments.

For the past several years, the spinel vanadates, AV2O4, have been central to the study of orbital degeneracy and the complex coupling of spin, charge and lattice degrees-of-freedom in frustrated antiferromagnets. They are of interest not only to condensed matter physicists who study orbital order and frustration, but also applied physicists who seek to take of advantage of the useful multiferroic effects which often result. Systems with diamagnetic (e.g. Zn2+, Cd2+, Mg2+) and spin-only (e.g. Mn2+) cations on the A-site sublattice have been studied extensively, demonstrate multiple magnetic and structural phase transitions, and reveal ground state properties heavily influenced by V3+ orbital degrees-of-freedom. Here, I report on elastic and inelastic neutron scattering investigations of a relatively new member of the spinel family, FeV2O4. In addition to the orbital degeneracy of vanadium cations, this system has a orbital doublet degree-of-freedom on the iron sublattice. The resultant interactions lead to complex and interesting behavior, including reports of four separate structural phase transitions and the emergence of net magnetic and electric dipole moments at lowest temperatures. Our data confirm the existence of three of the four reported structural transitions, and associate the lowest two with the onset of collinear and canted ferrimagnetic structures. Through consideration of local crystal and spin symmetry and the magnetic excitation spectrum, we are able comment on the physics driving each of the reported transitions and the likely ordering of electron orbitals at all temperatures. I will discuss each of these observations in the context of the current literature on other spinel-vanadates, and lay out potentially interesting paths for future research.

Recent advances in nanolithography allow researchers to fabricate artificially tailored magnetic metamaterials. These artificial metamaterials have gathered considerable interest from high tech as well as from basic science community. Although substantial progress has been made in last 15 years or so in the fabrication and the study of different types of magnetic metamaterials, the focus has been limited to only periodic metamaterials. In this seminar, I will present our group’s recent results on novel artificial quasicrystal—Penrose P2 tiling—magnetic metamaterials. In particular, I will show how such complex artificial quasicrystals give reproducible knee anomalies in the DC magnetization—obtained using SQUID magnetometer and static micromagnetic simulations—and their possible dynamic signatures—obtained using ferromagnetic resonance experiment and simulation. Furthermore, I will also discuss occurrences of chiral loops in these metamaterials, and how artificial magnetic quasicrystals can be viewed as a candidate for artificial spin ice and our recent results on that.

Joe Straley (UK)