## Introduction

I am an experimental condensed matter physicist, working in the general area of scattering studies of exotic ground states in new, mostly magnetic, materials. As described below, this means that we (my grad students, postdocs, collaborators and myself) make new materials which we think will have interesting and exotic ground states, and then take these materials to forefront neutron and x-ray scattering facilities in North America and around the world. We perform scattering experiments on these new materials and then work either independently or with our friends in theory to interpret the experiments, and thereby shed light on the exotic properties of the new materials.

How do we generate materials which exhibit exotic ground states? Well, we try to incorporate features into the crystal structure and the nature of the magnetic moments which encourage fluctuations, and thereby make it difficult for the material to find an ordered state at low temperatures. We have three features we can work with: we can make crystal architectures which are likely to show geometrical frustration; we can make magnetic crystals which have quantum magnetic moments in them, especially s=1/2 magnetic moments; and we can make three dimensional crystals which are made up of an assembly of low dimensional substructures, like stacks of quasi-two dimensional planes of atoms.

At present we have three themes to our work:

Geometrically frustrated magnets: these are magnetic materials which possess local geometries and magnetic interactions whose combination is incompatible with long range order. The easiest to appreciate occurrence of geometrical frustration happens with the combination of antiferromagnetism and triangular geometries. The tetrahedron is to three dimensions what the triangle is to two dimensions, so this is a common, but poorly understood occurance in three dimensional crystal structures made up of networks of interconnected tetrahedra.

We have been particularly active studying cubic “pyrochlore” magnets, which can be thought of in terms of magnetic moments decorating a network of corner sharing tetrahedra. Such materials have much difficult reaching a magnetically ordered state at low temperatures, and can display a host of exotic, disordered magnetic ground states such as spin liquid, spin glass, and spin ice states. We have devoted much effort to studying the rare earth titanate family of cubic pyrochores. You can look up our recent work on Yb2Ti2O7, Ho2Ti2O7, Er2Ti2O7, and Tb2Ti2O7 under publications. Grad students Jacob, Pat, Kate, and Katharina, and postdoc Jeremy have been leading these and related projects.

Quantum Magnets with singlet ground states: these are magnetic materials comprised of s=1/2 quantum magnetic moments decorating various lattices. One interesting and basic result of quantum mechanics is that while the classical picture of ferromagnetism corresponding to all spins in a solid pointing in the same direction is also valid when quantum mechanics is taken into account, the classical Neel state for antiferromagnetism is not correct when a fully quantum treatment of antiferromagnetism is necessary.

In these cases, which is really all cases as quantum mechanics applies to everything, antiferromagnetic interactions between the quantum moments can result in the formation of local singlets and an overall non-magnetic ground state. While the ground state is a non-magnetic singlet, the excited states, which we can probe by neutron spectroscopy, are triplet states and multi-triplet states. Application of a magnetic field Zeeman-splits the triplet state and a strong enough magnetic field can drive the energy of one of the triplet of excited states below the ground state. The net effect is that triplets can begin to condense into a “sea” of singlets and crystallize within the non-magnetic ground state in phenomena very closely related to Bose condensation.

We’ve focused on two types of quantum antiferromagnets which display singlet non-magetic ground states: the quasi-two dimensional Shastry-Sutherland system SrCu2(BO3)2 and quasi-one dimensional spin-Peierls systems. In the first case, the s=1/2 magnetic moments are already arranged into pairs which then form singlets at low enough temperatures. In the spin-Peierls case, uniform chains of s=1/2 magnetic moments must spontaneously “dimerized” to form a necklace of pairs of ions which then form singlets. In the latter case, the quantum magnetism and the lattice on which the s=1/2 moments reside are strongly coupled. You can look up some of our recent publications for both these materials. The SrCu2(BO3)2 was led by Sara Haravifard, who just finished her PhD and is now a postdoc at the University of Chicago. The spin-Peierls work on TiOBr and TiOCl is being led by Pat Clancy.

High temperature superconductors: Actually high temperature superconductors are also quantum magnets – doped quantum magnets, decorating a low dimensional structure, a two dimensional one in this case. So these materials combine a couple of the general themes we are interested in.

Many scientists have been interested in these materials for more than 20 years, mostly because they display superconductivity at temperatures as high as ~ 150 K. We have focused on the magnetism in the so-called “parent” materials in the High Tc family, and on how this magnetism is modified at relatively low doping. The “doping” means that we start out with a pure “parent” compound, La2CuO4, and then replace a small percentage (like 1 -10 %) of the La3+ with Ba2+. Its known that the effect of this doping is to remove s=1/2 quantum magnetic moments from the CuO2 plane in these materials. The magnetic phase diagram of these materials in this low doping regime is remarkable (at least to me!), in that the magnetism evolves from a strong, three dimensional, commensurate antiferromagnet through a couple of different, but related two dimensional, incommensurate antiferromagnetic states, one of which also displays the superconductivity. Our work on La(2-x)Ba(x)CuO4 is being led by grad students Greg, Jerod and Kate.