Research
This page offers a general summary of the research problems I've worked on, roughly in reverse chronological order. The intent is to provide a brief, generally-accessible background, since anyone with further interest or specialist knowledge can look up the relevant journal articles (and hopefully the introductions in those articles are written clearly enough that the level-of-detail continuum is complete). My speciality is in growing and oxygen-annealing single crystals of interesting materials, most frequently transition metal oxides. I typically study these materials' magnetic and electrical transport properties, do diffraction where required to determine their crystal or magnetic structures, then hand the samples off to collaborators for more specialized or in-depth work. I have participated in x-ray absorption and x-ray inelastic scattering measurements, but have managed to stay out of inelastic neutron scattering.
In many cases, the materials I was working on had possible industrial applications, such as lossless power transmission, extremely narrow-frequency filters for communication between cellphone base stations and satellites, fuel cells, magnetic memory devices, or quantum computation (the main proposed application of which, so far, is cryptography). However, I was not working toward these applications. I've done curiosity-driven research exclusively, trying to figure out how the world works and why, to expand human knowledge. This type of research often leads to new technologies and products, and major game-changing discoveries are more likely to come from basic than applied research, but commercialization is not a goal here. Once we know what something does, other people may see that newly discovered information as an opportunity for new technologies that we hadn't thought of.
Correlated Transition Metal Oxides and Frustrated Magnetism
The 3d, 4d and 5d transition metals, in the middle of the periodic table, exhibit many types of unusual magnetic behaviour. 3d orbitals have the radial extent of a tiny 1s orbital, but ten electrons can be packed in instead of two. Since electrons repel each other and this forces a lot of them into very close quarters, they interact very strongly. In some systems, these interactions can lead to fundamental changes in the electronic properties, for instance turning what should be a conductor into a wide-gap insulator because the electrons can't stand to share an atom. In 5d systems, these interactions are much weaker, but interactions between each electron's spin and the orbital state it occupies become very strong instead. In the 4d metals, the two effects can have roughly the same strength. There's a lot of interesting physics available here, and plenty of strange effects have been seen. I concentrated on magnetic effects that had been predicted but not observed, on d1, d4 and d5 systems.
Part of my interest here is because d1 systems are closely analogous to the d9 cuprate high-temperature superconductors, but no similar superconductivity has been observed.
Most of my time in Stuttgart was spent on SrFeO3-x and Sr3Fe2O7-y. These are rare Fe4+ compounds, and exhibit helical magnetism, where neighbouring spins are neither parallel nor antiparallel, but tilted so that they form a spiral. In such systems, special spin excitations called Skyrmions, which look vaguely like spin hedgehogs, are possible. The Stuttgart group had studied these materials for some time, but there was room for significant improvement in oxygen doping and oxygen order. We determined for the first time the magnetic phase diagram of Sr3Fe2O7-y with doping, improved the crystal growth technique for SrFeO3-x, and found a charge-order distortion that had eluded researchers for some time despite compelling evidence that it had to be there. We found some new magnetic phases, and worked out more details on some known phases.
The research in Seoul concentrated on Mn2Sb2O7, which normally forms in a noncentrosymmetric (and chiral) structure, based on kagome planes. The planes are linked through additional triangles dangling off the side of the kagome-plane triangles, making the most basic structural building block an extremely unusual Mn4 armchair unit. This material has multiple magnetic transitions at low temperature, one of which is also antiferroelectric (altering the electric polarization) -- the material is multiferroic. It is also possible to produce a much more symmetric version, in the pyrochlore structure, the most frustrated known structure in three dimensions. This version has corner-linked Mn4 tetrahedra, and at low temperatures it becomes a spin glass: the spins freeze without ordering. This version is actually particularly interesting because the spins are Heisenberg spins, meaning there's no orbital magnetism that can couple to them. It is exceedingly rare to find a pyrochlore lattice of Heisenberg spins. All previous work on the pyrochlore had actually studied trace Mn3O4 impurities by mistake. These are ferrimagnetic, which gives a very strong magnetic signal even if the amounts are undetectably small otherwise. On the chiral armchair version, I'd spent something like a year figuring out what that extra transition was and how to get rid of it, so I did the same thing to the pyrochlore version. I was then able to figure out what it actually did.
Noncentrosymmetric Superconductors
The vast majority of superconductors (materials that conduct electricity without any resistive losses below some temperature and expel magnetic fields) studied to date have inversion symmetry. This means that there's at least one point in the crystal structure where, if you move every atom to exactly the same position on the opposite side of that special point, you get exactly the same material. This is an extremely common symmetry element to have, but not all superconductors have it, and the physics can get very strange if it's not there. The first image here shows a material with A-B-B-A stacking — electric fields in the material may not be zero everywhere, but for every atom feeling such a field, there's another atom opposite the inversion centre (i) with exactly opposite properties, and they'll cancel. Without an i element, as in the second image, it's possible for every B atom, for instance, to experience an electric field downward, and the effects do not cancel.
Superconductivity is a macroscopic quantum state, which means that the entire superconductor can be described by a single wavefunction (the order parameter) that the electrons are all part of, acting coherently. When an inversion centre exists, this overall wavefunction obeys parity. That means that if you compare a particle in a state at some momentum with a particle having exactly opposite momentum, their quantum mechanical description, and the superconductivity in general, can either be identical or differ by a minus sign (a quantum mechanical phase). The sign of the superconducting order parameter is irrelevant for most measurements, but there a handful that are sensitive to it, and the material behaves quite differently if the order parameter changes sign, since that tends to mean it has to pass through zero for certain directions. This is the case in the cuprate high-temperature superconductors, as one example (the image compares this case, "d-wave", with the more-common s-wave scenario).
One key property of electrons is that if I swap two electrons, I have to get a minus sign in the wavefunction. In superconductors, the electrons are paired, so the pairing has to have this rule built in. The consequence for superconductors with inversion symmetry is that order parameters that do change sign require a spin state that does not (triplet), and an order parameter that does not change sign requires a spin state that does change sign when the electrons are swapped (singlet). Singlet and triplet superconductors behave in very different ways, and one of the first things people look at when finding a new superconductor is whether it's behaving like a singlet or triplet. s-Wave and d-wave both correspond with singlet pairing states.
If there is no inversion centre, then there's no reason for the superconducting order parameter to obey parity, and 'singlet' and 'triplet' aren't meaningful descriptions. If you chose to stick with those words, there will generally be some mixture. Spin-orbit interactions that would otherwise cancel at least globally can split the electronic structure by electron spin (in the image, the top two drawings show an example of this splitting in the band structure vs. energy and in the resulting Fermi surface vs. momentum). This leads to pairing of electrons primarily within each spin-specific Fermi surface (bottom). Note that singlet has a (↑↓ - ↓↑) form, not ↑↓. In any case, the unusual pairing leads to particularly weird effects in magnetic fields -- the Fermi surfaces shift, so all the pairs in each Fermi surface have a non-zero momentum, and you can get currents, possibly spin currents, and spatial oscillations in the order parameter. You can have places in the sample where the superconductivity goes to zero, and they might form spirals around lines of magnetic flux. This are just a couple examples of the weird behaviour possible in such a material. A significant number of really strange properties have been predicted and a few have been observed, but there's a great deal of work yet to be done on both the experimental and theoretical sides, and a lot of very strange physics yet to be discovered. I remain interested in these materials, and continue working on them.
Overdoped Cuprate Superconductors
The cuprates have the highest known superconducting transition temperatures, and are the only family which superconduct above nitrogen's boiling point, making them both scientifically extremely interesting and simultaneously potentially very important for applications. They were discovered in 1986, and to this day we don't have an agreed-upon explanation for their superconductivity.
The parent compound for the cuprates has 9 of a possible 10 3d electrons, which would normally make it a metal. However, the strong electron-electron interactions mentioned above prevent them from moving around, and the material is a Mott-Hubbard antiferromagnetic insulator -- the spins on adjacent copper atoms anti-align to lower their energy. When you start taking out electrons (adding holes, characterized by the extra holes per Cu atom p), the new holes are initially shared by oxygen atoms, to avoid having to share a copper atom with an existing hole. The insulating state is suppressed, then superconductivity appears. The superconducting transition temperature rises ("underdoped" regime), peaks at what we call "optimal doping", then falls back toward zero ("overdoped" regime), roughly following a parabola. There are a number of other strange phases around as well, and the two phases from which superconductivity develops up as far as optimal doping are not understood. On the overdoped side, it's possible that the superconductivity might emerge from an ordinary metallic (Fermi liquid) phase, which would offer a unique foothold for understanding. Unfortunately, for chemical reasons, it's very difficult to get most cuprate superconductors very far into the overdoped regime, and some that do make it there become extremely inhomogeneous.
An exception to this is Tl2Ba2CuO6+x (Tl-2201), which self-dopes in such a way that it starts around optimal doping and goes up from there. It has very flat CuO2 planes (the part that superconducts -- in most materials this layer is buckled), and only one single, isolated CuO2 plane (many cuprates have two or more together, interacting with each other, which is good for superconductivity but complicated for those of us trying to understand it). And for my MSc and PhD degrees, I grew single crystals of Tl-2201.
Cuprate Superconductors for Study with Neutrons
My first research work involved growing cubic-centimetre-sized crystals of the underdoped cuprate superconductor YBa2Cu3O7-x (YBCO). This was the first superconductor discovered with a transition temperature above the boiling point of nitrogen, has been particularly thoroughly studied, and is available in the highest quality of any cuprate superconductor. However, accessing underlying magnetic excitations by neutron scattering generally requires a mass on the order of tens of grams, which would require growing and individually aligning hundreds or even thousands of conventional-sized crystals. Large crystals grown by a very different method were available, but these generally contained about 30% other stuff, and that other stuff exhibited magnetism. We grew cubic-centimetre-size crystals with roughly 2% other stuff, and were able to detwin the crystals such that the a and b axes were largely aligned throughout the crystals (these axes are very similar, so a crystal usually has many tiny domains of both orientations, making it difficult to extract properties unique to one direction). These crystals have been used extensively by our neutron scattering collaborators and continue to yield interesting results.