The interaction between the neutron community and the theoretical community working in this field, using tools from statistical mechanics (including Monte-Carlo and molecular dynamics simulations) has a long history. In the field of polymers1, neutrons have long been the tool of choice for studying (in particular) single chain conformation and dynamics, a cornerstone in the theory of polymer melts. Similarly, our understanding of the structure of liquids is largely the result of a combination of neutron scattering, statistical mechanics, and simulation of model systems, as illustrated in the famous books on the liquid state by P.E. Egelstaff or J-P. Hansen and I.R. McDonald2. In glasses, neutron spin echo has been instrumental in revealing, beyond structural aspects, the complex dynamics that takes place on a time scale of a few nanoseconds3, in a time regime that permits comparison with mode coupling approaches and numerical simulations.
Today, the growing interest in nanoscience, and nanostructured materials, together with the availability of increasingly sophisticated local probes, are pushing soft matter studies towards the exploration of more and more complex situations, involving confinement, heterogeneities and interfaces. This complexity ranges from the model situations offered by regular porous materials, to the sophisticated architectures of biological assemblies. The behaviour of soft materials under external solicitations, mechanical deformation or flow, is also of considerable interest.
Electronic structure and magnetism
Neutrons scattering has always been one of the most valuable tool for the study of the electronic structures. This is even more the case when the system contains unpaired (magnetic) electrons, since both the ground state (DIF) and the excitations can be studied (TOF, TAS). The interaction between the neutron experimental community and the ab initio electronic structure theoreticians is characterized by the fact that in the ab-initio calculations the whole complexity of the real system (chemical as well as structural aspects) are taken into account, allowing not only a direct confrontation between the theoretical predictions and the experimental observations, but also the possibility to extract from the calculations the degrees of freedom that are pertinent for the system low energy physics and their interactions. For instance, in magnetic systems, wave-function based ab-initio calculations allow the determination of the different direct as well as super-(or double-) exchange paths, their relative importance/amplitude and thus the pertinent magnetic Hamiltonian to be used for the experimental interpretation. Similarly, in multiferroic systems, it is possible to obtain information on the microscopic origin of the electro-magnon excitations, since the variation of the different terms entering the exchange integrals can be obtained as a function of the atomic displacements associated with a phonon mode.
Understanding the properties of a system often means building up a simple representation of this system, where a few pertinent degrees of freedom are related through dominant interactions. It also means understanding how external parameters (pressure, chemical doping, applied fields, changes in composition or structure, etc...) act on these degrees of freedom and modify them. Ab initio theoretical calculations help to build up such a picture, bridging the gap between real systems (specific composition, specific geometry, etc...) and the models of the theoretical physics. It also allows to tackle a large variety of systems (from atoms and molecules to crystals and non periodic infinite systems), of problems (from chemistry and reactivity to magnetism and strongly correlated fermions), etc. It does also allows the hope of answering more technical problems such as the importance of the non sphericity (dependance on the orbitals shape) of the atomic/magnetic form factor in neutron scattering.
Neutron scattering provides a powerful probe of the properties of the condensed state. While the fundamental theory underpinning its use is well established, there remain many areas where a fruitful interaction between theorists and experimental communities is essential, in my view. As an example, many of the current materials of interest, either fundamental or applied, may only exist in the form of films or nano-scaled devices. The challenge is for the experimentalists to develop new ways of studying such samples or more conventional samples subject to extreme conditions (eg high magnetic field). Theorists can, ideally, help bring new ideas to motivate novel experiments and help interpret newer techniques, such as grazing incidence scattering from films. In strongly correlated solids there is currently a great deal of theoretical activity in the area of “spin liquids”. Such exotic states of matter are fascinating theoretical constructs but the number of physical realizations extremely few – they are established only for spin chains or for electrons for very high magnetic fields and low temperatures. Where theorists can help is to look for better candidate materials (for example in very frustrated spin systems) and also better define the experimental signatures in the “real” world of physical materials with all their complications. Some such exotic states of matter are defined in terms of correlation functions that are not immediately accessible to neutron scattering, for example three or four-spin correlations. A more obvious obstacle to their study is the presence of anisotropies and spin-orbit interactions whose effects must be included in the effective magnetic Hamiltonians. This may seem to be adding details of little intrinsic interest, but the same interactions lead to exciting new effects by mixing lattice and electronic degrees of freedom to produce, for example, multi-ferroic materials, or spin-dependent skew scattering of importance to potential spintronic devices. The polarization properties of the neutron make it, in principle, the ideal probe to disentangle such details on an atomic scale but there are many challenges because of sample or environmental difficulties. In most cases complementary techniques are needed to really understand what is going on and theory should help linking to the results of such other techniques. In some cases neutron techniques have advanced, for example, in resolution of inelastic scattering to a point where intrinsic lifetimes of excitations can be measured and this allows us to re-examine detailed theories for correlated systems that can now be tested.