This is an artistic interpretation combining the structure and Haldane gap excitation spectrum of Nd2BaNiO5 made by my friend and collaborator Andrey Zheludev for the cover of Neutron News.
The main ingredient of this material is Ni (S=1) ions arranged in chains, making it a near perfect example of 1D Heisenberg antiferomagnet. It was predicted by Haldane that 1D antiferromagnet with integer (as opposed to half-integer) spin will be in a quantum-disordered state, where the long range antiferromagnetic order is completely destroyed by quantum fluctuations. In this disordered state what used to be a doublet of gapless magnons (spin waves) is now a triplet of excitations with a finite energy gap at the AFM zone center.
This is exactly what was observed in Y2BaNiO5 (a closest relative of our material in which magnetic Nd rare-earth ion was replaced by the non-magnetic Y). This material does not develop AFM long range order and has all features of quantum disordered ground state, described by Haldane. Now the Nd-based material does order at 48K and at a first thought should have no energy gap in it's excitation spectrum below ordering temperature. However, the experiment tells us that not only that it's spin-excitation spectrum has an energy gap around 10 meV, but this gap even grows as T is decreased below TN!
This somewhat counterintuitive behavior can be explained in terms of a simple picture of a Haldane chain in a staggered magnetic field produced by the Nd sublattice.
We have succeeded in:
 | Working out the basic model and interpreting the results of neutron scattering experiments: cond-mat/9706047, cond-mat/9710015 (long review paper). |
| Experimental measurement of the staggered magnetization curve of an S=1 antiferromagnetic chain: cond-mat/9801068. |
| Deriving quantitative theoretical predictions for the increase in Haldane gap as a function of the staggered moment, induced by the external staggered field, as well as the overall shape of the staggered magnetization curve. These predictions, based on the existing numerical data, describing the shape of effective potential in O(3)-symmetric field theory, are in a beautiful agreement with the experimental data in Nd2BaNiO5: cond-mat/9803393. |
| Describing the intensity of collective Ni-Nd excitations as a function of the wave vector component perpendicular to chains. What happens here is that Haldane-gapped magnons on Ni-chains couple with the higher energy crystal-field excitations of Nd ions. This results in intensity modulation: |
We successfully explained
the following properties of this material:
| A commensurate-incommensurate phase transition of that spiral in external vertical magnetic field. As usual it happens via a formation of soliton (domain wall) lattice. For details see: cond-mat/9701127, cond-mat/9706146. |
| A peculiar way in which the spin plane and propagation of the spiral can be manipulated by applying a very weak horizontal magnetic field. An extremely weak in-plane anisotropy of order of 10 neV (yes nanovolts!) per spin. For details see cond-mat/9707166 . |
| The very weak deformation of the spiral in zero vertical field manifested in the third order satellites of main Bragg reflections and the details of the spin-wave spectrum around the AFM zone center. We explained this deformation by taking into account the correction to Dzyaloshinskii-Moria interaction predicted by Kaplan, and later by Shekhtman, Entin-Wohlman, and Aharony. This correction, which we refer to as KSEA interaction (initials of the four authors above) restores the local O(3) symmetry to every nearest-neighbor bond. It can be written as (D·S1)(D·S2)/2J. For details see cond-mat/9805236, and cond-mat/9810122. |
As one can see, the AC conductivity increases with frequency in all but the very thickest of the films, in which the Drude fall-off obscures this effect. One possible source of such conductivity increase is due to localization effects. Indeed, as frequency is increased the corresponding diffusion length scale decreases and the coherent backscattering of electrons is suppressed. However, the observed effect turns out to be to strong and the thickness dependence of the slope too bizarre to be explained in terms of localization alone. We believe that a much more mundane effect well known in more granular systems (such as films deposited at room temperature) is mainly responsible for this effect. Simply speaking at small length scale our films are far from homogeneous. They are composed of grains of Pb with horizontal dimensions of order of ~100-200Å. These grains are coupled to each other both capacitively and resistively (through direct contact or tunneling). Of course, the capacitive coupling does not contribute to the DC conductivity. But for for the IR frequencies it simply cannot be ignored! the higher is the frequency - the stronger is this capacitive coupling and higher is the AC conductive. Quantitative predictions for the frequency dependent conductivity in such purely classical systems were previously derived in the framework of the percolation theory. Our experimental data are consistent with these predictions.
