click on figure for more detailsIn the early experiments, the main area of interest concerned the structures present at low temperatures and fields. Here it was found that the structure is best described by a model in which the modulation vectors are coupled together to form a quadruple-q system, with different lengths and directions for each modulation (shown below).
click on figure for more details
A single layer of double-q structure formed: a)from q1 and q2, b)from q3 and q4. In each case the extra lines represent a repeat distance corresponding to 2q1.
Why this 4-q phase exists is still not clear, but a strong clue may lie in the observation that, to within experimental error q3 + q4 - 2q1 = 0 which may be attributed to a term in the free-energy expansion of the form µ3µ4µ1^2 (µi = the moment associated with the i^th q-vector), so providing the coupling energy necessary to lock together three of the four components of the quadruple-q structure.
Later experiments using D20 have investigated the magnetic structures at fields of up to 4.7 Tesla in a,b and c directions, the latter requiring the use of the vertical field cryomagnet. As a result, we have now examined much of the neodymium B-T phase diagram, with good agreement between the positions of the various structures and the phase boundaries by bulk measurements.
Certainly the most suprising and spectacular finding at low temperatures was that, as the field is reduced through 4 Tesla, the structure undergoes a remarkable period doubling and redoubling (shown below).
click on figure for more details
Magnetic satellites near (100) in Nd at T = 1.8K with B = 3.5T, applied 5° from a {100} direction.
At fields of about 5 Tesla, q and its third harmonic are the only ordering wavevectors seen. At such high fields the structure is no longer quadruple-q and only a single-q structure mainly from the moments on the hexagonal sites is seen. As the field is reduced a series of subharmonics develop, until at 3.5 Tesla there are at least nine different wavevectors visible, forming a chain - an "archipelago" -stretching away from the (100) brag reflection. These are at q/4 and some (but not all) of its harmonics.
Qualitatively, the effect is reminiscent of the period doubling which is seen in non-linear systems approaching the onset of chaos. The underlying reason for this behaviour is not clear, but loss of order on the cubic sites with increasing fields and the single to double-q transition on the hexagonal sites with decreasing fields have both been seen to destroy the effect.