Magnetic phase transitions in double hexagonal close packed neodymium metal-commensurate in two dimensions

In elemental neodymium, a series of phase transitions between multi-q modulated magnetic structures takes place below the magnetic ordering temperature TN. Based on extensive neutron diffraction studies of the temperature dependence of the length and orientation of the modulation vectors associated with these structures we suggest that there exists a simple phenomenological relationship between the symmetry of the double hexagonal crystal lattice and the symmetry of the corresponding magnetic lattice.

The model has a resemblance to the situation found for monolayer films on solid surfaces (orientational epitaxy) when considering the spin system as the adsorbate and the atomic structure as the substrate. In one dimension, the modulated magnetic structures are sequences of a commensurate to incommensurate transition followed by incommensurate to incommensurate transitions followed by an incommensurate to commensurate transition.

However, in two dimensions, all the modulated magnetic structures are equally well described as higher-order commensurate to commensurate transitions, where the magnetic unit cell is commensurate with the crystallographic unit cell, but rotated by some angle around the hexagonal axis with respect to the crystallographic unit cell.

The rotation angle as well as the magnetic unit cell depend on temperature. The data suggest that the rotation angle is zero whenever there is a change from one type of multi-q structure to another, i.e., in this case, the magnetic and the crystallographic unit cells are commensurate in both one and two dimensions.

Previous and recent results for the light rare earth metals neodymium and praseodymium and alloys thereof, which lend support to this interpretation, are reviewed.