Theory of commensurable magnetic structures in holmium.

The tendency for the period of the helically ordered moments in holmium to lock into values which are commensurable with the lattice is studied theoretically as a function of temperature and magnetic field. The commensurable effects are derived in the mean-field approximation from numerical calculations of the free energy of various commensurable structures, and the results are compared with the extensive experimental evidence collected during the last ten years on the magnetic structures in holmium. In general the stability of the different commensurable structures is found to be in accord with the experiments, except for the τ = 5/18 structure observed a few degrees below TN in a b-axis field. The trigonal coupling recently detected in holmium is found to be the interaction required to explain the increased stability of the τ = 1/5 structure around 42 K, and of the τ = 1/4 structure around 96 K, when a field is applied along the c-axis. 75.10.-b 75.25.+z 75.30.Gw Typeset using REVTEX