Theory of commensurable magnetic structures in holmium

Abstract

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 tau=5/18 structure observed a few degrees below T_N 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 tau=1/5 structure around 42 K, and of the tau=1/4 structure around 96 K, when a field is applied along the c-axis.Comment: REVTEX, 31 pages, 7 postscript figure

Field-induced magnetic phases in the normal and superconducting states ofErNi2B2C

“…It has previously turned out to be of great value to assist the analysis of diffraction experiments by theoretical model calculations of the stability of the structures which may occur. [15][16][17] The method consists in calculating the free energies of different commensurable structures within the mean-field approximation, by the application of a straightforward iteration procedure. The results are compared to each other and thereby the most stable structure may be identified.…”

Field-induced chirality in the helix structure of Ho/Y multilayers

“…Similar to the Dy, the moments in Ho are ferromagnetically coupled within the basal (ab)-plane, but their orientation rotates at a certain angle while moving along the c-axis. It was, however, shown that, contrary to the Dy, the magnetic order in bulk Ho is strongly affected by the crystal-field anisotropy [6,14,15]. The magnetic moments is bunching along the six easy axes in the basal plane due to the crystal-field anisotropy, what leads, firstly, to the lockin of the wave vector into values commensurable with the atomic lattice in certain temperature intervals, and, secondly, to the formation of a series of long period commensurate spin-slip structures [6,14,15].…”

Magnetic phase diagram ofHoxTm1−xalloys

“…9,12 The only crystal-field terms allowed for the hcp structure have lϭ2, 4, 6 and mϭ0 and l ϭmϭ6. The Heisenberg exchange and the dipolar coupling are both two-ion interactions.…”