Magnetic Structures of Thulium

Abstract

Neutron diffraction studies on polycrystalline and single-crystal specimens of thulium have been made at temperatures ranging from room temperature to 1.3\ifmmode^\circ\else\textdegree\fi{}K. The results are interpreted by means of a method which exhibits explicitly the Fourier components of the distribution of magnetic moments on the lattice sites. At about 56\ifmmode^\circ\else\textdegree\fi{}K, the N\'eel temperature, a simple oscillating $z$-component-type antiferromagnetic structure is developed. At approximately 40\ifmmode^\circ\else\textdegree\fi{}K, nonzero Fourier coefficients of overtones of the fundamental observed at higher temperatures are first detected. At 4.2\ifmmode^\circ\else\textdegree\fi{}K the magnetic structure of thulium is a type of antiphase domain structure in which several layers of moments parallel to the $+{a}_{3}$ direction are followed by several layers in which the moments are oppositely directed. The sequence in thulium is -4, +3, -4, +3,... etc. Each atom has, within the precision of the experiments, an ordered moment of $7{\ensuremath{\mu}}_{\mathrm{B}}$, and the ferrimagnetic structure has a net moment, parallel to the $c$ axis, of $1{\ensuremath{\mu}}_{\mathrm{B}}$ per atom. The fundamental period of the modulation remains constant over the whole range of temperatures at a value corresponding to $3.5 {a}_{3}$ periods. In the course of this study the scattering amplitude of thulium was determined to be ${b}_{\mathrm{Tm}}=(0.69\ifmmode\pm\else\textpm\fi{}0.02)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ cm.