Magnetic Structures of Thulium

Neutron diffraction studies on polycrystalline and single-crystal specimens of thulium have been made at temperatures ranging from room temperature to 1.3°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°K, the Néel temperature, a simple oscillating $z$-component-type antiferromagnetic structure is developed. At approximately 40°K, nonzero Fourier coefficients of overtones of the fundamental observed at higher temperatures are first detected. At 4.2°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 $7{\mu }_{\mathrm{B}}$, and the ferrimagnetic structure has a net moment, parallel to the $c$ axis, of $1{\mu }_{\mathrm{B}}$ 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 $b_{\mathrm{Tm}}=(0.69\mathrm{}\pm 0.02)\times {10}^{-12\mathrm{}}$ cm.