Noncollinear two- and three-dimensional magnetic ordering in the honeycomb lattices ofErX3(X=Cl,Br,I)

Abstract

Unusual magnetic ordering phenomena have been observed in the three title compounds in the milli-Kelvin temperature range. The ratio of interlayer to intralayer coupling and thus the critical behavior and the nature of the magnetic order can be tuned by chemical variation. In all three lattices the two-dimensional (2D) magnetic order within the layers is a two sublattice 120\ifmmode^\circ\else\textdegree\fi{} antiferromagnetic order with an infinite rotational degeneracy. The ordered magnetic moments increase from 3.3 to 4.7 and $5.5{\ensuremath{\mu}}_{B}/{\mathrm{Er}}^{3+}$ for ${\mathrm{ErCl}}_{3},$ ${\mathrm{ErBr}}_{3},$ and ${\mathrm{ErI}}_{3},$ respectively. ${\mathrm{ErCl}}_{3}$ shows a transition to 3D magnetic order at 350 mK with a k vector of $(\frac{2}{3},\phantom{\rule{0ex}{0ex}}0,\ensuremath{-}\frac{1}{12}).$ ${\mathrm{ErBr}}_{3}$ and ${\mathrm{ErI}}_{3}$ are the first examples of rare-earth trihalides displaying short-range 2D magnetic order from 400 mK up to several Kelvin, long-range 2D order between 280 mK and 400 mK, long-range 2D and short-range 3D order with $\mathbf{k}=(\frac{1}{3},\frac{1}{3},0),$ and a correlation length of 15 \AA{} below 280 mK. The differences are attributed to the different layer stackings in ${\mathrm{ErCl}}_{3}$ and ${\mathrm{ErBr}}_{3}{/\mathrm{E}\mathrm{r}\mathrm{I}}_{3}$ as well as the variation of interlayer distances.