Spin dynamics of S=2 triangular and honeycomb lattices

Abstract

Spin dynamics of $S=2$ triangular and honeycomb lattices realized in ${\mathrm{BaNa}}_{2}\mathrm{Fe}{[{\mathrm{VO}}_{4}]}_{2}$ and ${\mathrm{BaNa}}_{2}{\mathrm{Fe}}_{2/3}{\mathrm{Mg}}_{1/3}{[{\mathrm{VO}}_{4}]}_{2}$, respectively, are investigated by magnetization, heat capacity, and particularly $^{57}\mathrm{Fe}$ M\"ossbauer spectroscopy measurements from which spin fluctuation rates are derived. Slight distortions of the $[{\mathrm{FeO}}_{6}]$ polyhedra from ${D}_{3d}$ symmetry probe the respective anisotropy of the electronic ground state. ${\mathrm{BaNa}}_{2}\mathrm{Fe}{[{\mathrm{VO}}_{4}]}_{2}$ and ${\mathrm{BaNa}}_{2}{\mathrm{Fe}}_{2/3}{\mathrm{Mg}}_{1/3}{[{\mathrm{VO}}_{4}]}_{2}$ reveal magnetic decoupling of the underlying magnetic lattices. Down to the lowest temperature of our experiments (3.3 K) only the triangular lattice exhibits long-range order (${T}_{c}=6.5$ K). The long-range order involves only 2/3 of the Fe sites (static, ${H}_{hf}\ensuremath{\approx}190$ kOe), and 1/3 of the Fe sites fluctuate faster than the observation time window of the M\"ossbauer spectroscopy experiment. For the honeycomb lattice two distinct iron sites alternate. The moments oriented within the plane slow down considerably with ${H}_{hf}\ensuremath{\approx}120$ kOe whereas the moments on Fe sites aligned along the $c$ axis retain a three times larger fluctuation frequency. In both cases the orthogonal moments, obtained from the orientation of the hyperfine fields with respect to the electric field gradient, couple through Dzyaloshinskii-Moriya interaction. Magnetization data for both compounds show signs of ferromagnetic alignment of the reduced moments, $M$(0 kOe) $\ensuremath{\approx}2\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ per Fe. The evaluation of the specific heat data and M\"ossbauer spectra for the ${\mathrm{BaNa}}_{2}\mathrm{Fe}{[{\mathrm{VO}}_{4}]}_{2}$ supports the presence of short-range antiferromagnetic interactions below 50 K and suggests a crossover into competing ferromagnetic exchange below 10 K preceding the emerging long-range order.