Multiferroic FeTe${}_2$O${}_5$Br: Alternating spin chains with frustrated interchain interactions

A combination of density functional theory calculations, many-body model considerations, and magnetization and electron-spin-resonance measurements shows that the multiferroic FeTe${}_2$O${}_5$Br should be described as a system of alternating antiferromagnetic $S=5/2$ chains with strong Fe-O-Te-O-Fe bridges weakly coupled by two-dimensional frustrated interactions, rather than the previously reported tetramer model. The peculiar temperature dependence of the incommensurate magnetic vector can be explained in terms of interchain exchange striction being responsible for the emergent net electric polarization.

Figure 1

(a) Crystal structure of FeTe${}_2$O${}_5$Br along the $bc$ plane, where light yellow polyhedra denote [Fe${}_4$O${}_{16}$]${}^{20-}$ tetramer units. For clarity only Fe and Te atoms are shown. (b) The DFT magnetic exchange network, where the strongest $J_2$ and $J_4$ (thick lines) form alternating spin chains coupled by weaker frustrated interactions (thin lines). The marked unit cell contains eight magnetic Fe${}^{3+}$ ions.

Figure 2

(a) Measured magnetic susceptibility (circles) and comparison to the quantum Monte Carlo (solid line) and the classical (dashed line) calculations for an alternating $S=$ 5/2 chain with $J_4/J_2=$ 0.6 and $J_2=$ 16 K. The inset shows the high-field magnetization measured at $T=$ 1.5 K (circles) and the simulation to the model described in the text (solid line). The dashed line indicates the position of $B_{\mathit{SF}}$. Temperature evolution of ESR spectra at (b) 190 GHz and (c) 405 GHz for $B\left|\right|b$. Arrows indicate antiferromagnetic resonance modes emerging below the Néel transition temperature.

Figure 3

(a) Field dependence of AFMR spectra at 1.5 K for $B\left|\right|b$ and various resonant frequencies between 95 and 405 GHz. (b) Frequency-field dependence for intense (solid circles) and weak (open circles) AFMR modes. Solid lines are simulations to the model described in the text. The dashed line indicates $B_{\mathit{SF}}$.

Figure 4

Dependence of $q_{\mathrm{ICM}}^y$ on interchain exchange coupling constant ratios $J_i/J_i^0$ for $i=$ 1, 3, 6, calculated by direct minimization of the classical energy, where $J_i^0$ are exchange parameters used in AFMR simulations. The inset shows the same dependence calculated for $J_5$.

Figure 5

Refinement results for the O-Fe distances obtained from synchrotron x-ray diffraction, corresponding to (a)–(d) $J_1$ and (d) $J_3$ exchange pathways.

Figure 6

Measured magnetic susceptibility (circles) and classical (dashed line) and quantum (solid line) Monte Carlo results for an alternating $S=5/2$ chain with 60 spins, $J_4/J_2=0.6$, and $J_2=16$ K. Here we also include results for a two-dimensional $64\times 64$ lattice of classical spins (dotted line), using the exchange ratios determined from the ground-state minimization and AFMR calculations, but with $D=0$ and scaled to $J_2=12$ K. The statistical errors of the Monte Carlo sampling procedure are well below the width of the lines.