$\mathrm{M}{\mathrm{n}}_2\mathrm{Te}{\mathrm{O}}_6$: Complex antiferromagnetism as a consequence of the Jahn-Teller distortion

Structural and magnetic transitions in the distorted inverse trirutile $\mathrm{M}{\mathrm{n}}_2\mathrm{Te}{\mathrm{O}}_6$ have been studied between 1.5 and 300 K using magnetization, dielectric permittivity, and specific heat measurements combined with synchrotron x-ray- and neutron-diffraction techniques on polycrystalline samples. A first-order structural transition, strongly hysteretic, occurs progressively over a large temperature span and is characterized by a broad maximum peaking at 53 K in the specific heat data. This structural transition is followed by two antiferromagnetic transitions, to commensurate and incommensurate magnetic orders, at 48 and 26 K, respectively. This succession of structural and magnetic transitions is interpreted as originating from a delicate balance between Jahn-Teller distortion of $\mathrm{Mn}{\mathrm{O}}_6$ octahedra, rigid $\mathrm{Te}{\mathrm{O}}_6$ units, and their consequences on orbital and spin orderings.

Figure 1

Room-temperature monoclinic structure of $\mathrm{M}{\mathrm{n}}_2\mathrm{Te}{\mathrm{O}}_6(P{2}_1/c$ space group with $a=9.103\AA ,b=13.046\AA ,c=6.466\AA$, and $\beta =90.{03}^{\circ })$ [9] projected along $a$ (a) and $c$ (b). Elongated and compressed $\mathrm{Mn}{\mathrm{O}}_6$ octahedra are highlighted by dashed and full black lines corresponding to long and short Mn-O distances, respectively. Two types of $\text{−}{\left(\mathrm{Mn}\text{−}\mathrm{Mn}\text{−}\mathrm{Te}\right)}_{\infty }\text{−}$ chains run along $a,\mathrm{Mn}{\mathrm{O}}_6$, and $\mathrm{Te}{\mathrm{O}}_6$ octahedra are in pink/orange/yellow/purple, and dark/light green, respectively.

Figure 2

(a) Magnetic susceptibility curves of several $\mathrm{M}{\mathrm{n}}_2\mathrm{Te}{\mathrm{O}}_6$ samples (as-prepared sample in dark pink and ${\mathrm{O}}_2$-annealed samples from gray to green with increasing time of the plateau at 700 °C) recorded in zero-field-cooled warming, 0.01 T [χ$\left(T\right)$, left $y$ axis] and associated inverse curves with Curie-Weiss fitting (dotted lines) [1/χ$\left(T\right)$, right $y$ axis]. (b) SXRPD patterns (in a small selected 2θ range) of as-prepared and annealed samples, indexation corresponding to the space group and lattice parameters given on each side. (c), (d) Corresponding SEM images.

Figure 3

(a) $\mathrm{M}{\mathrm{n}}_2\mathrm{Te}{\mathrm{O}}_6$χ$\left(T\right)$ curves recorded in 1-zfcw, 2-fcc, and 3-fcw modes (left $y$ axis), and corresponding $T$ derivative (d2-fcc and d3-fcw) curves (right $y$ axis). (b) Comparison of the χ$\left(T\right)$ curves measured in 0.01 T—like in panel (a)—with the curves measured in 5 T (4-fcc and 5-fcw). (c) ac susceptibility curves while cooling or warming measured at three frequencies between ${10}^2$ and ${10}^4$ Hz.

Figure 4

Dielectric permittivity ε′ versus temperature, recorded while cooling or warming between 10 and 100 K, in zero magnetic field (left $y$ axis). Inverse of fcc and fcw magnetic susceptibility measured in 0.01 T, in the same temperature range, with the corresponding Curie-Weiss fitting as dotted lines (right $y$ axis).

Figure 5

Isothermal half-loop magnetization curves versus magnetic field, applied from 0 to 14 T then back to 0 T. Curves are split into two panels for clarity: (a) $T=5$ and 60 K, (b) $T=30$, 40, and 50 K.

Figure 6

Temperature evolution of the specific heat $C_{\mathrm{p}}/T$ of $\mathrm{M}{\mathrm{n}}_2\mathrm{Te}{\mathrm{O}}_6$, in QD mode (black symbols) and PBP mode (red line) applied to the heating branches of 50 overlapping pulses (details in the Experimental section). Red and black triangles indicate first- and second-order transitions, respectively. Inset: Zoom in the 20–40 K range.

Figure 7

Synchrotron x-ray data of $\mathrm{M}{\mathrm{n}}_2\mathrm{Te}{\mathrm{O}}_6$ versus temperature: (a) cooling and (b) warming runs, showing the strong hysteresis of the structural transition. Intensities are displayed in logarithmic scale to highlight the weak reflections growing below $T_{\mathrm{N}2}$. The extended temperature range in which the structural transition takes place is highlighted by the white vertical arrows delimiting the coexistence of the two (RTM+LTM) phases (based on a 10% threshold).

Figure 8

Synchrotron x-ray data of $\mathrm{M}{\mathrm{n}}_2\mathrm{Te}{\mathrm{O}}_6$ in the $1.2–2.8\text{−}{\AA }^{-1}$ range, at 10 K (blue), 50 K (dark yellow), 120 K (green), and 300 K (red) (data are shifted for clarity). Inset: Zoom-in on the low-intensity area of 10 and 300 K patterns. The small Bragg peaks outlined by empty down triangles result from the doubling along the $b$ axis of the inverse trirutile cell (HTT) and are indexed in the RTM cell. The superstructure Bragg peaks only observed in the LTM phase are shown by small black arrows.

Figure 9

Temperature evolution of the cell parameters of $\mathrm{M}{\mathrm{n}}_2\mathrm{Te}{\mathrm{O}}_6$ extracted from Le Bail refinements of the synchrotron x-ray data collected during the warming run: (a) cell parameter $a$ and monoclinic angle β, (b) cell parameter $b$, and (c) cell parameter $c$ and cell volume $V$. The shaded pink area corresponds to the biphasic domain, using a 10% phase threshold as in Fig. 7.

Figure 10

Temperature evolution of the neutron-diffraction patterns (G4.1 data) in the $0.2–1.8\text{−}{\AA }^{-1}$ range (patterns recorded in warming). $T_{\mathrm{S}}$ is marked in yellow, $T_{\mathrm{N}1}$ in purple, and $T_{\mathrm{N}2}$ in black. Propagation vectors (circles and squares for ${\mathbf{k}}_{\mathbf{1}}$ and ${\mathbf{k}}_{\mathbf{2}}$, respectively) are given for the main magnetic Bragg peaks.

Figure 11

Le Bail fitting of the LTM crystal structure of $\mathrm{M}{\mathrm{n}}_2\mathrm{Te}{\mathrm{O}}_6$ at 27 K (WISH data), with magnetic peaks indexed with ${\mathbf{k}}_{\mathbf{1}}=\left(1/200\right)$ and ${\mathbf{k}}_{\mathbf{2}}=\left(01/20\right)$. Gray stars outline weak additional magnetic peaks that are enlarged in the inset.

Figure 12

(a) Temperature evolution of chosen integrated magnetic Bragg peaks (from G4.1 data). The arrow shows the maximum seen on the intensity of the $\left(\overline{1}\overline{2}1\right)\left(\overline{1}21\right)+{\mathbf{k}}_{\mathbf{1}}$ Bragg peak. (b), (c) Views of the magnetic order derived from symmetry analysis. Octahedra are drawn around Mn (pink) only (not for Te in green), the ellipse underlines a pair of edge-sharing $\mathrm{Mn}{\mathrm{O}}_6$ octahedra, and both sets of structural axis (RTM and HTT) are given for comparison with the closely related model proposed in Ref. [8].