Honeycomb-lattice antiferromagnet Mn₂V₂O₇: a temperature-dependent x-ray diffraction, neutron diffraction and ESR study

The quality of synthesized sample Mn₂V₂O₇ was examined by XRD. Figure 1 shows the XRD patterns measured at 300 K and 10 K, respectively. By adopting Rietveld refinement method, there is a good agreement between observed XRD pattern and calculated one with a weighed pattern factor R_wp  =  16.9% (10 K) and R_wp  =  14.6% (300 K), respectively. At 300 K, Mn₂V₂O₇ crystallizes in monoclinic (C2/m) structure and the derived lattice parameters are a  =  6.7236(4) Å, b  =  8.7211(5) Å, c  =  4.9641(3) Å and β  =  103.775(3)°, whereas the symmetry of the system is lowered to triclinic (P-1) at 10 K and the lattice parameters are a  =  6.8660(4) Å, b  =  7.9351(2) Å, c  =  10.9029(2) Å, α  =  87.407(7)°, β  =  72.001(9)°, and γ  =  83.238(2)°. The refined atomic positions for 300 K (β-monoclinic phase) and 10 K (α-triclinic phase) are listed in tables 1 and 2, respectively.

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The temperature dependent XRD patterns were collected by cooling the sample first, and then heating the sample within a temperature range between 300 and 10 K. Figure 2 plots the temperature evolution of the two strongest peaks, A and B. The peak A is composed of (2 0 0), (1 1 1) and (0 2 1) reflections, and the peak B is a single (−2 0 1) reflection, according to the monoclinic β-phase. As the sample is cooled down from 300 K, the intensity of A and B is slightly reduced (see figure 2(a)). Meanwhile, the reflections A and B move to higher Bragg angles. All reflections in the XRD patterns between 300 and 280 K can be properly indexed with the monoclinic structure model. Once the temperature decreases below 270 K, a new peak located between A and B appears and it splits into two peaks (D and E) with a further decrease in temperature, accompanied with the complete suppression of peak B. According to the low-temperature triclinic structure model, peak C consists of (2 1 1), (2 0 0), (2 0 2) and (1   −  2 0) reflections, peak D consists of (0   −  1 3), (0 2 2), (1   −  1 3) while peak E consists of (2 1 0), (0   −  2 2) and (2 1 2) reflections. Both peaks D and E shift slightly toward higher Bragg angle with decreasing temperature, suggesting a decrease in the lattice parameters. The peak splitting in XRD patterns provides direct evidence of monoclinic (β)-triclinic (α) structural phase transition. The system is monoclinic above 270 K but it transforms into triclinic structure below 210 K, while two phases coexist between 270 and 210 K.

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As the Mn₂V₂O₇ sample is warmed up from 10 K (see figure 2(b)), the pure α-phase holds until 240 K. Above this temperature the β-phase appears and coexists with the α-phase up to 300 K. The obvious difference in the XRD patterns between cooling and heating procedures suggests that the monoclinic (β) to triclinic (α) structural phase transition is strongly thermally hysteretic, thus confirming the first-order character of the structural phase transition. A scrutiny of structural features reveals that the honeycomb layers in the β-Mn₂V₂O₇ are parallel to the (0 0 1) plane and those in the α-Mn₂V₂O₇ are parallel to the (1   −  1 0) plane. The primitive vectors, a, b and c, in the β-phase can be converted into a', b' and c' in the α-phase by the following correlation equations: a'  =  1/2(a  −  b  +  2c), b'  =  1/2(a  −  b  −  2c) and c'  =  a  +  b. Figure 3 shows the temperature dependence of the lattice parameters a', b', c' and the unit-cell volume in the α-phase representation. In the pure β-phase zone, the lattice parameters have no significant change (see figure 3(a)), while the lattice parameters exhibit a decrease upon cooling in the pure α-phase zone. In the region of coexistence of the two phases, the lattice parameters of the two different structures deviate largely from each other.

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We now discuss how the honeycomb lattice is distorted during the temperature-induced first-order structural phase transition. We choose two temperatures (10 K and 300 K) far away from the critical temperature to analyze this distortion by comparing the manganese hexagon. The honeycomb lattice at 300 K has a higher crystallographic symmetry, the distance of nearest-neighbor Mn²⁺ ions along the b-axis is 3.3097 Å, while the other four edges of manganese hexagon are all 3.5223 Å in length. With decreasing temperature, the lattice starts to deform and reaches maximum in magnitude at 10 K. Our Rietveld refinement for the structural parameters shows that there are two different kinds of Mn–Mn bond lengths in the manganese hexagon (3.3097 Å and 3.3097 Å) at 300 K, while at 10 K the manganese hexagon consists of three kinds of Mn-Mn bond lengths (3.3278 Å, 3.4173 Å and 3.3900 Å).

The magnetization measurement confirms the AFM ordering at T_N  =  23 K. The top inset of figure 4 shows that the 1/χ(T) curve above 50 K follows the Curie–Weiss law with Weiss constant θ_p  =  −32 K and an effective magnetic moment µ_eff  =  5.4 μ_B/Mn²⁺, in good agreement with previous report [21]. The main panel of figure 4 is the field dependence of magnetization measured at 2 K under applied magnetic field up to 9 T. The M–H curve is linear in low field because of the AFM ground state. A field-induced spin-flop transition takes place at H_sf  =  2.5 T, indicating the existence of magnetic anisotropy, which is also confirmed by the frequency-dependent EPR spectra collected at 2 K. The spin-flop transition reveals the spin structure variation at low temperature. The critical field is similar with the value obtained from single crystal along [0 0 1] direction of α-phase [29]. Above H_sf, the magnetization increases continuously. The extrapolation of the linear part points to the origin, which is expected for the spin-flop transition in AFM state. The M–T curves of magnetically aligned sample measured at 0.1 T are shown in the bottom inset of figure 4, which also reveals the presence of a big magnetic anisotropy in this compound.

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In order to study microscopic magnetism of Mn₂V₂O₇, we performed neutron diffraction experiment with a polarization analysis. The neutron diffraction patterns of α-Mn₂V₂O₇ at 3 K (<T_N) are shown in figure 5. The nuclear coherent, spin incoherent and magnetic signals are well separated from the total neutron scattering of the sample. In contrast to the spin incoherent scattering, which is almost featureless in the whole Q range from 0.4 to 2.6 Å⁻¹, both the nuclear and magnetic contributions are significant. Owing to the formation of long-range ordering of Mn²⁺ moments, the magnetic scattering reflections are clearly observed and some of them exhibit similar intensities compared to nuclear reflections. Apparently, most of the magnetic reflections locate in low Q range, suggesting the presence of a magnetic superstructure. It was found that the magnetic structure of α-Mn₂V₂O₇ might be incommensurate in nature since the magnetic reflections cannot be indexed properly with commensurate propagation vector. Given the fact that α-Mn₂V₂O₇ possesses very low symmetry and four different Mn sites, it is nontrivial to determine the magnetic structure of Mn₂V₂O₇ based on barely the neutron powder diffraction data. Future single crystal neutron diffraction studies are necessary to unambiguously solve the magnetic structure.

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Figure 6 shows the evolution of magnetic Bragg reflections in low-Q range at different temperatures. Upon the increase in temperature, the long-range magnetic order diminishes gradually and an order–disorder transition takes place as indicated by the decrease of intensity of magnetic reflections. The temperature dependence of integrated intensity of magnetic reflections around 0.7 Å⁻¹ was plotted in the inset of figure 6, showing the onset of magnetic order at T_N  =  23(2) K.

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The high-field ESR is a powerful tool to reveal the ordered state of magnetic systems with large magnetic anisotropy. Figure 7 shows the temperature-dependent resonance spectra measured at 120 GHz. A single PM resonance peak is observed at high temperature. The g value is derived to be g  =  1.99, a typical value of PM Mn²⁺ ion. Decreasing temperature leads to a broadening of the peak. Below T_N  =  23 K, the resonance peak splits into three modes. The mode 2 is stronger in intensity than the other two modes. With decreasing temperature, there is no shift of mode 1, whereas mode 2 shifts significantly toward the low field. The third mode also exhibits a slight shift and it could be ascribed to the EPR with a larger g value (see below), due to a small amount of paramagnetic impurities present in the sample.

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The frequency dependence of the ESR spectra measured at 2 K is shown in figure 8. Above 85 GHz, mode 1 and mode 2 as well as the EPR mode are observed. With increasing frequency, the difference of resonance fields between mode1 and mode 2 becomes smaller. Below 85 GHz, a new mode, which is denoted as mode 3, appears and its resonance field increases with decreasing frequency. There is an additional mode, which is marked by asterisks in figure 8, and its origin is not clear. Figure 9 gives the frequency-field (f-H) relationship, which indicates that the observed resonances are AFM resonance modes with easy-axial type anisotropy [30–37]. The EPR mode is linear and passes through the origin with g  =  2.11.

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The AFM resonances with easy-axis anisotropy can be understood within the framework of the conventional molecule-field theory [38, 39]. For a simple two-sublattice collinear antiferromagnet, the zero-field gap is given by Δ  =  gμ_BH_sf/h for AFM state [40], in which h is the Plank constant. With H_sf  =  2.5 T from the magnetization data, the AFM gap is derived to be about Δ  =  75 GHz. According to [41], mode 1 and mode 3 belong to H_// easy axis and follow hf/gμ_B  =  $\sqrt{H_{\text{Res}}^{2}-{{ \Delta }^{2}}}$ and hf/gμ_B  =  $\sqrt{{{ \Delta }^{2}}-H_{\text{Res}}^{2}}$, respectively. The mode 2 corresponds to H_⊥ easy axis and can be described as hf/gμ_B  =  $\sqrt{H_{\text{Res}}^{2}+{{ \Delta }^{2}}}$, where H_Res is the resonance field. The zero-field AFM gap originates from the exchange interaction H_E and magnetic anisotropy H_A, it can be expressed as Δ  =  $\sqrt{2{{H}_{\text{E}}}{{H}_{\text{A}}}}$. Figure 9 shows that our ESR data do not match with the theoretical model completely. This is probably because our treatment using a two-sublattice model is only an approximation. In fact, there are four different Mn ions in α-Mn₂V₂O₇ and the magnetic structure is very complicated based on our neutron scattering experiments.