New ($\alpha \beta \gamma$)-incommensurate magnetic phase discovered in the ${\mathrm{MnCr}}_2{\mathrm{O}}_4$ spinel at low temperatures

The nuclear and magnetic structure of the spinel $\mathrm{Mn}{\mathrm{Cr}}_2{\mathrm{O}}_4$ is reinvestigated by magnetization, specific heat, and neutron diffraction experiments at different temperatures. Four samples of this spinel synthesized under different atmospheres are analyzed. Through these experiments, a new magnetic phase, with propagation vector ${\vec{k}}_{\mathrm{I}2}=\left(0.6597\left(1\right)0.5999\left(1\right)0.1996\left(2\right)\right)$, not previously reported, is identified below 18 K when the sample is synthesized under a reductive atmosphere. A possible explanation for the different magnetic ground states observed is given based on the competition among the main exchange interactions present in the system. Using the magnetic superspace group formalism, the symmetry of the nuclear and magnetic structures is determined. The presence of transverse conical magnetic structures in the lower-temperature phases allows for multiferroicity in this compound, and the electric polarization direction is determined for each magnetic phase.

Figure 1

Nuclear structure of $\mathrm{Mn}{\mathrm{Cr}}_2{\mathrm{O}}_4$ showing the octahedral (${\mathrm{CrO}}_6$), in blue, and tetrahedral (${\mathrm{MnO}}_4$), in purple, positions.

Figure 2

Temperature dependence of the magnetization with an applied magnetic field $H=200$ Oe measured after zero field cooling (ZFC) (black dots) and field cooling (FC) (red dots) procedures for samples S1R (a), S1A (b), S2R (c), and S2A (d). $T_{\mathrm{N}}$ is showed with a purple line, while $T_{\mathrm{I}1}, T_{\mathrm{I}2}$, and $T_{\mathrm{L}}$ are showed with blue, pink, and grey lines in the inserts.

Figure 3

Temperature dependence of heat capacity $C_P$ (blue dots) at zero field and ZFC (black dots) and FC (red dots) magnetization curves at $H=200$ Oe for SC1R sample. The heat capacity curve shows clearly three transitions temperatures $T_{\mathrm{N}}=40$ K, $T_{\mathrm{I}1}=20$ K, and $T_{\mathrm{I}2}=18$ K.

Figure 4

Low $Q$ part of diffraction patterns obtained at different temperatures for S1R sample at G.4.1 (a), S2R sample measured at NOVA (b), S1A sample at S-HRPD (c), and S2A sample at NOVA (d). Reflections due to the ${\mathrm{Cr}}_2{\mathrm{O}}_3$ impurity in (c) and (d) are labeled with a yellow diamond. The satellite reflections due to ${\vec{k}}_{\mathrm{I}1}$ and ${\vec{k}}_{\mathrm{I}2}$ are, respectively, indicated in the upper part of each figure with red and blue symbols (asterisk and circles). The reflections mentioned in Fig. 5, $\left(220\right)+{\vec{k}}_{\mathrm{N}}, \left(002\right)+{\vec{k}}_{\mathrm{I}1}$ and $\left(1\overline{1}1\right)+{\vec{k}}_{\mathrm{I}2}$ are, respectively, marked with black, red, and blue circles.

Figure 5

Evolution with temperature of the intensity of some magnetic reflections; $\left(220\right)+{\vec{k}}_{\mathrm{N}}$ in black, $\left(002\right)+{\vec{k}}_{\mathrm{I}1}$ in red and $\left(1\overline{1}1\right)+{\vec{k}}_{\mathrm{I}2}$ in blue for each sample. The transition temperatures determined from the magnetization measurements $T_{\mathrm{N}}, T_{\mathrm{I}1}, T_{\mathrm{I}2}$, and $T_{\mathrm{L}}$ are showed with purple, blue, pink, and grey lines.

Figure 6

Temperature-dependent changes in the lattice parameters for samples S1R and S1A. To enable easy comparison at lower temperature values, the temperature axis is presented on a logarithmic scale. The lattice parameters are referred to the standard setting of the paramagnetic group.

Figure 7

Representative Rietveld refinements at selected temperatures for sample S1R. In red are shown the observed points and in back continuous line the calculated pattern with the parameters shown in Table 2. The blue continuous line and the green ticks indicate the difference between the observed and calculated profile and the nuclear and satellite peaks generated by the magnetic superspace group, respectively.

Figure 8

High-resolution diffractogram collected at $T=9.1$ K for sample S1A at the instrument S-HRPD. In red are shown the observed points and in back continuous line the calculated pattern with the parameters shown in Table 1. The blue continuous line and the green ticks indicate the difference between the observed and calculated profile and the nuclear and satellite peaks generated by the magnetic superspace group, respectively. The insert shows a zoom of the low-$Q$ part, where the scale is the same as in Fig. 7.

Figure 9

Views of the magnetic structures determined for each phase: (a) $\left(000\right)$, (b) $\left(\delta \delta 0\right)$, and (c) $\left(\alpha \beta \gamma \right)$.

Figure 10

Temperature evolution of the parameters defining the magnetic structures: $M_j$ (a), $\alpha$ (b), and $M_{j,0}$ (c) extracted from the Rietveld analysis of sample S1R. A comparison between the magnetization obtained from the fits to the NPD data (red) and the susceptibility measured at ZFC (black) is shown in (d).

Figure 11

Magnetic phases observed for each sample together with their phase transition temperatures. Green: paramagnetic order, purple: $\left(000\right)$ - FIM phase, pink: $\left(\delta \delta 0\right)$ - incommensurate phase, blue: $\left(\alpha \beta \gamma \right)$ - incommensurate phase. For samples S2R and S2A, the percentages of each incommensurate phase present at the lowest temperature measured is given.