Pressure-induced commensurate order in ${\mathrm{TbMn}}_2{\mathrm{O}}_5$ and ${\mathrm{DyMn}}_2{\mathrm{O}}_5$: Influence of rare-earth anisotropy and $\mathit{3}\mathit{d}\mathit{\text{−}}\mathit{4}\mathit{f}$ exchange

The magnetic structure of ${\mathrm{TbMn}}_2{\mathrm{O}}_5$ and ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ multiferroics has been studied by high-pressure neutron diffraction in a large pressure range up to 6.6 GPa. In both cases, we observe a pressure-induced commensurate magnetic phase with propagation vector $\left(\frac{1}{2}0\frac{1}{2}\right)$, growing with pressure at the expense of the ambient pressure phases. Being previously observed in ${\mathrm{YMn}}_2{\mathrm{O}}_5$ and ${\mathrm{PrMn}}_2{\mathrm{O}}_5$, this phase is most likely a generic feature of the $R{\mathrm{Mn}}_2{\mathrm{O}}_5$ multiferroic family. A simple model is proposed to explain qualitatively the emergence of this pressure-induced phase. Differences between ${\mathrm{TbMn}}_2{\mathrm{O}}_5$  and ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ behaviors at ambient and low pressures provide clues on the interaction scheme.

Figure 1

Sequence of phases observed in ${\mathrm{TbMn}}_2{\mathrm{O}}_5$: With decreasing temperature, a transition from a paramagnetic to an incommensurate spin structure occurs at $T_{N1}\left(43\mathrm{K}\right)$. The incommensurate (ICM) modulation is along ($a,b$), and ${\mathrm{TbMn}}_2{\mathrm{O}}_5$ remains paraelectric in this range. Below $T_{C1}\left(33\mathrm{K}\right)$, a transition to a commensurate (CM) magnetic phase is observed. The propagation vector is $\mathbf{k}=\left(\frac{1}{2}0\frac{1}{4}\right)$, and ${\mathrm{TbMn}}_2{\mathrm{O}}_5$ becomes ferroelectric. At $T_{C2}\left(24\mathrm{K}\right)$, a third transition back to an ICM structure occurs with $\mathbf{k}=\left(\frac{1}{2}+\delta 0\frac{1}{4}+\epsilon \right)$.

Figure 2

${\mathrm{TbMn}}_2{\mathrm{O}}_5$. Refined diffraction patterns measured at ambient pressure. (a) High-resolution pattern at ambient temperature; (b) $T=1.5\mathrm{K}$; (c) $T=25\mathrm{K}$. The patterns were refined with (b) LT-ICM and (c) CM phases, according to Ref. [33] for LT-ICM and Refs. [3, 20] for CM. The solid black line is a fullprof refinement; the tick marks show the Bragg peak positions for the structural (blue) and magnetic (red) phases. The solid blue line is the difference between the calculated and the measured patterns.

Figure 3

${\mathrm{TbMn}}_2{\mathrm{O}}_5$ refined magnetic structure. (a) at 1.5 K on the ($a,b$) plane; (b) at 25 K on the ($a,b$) plane; (c) at 25 K along the $\mathit{c}$ axis. ${\mathrm{Mn}}^{3+}$ moments and ${\mathrm{Mn}}^{4+}$ moments form AF zigzag chains. The blue (respectively, green) arrows correspond to ${\mathrm{Mn}}^{3+}$ (respectively, ${\mathrm{Mn}}^{4+}$) moments. The Tb moments (red arrows) have been reduced by a factor of 2 at 1.5 K for the sake of clarity. The black lines are guides for the eye.

Figure 4

${\mathrm{TbMn}}_2{\mathrm{O}}_5$ (a) Magnetic patterns at low temperatures showing the onset of a PCM phase at the expense of the ambient pressure ICM phase. Patterns were normalized to a structural peak, and a pattern in the paramagnetic phase was subtracted. (b) Pressure dependence of the relative amount of the PCM phase around 5 K.

Figure 5

${\mathrm{TbMn}}_2{\mathrm{O}}_5$. (a) Refined pattern at 5.6 GPa and 20 K. Red ticks: structural peaks; green ticks: magnetic peaks. The blue ticks mark the position of the Pb structural peaks (not shown here) used to probe the pressure. (b) PCM structure. ${\mathrm{Mn}}^{3+}$moments (blue arrows) and ${\mathrm{Mn}}^{4+}$ moments (green arrows) form AF zigzag chains. Tb moments are shown by red arrows.

Figure 6

${\mathrm{DyMn}}_2{\mathrm{O}}_5$. Sequence of phases with temperature as described in Ref. [34]. Between 8 and 42 K commensurate ($\epsilon =0$) and incommensurate ($\epsilon =\pm 0.015$) phases are very close to each other. They evolve differently on cooling and warming.

Figure 7

${\mathrm{DyMn}}_2{\mathrm{O}}_5$ at ambient pressure. (a) Magnetic structure with ${\mathbf{k}}_1=\left(\frac{1}{2}0\frac{1}{4}\right)$ taken from Ref. [37]; (b) magnetic structure with ${\mathbf{k}}_2=\left(\frac{1}{2}00\right)$; (c) powder magnetic pattern measured at 3.5 K. The pattern is refined by assuming the coexistence of the two phases described in (a) and (b). The solid black line is a fullprof refinement; the tick marks show the Bragg peak positions for the structural (blue), CM (red), and ICM (green) phases. The solid blue line is the difference between the calculated and the measured patterns. In the inset: zoom on the low-$Q$ area.

Figure 8

${\mathrm{DyMn}}_2{\mathrm{O}}_5$ neutron-diffraction patterns at 6.6 GPa for several temperatures.

Figure 9

${\mathrm{DyMn}}_2{\mathrm{O}}_5$. (a) Refined pattern at 6.6 GPa and 18 K assuming a planar model. Red ticks: structural peaks; green ticks: magnetic peak. The blue ticks mark the position of the Pb structural peaks used to probe the pressure. (b) PCM structure: ${\mathrm{Mn}}^{3+}$ moments: blue arrows; ${\mathrm{Mn}}^{4+}$ moments: green arrows; and ${\mathrm{Dy}}^{3+}$ moments: red arrows. For the sake of clarity the Dy arrows were increased by a factor of 3.

Figure 10

Temperature-pressure phase diagrams for ${\mathrm{TbMn}}_2{\mathrm{O}}_5$ (top) and ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ (bottom) deduced from the neutron data. The colored circles show the temperature-pressure data points and the coexistence of the magnetic phases. The phases of amounts less than 10% have been discarded. The rectangles on the left show the ambient pressure states.

Figure 11

Scheme of the different magnetic interactions in $R{\mathrm{Mn}}_2{\mathrm{O}}_5$.

Figure 12

One-dimensional (1D) chains which schematically represent the $R{\mathrm{Mn}}_2{\mathrm{O}}_5$ structure along the $\mathit{c}$ axis and illustrate the energy gains for different components $k_z$ of the propagation vector. In the simplified expressions of the energy, we consider Ising spins of unit length oriented along a given axis of the ($a,b$) plane, which coincides with the uniaxial anisotropy axis of the $R$ ion. $H_R$ is proportional to the molecular field on the $R$ site.