Figure 1

Phase diagram of ${\mathrm{T}\mathrm{b}\mathrm{M}\mathrm{n}}_2{\mathrm{O}}_5$. (a) Propagation vector components along $a^{*}$ (open circle) and $c^{*}$ (filled circle). (b) Integrated intensity of the (100)-$\mathbf{k}$ reflection (filled circle) and background level integrated over $0.76<Q<0.87{\AA }^{-1}$ (open circles). Dielectric constant [panel (c)] and spontaneous polarization [panel (d)] in zero magnetic field (solid line) and 3 T (cross symbol) (see Ref. 7 for details). Vertical dotted lines mark the transition temperatures (see text).Reuse & Permissions

Figure 2

Temperature dependence of selected structural parameters. Left panel represents variation of lattice parameters. Right panel shows an equivalent atomic displacement parameter for selected atoms. Lines are guides to the eye.Reuse & Permissions

Figure 3

Refined magnetic structure (black arrows) and proposed polar displacements (white arrows) at 27 K. The refined magnetic moments of 1.81 and $2.40{\mu }_B$ for ${\mathrm{M}\mathrm{n}}^{4+}$ and ${\mathrm{M}\mathrm{n}}^{3+}$ are significantly lower than the expected fully ordered spin values, indicating that a significant component of the moment remains disordered. The canting angles with respect to the $a$ axis are of $24°$ and $10°$. The $c$-axis stacking of these layers can be interpreted as a pure $\dots ++--++--\dots$ sign modulation. Through the Tb layer, the coupling alternates between AFM (as in ${\mathrm{B}\mathrm{i}\mathrm{M}\mathrm{n}}_2{\mathrm{O}}_5$) and FM (as in ${\mathrm{D}\mathrm{y}\mathrm{M}\mathrm{n}}_2{\mathrm{O}}_5$). A small induced moment on Tb ($1.6{\mu }_B$) is present with the FM interlayer coupling and absent for the AFM one. This detail is essential to obtain a perfect fit of the data (Fig. 4), but the refinement is rather insensitive to the moment orientation. The Tb moment is omitted in the drawing for clarity. Roman numerals refer to the $a$-axis AFM chains (see text).Reuse & Permissions

Figure 4

Rietveld refinement pattern for ${\mathrm{T}\mathrm{b}\mathrm{M}\mathrm{n}}_2{\mathrm{O}}_5$ at 27 K. The data from three banks of detectors have been grouped on a common scale. The top and bottom rows of tick marks refer to nuclear and magnetic reflections, respectively. The inset shows the field dependence of a nuclear peak at 1.5 K.Reuse & Permissions