Magnetic structures of the rare-earth quadruple perovskite manganites $R{\mathrm{Mn}}_7{\mathrm{O}}_{12}$

We report a neutron powder diffraction study of $R{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ quadruple perovskite manganites with $R=\mathrm{La}$, Ce, Nd, Sm, and Eu. We show that in all measured compounds concomitant magnetic ordering of the $A$ and $B$ manganese sublattices occurs on cooling below the Néel temperature. The respective magnetic structures are collinear, with one uncompensated ${\mathrm{Mn}}^{3+}$ moment per formula unit as observed in bulk magnetization measurements. We show that both ${\mathrm{LaMn}}_7{\mathrm{O}}_{12}$ and ${\mathrm{NdMn}}_7{\mathrm{O}}_{12}$ undergo a second magnetic phase transition at low temperature, which introduces a canting of the $B$-site sublattice moments that is commensurate in ${\mathrm{LaMn}}_7{\mathrm{O}}_{12}$ and incommensurate in ${\mathrm{NdMn}}_7{\mathrm{O}}_{12}$. This spin canting is consistent with a magnetic instability originating in the $B$-site orbital order. Furthermore, ${\mathrm{NdMn}}_7{\mathrm{O}}_{12}$ displays a third magnetic phase transition at which long-range ordering of the Nd sublattice modifies the periodicity of the incommensurate spin canting. Our results demonstrate a rich interplay between transition-metal magnetism, orbital order, and the crystal lattice, which may be fine-tuned by cation substitution and rare-earth magnetism.

Figure 1

The ${\mathrm{LaMn}}_7{\mathrm{O}}_{12}$ temperature dependence of (a) field-cooled magnetic susceptibility, (b) the $A$- and $B$-site ordered magnetic moments, (c) the global tilt of the $\mathbf{k}=(0,0,0)$ magnetic structure component, and (d) the canting angle of the Mn4 and Mn5 moments due to the evolution of the $\mathbf{k}=(0,1,0)\alpha$ mode, defined as ${tan}^{-1}(m_{\alpha }/m_{\chi })$.

Figure 2

Neutron powder diffraction data measured from ${\mathrm{LaMn}}_7{\mathrm{O}}_{12}$ in bank 2 (average $2\theta =58.3^{\circ }$) of the WISH diffractometer. Diffraction data (red points) collected in the (a) paramagnetic, (b) AFM I, and (c) AFM II phases are shown. The fitted nuclear (top tick marks) and magnetic (bottom tick marks) structural models are shown as a solid black line. Tick marks corresponding to ${\mathrm{Mn}}_3{\mathrm{O}}_4$ (3.4 wt %), ${\mathrm{LaMnO}}_3$ (0.5 wt %), and La(${\mathrm{CO}}_3$)(OH) (0.9 wt %) impurity phases have been omitted for clarity. A difference pattern ($I_{\mathrm{obs}}-I_{\mathrm{calc}}$) is given as a blue solid line at the bottom of each panel.

Figure 3

(a)–(c) Antiferromagnetic modes of the $B$-site sublattice, where yellow and black spheres represent moments of opposite sign. The refined magnetic structures of (d) the AFM I and (e) AFM II phases of ${\mathrm{LaMn}}_7{\mathrm{O}}_{12}$ are shown, with the $A$ sublattice on the left and the $B$ sublattice on the right. The orthogonal $\chi$ and $(\alpha +\gamma )$ components of the ground-state $B$ sublattice magnetic structure are shown as thin black and red arrows, respectively. In all panels the $I2/m$ quadruple perovskite unit cell is drawn with black lines.

Figure 4

The ${\mathrm{NdMn}}_7{\mathrm{O}}_{12}$ temperature dependence of (a) field-cooled magnetic susceptibility, (b) the $A$-site, $B$-site, and Nd ordered magnetic moments, (c) the global tilt of the $\mathbf{k}=(0,0,0)$ magnetic structure component, and (d) the maximum canting angle of the Mn4 and Mn5 moments due to the evolution of the $\mathbf{k}=(k_x,1,k_z)\alpha$ mode, defined as ${tan}^{-1}(m_{\alpha }/m_{\chi })$. The inset of (d) gives the temperature dependence of the incommensurate propagation vector components, $k_x$ and $k_z$.

Figure 5

Neutron powder diffraction data measured from ${\mathrm{NdMn}}_7{\mathrm{O}}_{12}$ in bank 2 (average $2\theta =58.3^{\circ }$) of the WISH diffractometer. Diffraction data (red points) collected in the (a) paramagnetic, (b) AFM I, (c) AFM II, and (d) AFM ${\mathrm{II}}^{\prime }$ phases are shown. The fitted nuclear (top tick marks) and magnetic (bottom tick marks) structural models are shown as a solid black line. A difference pattern ($I_{\mathrm{obs}}-I_{\mathrm{calc}}$) is given as a blue solid line at the bottom of each panel. The dashed line in the inset to (d) shows the calculated peak position for the commensurate propagation vector $(1/3,1,0)$.

Figure 6

(a) The refined $A$-site magnetic structure of the AFM ${\mathrm{II}}^{\prime }$ phase of ${\mathrm{NdMn}}_7{\mathrm{O}}_{12}$. (b) The incommensurate “rocking” of $B$-site magnetic moments along the crystallographic $a$ axis ($\parallel k_x$). In all panels the $I2/m$ quadruple perovskite unit cell is drawn with black lines.

Figure 7

The temperature dependence of the 1-T field-cooled magnetic susceptibility (blue lines) and the AFM I $A$- and $B$-site magnetic moments (black circles and red squares, respectively) of ${\mathrm{CeMn}}_7{\mathrm{O}}_{12}$, ${\mathrm{SmMn}}_7{\mathrm{O}}_{12}$, and ${\mathrm{EuMn}}_7{\mathrm{O}}_{12}$.

Figure 8

Neutron powder diffraction data measured from ${\mathrm{CeMn}}_7{\mathrm{O}}_{12}$, ${\mathrm{SmMn}}_7{\mathrm{O}}_{12}$, and ${\mathrm{EuMn}}_7{\mathrm{O}}_{12}$ in bank 2 (average $2\theta =58.3^{\circ }$) of the WISH diffractometer. Diffraction data (red points) collected in the (a)–(c) paramagnetic and (d)–(f) AFM I phases are shown. The fitted nuclear and magnetic structural models are shown as solid black lines, with the respective peak positions shown by a single sets of black tick marks. A difference pattern ($I_{\mathrm{obs}}-I_{\mathrm{calc}}$) is given as a blue solid line at the bottom of each panel. Tick marks from impurity phases have been omitted for clarity.

Figure 9

The magnetic moment per formula unit of our polycrystalline ${\mathrm{LaMn}}_7{\mathrm{O}}_{12}$ sample, measured as a function of magnetic field above and below $T_2$.