Magnetoelastic Coupling and Symmetry Breaking in the Frustrated Antiferromagnet $\alpha \mathrm{\text{−}}{\mathrm{NaMnO}}_2$

The magnetic and crystal structures of the $\alpha \mathrm{\text{−}}{\mathrm{NaMnO}}_2$ have been determined by high-resolution neutron powder diffraction. The system maps out a frustrated triangular spin lattice with anisotropic interactions that displays two-dimensional spin correlations below 200 K. Magnetic frustration is lifted through magneto-elastic coupling, evidenced by strong anisotropic broadening of the diffraction profiles at high temperature and ultimately by a structural phase transition at 45 K. In this low-temperature regime a three-dimensional antiferromagnetic state is observed with a propagation vector $\mathbf{k}=(\frac{1}{2},\frac{1}{2},0)$.

Figure 1

$\alpha \mathrm{\text{−}}{\mathrm{NaMnO}}_2$: (a) crystal structure in the $a_m{b}_m$ plane at room temperature. Mn and O atoms are represented as large black and small red spheres, respectively. ${\mathrm{MnO}}_6$ octahedra are shown in transparent gray together with $d_{3r^2-z^2}$ orbitals. The green and blue lines show inequivalent ($J_1$, $J_2$) magnetic interactions along $b_m$ and $[110{]}_m$ (subscript $m$ for monoclinic). (b) Temperature evolution of the magnetic susceptibility, $\chi$ ($H=1\mathrm{T}$; zero-field cooled data). Inset: the derivative of $\chi T$ vs $T$.

Figure 2

Rietveld refinement of neutron powder diffraction data obtained at 4 K for $\alpha \mathrm{\text{−}}{\mathrm{NaMnO}}_2$ in the triclinic cell. The red points and black line represent the data and calculated profile, respectively. The blue line at the bottom is the difference between observed and calculated patterns. Tick marks show the position of Bragg peaks for the nuclear (top line) and magnetic phases (bottom line). The * symbol marks the position of the $(0,\frac{1}{2},0{)}_t$ magnetic Bragg peak, indexed in the triclinic cell (subscript $t$). Inset: temperature evolution of the Warren scattering (gray symbols); black lines are fit to the data (see text for details).

Figure 3

Schematic representation of the magnetic order in the $ab$ plane for $\alpha \mathrm{\text{−}}{\mathrm{NaMnO}}_2$. The $+$ and $-$ signs indicate the direction of the magnetic moments along the $d_{3r^2-z^2}$ orbital shown in gray. The blue lines mark the high-temperature monoclinic ($a_m$, $b_m$) and low-temperature triclinic ($a_t$, $b_t$) unit cells. Red arrows show the strain directions.

Figure 4

Variation of magnetic and structural parameters vs temperature for $\alpha \mathrm{\text{−}}{\mathrm{NaMnO}}_2$. (a) Mn magnetic moment in the 3D ordered phase. (b) Correlation length of the magnetic domains in the 2D magnetic phase. (c) Selected microstrain coefficients in the 2D magnetic regime (see text for details). (d) Mn-Mn interatomic distances along the $a$ (square symbol) and $b$ axis (triangles) in the triclinic cell; the filled circles show the distances in the monoclinic phase.