Frustration-driven magnetic order in hexagonal InMnO${}_3$

InMnO${}_3$ is a peculiar member of the hexagonal manganites h-$R$MnO${}_3$ (where $R$ is a rare-earth metal element), showing crystalline, electronic, and magnetic properties at variance with the other compounds of the family. We have studied high quality samples synthesized at high pressure and temperature by powder neutron diffraction. The position of the Mn ions is found to be close to the threshold $x=1/3$ where superexchange Mn-Mn interactions along the $\mathit{c}$ axis compensate. Magnetic long-range order occurs below $T_{\mathrm{N}}=120\left(2\right)$ K with a magnetic unit cell doubled along $\mathit{c}$, whereas short-range two-dimensional dynamical spin correlations are observed above $T_{\mathrm{N}}$. We propose that pseudodipolar interactions are responsible for the long period magnetic structure.

Figure 1

Observed and fullprof calculated NPD pattern at room temperature. The Bragg reflections (tics) and the difference between the observed and calculated patterns are plotted at the bottom.

Figure 2

Refined position $x$ of Mn versus temperature in reduced units of the cell parameter $a$. The horizontal black line is located at $x=1/3$, the red line is a guide to the eyes.

Figure 3

Interplane exchange paths versus Mn position. Two exchange paths $J{z}_1$ and $J{z}_2$ are in competition and the $x=1/3$ Mn position corresponds to the specific case $J{z}_1=J{z}_2$. Inset: in-plane exchange paths leading to the 120${}^{\circ }$ magnetic configuration.

Figure 4

Upper panel: integrated intensity of the (1 0 1/2) Bragg reflection versus temperature. The red dashed line is a guide to the eyes. Lower panel: observed NPD pattern at low temperature ($T=1.5$ K). The $\mathbf{k}=(0$ 0 $\frac{1}{2}$) propagation vector is easily observed through the existence of (1 0 $\frac{(l+1)}{2}$) Bragg reflections.

Figure 5

Magnetic structures associated to the four unidimensional irreductible representations of the $P{6}_{3}cm$ space group. Red arrows indicate magnetic moments with real Fourier components, black arrows indicate moments with imaginary Fourier components.

Figure 6

${}^{57}$Fe Mössbauer spectra in InMn${}_{0.99}$Fe${}_{0.01}$O${}_3$ below and above $T_N=120$ K. At $T=140\text{K}$ a quadrupolar doublet characteristic of paramagnetic Fe${}^{3+}$ is observed. At $T=4.2\text{K}$ the spectrum shows a six-lines hyperfine pattern perfectly reproduced by a single hyperfine magnetic field.

Figure 7

Observed and fullprof calculated NPD patterns at several temperatures. Above $T_{\mathrm{N}}$ a strong diffuse scattering is observed on the patterns recorded on 3T2 spectrometer (top) with $\lambda =1.225\text{Å}$. This scattering is not visible on the G6.1 patterns (bottom) for which $\lambda =4.74\text{Å}$.

Figure 8

Refined correlation length versus temperature (red dots) and fit of the critical exponent $\nu$ (solid line). Inset: intensity recorded at $T=130$ K on the 3T2 spectrometer. The dashed line is a fit of the diffuse intensity with a Warren function.

Figure 9

Left: numerical calculation of the dynamical structure factor of spin waves along the (0 0 $q$${}_l$) direction in case of pseudodipolar coupling between Mn. Right: numerical calculation of the dynamical structure factor of spin waves along the (0 0 $q$${}_l$) direction in the case of antiferromagnetic interplane exchange coupling between Mn.