Long-range magnetic ordering in Li2MnGeO4 and precursor short-range spin correlations

Abstract

Long-range magnetic ordering and short-range spin correlations in layered noncentrosymmetric orthogermanate ${\mathrm{Li}}_{2}\mathrm{MnGe}{\mathrm{O}}_{4}$ were studied by means of polarized and unpolarized neutron scattering. The combined Rietveld refinement of synchrotron and neutron powder diffraction data at room temperature within the $Pmn{2}_{1}$ space group allowed us to specify the details of the crystal structure. According to the additional Bragg peaks in low-temperature neutron diffraction patterns a long-range antiferromagnetic ordering with the propagation vector $k=\phantom{\rule{0.16em}{0ex}}(1/2\phantom{\rule{0.16em}{0ex}}1/2\phantom{\rule{0.16em}{0ex}}1/2)$ has been found below ${T}_{N}\ensuremath{\approx}8\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Symmetry analysis revealed the model of the ground state spin structure within the ${C}_{a}c$ (no. 9.41) magnetic space group. It is represented by the noncollinear ordering of manganese atoms with a refined magnetic moment of $4.9\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}/{\mathrm{Mn}}^{2+}$ at 1.7 K, which corresponds to the saturated value for the high-spin configuration $S=5/2$. Diffuse magnetic scattering was detected on the neutron diffraction patterns at temperatures just above ${T}_{N}$. Its temperature evolution was investigated in detail by polarized neutron scattering with the following XYZ-polarization analysis. Reverse Monte Carlo simulation of diffuse scattering data showed the development of short-range ordering in ${\mathrm{Li}}_{2}\mathrm{MnGe}{\mathrm{O}}_{4}$, which is symmetry consistent on a small scale with the long-range magnetic state below ${T}_{N}$. The reconstructed radial spin-pair correlation function $S(0)\phantom{\rule{0.16em}{0ex}}S(r)$ displayed the predominant role of antiferromagnetic correlations. It was found that spin correlations are significant only for the nearest magnetic neighbors and almost disappear at $r\ensuremath{\approx}12\phantom{\rule{0.16em}{0ex}}\AA{}$ at 10 K. Temperature dependence of the diffuse scattering implies short-range ordering long before the magnetic phase transition. Besides, the spin arrangement was found to be similar in both cases above and below ${T}_{N}$. As a result, an exhaustive picture of the gradual formation of magnetic ordering in ${\mathrm{Li}}_{2}\mathrm{MnGe}{\mathrm{O}}_{4}$ is presented.