Magnetic ordering in La1.5Ca0.5CoO4 revealed by resonant magnetic x-ray scattering and neutron diffraction

We report a comprehensive study on the magnetic ground state of ${\mathrm{La}}_{1.5}{\mathrm{Ca}}_{0.5}\mathrm{Co}{\mathrm{O}}_{4}$ combining single crystal neutron diffraction and resonant magnetic x-ray scattering at the $\mathrm{Co}\phantom{\rule{0.16em}{0ex}}{L}_{2,3}$ edges. Three single-crystal samples obtained from the same boule were investigated exhibiting magnetic phase transitions from a high-temperature paramagnetic phase to an antiferromagnetic phase at ${T}_{\mathrm{N}}\ensuremath{\approx}52\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Single crystal neutron diffraction reveals that the crystal structure at room temperature shows an orthorhombic $A$-centered lattice but with $a$ and $b$ axes almost equal in length. The structural phase transition (charge-ordering-like) from the parent tetragonal cell takes place above 523 K into the space group $A2mm$ where two nonequivalent compressed and expanded $\mathrm{Co}{\mathrm{O}}_{6}$ octahedra are ordered showing a checkerboard pattern in the $ab$ plane. The charge segregation between the nonequivalent Co sites is about 0.4(1) electrons. Resonant magnetic x-ray reflections indexed as ${(1/4,\phantom{\rule{0.16em}{0ex}}1/4,\phantom{\rule{0.16em}{0ex}}0)}_{\mathrm{t}}$, ${(1/4,\phantom{\rule{0.16em}{0ex}}1/4,\phantom{\rule{0.16em}{0ex}}1)}_{\mathrm{t}}$, and ${(1/4,\phantom{\rule{0.16em}{0ex}}1/4,\phantom{\rule{0.16em}{0ex}}1/2)}_{\mathrm{t}}$ in the parent tetragonal cell were observed at low temperature at the $\mathrm{Co}\phantom{\rule{0.16em}{0ex}}{L}_{2,3}$-edge energy range. The resonant spectral shape, with a noticeable absence of any resonant enhancement at the $\mathrm{Co}\phantom{\rule{0.16em}{0ex}}{L}_{2}$ edge, indicates that only ${\mathrm{Co}}^{2+}$-like ions participate in the magnetic ordering. The polarization analysis discloses that the orientation of Co magnetic moments is the same for the three magnetic orders and they are long-range ordered along the diagonal in the $ab$ plane of the parent tetragonal cell with a slight tilt in the $c$ axis. Despite the onset temperatures for the three resonant magnetic reflections being the same, $\ensuremath{\approx}55\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, different thermal behavior is observed between ${(1/4,\phantom{\rule{0.16em}{0ex}}1/4,\phantom{\rule{0.16em}{0ex}}1/2)}_{\mathrm{t}}$ and ${(1/4,1/4,L)}_{\mathrm{t}}$ ($L=\mathrm{integer}$) reflections whose intensities maximize at different temperatures, suggesting the coexistence of two magnetic arrangements. Moreover, the intensity of the ${(1/4,\phantom{\rule{0.16em}{0ex}}1/4,\phantom{\rule{0.16em}{0ex}}1/2)}_{\mathrm{t}}$ magnetic reflection is at least ten times larger than that of the ${(1/4,1/4,L)}_{\mathrm{t}}$ $(L=\mathrm{integer})$ ones. On the other hand\, neutron diffraction measurements only detect a single type of antiferromagnetic ordering following the propagation vector $\mathbit{k}={(1/4,\phantom{\rule{0.16em}{0ex}}1/4,\phantom{\rule{0.16em}{0ex}}1/2)}_{\mathrm{t}}$ that involves half of the Co atoms in the unit cell. We conclude that the bulk magnetic order in ${\mathrm{La}}_{1.5}{\mathrm{Ca}}_{0.5}\mathrm{Co}{\mathrm{O}}_{4}$ corresponds then to this propagation vector $\mathbit{k}={(1/4,\phantom{\rule{0.16em}{0ex}}1/4,\phantom{\rule{0.16em}{0ex}}1/2)}_{\mathrm{t}}$ while ${(1/4,\phantom{\rule{0.16em}{0ex}}1/4,\phantom{\rule{0.16em}{0ex}}0)}_{\mathrm{t}}$ and ${(1/4,\phantom{\rule{0.16em}{0ex}}1/4,\phantom{\rule{0.16em}{0ex}}1)}_{\mathrm{t}}$ magnetic reflections correspond to a minority magnetic phase that must be due to changes in the oxygen stoichiometry near the surface.