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 $\mathrm{Co}{L}_{2,3}$ 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 $T_{\mathrm{N}}\approx 52\mathrm{K}$. 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 ${\left(1/4,1/4,0\right)}_{\mathrm{t}}$, ${\left(1/4,1/4,1\right)}_{\mathrm{t}}$, and ${\left(1/4,1/4,1/2\right)}_{\mathrm{t}}$ in the parent tetragonal cell were observed at low temperature at the $\mathrm{Co}{L}_{2,3}$-edge energy range. The resonant spectral shape, with a noticeable absence of any resonant enhancement at the $\mathrm{Co}{L}_2$ 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, $\approx 55\mathrm{K}$, different thermal behavior is observed between ${\left(1/4,1/4,1/2\right)}_{\mathrm{t}}$ and ${\left(1/4,1/4,L\right)}_{\mathrm{t}}$ ($L=\mathrm{integer}$) reflections whose intensities maximize at different temperatures, suggesting the coexistence of two magnetic arrangements. Moreover, the intensity of the ${\left(1/4,1/4,1/2\right)}_{\mathrm{t}}$ magnetic reflection is at least ten times larger than that of the ${\left(1/4,1/4,L\right)}_{\mathrm{t}}$ $(L=\mathrm{integer})$ ones. On the other hand\, neutron diffraction measurements only detect a single type of antiferromagnetic ordering following the propagation vector $\mathit{k}={\left(1/4,1/4,1/2\right)}_{\mathrm{t}}$ 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 $\mathit{k}={\left(1/4,1/4,1/2\right)}_{\mathrm{t}}$ while ${\left(1/4,1/4,0\right)}_{\mathrm{t}}$ and ${\left(1/4,1/4,1\right)}_{\mathrm{t}}$ magnetic reflections correspond to a minority magnetic phase that must be due to changes in the oxygen stoichiometry near the surface.

• Received 22 January 2021
• Revised 24 March 2021
• Accepted 5 May 2021

DOI:https://doi.org/10.1103/PhysRevB.103.184422