Powder neutron diffraction studies of undoped ${\mathrm{La}}_2$ ${\mathrm{CuO}}_{4\mathrm{-}\mathrm{y}}$ have revealed new superlattice peaks below ∼220 K. The absence of corresponding x-ray superlattice lines and an observed susceptibility anomaly near 220 K suggest the occurrence of antiferromagnetism. From the magnetic peak intensities we deduce a structure consisting of ferromagnetic sheets of Cu spins alternating along the [100] orthorhombic axis, with the spins aligned along the [001] orthorhombic axis, The low-temperature magnetic moment is approximately 0.5${\mathrm{\mu }}_{\mathrm{B}}$/(Cu atom). The tetragonal-orthorhombic transition at 505 K has also been studied.

Neutron-diffraction experiments on ceramic powders of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ (nonsuperconducting, with $x=0.0\mathrm{} \mathrm{and} 0.15$ have confirmed the existence of long-range, three-dimensional, antiferromagnetic order of the Cu spins. The structure determination was aided by the use of uniaxially oriented powders. The ordering wave vector within a Cu${\mathrm{O}}_2$ plane is (½ ½) and the planes are coupled antiferromagnetically along the $c$ axis. The Néel temperature is 400±10 K for the $x=0.15\mathrm{}\pm 0.05$ sample and ≳500 K for $x=0.0\mathrm{}$.

Millimeter-sized ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ single crystals are grown out of a Bi-Te flux and characterized using magnetic, transport, scanning tunneling microscopy, and spectroscopy measurements. The magnetic structure of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ below $T_N$ is determined by powder and single-crystal neutron diffraction measurements. Below $T_N$ = 24 K, ${\mathrm{Mn}}^{2+}$ moments order ferromagnetically in the $ab$ plane but antiferromagnetically along the crystallographic $c$ axis. The ordered moment is 4.04(13)${\mu }_B$/Mn at 10 K and aligned along the crystallographic $c$ axis in an A-type antiferromagnetic order. Below $T_N$, the electrical resistivity drops upon cooling or when going across the metamagnetic transition in increasing magnetic fields. A critical scattering effect is observed in the vicinity of $T_N$ in the temperature dependence of thermal conductivity, indicating strong spin-lattice coupling in this compound. However, no anomaly is observed in the temperature dependence of thermopower around $T_N$. Fine tuning of the magnetism and/or electronic band structure is needed for the proposed topological properties of this compound. The growth protocol reported in this work might be applied to grow high-quality crystals where the electronic band structure and magnetism can be finely tuned by chemical substitutions.

The structures of five phases in the ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{K}}_{\mathit{x}}$ ${\mathrm{BiO}}_3$ system for 0≤x≤0.5 and temperatures below 473 K have been determined by neutron powder diffraction. Bulk superconductivity occurs only in a cubic perovskite phase which exists for x≥0.37 (at 10 K). At room temperature, as the potassium concentration is decreased, the cubic structure distorts first by ${\mathrm{BiO}}_6$ octahedral tilting and then by symmetric oxygen breathing-mode distortions. Semiconducting behavior for the monoclinic phase at 0≤x≤0.1 can readily be explained on the basis of a commensurate charge-density wave. The semiconducting orthorhombic phase, which extends from the monoclinic phase to the cubic superconducting phase, contains only octahedral tilting distortions that would not be expected to destroy metallic behavior. Thus, this commensurate structure provides no explanation for the metal-insulator transition. An incommensurate modulation extending across the semiconducting region of the phase diagram has been observed by electron diffraction, but is not observed by neutron diffraction. It is not clear whether this incommensurate modulation is responsible for the nonmetallic behavior.

Neutron diffraction has been used to study antiferromagnetic ordering in $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ as a function of $x$. Evidence for such ordering has been observed only in the tetragonal, nonsuperconducting phase ($x\lesssim 0.4$). The magnetic origin of the superlattice reflections has been confirmed with polarized beam measurements. A single antiferromagnetic structure was observed throughout the ordered phase, with a maximum Néel temperature of ∼500 K and average ordered moment of ${(0.66\mathrm{}\pm 0.07)}_{\mathrm{\mu }\mathit{B}}$ per magnetic Cu atom at $x\approx 0$. Magnetic susceptibility measurements suggest that two-dimensional correlations are strong, as in ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_{4-y}$, and may survive into the orthorhombic phase.