A quantum magnet, ${\mathrm{LiCuSbO}}_4$, with chains of edge-sharing spin-$\frac{1}{2}$ ${\mathrm{CuO}}_6$ octahedra is reported. While short-range order is observed for $T<10\mathrm{K}$, no zero-field phase transition or spin freezing occurs down to 100 mK. Specific heat indicates a distinct high-field phase near the 12 T saturation field. Neutron scattering shows incommensurate spin correlations with $q=(0.47\pm 0.01)\pi /a$ and places an upper limit of $70\mu \mathrm{eV}$ on any spin gap. Exact diagonalization of 16-spin easy-plane spin-$\frac{1}{2}$ chains with competing ferro- and antiferromagnetic interactions ($J_1=-75\mathrm{K}$, $J_2=34\mathrm{K}$) accounts for the $T>2\mathrm{K}$ data.

The nature of the spin-flop (SF) transition in the magnetoelectric quasi-2D Heisenberg system LiMnPO${}_4$ is studied in fields applied along the $a$ axis. A refinement of the magnetic structure using neutron diffraction data in the SF phase reveals that the spins reorient from being parallel to the $a$ axis to be nearly along the $c$ axis at magnetic fields between 4 and 4.7 T, depending on temperature. The low-field antiferromagnetic phase boundary is shown to join the spin-flop line tangentially at the so-called bicritical point, where there is a suppression of the ordering temperature. At the bicritical field, we observe an increased intensity of the Lorentz broadened elastic scattering at magnetic Bragg peaks above $T_N$ as compared to zero field and 10 T, without an increase in peak width. This suggests an increased density of fluctuations at the bicritical field as compared to zero field.

We report significant details of the magnetic structure and spin dynamics of ${\mathrm{LiFePO}}_4$ obtained by single-crystal neutron scattering. Our results confirm a previously reported collinear rotation of the spins away from the principal $b$ axis, and they determine that the rotation is toward the $a$ axis. In addition, we find a significant spin-canting component along $c$. The possible causes of these components are discussed, and their significance for the magnetoelectric effect is analyzed. Inelastic neutron scattering along the three principal directions reveals a highly anisotropic hard plane consistent with earlier susceptibility measurements. Using a spin Hamiltonian, we show that the spin dimensionality is intermediate between $XY$- and Ising-like, with an easy $b$ axis and a hard $c$ axis. It is shown that both next-nearest neighbor exchange couplings in the $bc$ plane are in competition with the strongest nearest neighbor coupling.