For the spin-chain compound ${\mathrm{Ca}}_3{\mathrm{Co}}_2{\mathrm{O}}_6$, the magnetization curves as a function of the magnetic field are strongly out-of-equilibrium at low temperature, and they exhibit several steps whose origins are still a matter for debate. In the present paper we report on a detailed investigation of the temperature and time dependence of these features. First, it is found that some of the magnetization steps can disappear as the characteristic time of the measurement is increased. A comparison of the influence of temperature and time points to the existence of a thermally activated process that plays an important role in determining the form of the magnetization curves. Second, direct investigations of the magnetic response as a function of time show that this thermally activated process competes with a second relaxation mechanism of a very different nature, which becomes dominant at the lowest temperatures. These results shed new light on the peculiar magnetization process of this geometrically frustrated, Ising-like spin-chain compound.

The magnetic behavior of the Ca₃Co₂O₆ spin chain compound is characterized by a large Ising-like character of its ferromagnetic chains, set on a triangular lattice, that are antiferromagnetically coupled. At low temperature, T < 7 K, the 3D antiferromagnetic state evolves towards a spin frozen state. In this temperature range, magnetic field driven magnetization of single crystals (H // chains) exhibits stepped variations. The occurrence of these steps at regular intervals of the applied magnetic field, H_step = 1.2 T, is reminiscent of the quantum tunneling of the magnetization (QTM) of molecular based magnets. Magnetization relaxation experiments also strongly support the occurrence of this quantum phenomenon. This first observation of QTM in a magnetic oxide belonging to the large family of A₃BB′O₆ compounds opens new opportunities to study a quantum effect in a very different class of materials from molecular magnets.

Elucidating order within disorder: In some materials, the geometry of the crystal lattice gets in the way of magnetic ordering. Their spins, although magnetically interacting, remain seemingly disordered and form a so-called spin liquid. Paddison et al. propose a different model for the spin-liquid compound Gd ₃ Ga ₅ O ₁₂ . Neutron diffraction measurements and numerical techniques revealed that even though individual spins in this material were disordered, they formed 10-spin loops that were correlated with one another. The nature of this “hidden order” was such that it escaped direct detection by conventional techniques Science , this issue p. 179

We present a detailed powder and single-crystal neutron diffraction study of the spin chain compound ${\mathrm{Ca}}_3{\mathrm{Co}}_2{\mathrm{O}}_6$. Below 25 K, the system orders magnetically with a modulated partially disordered antiferromagnetic structure. We give a description of the magnetic interactions in the system which is consistent with this magnetic structure. Our study also reveals that the long-range magnetic order coexists with a shorter-range order with a correlation length scale of $\sim 180\AA$ in the $ab$ plane. Remarkably, on cooling, the volume of material exhibiting short-range order increases at the expense of the long-range order.

$\mathrm{RbFe}({\mathrm{MoO}}_4{)}_2$ is a rare example of a nearly two-dimensional Heisenberg antiferromagnet on a triangular lattice. Magnetic resonance spectra and magnetization curves reveal that the system has a layered spin structure with six magnetic sublattices. The sublattices within a layer are arranged in a triangular manner with the magnetization vectors $120°$ apart. The $H-T$ phase diagram, containing at least five different magnetic phases is constructed. In zero field, $\mathrm{RbFe}({\mathrm{MoO}}_4{)}_2$ undergoes a phase transition at $T_N=3.8\mathrm{}\mathrm{K}$ into a noncollinear triangular spin structure with all the spins confined in the basal plane. The application of an in-plane magnetic field induces a collinear spin state between the fields $H_{c1\mathrm{}}=47\mathrm{}\mathrm{kOe}$ and $H_{c2\mathrm{}}=71\mathrm{}\mathrm{kOe}$ and produces a magnetization plateau at one-third of the saturation moment. Both the ESR and the magnetization measurements also clearly indicate an additional first-order phase transition in a field of 35 kOe. The exact nature of this phase transition is uncertain.

We predict that an external field can induce a spin ordering in highly frustrated classical Heisenberg magnets. We find analytically stabilization of collinear states by thermal fluctuations at a one-third of the saturation field for kagome and garnet lattices and at a half of the saturation field for pyrochlore and frustrated square lattices. This effect is studied numerically for the frustrated square-lattice antiferromagnet by Monte Carlo simulations for classical spins and by exact diagonalization for $S=1\mathrm{}/2$. The field induced collinear states have a spin gap and produce magnetization plateaus.