We present a study of the transport and magnetic properties of a series of $R\mathrm{NiBC}$ compounds $(R=\mathrm{Er},$ Ho, Dy, Tb, and Gd). All the materials investigated have long range magnetic order at sufficiently low temperatures. Magnetoresistance measurements are presented for a large range of temperatures (T) and magnetic fields (H). We show that below the critical temperature, the temperature dependence of the resistivity is determined by electron scattering due to the elementary excitations (spin waves) of the ordered magnetic phase and the values of the gap in the magnon spectra were derived. Finally we discuss the $H\times T$ phase diagram of these materials.

By means of nuclear spin-lattice relaxation rate T1-1, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl2-4SC(NH2)2 and the spin-ladder system (C5H12N)2CuBr4. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, T1-1 exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for T1-1, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

We study the Kondo lattice from the point of view of the scaling theory of critical phenomena. The coherence temperature ${\mathrm{scrT}}_c$ is associated with a crossover from a paramagnetic state with local moments to a Fermi-liquid regime with strong magnetic correlations. We obtain an expression for ${\mathrm{scrT}}_c$ in terms of the Kondo-lattice parameters and a crossover exponent ${\phi }_t$. The effect of a magnetic field is investigated and characterized by another critical exponent. These exponents obey scaling relations with a shifted dimensionality.

The occurrence at low temperatures of an ultrasharp field-induced transition in phase-separated manganites is analyzed. Experimental results show that magnetization and specific-heat steplike transitions below $5\mathrm{K}$ are correlated with an abrupt change of the sample temperature, which happens at a certain critical field. This temperature rise, a magnetocaloric effect, is interpreted as produced by the released energy at the transition point and is the key to understand the existence of the abrupt field-induced transition. A qualitative analysis of the results suggests the existence of a critical growing rate of the ferromagnetic phase, beyond which an avalanche effect is triggered.