Using a capacitive dilatometer we investigated the magnetoelastic behaviour of single-crystalline ErNi 2 B 2 C in the temperature range 1.8 K T 16 K and for external magnetic field in the tetragonal ab-plane µ 0 H 6 T. For T T N = 6.4 K the longitudinal magnetostriction coefficient is negative, whereas the transverse one is positive. The thermal evolution of the lattice distortion ε γ = (λ ⊥ − λ)/ √ 2 is in agreement with that of the previously reported spontaneous tetragonal-to-orthorhombic distortion determined by neutron diffraction. The behaviour is influenced by the distribution of the magnetic domains in the crystal. The H-T phase diagram, constructed from the magnetostriction curves, shows the well-known cascade of metamagnetic transitions between several phases (antiferromagnetic AF1, ferrimagnetic F1, F2) in the field range 0 < µ 0 H < 2.1 T below T N. On the basis of a Hamiltonian consisting of an exchange, a crystal-field, a Zeeman, and a magnetoelastic term, we were able to reproduce reasonably well the H-T phase diagram as well as various forced magnetostriction curves.

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With the purpose of investigating coexistence between magnetic order and superconductivity, we consider a model in which conduction electrons interact with each other, via an attractive Hubbard on-site coupling U, and with local moments on every site, via a Kondo-like coupling, J. The model is solved on a simple cubic lattice through a Hartree-Fock approximation, within a 'semi-classical' framework which allows spiral magnetic modes to be stabilized. For a fixed electronic density, n , the small J region of the ground state (T  =  0) phase diagram displays spiral antiferromagnetic (SAFM) states for small U. Upon increasing U, a state with coexistence between superconductivity (SC) and SAFM sets in; further increase in U turns the spiral mode into a Néel antiferromagnet. The large J region is a (singlet) Kondo phase. At finite temperatures, and in the region of coexistence, thermal fluctuations suppress the different ordered phases in succession: the SAFM phase at lower temperatures and SC at higher temperatures; also, reentrant behaviour is found to be induced by temperature. Our results provide a qualitative description of the competition between local moment magnetism and superconductivity in the borocarbides family.