M. Matlak

Phase Transitions in Correlated Electron Systems. Chemical Potential Evidence

We consider a model describing two kinds of correlated electrons characterized by the average occupation numbers n (1) = Σ and n (2) = Σ using the constraint n (1) + n (2) = n where n is the average number of electrons per magnetic ion. Depending on the model parameters, the model can describe second order phase transitions from ferromagnetic and normal phase to paramagnetic and normal (critical temperature T C ), from paramagnetic and superconducting phase to paramagnetic and normal (critical temperature Ts), as well as combined, reentrant, phase transitions with three critical temperatures T S1 , T C and T S2 (T S1 < T C < T S2 ). We consider two cases: (1) n (1) ¬= 0, n (2) ¬= 0 (two sorts of interacting electrons) and (2) n (1) ¬= 0, n (2) = 0 (one sort of interacting electrons resulting from the shift of the center of gravity for the second band to higher energies). In both cases ((1) and (2)) the chemical potential μ exhibits small but distinct kinks at all critical temperatures of the system. This effect suggests a new possibility to detect all critical temperatures of a real solid (structural phase transitions included) exclusively from the experimental measurement of the chemical potential as function of temperature. In the case (1) the critical temperatures of the system are also visible from the kinks in the temperature dependence of the average occupation numbers n (1) and n (2) (the effect of critical electron redistribution at critical temperatures). Considering the phase transition from paramagnetic superconductor to normal system within our model, we can reproduce the same temperature dependence of the chemical potential as measured for the high-temperature superconductor YBa 2 Cu 3 O 7-δ . This result entirely supports the statement about the applicability of the chemical potential as a detector of phase transitions in real solids.

Reentrant Superconductivity in HoMo6S8

A simplified version of the s-f model, supplemented by the intersite Cooper pair interaction between conduction electrons with opposite spins, is used to investigate the competition between ferromagnetism and anisotropic superconductivity in a single-domain ferromagnet. The calculations of the temperature dependence of the magnetizations m f (localized 4f electrons), m d (conduction electrons) and the superconducting order parameter show the existence of three critical temperatures: T C (Curie temperature), T S1 and T S2 (lower and upper superconducting transition temperatures). The critical temperatures fulfil the relation T S1 T S2 paramagnetic and normal. The superconducting order parameter possesses a distinct maximum between T S1 and T S2 and vanishes for T T S2 in agreement with the recent experimental results for HoMo 6 S 8 . The calculated temperature dependence of the dc resistivity shows a typical reentrant behaviour, characteristic for such ferromagnetic superconductors as ErRh 4 B 4 and HoMo 6 S 8 . Using a suitable choice of the model parameters we can obtain a reasonable fit of the recent experimental results for HoMo 6 S 8 , concerning the temperature dependence of the superconducting order parameter and dc resistivity.

Thermodynamical Cross-Relations for Superconductors at the Critical Point

We investigate superconducting systems with the use of the phenomenological Landaus theory of second order phase transitions, including into the considerations the critical behaviour of the chemical potential. We derive in this way a variety of new thermodynamical relations at the critical point. Twelve basic relations connect critical jumps of different thermodynamical quantites (specific heat, chemical potential derivatives with respect to temperature, pressure (volume) and number of particles, volume (pressure) derivatives with respect to temperature and pressure (volume)) with the critical temperature or its derivatives with respect to the number of particles or pressure (volume). These relations allow to find plenty of cross-relations between different quantities at the critical point. The derived formulae can practically be used in many cases to find such thermodynamical quantities at the critical point which are extremely difficult to measure under the assumption that the other ones are already known. We additionally perform a test of the two derived relations by using two-band microscopic model, describing superconducting systems. We calculate the specific heat, order parameter and chemical potential as functions of temperature to show that the tested relations are very well fulfilled.

Phase Diagrams of the Reentrant Superconducting Re(1)1—xRe(2)xX (X = Rh4B4) Alloys.Application to Er1—xHoxX, Er1—xGdxX, Er1—xTmxX, HoxLu1—xX and Sm1—xErxX

We consider a simplified version of the s-f model, supplemented by the intersite Cooper pair interaction between conduction electrons with opposite spins to investigate the ferromagnetic and superconducting properties of an alloy Re 1-x (1) Re x (2) X (Re (1) , Re (2) rare earth elements, X = Rh 4 B 4 ) using the virtual crystal approximation (VCA). For a suitable choice of the model parameters we can reproduce the phase boundaries of the experimentally measured phase diagrams for Er 1-x Ho x X, Er 1-x Gd x X, Er 1-x Tm x X, Ho x Lu 1-x X and Sm 1-x Er x X alloys.