Reentrant behaviour

Some of these phases occur in reentrant phase diagrams showing single [30] and sometimes multiple reentrant behaviour, described by the phase sequence I-N-Aa-N-Aa-N-Ai-C-A2-C2 on cooling [46, 57],... 

Fig. 6. Resistance-vs.-temperature curves of a GdMO(,Sg sample for different values of the applied magnetic field, indicating near-reentrant superconductivity i.e. reentrant behaviour at finite field only (nominal composition...

Fig. 38. (a) Resistivity vs. temperature measured at different magnetic fields H on a polycrystalline HoNi2B2C sample. Tc is the superconducting transition temperature at H = 0. A near-reentrant behaviour occurs around a temperature Tn. (b) Temperature dependence of the specific heat Cp of a HoNi2B2C single crystal (2 mm x 3 mm x 0.1 mm in size), measured at zero magnetic fiekL Above the main peak of Cp(T) at Tn. two additional features appear (marked by arrows). Samples prepared by I. Freudenberger. 

It is well known that ferromagnetism favors reentrant behaviour (see subsection 1.3). The formation of such secondary phases is supported by nonstoichiometry. Therefore the chemical characterization of the sample is of prime importance. However, due to the presence of the two light elements B and C the various classical characterization techniques as chemical analysis, intensity analysis of x-ray or neutron diffraction, transition electron... 

Fig. 42. Reentrant behaviour in modified H0N12B2C samples, (a) Annealing of polycrystalline H0N12B2C1.1 at 1 IOO°C for 10 days or 20 days results in reentrant behaviour whereas less intensely annealed material (A and +) shows no reentrant behaviour (Schmidt et al. 1997). (b) Reentrant behaviour caused by substitution of Ni by Co (Schmidt 1997). x — ac susceptibility, p — electrical resistivity.

Fig. 43. (a and b) Resistivity versus temperature curves for HoNi2B2C and Yo.isHoo.8sNi2B2Ct respectively, showing reentrant behaviour, (c and d) The comparison with the neutron diffraction peak intensities shows that the a structure is strongly related to the reentrant behaviour, (e and f) Upper critical field determined from the resistive transitions shown in (a) and (b) (Eversmann et al. 1996 Milder et al. 1997 Kreyssig et al. 1997). 

As a general empirical rule for HoNi2B2C samples, the appearance of reentrant behaviour caused by stoichiometric effects or pressure or magnetic field is always connected with a reduced value of Tc. 

It is obvious that the commensurate antiferromagnetic structure of fig. 39a coexists with superconductivity in HoNi2B2C, similar as in DyNi2B2C. On the other hand, as can be seen in fig. 43(a and c) the superconductivity is suppressed in the small temperature range where the two incommensurate magnetic structures of fig. 39(b and c) occur. Now the question is which of these two structures is more relevant for the near-reentrant behaviour. In Y().i5Hoo.85Ni2B2C the situation is totally different (fig. 43(b and d)). Here the a ... 

In [96] exactly solvable models based on Dyck paths and Motzkin paths in two dimensions, and a partially directed walk model in three dimensions are given. Orlandini et al. [96] observe re-entrant behaviour in three dimensions, but not in two. Reentrant behaviour is shown in figure 10 below ... 

Reentrant behaviour refers to the fact that the force temperature diagram at first increases with increasing temperature, and then decreases. It thus has a finite maximum at a positive temperature. 

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