Coexistence of Spin-Glass and Ferromagnetic Orderings

Abstract

The phase diagram of the infinite-range model of spin-glasses exhibits two mixed phases. In these mixed phases, ferromagnetism and spin-glass order coexist, due to freezing of the transverse degrees of freedom or replica symmetry breaking. This may help to interpret a number of recent experimental findings, e.g. , in AuFe.PACS numbers: 75.50.Kj, 05.50.+q Many disordered magnetic materials have been systematically investigated as a function of the concentration of the constituents. In the phase diagrams of these materials, one often finds a spin-glass phase for some range of concentration and a phase with long-range order (ferromagnetic or antiferromagnetic) for other concentrations. ' " Recently, a number of experiments have been performed to study the border region between the spin-glass and ferromagnetic phases, and many interesting data are now available. Unfortunately these data are most often interpreted, qualitatively'"'" and even quantitatively, "'~' with the help of a theory" which, though of great merit in its days, is now obsolete (it has been proven to be incorrect, " at low temperatures, as a solution of its model). Moreover, these theoretical predictions are inadequate because they are concerned with Ising spins, whereas experimental spine are Heisenberg-like (isotropic vector spins). The purpose of this Letter is to draw attention to recent studies, "" which should provide a more satisfactory theoretical basis, and to present new results concerning the nature of two mixed phases, with both spin-glass and ferromagnetic characters. The existence of such intermediate phases may help explain a number of phenomena already observed experimentally, but hitherto ambiguously interpreted.In the spirit of a mean-field theory, we consider the famous infinite-range model" for N classical vector spins S,. Each S; has m components S;" (p. =1, . .. , m) satisfying, for convenience, the following normalization condition: They interact via independent random interactions J;, . distributed according to the following law: P(Z ) = -~e xp --J 2wj 2 (2) so that (J, , ), = J,/N and (J, .~) , =1/N, where ( ),denotes an average over the bond disorder, that is, over P(J,~). In the presence of an external magnetic field H applied along the p, = 1 direction, the Hamiltonian of the model reads where the sum over (ij ) denotes a summation over the N(N -1)/2 distinct pairs of sites.In the limit of large and positive J" the interactions are mainly ferromagnetic and the system exhibits a ferromagnetic phase. For J0=0, the interactions are random in sign and the ordering is of spin-glass type. The border region between ferromagnetic and spin-glass phases occurs for Jo =1. However, it has been shown" how the properties of the model for J, g0 can be simply derived from the case J, = 0, which we therefore first consider.

Phase diagram of a dilute ferromagnet model with antiferromagnetic next-nearest-neighbor interactions

“…Therefore we identify this phase transition as a Gabay and Toulouse (GT) transition [29] and the low temperature phase as a mixed (M) phase of the FM and a transverse SG. It is also noteworthy that, for x = 0.79 and x = 0.80, we estimate respectively T SG /J 1 = 0.10 ± 0.01 and T SG /J 1 = 0.098 ± 0.005, whereas respectively T R /J 1 = 0.15 ± 0.01 and T R /J 1 = 0.125 ± 0.005 [28].…”

Magnetic short- and long-range order inPbFe0.5Ta0.5O3

“…For example, for reentrant spinglasses in amorphous metallic compounds Fe-Mn 10,11 , Fe-Zr 12,13 , Au-Fe 15,16 a spin canting along with transverse spin freezing was considered as a mechanism of coexistence. Random transverse spin freezing scenario for occurrence of such a ground state is predicted by mean-field theory 2 .…”

“…Coexistence of long-range and spinglass orders have been studied in disordered ferromagnetic materials both theoretically and experimentally 2,[10][11][12][13][14][15][16] . For example, for reentrant spinglasses in amorphous metallic compounds Fe-Mn 10,11 , Fe-Zr 12,13 , Au-Fe 15,16 a spin canting along with transverse spin freezing was considered as a mechanism of coexistence.…”

“…Studies of disordered materials have gained interest due to novel phases and phase transitions they exhibit [1][2][3][4] . AB x B 1−x O 3 are complex perovskites which have inherent disorder at the B-site resulting in unusual properties.…”

Structural and Magnetic Properties of Dilute Spinel Ferrites: Neutron Diffractometry and Magnetometry Investigations

“…From the viewpoint of the molecular field acting on iron ions, the random substitution remarkably reduces its mean value in comparison with the variation of its dispersion, as discussed above. In such cases, a well-known phase diagram with reentrant spin-glass transitions has been predicted [20]. In this context, the observed behavior of the dilute spinel ferrites can be interpreted in the framework of the reentrant spin-glass picture.…”