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The fibre bundle approach has been applied to derive the explicit formulas presenting all the eight fundamental magnetic structures and their symmetry groups including the spin glass state. The explanation of the uniqueness of the spin glass state has its roots in the appearance of the probability function p(i, j) in the second term of the assumed Hamiltonian. This term actually describes the random distribution of either dopants or defects in the ferromagnetic matrix under the percolation threshold. On this basis the Gaussian type randomness was derived for both the general global magnetic coupling constant and the magnetization vector, the latter effect bringing to the statistical features of the magnetic structure and the magnetic symmetry group of the spin glass state.

The spinel stoichiometric compounds of the CuCr 2 − x Sb x Se 4 family were obtained for the first time and prepared with the assumption of the valence of Sb ions equal to 3. The magnetization isotherms at 4.2 K and at the magnetic stationary fields up to 14 T as well as the temperature dependencies of magnetic susceptibility were studied in the temperature range of 4.2 ÷ 400 K. These results were compared with analogous measurements performed earlier by the authors for the nonstoichiometric spinel family built of the same elements and obtained under the assumption of the valence of Sb ions equal to 5. From this comparison it follows that these two spinel series reveal significant differences: (1) The interval of possible concentrations of Sb ions in the obtained stoichiometric spinel samples under study is up to 1.0, whereas for the nonstoichiometric spinels is (0.30 ÷ 0.48). (2) The corresponding intervals for the appearance of the spin glass states are: (0.2 ÷ 1.0) and (0.30 ÷ 0.48), whereas the freezing temperatures do not differ significantly. (3) The magnetization processes in the stoichiometric samples depend strongly on the Sb concentration, whereas in the nonstoichiometric samples they run very hardly.

The experimental evidence of metamagnetism, giant negative magnetoresistance and spin glass state is presented for the compounds under study. An attempt is made to explain the jump-like phase transition of the colossal negative magnetoresistance of −4433% at 153.2 K into the colossal positive magnetoresistance of +980% at 154.2 K for the spinel sample with selenium. It was emphasized that in all the phenomena described in this paper the double exchange magnetic interaction plays the main role.

In this article is pointed out the particularly important role of the double exchange magnetic interaction in the appearance of the phenomenon of the coexistence of the negative giant magnetoresistance and the spin glass state in the selected RE-manganites and the spinels with chromium. To explain this phenomenon, its statistical background and the types of magnetic interactions in the compounds under study are taken into account. The particular importance of the double exchange magnetic interaction “cooperating” with the strong external magnetic induction results here from that: i. its coupling constant is several times greater than the superexchange one, ii. the spin orientation of the hopping electrons is conserved (always ferromagnetic coupling!) and the charge transfer makes the p-type metallic conductance.

Motto The first address of Satan to the human race began most modestly with the word: why? Adam Mickiewicz (1798–1855) The resistance, magnetoresistance and magnetization measurements have been performed in the temperature range of 4.2–300 K and in the external magnetic inductions up to 14 T for the Sm1− x Sr x MnO3 (x = 0.33, 0.45) and RE0.55Sr0.45MnO3 (RE0.55 = Eu0.397Nd0.153, Tb0.25Nd0.30) manganites. In these samples the metal–semiconductor phase transitions as well as two kinds of the magnetic phase transitions the ferromagnetic–paramagnetic and metamagnetic (both spin-flip and spin-flop) have been observed. It was found that correlations between the magnetic and electrical phase transitions appear at high values of the external magnetic inductions. These correlations consist, simultaneously, of the large negative magnetoresistance and metamagnetic phase transitions. The existence and reconstruction of the ferromagnetic and antiferromagnetic clusters under the influence of the external magnetic induc...

High degree of defectiveness both in the stoichiometric CuCr 2− x Sb x S 4 ( x = 0.3, 0.4, 0.5) and nonstoichiometric Cu 1 + x Cr 1.5 + y Sb 0.5 + z Se 4 + t (where: −0.02 ≤ x ≤ 0.01, 0.03 ≤ y ≤ 0.35, −0.2 ≤ z ≤ −0.02, 0.01 ≤ t ≤ 0.08) spinels doped with Sb has been determined with the aid of the vacancy model. From the analysis carried out of the effective magnetic moments and the exchange integrals, it follows that in the spinels with sulphur mainly the cation subarrays are defected whereas in the spinels with selenium the defectiveness appears mainly in the anion subarrays. It turned out that in the spinels with sulphur the ferromagnetic cluster spin glass states appear accompanied by the large negative magnetoresistance, whereas in the spinels with selenium the corresponding clusters are antiferromagnetic and the giant magnetoresistance has been observed both positive and negative. A jump-like phase transition was here observed changing both the sign and the measured value of the magnetoresistance from −4433% at 153.2 K up to +980% at 154.24 K. Moreover, in the spinels with selenium both semiconductor–metal and metal–semiconductor phase transitions have been observed from the temperature dependence of the resistance.

The relation of the magnetic coupling constants and the random distribution of dopants and defects under the percolation threshold is studied. The relation of the 2nd non-linear static magnetic susceptibility and the 2nd harmonic of the dynamic magnetic susceptibility is used for the interpretation of experimental data concerning the spin-glass state obtained as a result of different types of the competitions of the magnetic interactions. Statistical background of the electrical properties as a result of their correlation with the magnetic properties is discussed.

The X-ray absorption K-edges of sulfur in CuCr2−xSbxS4 (x = 0.3, 0.4, 0.5) have been measured and compared to linearized augmented plain wave (LAPW) numerical calculations. The near edge region is generated by magnetically polarized and hybridized S 2p energy levels and shows small change with increased Sb content, which can be attributed to the movement of Cr 3d spin-down states up on the energy scale. The LAPW result confirms this effect. Moreover, the calculations show that the antimony in those spinels is rather in +3 than in +5 valence state. The calculated magnetic moment on Cr equals to 2.72μB. In EXAFS, there is no visible change between x = 0.3 and 0.5 spectra, which indicates that the local structure does not change significantly.

The considerations using such quantities like a. o. correlation function (Green function), certain subspace in Hilbert space, have been applied in terms of the mean field theory both to the Hubbard and Heisenberg spin Hamiltonian. This procedure results in that the magnetization of the system under consideration occurs only if the corresponding topological invariants assume special values. Several examples are discussed using this approach for different types of the magnetic ordering. A general hypothesis has been put forward that particular condensed matter phases (not only magnetic) in a given system take place if certain topological invariants of a given subspace defined in the space of states assume special values.

Powder samples of CuCr 2− x Sb x S 4 were obtained for x =0.3, 0.4 and 0.5. All the samples have spinel structure. The magnetization measurements were carried out with the use of the induction method in the temperature range of 4.2–300 K in stationary fields with inductions up to 14 T. Both the electrical conductivity and the magnetoresistivity were measured in the same range of temperatures with the use of the four-point method. For the magnetoresistivity measurements both stationary fields up to 14 T and pulsed fields of 38 T were applied. A lack of magnetic saturation is observed for all the samples. Moreover, an increase of the antiferromagnetic component of the magnetization is observed with the increase of the Sb concentration. The absolute values of magnetoresistivity as a function of x exhibit at 4.2 K and 14 T a maximum at about x =0.4, assuming zero at x =0.5. For the two concentrations, i.e. for x =0.3 and 0.5, the magnetoresistivity at room temperature changes its sign twice as a function of the magnetic field. A peak clearly seen in the temperature dependence of the relative derivatives of both the magnetization and susceptibility seems to testify to a spin-flip transition at 13 K and 1 T.

A set of vortices in the superconducting system being a two-dimensional region with a boundary has been considered. Here the system under study is described by the model of the Ginzburg-Landau potential in the dual point. This model predicts that in the bounded superconducting system non-interacting vortices appear. These vortices make the absolute minima of this potential. It turned out that in the thermodynamic equilibrium for the fixed number of vortices, the temperature of the system and the geometry of the boundary are related to each other. The simultaneous change of the temperature of the system and of the geometry of the boundary has been investigated under the assumption that the number of vortices is fixed. In the case of the flat disc the explicit form of the temperature vs. area relation has been obtained for two different boundary conditions.

An attempt was made to explain the physical sense of the special r o /r a vs. r t /r a plot being a phase diagram for the variety of chromium compounds, especially spinels, Krok-Kowalski et al., J. Alloys Compd. 315, 62 (2001). Here r t is the ionic radius of cations in the tetrahedral positions, r o the ionic radius of cations in the octahedral positions, r a the ionic radius of anions. Therefore, a model was proposed in which only the direct and RKKY exchanges were taken into account. The predictions of the presented model are adequate to the experimental data contained in this plot.

A hypothesis is put forward concerning the existence of the general relation between aperiodic crystal structures and the invariants of the group of the automorphisms of the d-dimensional torus. A relation is proved between the one-dimensional and two-dimensional displacive modulations and the rationality of some invariants of the group of automorphisms of both the circle S 1 and the torus T 2 .

In the spinels under study the spin glass state was observed at x =0.3, 0.4. The spin-freezing temperature is equal to about 47.4 and 30 K for x =0.3 and 0.4, respectively. The temperature range, in which the spin glass state appears, is much narrower for x =0.3 than for x =0.4. The negative magnetoresistance decreases significantly with the decrease of Sb concentration.

The percolation limit of the appearance of the spin glass state in the compounds under study has been obtained experimentally. The conditions of stability of the spin glass state have been analyzed here on the basis of the de Almeida-Thouless theory for two spinels differing in the magnetic coupling constants. It turned out that for the higher value of the coupling constant the magnetic field influences the freezing temperature more strongly. Moreover, the greater the coupling constant the broader the range of the possible values of freezing temperatures, in other words the greater the temperature range of the appearance of the spin glass states. It was proved that for the stability of the spin glass state the existence of a small magnetic field is necessary. In our case the value of this field is equal to 3.46 × 10(-23)T(G). For the compounds under study the value of the magnetic coupling constant J cannot exceed 130 K for the spin glass state to appear.

The evolution of a probe D-brane in the p-brane background is considered. The anisotropic evolution of the world-volume of the D-brane with a given topology of a world-volume in the form of a direct product of a n-dimensional flat space and (3 − n)-dimensional sphere is formulated. In this case the anisotropy is described with the aid of two parameters (Hubble parameters) The special case of this evolution, namely the isotropic evolution corresponds to equality of these two parameters. In the latter case the masses and charges of the background p-branes are obtained.