STUDIES ON STATIC AND DYNAMIC PROPERTIES OF SPIN-GLASSES

Abstract

The spin-glass is a random magnetic system wherein the spins are frozen in random directions without any long range order, at a well-defined temperature T f. The spin- glass state is a new magnetic phase which appears at Tf in the absence of an external magnetic field. It seized public attention with the susceptibility results of Cannella and Mydosh (1).. Spin-glass phase has been found in many systems like noble metal hosts with transition metal impurities, transition metal hosts with transition metal impurities,rare-earth combinations, amorphous compounds and insulating mate-riaLs. It was originally thought that the spin-glass transitio: was related to the long range oscillatory behavior of the RKKY interaction between the magnetic impurities on random sites, but with the discovery of insulating spin-glass systems it is felt that the 'randomness' of spins and the 'conflict' in the interactions between the spins are the only basic requirements for the spin-glass phase to occur. In recent years spin-glass has been subjected to intense experimental and theoretical investigations. In spite of that the question, whether there is a sharp or a continuous freezing of moments remain unanswered. Some experiments like low-field susceptibility, anomalous Hall effect, Mobssbaur effect and muon spin relaxation support than view that there is a sharp freezing of spins at a characteristic temperature. Somc other experiments, eg.- th(-. specific heat measurement, and the neutron scattering studies do not favour the idea of a sharp freezing--temperature. Since the question of a sharp transi-tion is unresolved experimentally, the theoretical models can be accordingly divided into two classes : (i) those supporting the view of sharp transition and (ii) others relying on the continuous freezing process. . In the first category, the theory of Edwards and Anderson (2) (EA) is quite popular. They have treated the bond-disorder problem for the quenched .system within a novel form of mean-field theory employing the 'replica trick'. The work has been extended by several authors. A cusp is found both in the susceptibility and the specific heat. The rounding-off of the cusp is an order of magnitude smeller than that predicted by the experiment. The cusp in the susceptibility is supported by the experiments but no such cusp has been observed in the specific heat measurements. The EA theory has generated intense research activity. Several experimental phenomena in spin-glass systems have been analysed within the framework of EA-theory. With this very aim the present thesis undertakes to examine some spin-glass properties like electrical resistivity, thermoelec-tric power, magnetoresistance, susceptibility, specific heat and neutron scattering intensity on the basis of the EA-theory. Several workers have measured the magnetoresistance in spin-glass materials. The study of the magnetoresistance in spinwglasses is important because the susceptibility peak and the Hall effect show unexpectedly high sensitivity with the external magnetic field. In Chapter II of the thesis we (iv) have calculated the magnetoresi stance of spin-glasses by the method of double-time Green's function and by employing Kubo-Greenwood formula. The higher order Green's functions have been decoupled into the lower order Green's functions using Nagaoka's decoupling approximation. In the first approxima-tion, the correlation function describing the quasibound states between the conduction electron and the impurity spin has been neglected. The selfenergy of the Green's function has been obtained to the second order in normal and exchange interactions and in the framework of .EA-•theory. It is found that the self-energy consists of two parts : one involving spin-glass order parameter Q and the other spin-deviation correlation function. xn expression for the transverse magnetoresistance has been obtained by evaluating the relaxa-tion time at the Fermi surface. A comparison has been made between our result and the experimental data. A qualitative agreement is found. In spin-glass materials, the electrical resistivity shows maximum at a. temperature Tm greater than the spin-glass transition temperature and the thermoelectric power does not show any features which could be attributed to the spin-glass phase. In Chapter III we have studied the electrical resisti-vity and the thermoelectric power by using the method of double-time Green's functions. The decoupling scheme of Nagaoka has been employed and the terms representing the quasi-bound states have been retained. Using the EA-theory, the self-energy for the spin-glass phase has been derived in the (v) multiple scattering approximation. A self-consistent expre-ssion for the t-matrix has been obtained following the approach of Hamann. The temperature Tm is found to be in accord with the calculation of other workers. The calculation of the thermopower to order J3V0 does not show any marked feature for the spin-glass, which is consistent with the experiments. The calculation of Lorenz number shows a maximum at a temperature smaller than the freezing temperature. To our knowledge the experimental result for the Lorenz number is not available. Experimentally, the susceptibility cusp is found to be very sensitive to the magnetic field. In Chapter IV we have studied the effect of the magnetic field on the suscepti-bility and specific heat within the framework of EA-theory. The quantum Heisenberg Hamiltonian in the presence of an external magnetic field has been employed with the exchange interaction distributed randomly about a positive mean. Following closely the treatment given by Sherrington and Southern, an expression for the free-energy has been obtained. Then the expressions for the spin-glass order parameter Q, the magnetisation 1V11, the susceptibility x and the specific heat C have been obtained in the presence of the magnetic field. The field dependence of the susceptibility and the specific heat has been calculated near the spin-glass transition temperature. It is found that the EA-theory is not adequate to explain the high sensitivity of the cusp. The small angle neutron scattering measurements on AuFe alloys by Murani show a q-dependence of temperatures (vi) corresponding to sharp discontinuities in the scattering intensity I(q, T ). This behavior seems to be in contrast to a unique freezing temperature. In Chapter V, the general expression for the static correlation function due to Frank and Mitran has been used by us to calculate I(q,T) in the framework of EA-theory. The essential features of the obser-ved spectra is found to be explainable within this theory.