GROUND AND EXCITED STATE PROPERTIES OF SPIN-1/2 FALICOV-KIMBALL MODEL ON A TRIANGULAR LATTICE

Abstract

In recent years, the electronic and magnetic properties of certain correlated electronic systems such as NaTiO2, NaV O2, NaCoO2, GdI2 and GdI2Hx etc., have drawn a huge attention of the condensed matter physicists. These are layered systems with a triangular lattice and can often be characterized by the presence of two types of electrons (i.e. itinerant and localized). These systems, by tuning the U/t ratio (where U is on-site Coulomb repulsion between itinerant and localized electrons and t is hop- ping parameter) and position of energy level Ef of localized electrons, exhibit several interesting exotic properties like metal-insulator transition, charge and magnetic or- der, instability to the formation of excitons and non-Fermi liquid behaviour etc., as have been observed experimentally. Therefore we believe that these systems can very well be modeled by the spin-independent and spin-dependent Falicov-Kimball model (FKM) on a two-dimensional triangular lattice. This thesis studies the ground and excited state properties of spin-1/2 FKM with various extended interaction terms relevant for the above mentioned systems on a non-bipartite (triangular) lattice. This thesis consists of six chapters which are discussed one by one in the following. i ii Chapter 1 is an introductory chapter containing a discussion on the electron correlation and correlated systems. An overview is presented on various theoretical approaches such as Mott hypothesis, Hubbard model and FKM etc. that are used to study such correlated systems. Correlated systems like transition metal dichalco- genides, cobaltates, GdI2 and its doped variant GdI2Hx, NaTiO2 and NaV O2 etc have attracted a huge attention of the condensed matter physicists for their exotic properties like metal-insulator transition, charge and magnetic order, instability to the formation of excitons and non-Fermi liquid behaviour etc. Some of these systems where we believe the model studied in this thesis is applicable, have been discussed in detail. Their crystal structures and basic electronic structures have also been dis- cussed to explain the applicability of spin-1/2 FKM for these systems. In the later part of the chapter we have discussed the methodology used in our calculations to evaluate the ground state and finite temperature properties of spin-1/2 FKM on a triangular lattice. Details of the numerical techniques used in our calculations such as exact numerical diagonalization and Monte Carlo method with Metropolis algorithm are also given. In Chapter 2 we have discussed our observations on the ground state magnetic properties of spin-1/2 FKM on a triangular lattice. Magnetic properties have been explored as a function of following parameters: on-site Coulomb correlation U, ex- change interaction strength J and filling of electrons. We have observed that the ground state magnetic configurations exhibit long range Neel anti-ferromagnetic or- der, ferromagnetic order or a mixture of both as J is varied. The magnetic moments of itinerant (d-) and localized (f-) electrons are also estimated. In one-fourth filling case for U less than a critical value, we observed no net magnetic moment from d- and f-electrons. iii In Chapter 3 we have discussed our study on the ground state magnetic proper- ties of spin-1/2 FKM on a triangular lattice, where we have incorporated an additional term in the Hamiltonian describing the superexchange interaction (Jse) between lo- calized f- electrons. Transitions from anti-ferromagnetic (AFM) to ferromagnetic (FM) again to re-entrant AFM phase is observed in a wide range of parameter space. We have also calculated the density of d- electrons at each site for two fillings, i.e one-fourth and half-filled case. Magnetic moments of d- and f- electrons are observed to depend strongly on the value of J, Jse and also on the total number of d- electrons. Chapter 4 In this chapter we present our study on the thermodynamic prop- erties of the spin-1/2 FKM on a triangular lattice. We have observed the phase transition from low temperature (inhomogeneous) phases to high temperature (dis- ordered/homogeneous) phases at a critical temperature which varies with Coulomb correlation U, exchange interaction strength J and electron filling. We have also calculated the temperature dependence of specific heat and observed a sharp jump at Tc indicating the phase transition. We have also observed that Tc increases with increase in on-site Coulomb correlation. iv Chapter 5 Here we have further extended the spin-1/2 Falicov-Kimball model (FKM) by incorporating the correlated hopping (t′) term between d- and f- electrons. Correlated hopping (t′) term includes the effect of the occupation of nearest neighbor sites by localized (f-) electrons on hopping of itinerant (d-) electrons. Various inter- esting ground state magnetic configurations e.g. long range FM order, discrete FM domains with AFM alignment among themselves, FM and AFM binary alloy type etc. and segregated phase of localized (f-) electrons are observed at different values of t′. Positive value of t′ is observed to drive the system towards phase segregation and also from AFM to FM and this effect is seen at all fillings studied here. As phase segregation is observed experimentally in many correlated systems discussed above, we believe our study discussed in this chapter could be very useful in this regard. Chapter 6 contains an overall summary and conclusions along with future plans.