حل ميدان ميانگين مدل اندرسون براي دو اربيتال جايگزيده متفاوت dو F

چكيده انگليسي :

Anderson Model For Two Different Localized Magnetic Impurities d and f Payam Derakhshan p derakhshan@ph iut ac ir Date of Submission 2011 03 12 Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Akbar Jafari sa jafari@cc iut ac ir Abstract In this thesis we study the magnetic properties of materials in electron electron interaction frame by use of perturbation and retarded Green function and Anderson model At first we suppose the host metal as a electron gas and ignore the correlation between electrons because of spatial divergence of s orbital Then we add the impurity of d orbital kind in this stage we try to divide magnetic and non magnetic regions by the mean field approximation based on impurity and metal properties We ll see that there is a sharp transition between magnetic and non magnetic region that depends on the density of free electron states the elements of s orbital and d orbital s overlapping matrix or in a better word John Tyler factors and also coulomb correlation integral in the interval d orbital shell The use of retarded green function and their equation of motions can help us to tackle this problem We solve the equations self consistently Moreover we add f impurity to host metal and like above in low temperature obtain the magnetic of two impurities orbital We try to compare the magnetic and non magnetic phase with the change of properties of one impurity The embedding of two magnetic atoms in normal metal leads to variety of interesting effects Two different magnetic impurity coupled to the Fermi sea of the host metal may lose or not its magnetic properties In two different localized magnetic states and in metals the conditions necessary for the presence or absence of localized moments are analyzed There is a special parameter that is the product of two John Tyler factors and if it becomes zero there would be no magnetization a self consistent Hartree Fock treatment for solute ions shows that there is a sharp and asymmetric transition between magnetic state and nonmagnetic state depending on the density of states of free electrons the s d and s f admixture matrix elements and the Coulomb correlation integral in the d and f shell in the fact a preserved two localized magnetic moment coupled to the Fermi sea can lead to a correlated non magnetic ground state of the whole system At last numerical analyze of Anderson model for two different localized magnetic impurities indicates this fact that by addition of the certain impurity on a non magnetic host metal if we are able to add another kind to get a maximum magnetization or not An answer to this question leads to find the process of magnetic change for different impurities Observed correlations and symmetries in the graphs would help us to evaluate different impurities to reach the maximum magnetization In a certain interval of energy there are some points that their and are correlated i e both magnetization tend from maximum to minimum value As the d orbital s energy increases symmetry would be lost and as the value of d impurity would dominate the magnetization The noticeable fact is existence of symmetry in an energy interval as the both kind of magnetizations are correlated they obey an special symmetry Also correlation or in the other word magnetic of two impurities won t change from maximum to minimum Keywords 1 Retarde Green function 2 Anderson model 3 Mean field 4 John Tyler 5 Equation of motion

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حل ميدان ميانگين مدل اندرسون براي دو اربيتال جايگزيده متفاوت dو F

تابع گرين تاخيري , يان تلر , معادله حركت