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The investigation of charge ordering in colossal magnetoresistance. Shih-Jye Sun Department of Applied Physics National University of Kaohsiung. 2005/9/30 in NCKU. Colossal Magnetoresistance. La 1-x (Ca,Sr…) x MnO 3. Phase diagram of CMR. Urushibara et al (1995). Cheong and Hwang (1999).
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The investigation of charge ordering in colossal magnetoresistance Shih-Jye Sun Department of Applied Physics National University of Kaohsiung 2005/9/30 in NCKU
Colossal Magnetoresistance La1-x(Ca,Sr…)xMnO3
Phase diagram of CMR Urushibara et al (1995) Cheong and Hwang (1999)
Mn3+ Mn3+ Mn3+ Mn3+ Mn4+ Mn4+ eg eg eg (1) (1) (2) eg eg eg t2g t2g t2g t2g t2g t2g （A） (2) O2- (2) (3) 2p （B） O2- (3) 2p （C） O2- (3) (1) Double exchange mechanism 2p
TC(TCO or TN) χ TC T The motivation La1-xCaxMnO3 PI para-insulator(PI) Temp I TC TCO FI CO II TN TCO CO AFM III x 0.5<x<0.85 x~0.2 Susceptibility instability From region I to II and II to III
Hamiltonian: (kinetic energy) (inter-Coulomb repulsion) (on-site Coulomb repulsion) Theoretical formulas derivation Itinerant spin Local spin
Greens function for susceptibilities Charge-charge susceptibility
Equation of motion method (1) (2) (3) (1)
Random Phase Approximation Wick’s theorem Fermi-Dirac distribution
PI to CO transition Similarly, for spin-spin susceptibility
(spin dependent in PI) PI to AFM In CO state Mn+3 Mn+4
CO to AFM x TC TN 0.55 222 156 0.60 260 143 0.65 265 130 0.70 250 125 0.75 215 113 0.80 180 106 0.85 130 102 Substituting to Experimental data To determine interaction relations Cheong and Hwang (1999)
Results and discussion Reflection different transitions
Consistent with John Teller distortion More distortion non-symmetry symmetry
Charge gap fluctuation The competition between HV and HU
Conclusions • Substituting experimental critical transition temperatures of TCOs and TNs to charge-charge and spin-spin susceptibility functions offer the determination of the inter-Coulomb repulsions and charge gaps for x > 0.5, respectively. • These Inter-Coulomb repulsions increase with x increasing but not in linear. • In small on-site repulsion U the phase transitions only occur pare-insulator to charge-ordering transitions and in large U only occur para-insulator to antiferromagnetic transitions. The consequential phase transitions for para-insulator to charge-ordering following charge-ordering to antiferromagnetic transitions occur in a moderate U. In charge ordering states the charge gaps are opened and are depressed by U. • The scale of the charge gap increases linearly with x increasing excluding a small range of deviation. This deviation comes from the charge gap fluctuation according to the competition between inter-Coulomb and on-site Coulomb interactions.