The investigation of charge ordering in colossal magnetoresistance

The investigation of charge ordering in colossal magnetoresistance Shih-Jye Sun Department of Applied Physics National University of Kaohsiung 2005/9/30 in NCKU 1

Colossal Magnetoresistance La 1 -x(Ca, Sr…)x. Mn. O 3 2

Phase diagram of CMR Urushibara et al (1995) Cheong and Hwang (1999) 3

Double exchange mechanism （A） Mn 3+ eg Mn 4+ O 2 - (1) 2 p (2) (3) eg t 2 g （B） Mn 3+ O 2 - eg (1) (3) 2 p eg (2) t 2 g （C） Mn 3+ Mn 4+ eg t 2 g O 22 p (1) (3) eg (2) t 2 g 4

John Teller distortion 5

The motivation La 1 -x. Cax. Mn. O 3 Temp PI para-insulator(PI) I TC TCO FI CO II TCO CO AFM x 0. 5<x<0. 85 x~0. 2 χ III TN TC(TCO or TN) Susceptibility instability From region I to II and II to III 6 TC T

Theoretical formulas derivation Hamiltonian: Itinerant spin Local spin (kinetic energy) (inter-Coulomb repulsion) (on-site Coulomb repulsion) 7

Hamiltonian in momentum representation 8

Greens function for susceptibilities Charge-charge susceptibility 9

Spin-spin susceptibility 10

Equation of motion method (1) (2) (3) (1) 11

(2) 12

Random Phase Approximation Wick’s theorem Fermi-Dirac distribution 13

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Spin dependent in PI state 17

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PI to CO transition Similarly, for spin-spin susceptibility 19

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(spin dependent in PI) PI to AFM In CO state Mn+3 Mn+4 23

CO to AFM x 0. 55 0. 60 0. 65 0. 70 0. 75 0. 80 0. 85 TC 222 260 265 250 215 180 130 TN 156 143 Substituting to 130 125 113 106 Experimental data 102 Cheong and Hwang (1999) 24 To determine interaction relations

Results and discussion Reflection different transitions 25

Consistent with John Teller distortion More distortion non-symmetry 26

Charge gaps are depressed by U 27

Charge gap fluctuation The competition between HV and HU 28

Conclusions l 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. l These Inter-Coulomb repulsions increase with x increasing but not in linear. l 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 parainsulator 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. l 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. 29

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