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

2 Colossal Magnetoresistance La 1-x (Ca,Sr…) x MnO 3

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

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

5 John Teller distortion

6 The motivation para-insulator(PI) CO AFM FI CO PI x Temp x~ <x<0.85 La 1-x Ca x MnO 3 TCTC T CO TNTN TCTC χ T C (T CO or T N ) T Susceptibility instability I II III From region I to II and II to III

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

8 Hamiltonian in momentum representation

9 Greens function for susceptibilities Charge-charge susceptibility

10 Spin-spin susceptibility

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

12 (2)

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

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17 Spin dependent in PI state

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

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

24 CO to AFM x TC TN Substituting to Experimental data To determine interaction relations Cheong and Hwang (1999)

25 Results and discussion Reflection different transitions

26 Consistent with John Teller distortion non-symmetrysymmetry More distortion

27 Charge gaps are depressed by U

28 Charge gap fluctuation The competition between H V and H U

29 Conclusions Substituting experimental critical transition temperatures of T CO s and T N s 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.

30 Thanks for your attendance!!