PHYS07200604007 Manas Kumar Dala - Homi Bhabha National ...

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Introduction 6 Figure 1.3: Phase diagram of temperature versus tolerance factor for the system R 0.7 A 0.3 MnO 3 , where R is a trivalent rare earth ion and A is a divalent alkaline earth ion [12]. a triple degenerate (lower energy levels) d xy , d yz , and d zx orbitals, called t 2g states and a double degenerate (higher energy levels) d x 2 −y 2 and d 3z 2 −r 2 orbitals, called e g states [13]. Energy separation between the t 2g states and e g states is 10Dq due to the crystal field splitting of MnO 6 octahedra. The schematic of the electronic structure from ionic point of view are shown in the Fig. 1.4. Since the e g orbitals point towards the six O atoms, they are expected to have a larger hybridization with the O 2p states (p x , p y , and p z ) and hence are more delocalized than the t 2g states. So the e g state electrons play an important role of conduction electrons in this type of crystals. In Mn 3+ ions three electrons occupy the t 2g states and one electron occupies the e g states. The strong Hund’s coupling (J H ) in these systems favors the alignment of the e g electron spins with the core-like t 2g spins. When the manganites are doped with holes through chemical substitution, the Mn 4+ ions are formed. In Mn 4+ ions, there are only three electrons occupying the t 2g orbitals. When the excess electron is present in case of Mn 3+ ion, a further distortion known as the Jahn-teller distortion may lower the crystal symmetry and break the degeneracy of the e g states. This can be energetically favorable as the excess electron will fill the lower energy orbital while the upper energy orbital remains empty.
Introduction 7 Figure 1.4: A schematic of the electronic structure of Mn 3+ (a) and Mn 4+ (b). 1.5 Double exchange mechanism The starting point for understanding the properties of manganites is the so-called ”double” exchange (DE) mechanism and was first proposed by C. Zener [5, 6] in 1951, which says the simultaneous hopping of e g elctrons from Mn 3+ sites to O 2− sites and then from O 2− to the empty e g orbitals of Mn 4+ sites. This transfer of e g electron from Mn 3+ to Mn 4+ by DE is the basic mechanism of electrical conduction in manganites. In 1955, the DE theory was expanded by P. W. Anderson, and H. Hasegawa [7], where the hopping probability (t ij ) of the e g electron from Mn 3+ to neighbouring Mn 4+ is, t ij = t cos( θ ij ), (1.3) 2 where θ ij is the angle between the Mn spins in the case of strong Hund’s coupling. The concept of double exchange mechanism is illustrated in Fig. 1.5. For parallel spin configuration (θ ij = 0) the hopping probability is maximum and for antiparallel spin (θ ij = 180 o ), the hopping probability is zero, that means the hopping cancels. Thus it predicts maximum conductivity at ferromagnetic state where as insulating behaviour at antiferromagnetic state. This provides the qualitative explanation for the close connection between the insulator-metal transition and the magnetic transition. It also explains why the external magnetic field will increase the conductivity since θ ij will be reduced as the external magnetic field polarizes the core (t 2g ) spins of the Mn ions. Using mean-field approximations, P. -G. degennes [8] in 1960 suggested that the interpolation between the antiferromagnetic state of the undoped limit and the ferromagnetic state at finite hole density, where the DE mechanism works, occurs
Page 1 and 2: SPECTROSCOPIC INVESTIGATIONS OF THE
Page 3 and 4: iii To My Parents
Page 5 and 6: Maharana, P. Khare, D. K. Basa, K.
Page 7 and 8: List of Publications/Preprints [1]
Page 9 and 10: Synopsis The perovskite type mangan
Page 11 and 12: to the t 2g and e g spin-up states
Page 13 and 14: Bibliography [1] R. von Helmolt, J.
Page 15 and 16: Contents CERTIFICATE Acknowledgemen
Page 17 and 18: List of Figures 1.1 Temperature dep
Page 19 and 20: 2.2 Schematic view of the energetic
Page 21 and 22: 3.4 O K edge x-ray absorption spect
Page 23 and 24: Chapter 1 Introduction 1
Page 25 and 26: Introduction 3 The temperature and
Page 27: Introduction 5 Figure 1.2: Schemati
Page 31 and 32: Introduction 9 Figure 1.6: Schemati
Page 33 and 34: Introduction 11 Figure 1.8: Differe
Page 35 and 36: Introduction 13 Figure 1.10: A sche
Page 37 and 38: Introduction 15 Figure 1.12: Schema
Page 39 and 40: Introduction 17 Figure 1.13: Phase
Page 41 and 42: Bibliography [1] R. von Helmolt, J.
Page 43 and 44: Introduction 21 [31] Damien Saurel,
Page 45 and 46: Chapter 2 Experimental Techniques 2
Page 47 and 48: Experimental Techniques 25 Figure 2
Page 49 and 50: Experimental Techniques 27 Let us n
Page 51 and 52: Experimental Techniques 29 and G(k,
Page 55 and 56: Experimental Techniques 33 point wi
Page 57 and 58: Experimental Techniques 35 negative
Page 59 and 60: Experimental Techniques 37 ∆E = E
Page 63 and 64: Experimental Techniques 41 ( ) dσ
Page 65 and 66: Experimental Techniques 43 The expe
Page 67 and 68: Experimental Techniques 45 are weld
Page 77 and 78: Bibliography [1] H. Hertz, Ann. Phy
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Experimental Techniques 57 [35] K.
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Chapter 3 Electronic Structure of P
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Electronic Structure of Pr 0.67 Ca
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Bibliography [1] I. G. Deac, J. F.
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Chapter 4 Electronic Structure of P
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Electronic Structure of Pr 1−x Ca
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Electronic Structure of Ca 0.86 Pr
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Bibliography [1] C. Zener, Phys. Re
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Summary and Conclusions 109 In this
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