Materials 286K Class 05. The Hubard model and magnetism On the insulating side of the M–I transition, magnetism of some sort (usually.

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Presentation transcript:

Materials 286K Class 05. The Hubard model and magnetism On the insulating side of the M–I transition, magnetism of some sort (usually antiferromagnetism) manifests.

Materials 286K Class 05. The Hubard model and magnetism In the limit that U >> t, the Hubbard model: Can be reduced to the Heisenberg Hamiltonian: where

Materials 286K Class 05. The Hubard model and magnetism [will return to these !] The example of LnNiO 3, Ln = La, Pr, Nd, Sm: Torrance, Lacorre, Nazzal, Ansaldo, Niedermayer, Phys. Rev. B. 45 (1992) 8209–8212.

Materials 286K Class 05. The Zaanen-Sawatzky-Allen phase diagram The position of transition metal d-states vs. anion p states: Zaanen, Sawatzky, Allen, Phys. Rev. Lett. 55 (1985) 418–421.

Materials 286K Class 05. The Zaanen-Sawatzky-Allen phase diagram The actual diagram. Note that T is what we have been calling W, and W is proportional to t in the Hubbard Model. Zaanen, Sawatzky, Allen, Phys. Rev. Lett. 55 (1985) 418–421.

Materials 286K Class 05. The Zaanen-Sawatzky-Allen phase diagram A simplified view: In the language of ZSA: Zaanen, Sawatzky, Allen, Phys. Rev. Lett. 55 (1985) 418–421. lower Hubbard upper Hubbard U Mott-Hubbard insulators: lower Hubbard upper Hubbard  Charge-transfer insulators: anion p states

Materials 286K Class 05. The Zaanen-Sawatzky-Allen phase diagram Examples of Mott-Hubbard: V 2 O 3, Ti 2 O 3, Cr 2 O 3 and most halides. Early transition metals, and lower oxidation states. Interestingly, these do display T-dependent M–I transitions. Examples of Charge-transfer: CuO, NiCl 2, NiS, etc. Later transition metals and higher oxidation states. CuO and NiCl 2 are always insulating. Zaanen, Sawatzky, Allen, Phys. Rev. Lett. 55 (1985) 418–421.

Materials 286K Class 05. The Zaanen-Sawatzky-Allen phase diagram. Periodic trends Zaanen, Sawatzky, Allen, Phys. Rev. Lett. 55 (1985) 418–421.

Materials 286K Class 05. The Zaanen-Sawatzky-Allen phase diagram and perovskites Optical studies of band gaps: Distinguishing d–d and p–d character: Arima, Tokura, Torrance, Phys. Rev. B. 48 (1993) 17006–17009.

Materials 286K Class 05. The Zaanen-Sawatzky-Allen phase diagram and perovskites

Materials 286K Class 05. The Zaanen-Sawatzky-Allen phase diagram and batteries The transition metal d and anion p levels manifest in Li-battery electrochemistry. Hayner, Zhao, Kung, Annu. Rev. Chem. Biomolec. Eng. 3 (2012) 445–471.

Materials 286K Class 05. The Zaanen-Sawatzky-Allen phase diagram and redox competition Ideas of Goodenough, Rouxel etc. M 4+ M 2+

Materials 286K Class 05. The Zaanen-Sawatzky-Allen phase diagram and redox competition