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Orbital Ordering and Exchange Interactions in RMnO 3 Perovskites

Orbital Ordering and Exchange Interactions in RMnO 3 Perovskites. J. B. Goodenough, U.T. Austin DMR-0555663. s. l. s. l. O 1. m. m. m. l. s. O 4. s. 1. O 4. l. R. l. m. O 4. s. O 3. m. m. m. s. R 2. l. R 2. O 2. c. f 1. R 2. s. l. R 1.

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Orbital Ordering and Exchange Interactions in RMnO 3 Perovskites

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  1. Orbital Ordering and Exchange Interactions in RMnO3 Perovskites J. B. Goodenough, U.T. Austin DMR-0555663

  2. s l s l O1 m m m l s O4 s 1 O4 l R l m O4 s O3 m m m s R2 l R2 O2 c f1 R2 s l R1 f2 b m m s l a O3 O4 s l y2 - z2 3x2 - r2 Dc xy, yz, zx Pbnm MnO6 Octahedra 1 La Pr Nd Sm Eu Gd Tb Ho Er Tm Yb Lu Y Dy P63cm Mn3+ ion MnO5 Bipyramid Crystallographic structure of RMnO3 Ds Synthesized under ambient pressure Synthesized under high pressure Synthesized under ambient pressure a c O4 O3 O4 3z2 - r 2 (x2-y2) ± ixy yz ± ixz

  3. Magnetic phase diagram of RMnO3 Perovskites Although the same orbital ordering takes place over entire family of RMnO3 perovskites, there are three magnetic phases: Type-A spin ordering, No classic spin ordering, Type-E spin ordering.

  4. The evolution of structural distortions versus ionic size of the A-site Rare Earth The structure refinement from data of neutron and x-ray diffraction.

  5. Jab = Jsab -Jpab Jc = -Jsc -Jpc g =30 -f , w= 180 - q Jsab ~ cos4(g/2)cos2(w/2)|3x12 - r12|H’|x22-z22|2/Ds The relationship between structural distortions and magnetic couplings in perovskite RMnO3 Js is sensitive to q Jp is much less sensitive to q q = (f1 + 2f2)/3

  6. Check some numbers from Structure, TN and TJT (For Type-A spin ordering phase) dlnTN/d(IR)  9 Ǻ-1 dln(cos2(w/2))/d(IR)  0.4 Ǻ-1 dln(cos4(g/2))/d(IR), wrong sign dln(Ds-1))/d(IR)  7 Ǻ-1 ( Ds ~ kTJT, mean-field theory) Conclusions * Type-A spin ordering phase for R=La-Gd Jsab is weakened primarily by Ds, not by the angle q. * No classic spin ordering phase for R= Tb, Dy A |Jsab| ~ |Jpab| leads to the exchange interaction frustration. * Type-E spin ordering phase for R= Y-Lu Segregation into Jsab dominant and Jpab dominant Mn-O-Mn bonds occurs.

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