1. Ryotaro Arita Dept. Applied Phys., Univ. Tokyo Theoretical materials design of ferromagnets comprising non-magnetic elements

2. R.Arita Collaborators Dr. Y. Suwa Prof. K. Kuroki Prof. H. Aoki (Univ. Tokyo)(Adv. Res. Lab. Hitachi)(Univ. Electro-Cummun.)

3. R.Arita Itinerant ferromagnetism in purely organic polymers ? C 60 -TDAEAlkali-metal loaded zeoliteRadical polymers (Al, Si, O) + KC, H, NT c ~16K T c ~8K Known materials (localized spin systems) T c ~O(1) K Theoretical materials design of ferromagnets comprising non-magnetic elements Motivation

4. R.Arita Guideline for materials design of ferromagnets : Rigorous results (theorem) for the Hubbard model Materials design by first-principles calculation + model calculation Flat-band ferromagnetism by Mielke & Tasaki (‘91,’92) Strategy

5. R.Arita (1) Half-filled dispersionless band at the bottom of the band structure (2) Connectivity condition satisfied (Wannier functions overlap no matter how they are linearly combined.) MaxLoc Wannier (Marzari&Vanderbilt) has overlaps with its neighbors ・・・ Overlapping “Wannier” orbits parallel spins favored due to Pauli’s exclusion rule Example: 1D triangular lattice ・・・   = -1 t=1 (1) (2) Ferromagnetism guaranteed for U > 0 when Mielke 91, Tasaki 92 Flat-band Ferromagnetism

6. R.Arita ・・・ t=1  Robustness of Flat-band Ferromagnetism ε 0 =-1 ε 0 ≠-1 Flat-band F Penc et al (1996) F survives : not pathological Finite band dispersion Ferromagnetic phase

7. R.Arita ・・・ t=1  Robustness of Flat-band Ferromagnetism U  Sakamoto-Kubo (1996), Watanabe-Miyashita (1997) 024 0 1 FM n=0.375 Flat-band Carrier doping ε 0 ≠-1 n=0.5 n≠0.5 Metallic ferromagnetism

8. R.Arita In realistic situations… Flat band ferromagnetism: Proved for the case where the flat band is at the bottom of the Band structure Flat band is not always at the bottom

9. R.Arita (RA et al, PRB 57 R6854(1998))  Ferro Ferro guaranteed only for U < U c Strong coupling regime: AF favored Ferromagnetism only for U<U c  Connected square lattice t’ When flat bands is in the middle of the band structure :

10. R.Arita In realistic situations… Flat band F: Proved for the case where the flat band is at the bottom of the Band structure Flat band is not always the bottom Stability of the flat-band ferromagnetism depends on the position of the flat band

11. R.Arita Asymmetric DOS favors F F fragile F robust Not only D(  f ) but also the position of the peak is in D important cf) Stoner criterion: UD(  f ) > 1 DMFT study by Wahle,Bluemer,Schlipf,Held, & Vollhardt (1998) F not favored F favored

12. R.Arita Materials design of flat-band ferromagnetism in real materials (1)Construct a tight-binding model having flat bands (2) Search for materials which correspond to the tight-binding model (first-principles calculation) (3) Ferromagnetic ground state ? (LSDA) Estimate U c and check that U c is not too small (model calculation)

13. R.Arita Five membered rings: connectivity condition satisfied for realistic parameters of t and  Chain of five-membered rings Energy Design of flat-band ferromagnetism in organic polymers  0 = +1 t  Many known polymers: polypyrrole, polyazole, polythiophene, etc Flat band N n S n N n NN H.. H Versatile possibilities of putting on various functional bases

14. R.Arita GGA calculation (TAPP, Tokyo Ab-initio Program Package) Plane wave basis + ultra-soft pseudo-potential  0 = +1 t  = N n N n NN.. XX or X=Na, K, Cl, F, OH, CH 3 (low electron affinity) No flat band ? dispersive Polymers of five-membered rings Difficult to make  0 ~+1

15. R.Arita = N n N n NN.. or X X X=CN, COOH, NH 2 (bases with  electrons) Flat band for polyaminotriazole N n NN.. NH 2 Polymers of decorated five-membered rings RA et al., PRL., 88,127202 (2002) Difficult to make  0 ~+1 Flat band for  0 < 0 ?

16. R.Arita tight-binding model Electronic Structure of Polyaminotriazole GGA calculation ( connectivity condition satisfied )

17. R.Arita Connectivity condition satisfied ?: How to see it Maximally localized Wannier fn. < size of unit cell Periodic part of Bloch fn. (u k ) = Same for all k

18. R.Arita Connectivity condition satisfied ?: How to see it Maximally localized Wannier fn. > size of unit cell Periodic part of Bloch fn. (u k ) depends on k

19. R.Arita Comparison of the Bloch wave functions connectivity condition satisfied for GGA GGA Tight-binding model Connectivity condition satisfied for the tight-binding model  X

20. R.Arita comparison of the total energies The ferromagnetic state is most stable Peierls instability is weak LSDA for doped PAT PAT = promising candidate for flat-band F with an appropriate carrier doping cf) polyethylene

21. R.Arita Magnetic phase diagram for the Hubbard model Ferromagnetism stable unless U is not too strong

22. R.Arita 4-Amino 1,2,4,Triazole color state melting point white crystals 86.3 - 87.3 C° http://www.purechagroup.com/ commercially available: Polymerization? N N N H2NH2N

23. R.Arita Polymethylaminotriazole Related materials Oligomer of Methylaminopyrrole Ferro ~ AF < P Flat band Ground state = High spin state (S=1) Suwa, RA, Kuroki, Aoki, PRB68 174419 (2003) Suwa, RA, Kuroki, Aoki, in prep. (2009)

24. R.Arita N NMe 2 N NMe 2 N NMe 2 n N NMe 2 N NMe 2 N NMe 2 n m m SbCl 6 - Experiments (actual synthesis) Nishihara group, Univ. Tokyo 4 holes/ 8 rings dimethylaminopyrrole

25. R.Arita N NMe 2 N NMe 2 N NMe 2 n N NMe 2 N NMe 2 N NMe 2 n m m SbCl 6 - Experiments (actual synthesis) Nishihara group, Univ. Tokyo 4 holes/ 8 rings dimethylaminopyrrole ESR

26. R.Arita N NMe 2 N NMe 2 N NMe 2 n N NMe 2 N NMe 2 N NMe 2 n m m SbCl 6 - Experiments (actual synthesis) Nishihara group, Univ. Tokyo 4 holes/ 8 rings dimethylaminopyrrole

27. R.Arita Polyaminotriazole: promising candidate for flat-band ferromagnetism Related materials: Oligomer of dimethylaminopyrrole: High-spin state ? Conclusions