Ryotaro AritaDept. Applied Phys., Univ. Tokyo

Theoretical materials design of ferromagnets comprising non-magnetic elements

R.AritaR.Arita

Collaborators

Dr. Y. SuwaProf. K. KurokiProf. H. Aoki

(Univ. Tokyo) (Adv. Res. Lab. Hitachi)(Univ. Electro-Cummun.)

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Itinerant ferromagnetism

in purely organic polymers ?

C60-TDAE Alkali-metal loaded zeolite Radical polymers

(Al, Si, O) + KC, H, N Tc~16K Tc~8K

Known materials (localized spin systems)

Tc~O(1) K

Theoretical materials design of ferromagnets comprising non-magnetic elements

Motivation

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Guideline for materials design of ferromagnets :

Rigorous results (theorem) for the Hubbard model

Materials design by

first-principles calculation

+ model calculation

†

,

.ij i j i ii j i

H t c c h c U n n

Flat-band ferromagnetism by Mielke & Tasaki (‘91,’92)

Strategy

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(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

†GS 0

iii

Example: 1D triangular lattice・・・・・・

= -1

t=1

(1) (2)

Ferromagnetism guaranteed for U > 0 when

Mielke 91, Tasaki 92Flat-band Ferromagnetism

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・・・・・・t=1

Robustness of Flat-band Ferromagnetism

ε0=-1

ε0≠-1

Flat-band F

Penc et al (1996)

F survives : not pathological

Finite band dispersion

Ferromagnetic phase

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・・・・・・t=1

Robustness of Flat-band Ferromagnetism

U

Sakamoto-Kubo (1996), Watanabe-Miyashita (1997)

0 2 4

0

-1

1

FM

n=0.375Flat-band

Carrier doping

ε0≠-1

ε0≠-1

n=0.5

n≠0.5

Metallic ferromagnetism

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In realistic situations…

Flat band ferromagnetism:Proved for the case where the flat band isat the bottom of theBand structure

Flat band isnot always at the bottom

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(RA et al, PRB 57 R6854(1998))

Ferro

Ferro guaranteed only for U < Uc

Strong coupling regime: AF favored

Ferromagnetism only for U<Uc

0

' cos

( 1 2sin )

t t

t

Connected square lattice

t’

When flat bands is in the middle of the band structure :

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In realistic situations…

Flat band F:Proved for the case where the flat band isat the bottom of theBand structure

Flat band isnot always the bottom

Stability of the flat-band ferromagnetismdepends on the position of the flat band

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Asymmetric DOS favors F

F fragileF 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

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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 Uc and check that Uc is not too small (model calculation)

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Five membered rings: connectivity condition satisfied for realistic parameters of t and

Chain of five-membered ringsEnergy

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

nN N

H

.. ..

H

Versatile possibilities of putting on various functional bases

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GGA calculation (TAPP, Tokyo Ab-initio Program Package)Plane wave basis + ultra-soft pseudo-potential

0 = +1

t

=N

n

N

nN N

.. ..X X

or

X=Na, K, Cl, F, OH, CH3

(low electron affinity)

No flat band

?

dispersive

Polymers of five-membered rings

Difficult to make 0~+1

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=N

n

N

nN N

.. ..or

X X

X=CN, COOH, NH2 (bases with electrons)

Flat band for polyaminotriazole

N

nN N

..

NH2

Polymers of decorated five-membered rings

RA et al.,PRL., 88,127202 (2002)

Difficult to make 0~+1

Flat band for 0 < 0 ?

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tight-binding model

Electronic Structure of Polyaminotriazole

GGA calculation

( connectivity condition satisfied )

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Connectivity condition satisfied ?: How to see it

Maximally localized Wannier fn.< size of unit cell

Periodic part of Bloch fn. (uk )

= Same for all k

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Connectivity condition satisfied ?: How to see it

Maximally localized Wannier fn.> size of unit cell

Periodic part of Bloch fn. (uk )

depends on k

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Comparison of the Bloch wave functions

connectivity condition satisfied for GGA

GGA

Tight-bindingmodel

Connectivity condition satisfied for the tight-binding model

X

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comparison of the total energies

The ferromagnetic state is most stablePeierls instability is weak

LSDA for doped PAT

PAT = promising candidate for flat-band F with an appropriate carrier doping

cf) polyethylene

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Magnetic phase diagram for the Hubbard model

Ferromagnetism stable unless U is not too strong

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4-Amino 1,2,4,Triazole

color

statemelting point

white

crystals

86.3 - 87.3 C°

http://www.purechagroup.com/commercially available:

Polymerization?

NN

NH2N

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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)

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N

NMe2

N

NMe2

N

NMe2

N

NMe2

N

NMe2

N

NMe2

N

NMe2

1) n-BuLi THF, reflux

2) NiCl2, r.t.

yield: 60% yield: 15%

1) n-BuLi / t-BuOK THF, -78 oC

2) NiCl2(dppp), r.t.

N

NMe2

N

NMe2

N

NMe2

N

NMe2yield: 23%

N

NMe2

N

NMe2

N

NMe2

N

NMe2

1) n-BuLi THF, reflux

2) NiCl2, r.t.

N

NMe2

N

NMe2

N

NMe2 n

N

NMe2

N

NMe2

N

NMe2 n

m

m SbCl6-

Experiments (actual synthesis)

Nishihara group, Univ. Tokyo4 holes/ 8 rings

dimethylaminopyrrole

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N

NMe2

N

NMe2

N

NMe2

N

NMe2

N

NMe2

N

NMe2

N

NMe2

1) n-BuLi THF, reflux

2) NiCl2, r.t.

yield: 60% yield: 15%

1) n-BuLi / t-BuOK THF, -78 oC

2) NiCl2(dppp), r.t.

N

NMe2

N

NMe2

N

NMe2

N

NMe2yield: 23%

N

NMe2

N

NMe2

N

NMe2

N

NMe2

1) n-BuLi THF, reflux

2) NiCl2, r.t.

N

NMe2

N

NMe2

N

NMe2 n

N

NMe2

N

NMe2

N

NMe2 n

m

m SbCl6-

Experiments (actual synthesis)

Nishihara group, Univ. Tokyo4 holes/ 8 rings

dimethylaminopyrrole

ESR

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N

NMe2

N

NMe2

N

NMe2

N

NMe2

N

NMe2

N

NMe2

N

NMe2

1) n-BuLi THF, reflux

2) NiCl2, r.t.

yield: 60% yield: 15%

1) n-BuLi / t-BuOK THF, -78 oC

2) NiCl2(dppp), r.t.

N

NMe2

N

NMe2

N

NMe2

N

NMe2yield: 23%

N

NMe2

N

NMe2

N

NMe2

N

NMe2

1) n-BuLi THF, reflux

2) NiCl2, r.t.

N

NMe2

N

NMe2

N

NMe2 n

N

NMe2

N

NMe2

N

NMe2 n

m

m SbCl6-

Experiments (actual synthesis)

Nishihara group, Univ. Tokyo4 holes/ 8 rings

dimethylaminopyrrole

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Polyaminotriazole:

promising candidate for

flat-band ferromagnetism

Related materials:

Oligomer of dimethylaminopyrrole:

High-spin state ?

Conclusions