Current Applied Physics 4 (2004) 539–542

www.elsevier.com/locate/cap

Theoretical study of spin-alignment control in molecular magnets q

Ping Huai *, Yukihiro Shimoi, Shuji Abe

Research Consortium for Synthetic Nano-Function Materials Project (SYNAF) and Nanotechnology Research Institute (NRI),

National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan

Received 20 November 2003; accepted 30 January 2004

Available online 24 March 2004

Abstract

We investigated theoretically the electronic control of spin-alignment in p-conjugated molecular magnets, stimulated by the

recent successful observation of the spin control in novel diradical molecules. To clarify the mechanism of the spin alignment, a

microscopic model was designed for a p-electron system interacting with two stable radical groups. We demonstrated that electronic

doping induces a transition from low-spin to high-spin states, depending on topological structures of molecules and the strength of

interaction. In the doped case, spins align in a different way from that predicted by the topological rule established in the half-filled

case. These theoretical results provide useful insights into molecular design of organic magnets controllable by external stimuli.

� 2004 Elsevier B.V. All rights reserved.

PACS: 75.50.Xx; 71.10.Fd; 75.20.Hr

Keywords: Molecular magnets; Spin-alignment control; Kondo–Peierls–Hubbard model; Exchange interaction

1. Introduction

Molecular magnetism has attracted considerable

interests for decades since the discovery of high spin

ground states in dicarbene [1,2]. Recently a new class of

purely organic molecular magnets has received increas-

ing attention as their spin alignment is controllable byexternal stimuli such as charge doping or photoexcita-

tion [3,4], as schematically shown in Fig. 1. Among these

pioneering studies, Izuoka and his co-workers have

succeeded in controlling intramolecular spin alignment

by charge doping in a newly designed organic molecule,

thianthrene bis(nitronyl nitroxide) [3]. This molecule,

consisting of p-conjugated moiety and two stable radi-

cals, is spin singlet (S¼ 0) in its ground state and be-comes spin quartet (S¼ 3/2) upon one-electron

oxidation. The control of spin alignment by photoexci-

tation has also been demonstrated in a similar type of

molecules by Teki et al. [4].

qOriginal version presented at QTSM&QFS 2003 (Quantum

Transport Synthetic Metals & Quantum Functional Semiconductors),

Seoul National University, Seoul, Korea, 20–22 November 2003.* Corresponding author. Fax: +81-298-61-5400.

E-mail address: p.huai@aist.go.jp (P. Huai).

1567-1739/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.cap.2004.01.019

The dominant mechanism of spin alignment in the

ground state of magnetic molecules has been well

established as a topological rule [5–7], based on the

dynamical antiferromagnetic spin polarization effect of

p electrons with on-site Coulomb repulsion. However,

the topological rule cannot be applied to doped or ex-

cited molecules, and most discussions on the spin-alignment control so far have been given on the basis of

individual molecular orbitals [8–12].

On the other hand, to design such novel functional

molecular magnets, it is necessary to clarify the mech-

anism of spin alignment not only in the ground state,

but also in the doped or excited states. Therefore in the

present study, we tried to shed light on the spin-align-

ment control by charge doping from the general point ofview.

2. Model and theoretical treatment

A microscopic model Hamiltonian approach [13] is

applied to study novel molecular magnets: a Peierls–

Hubbard model with N sites and Ne electrons, which is

coupled with two localized spins. That model is given in

the following Hamiltonian:

High Spin

Charge Doping Photoexcitation

Low SpinJ J

J J

π

hνe

Fig. 1. Schematic picture of spin-alignment control by charge doping

or photoexcitation.

(a)

S =0

S =3/2

R

RNe = N

Ne = N − 1

R

R

(b)

S =0

S =1/2

R

RNe = N

Ne = N − 1

R

R

Fig. 2. Schematic picture of spin-alignment control by hole doping in

polyene-based molecular magnets.

540 P. Huai et al. / Current Applied Physics 4 (2004) 539–542

H ¼ �X

i;s

t0ð1þ DiÞðCyi;sCiþ1;s þ h:c:Þ þ

X

i

Uni;"ni;#

þX

i

t02k

ðDi � Diþ1Þ2 �J2ðCy

i1rCi1 ST1

þ Cyi2rCi2 ST2Þ: ð1Þ

The Peierls–Hubbard model corresponds to the p-con-jugated moiety of an organic molecule, while the local-

ized spins (ST1 and ST2) correspond to the unpaired

electrons of stable radical groups (R) attached to it.

In the p electron system, the nearest-neighbor transfer

integral t0 is modified by the dimensionless lattice

deformation Di in the form of Su–Schrieff–Hegger (SSH)coupling. The electron–electron correlation is taken into

account by using on-site Coulomb repulsion energy U .

The lattice deformation is treated classically and its

elastic constant is given by the inverse of the dimen-

sionless SSH electron–lattice coupling constant k.The two localized spins interact indirectly to each

other through the exchange interaction (J ) with p elec-

trons, while a direct spin–spin interaction is neglected inthis model. We exactly diagonalized the electronic and

spin parts of the Hamiltonian by the Lanczos algorithm,

taking into account all of the correlation effect. The

lattice deformation is optimized by means of the Hell-

mann–Feynman force equilibrium condition.

Due to the electron–hole symmetry in this model,

electron doping (Ne ¼ N þ 1) gives the same results as

hole doping (Ne ¼ N � 1). Thus only the results for holedoping will be discussed in this paper.

3. Results and discussion

The main target of this study is to determine the

intramolecular spin alignment before (Ne ¼ N ) and after

(Ne ¼ N � 1) one electron oxidation in the p electronsystem. Two kinds of p-conjugated moieties are studied:

polyene with 10 carbons and anthracene with 14 car-

bons. Typical results are shown below with the follow-

ing parameters (in the unit of t0): U ¼ 2:5, J ¼ 0:2(ferromagnetic) while k ¼ 0:2 for polyene and k ¼ 0:0for anthracene.

Fig. 2 schematically shows the change in spin align-

ment in polyene-based molecular magnets obtained bythe exact-diagonalization calculations. Two molecules

with different radical positions are chosen in Fig. 2(a)

and (b) to examine the topological effect. In Fig. 2(a),

the half-filled ground state (Ne ¼ N ) is a spin singlet

(S¼ 0) with antiparallel alignment of the radical spins,

and bond alternation appears in the lattice. If an elec-

tron is removed from the p-conjugated moiety, the total

spin turns to be quartet (S¼ 3/2) with parallel alignmentof radical spins, leading to controllable spin alignment

between the low- and high-spin configurations by charge

doping.

In Fig. 2(b), the spin alignment of the half-filled

ground state is quite similar to that of the case (a), as

predicted by the topological rule. However, the doped

molecule is a spin doublet (S¼ 1/2) quite different from

that of case (a). Although the radical spins are in parallelalignment, they are antiferromagnetically coupled to the

net p spin, resulting in the spin doublet. Such doping-

induced spin alignment with different p topology cannot

be explained based on the topological rule.

Next we proceed to the spin-alignment control in

anthracene-based molecular magnets. To investigate the

topological effect, we change the position of one of the

radicals. Fig. 3(a) shows that the half-filled ground stateis a spin singlet (S¼ 0) with antiparallel alignment of

radical spins. Single hole doping into the p-electronsystem induces the spin alignment into parallel, resulting

in a transition from the low pin state (S¼ 0) to the high

spin one (S¼ 3/2).

Fig. 3(b) shows that the half-filled ground state is a

spin triplet (S¼ 1), while the doped molecule is a spin

quartet (S¼ 3/2). The spin alignment of the half-filledground state can be easily understood in terms of the

topological rule. However it is very interesting that the

Fig. 4. Spin density in doped Hubbard model for (a) polyene (b)

anthracene. The radius of circles is proportional to the absolute value

of spin density. Filled (open) circles correspond to positive (negative)

values.

S i1 S i2

J > 0 J > 0

S= 3/2

S i1 S i2

J > 0 J > 0

S=1/2

(a)

(b)

Fig. 5. Schematic picture of intramolecular spin alignment of doped

system with ferromagnetic coupling (J > 0): (a) S¼ 3/2 (b) S¼ 1/2.

R R

Ne =N−1R R

Ne =N

S=1

S=3/2

(b)

R

R

Ne =N−1R

RNe =N

S=0

S=3/2

(a)

Fig. 3. Schematic picture of spin-alignment control by hole doping in

anthracene-based molecular magnets.

P. Huai et al. / Current Applied Physics 4 (2004) 539–542 541

high spin also appears in the doped molecule similar to

the case in Fig. 3(a). In fact, we found more doping-

induced high spin (S¼ 3/2) in many other topological

structures in the anthracene case.

To understand the spin alignment in doped case, we

investigated spin density in p-conjugated moieties using

the Hubbard model. Fig. 4 shows the spin density in the

doped states (N" ¼ N=2, N# ¼ N=2� 1) for both poly-ene and anthracene with U=t0 ¼ 2:5. The electron–lat-

tice coupling in polyene is omitted as the dimerization is

fairly weakened in the doped case.

Since a down-spin electron is removed from the

p-conjugated moiety, all the spin density should be po-

sitive if the on-site Coulomb interaction is absent.

Nevertheless with the finite U , negative spin density

appears in polyene shown in Fig. 4(a). In terms of thespin density, the spin alignment can be justified in a

perturbative way shown in Fig. 5. The radical spin

prefers to be parallel to the p spin at the site to which the

radical is attached. If both attached sites have positive

spin density, the radical spins are in the parallel align-

ment with the net p spin, as shown in Fig. 5(a). On the

other hand, if the attached sites have negative spin

densities, the radical spins are in the antiparallel align-

ment with the net p spin, as shown in Fig. 5(b).

The spin alignment in anthracene can be clarified in

the similar way. If we take a closer look at the spindensity in Fig. 4(b), negative values appear only in the

sites that are impossible for radical to attach. Therefore

the radical spins always prefer parallel alignment with

the net spin in p-conjugated moiety, unless the exchange

coupling J is strong, leading to spin quartet (S¼ 3/2).

4. Summary

In summary, the spin-alignment control by charge

doping in p-conjugated molecular magnets has beenstudied in the theoretical model of the Peierls–Hubbard

model coupling with two radicals spins. Two kinds of p-conjugated moieties, polyene and anthracene, are

investigated to clarify the structural dependence of

intramolecular spin alignment. It is demonstrated that

electronic doping induces low-spin to high-spin transi-

tion, which depends on topological structures of mole-

cules. The spin density provides useful information todetermine the manner of spin alignment in the doped

case where the topological rule cannot be applied.

References

[1] K. Itoh, Chem. Phys. Lett. 1 (1967) 235.

[2] E. Wasserman, R.W. Murray, W.A. Yager, A.M. Trozzolo,

G. Smolinsky, J. Am. Chem. Soc. 89 (1967) 5076.

[3] A. Izuoka, M. Hiraishi, T. Abe, T. Sugawara, K. Sato, T. Takui,

J. Am. Chem. Soc. 122 (2000) 3234.

[4] Y. Teki, S. Miyamoto, M. Nakatsuji, Y. Miura, J. Am. Chem.

Soc. 123 (2001) 294.

[5] N. Mataga, Theoret. Chim. Acta 10 (1968) 372.

[6] A.A. Ovchinnikov, Theoret. Chim. Acta 47 (1978) 297.

[7] E.H. Lieb, Phys. Rev. Lett. 62 (1989) 1201.

542 P. Huai et al. / Current Applied Physics 4 (2004) 539–542

[8] H. Sakurai, A. Izuoka, T. Sugawara, J. Am. Chem. Soc. 122

(2000) 9723.

[9] Y. Teki, S. Miyamoto, M. Nakatsuji, Y. Miura, J. Am. Chem.

Soc. 123 (2001) 294.

[10] M. Matsushita, T. Nakamura, T. Momose, T. Shida, Y. Teki, T.

Takui, T. Kinoshita, K. Itoh, J. Am. Chem. Soc. 114 (1992) 7470.

[11] S. Yamanaka, T. Kawakami, M. Okumura, K. Yamaguchi,

Chem. Phys. Lett. 233 (1995) 257.

[12] H. Mizouchi, A. Ikawa, H. Fukutome, J. Phys. Soc. Jpn. 66 (1997)

881.

[13] P. Huai, Y. Shimoi, S. Abe, Phys. Rev. Lett. 90 (2003)

207203.