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IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011 2429

Ligand-Driven Exchange Coupling in �� Single-Molecule MagnetsNguyen Anh Tuan�, Ngo Thanh Tam�, Nguyen Huy Sinh�, and Dam Hieu Chi��

Faculty of Physics, Hanoi University of Science, Thanh Xuan, Hanoi, VietnamSchool of Materials Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa 923-1292, Japan

Distorted cubane ��

� � �� (� �; � ��; � ��; �� ) single-molecule magnets (SMMs) have been studied by first-principles calculations. Our earlier studies showedthat the basic mechanism of antiferromagnetic �� coupling � �� is determined by the type hybridization among the� orbitals at the �� sites and the �� orbitals at the �� site through the orbitals at the � �� ions. This result allows

us to predict that ferrimagnetic structure of ��

molecules will be the most stable with the ��

angle � , while synthesized ��

molecules have �! . One approach is suggested to design new ��

SMMs having a much more stable ferrimagnetic state. This approach is controlling the �� exchange path-ways by rational variations in ligands to strengthen the hybridization between Mn ions. In this paper, by combining variations in theL and Z ligands, ten new high-spin ��

�� " ��

� �#��#�� (� $#%��, $%�#�,$%��,$&�%��, or$%�&��;� �� or��#�#��$#��) molecules have been designed. Our calculated resultsshow that these ten modelling �� molecules have � and �� in the range of ( 231.6, 147.4) K, in which the moleculewith �� $#%�� #�#��$#�� has the highest �� of 231.6 K corresponding to '� () . This valueis over 3 times larger than that of synthesized �� SMMs. Our calculated results demonstrate combining variations in the L and Zligands as an effective way to tailor intramolecular exchange coupling of the �� molecules. The results would give some hints forsynthesizing new SMMs.

Index Terms—Computational materials design, exchange interaction, ferrimagnetic materials, single-molecule magnets.

I. INTRODUCTION

C LASSICAL magnets, e.g., metals, alloys, and metaloxides, play a significant role in the development of

modern society, science, and technology, producing a multi-bil-lion-dollar-per-year industry. However, magnetic anisotropyof classical magnetic particles is disappeared when their sizeis reduced to several nanometers due to the superparamag-netic effect. The development of molecule-based magnetsgives us possibilities to design magnets at nanoscale. Asfar as molecular nanomagnets are concerned, the past fewyears have withnessed an explosive growth of single-moleculemagnets (SMMs). SMMs are individual molecules that canfunction as magnets below their blocking temperature. They arebeing extensively studied due to their potential technologicalapplications to molecular spintronics [1]. They derive theirproperties from the combination of a high ground-state spin

with a large and negative Ising type of magnetoanisotropy,as measured by the axial zero-field splitting parameter .SMMs consist of magnetic atoms connected and surrounded byligands. The challenge of SMMs consists in tailoring magneticproperties by specific modifications of the molecular units. The

results from local spin moments at magnetic ions andexchange coupling between them . Moreover, has tobe important to well separate the ground spin state from the

Manuscript received February 21, 2011; accepted April 17, 2011. Date ofcurrent version September 23, 2011. Corresponding author: N. A. Tuan (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2011.2152377

excited states [2]–[4]. Therefore, seeking possibilities of theenhancement of will be a way to develop SMMs.

In the framework of computational materialsdesign, distorted cubane [

] ( ; ; ;) molecules [5], [6] is one of

the most attractive SMM systems because their interestinggeometric structure and important magnetic quantities can bewell estimated by first-principles calculations [7]–[10]. In ourearly studies [7], by using first-principles calculations withingeneralized gradient approximation, the basic mechanism ofthe antiferromagnetic (AFM) interaction between theion and the three high-spin ions inmolecules was analyzed. The AFM coupling

is determined by the type hybridization among theorbitals at the sites and the orbitals at

the site through the orbitals at theions. This result allows us to predict that ferrimagneticstructure of molecules will be the moststable with the angle

, while synthesized molecules have. To design new SMMs having

much more stable ferrimagnetic state, one approach issuggested: Controlling theexchange pathways by rational variations in ligands tostrengthen the hybridization between Mn ions. In our previouspaper [8], by employing N-based ligands to form theexchange pathways between Mn atoms, new six high-spin

( , , , , , or )molecules with of 9/2 have been designed. The calculatedresults confirm the expectation that tends to becomestronger when reaches to around 90 . The molecule with

has the highest of 174.47 K

0018-9464/$26.00 © 2011 IEEE

2430 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011

corresponding to . This value is about 2.5 timeslarger than that of synthesized SMMs.

In this paper, to seek more new molecules with, new ten high-spin

molecules have been designed bycombining variations in the L and Z ligands ( ,

, , , or ;or . Our calculated results show that allthese ten modelling molecules have andin the range of ( 231.6, 147.4) K, in which the molecule with

has the highestof 231.6 K corresponding to . This value

is over 3 times larger than that of synthesized SMMs.Our calculated results demonstrate combining variations in theL and Z ligands as an effective way to tailor intramolecularexchange coupling of the molecules. The results providesome hints for synthesizing new SMMs.

II. COMPUTATIONAL METHODS

To compute the geometric structure, electronic structure andeffective exchange coupling parameters of molecules, thesame reliable computational method as in our previous paper [7]is adopted. In this method, all calculations have been performedby using DMol [3] code with the double numerical basis setsplus polarization functional (DNP) [11]. For the exchange cor-relation terms, the generalized gradient approximation (GGA)RPBE functional was used [12]. All-electron scalar relativisticmethod was used to describe the interaction between the coreand valence electrons [13]. The real-space global cutoff radiuswas set to be 4.7 for all atoms. The spin-unrestricted DFTwas used to obtain all results presented in this study. Theatomic charge and magnetic moment were obtained by usingthe Mulliken population analysis [14], [18]. The charge densityis converged to in the self-consistent calculation.In the optimization process, the energy, energy gradient, andatomic displacement are converged to , and

, respectively. The total energy difference methodwas adopted to calculate the exchange coupling parameters of

molecules [7]. To determine exactly the magnetic groundstate of molecules, all possible spin configurationsof molecules are probed, which are imposed asan initial condition of the structural optimization procedure.The number of spin configurations should be considered de-pending on the charge state of manganese ions. In terms of theoctahedral field, ions could, in principle, have only thehigh-spin state with configuration , in which threeelectrons occupy three different orbitals. The possible spinstates of ion are the high-spin (HS) state with configura-tion and the low-spin (LS) state with configuration

. Additionally, the magnetic coupling between theion at the A site and ions at the B site can be

ferromagnetic (FM) or antiferromagnetic (AFM). Therefore,there are four spin configurations which should be consideredfor each molecule, including: (i) AFM-HS, (ii)AFM-LS, (iii) FM-HS, and (iv) FM-LS.

Fig. 1. The schematic geometric structures of the molecules �� and ��. The�� is highlighted in the balls.

III. RESULTS AND DISCUSSION

New distorted cubane molecules have beendesigned based on the synthesized [

] ( and )molecule [5], [6]. Firstly, the molecule is reduced to

( and ) by replacing eachring of dbm groups with one H atom to improve the com-putational performance. The schematic geometric structuresof molecules and are displayed in Figs. 1(a) and1(b), respectively. Then new molecules havebeen designed by variations in L and Z ligands of the mol-ecule . To preserve the distorted cubane geometry of the

core ofmolecules and the formal charges of Mn ions, ligands sub-stituted for the core ligand should satisfy followingconditions: (i) To have the valence of 2; (ii) The ionic radius ofthese ligands should be not so different from that of ion.From these remarks, N based ligands, NR ,should be the best candidates. Moreover, by variation in Rgroup, the local electronic structure as well as electroneg-ativity at N site can be controlled. As a consequence, the

coupling is expected to be tailored.In our previous paper [8], by employing N-based ligands toform the exchange pathways between Mn atoms, six high-spin

( , , , , , or ;) molecules with of 9/2 have been designed.

The calculated results confirmed the expectation that tendsto become stronger when reaches to around 90 . The mol-ecule with has the highest of 174.47K corresponding to . This value is about 2.5 timeslarger than that of and .

In this study, to seek more new moleculeswith , new ten high-spin moleculeshave been designed by combining variations in the L andZ ligands of the molecule . These ten molecules have ageneral chemical formula

( , ,, , or ; or

. They are labeled fromand , and their chemical formulas are tabulatedin Table I. It is noted that, the molecules and have

TUAN et al.: LIGAND-DRIVEN EXCHANGE COUPLING IN SINGLE-MOLECULE MAGNETS 2431

TABLE ITHE CHEMICAL FORMULAS OF �� MOLECULES AND THEIR L LIGANDS

�� , �� . Selected important magnetic and geometric parameters of �� molecules, the effective exchangecoupling parameter between the �� and �� ions �� , the magnetic moment at Mn sites (� and � ), the exchange coupling angle�� , the distance between the �� and �� ions �� , the �� and �� bond lengths (� and � ),and thedistortion factor of B sites �� .

Fig. 2. The typical geometric structures of molecules �� and �� . Hydrogenatoms are removed for clarity. This figure shows the difference in Z ligand be-tween the molecules �� and �� .

the same core L ligand but difference in the Z ligand. Themolecules has the , while the molecules

have . The typical geometricstructures of molecules and are shown in Fig. 2.

Our calculated results show that the most magnetic stablestate of all twelve molecules , , andis the AFM-HS. The three ions at the B sites exist inthe HS state with configuration , and theexchange coupling between the three ions and the

ion is AFM resulting in the ferrimagnetic structure inmolecules with the large of 9/2. Note that,

the HS state with configuration relatesto the appearance of the elongated Jahn-Teller distortions at

ions. Our calculated results confirm that each of threesites is an elongated octahedron along the

axis. Here, the distortion factor of the B sites is measured by, where, is the interatomic

distance between the and sites as labled in Fig. 3.The is the average interatomic distance between thesite and the two O sites of the group as shown inFig. 3. The values of , and is tabulated in Table I.The of molecules and is various in therange from 6.738% to 11.339%. The molecules andhave the highest and smallest values of , respectively. The

Fig. 3. Ligand configuration at the Mn sites of �� molecules. TheQ sites are located by the O atoms in the molecule ��, and by the N atoms inthe molecule �� .

HS spin state as well as the elongated Jahn-Teller distortions ations is known as one of the origin of the axial anisotropy

in Mn SMMs [15]–[17]. These results demonstrate that all newten molecules under consideration in this paperare expected to have axial anisotropy.

The geometric structures corresponding to the most stablestates of these molecules are displayed in Figs. 1 and 2, ofwhich has been synthesized before [5], [6]. The calcu-lated geometric structure of is in good agreement withthe experimental data reported in [5] and [6]. As displayedin Fig. 1(a), the molecule has symmetry, with the

axis passing through and ions. Thecore can be simply

viewed as a “distorted cubane”. The Z ligand consists of threecarboxylate (OAc) groups, forming three bridges between the

ion and the three ions. The molecule containsthree dbm groups. Each dbm group forms two coordinatebonds to complete the distorted octahedral geometry at eachB site. A comparison between and show that their

skeletons are nearly the same. For example,the difference in and of these molecules are very small,as shown in Table I. Also their magnetic moments at Mn sitesand are nearly the same. It is noted that the moleculeis obtained from the molecule by replacing each ringof dbm groups with one H atom. These results demonstrate thatvariation in outer part of dbm groups is not so much influenceon magnetic properties of molecules.

2432 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011

Our calculations show that the geometric structures ofmolecules and are similar to , asshown in Fig. 2. They also have symmetry, with theaxis passing through and , even if their L andZ ligands are different. Also the distorted cubane geometryof the core is preserved. However, their bond anglesand interatomic distances are different from those of ,especially the exchange coupling angle . The moleculehas , while the molecules andhave , as tabulated in Table I. These results allow usto predict that the exchange coupling parameter of themolecules and is significant larger thanthat of . Indeed, our calculated results show that theof molecules and is at least twice largerthan that of , as tabulated in Table I, in which the ofmolecule is over 3 times larger than that of the molecule

. Here it is noted that, the computational method adoptedin this study overestimate the by a factor of about 2 [7].Hence, the expected value of of the molecules underconsideration should be a half of our calculated results.

A comparison between molecules and shows thatthe of is larger than that of , while their and

are nearly the same, as shown in Table I. It poses a ques-tion what causes the significant difference between the of

and . It is noted that, in molecules, eachion with the configuration has one

unpaired electron occupying the orbital which can be delo-calized toward the nearest ligands and also toward the

ion [7]. This magnetic orbital may overlap strongly withhalf-filled orbitals of the ion resulting in the AFMcoupling between the and ions. Therefore, it isexpected that the stronger delocalization of electron occupyingthe orbitals, the smaller magnitude of the magnetic momentsof Mn ions, and the stronger AFM coupling between theand ions . A comparison between the molecules

and confirms this expectation, the molecule withsmaller and is always accompanied with a larger

, as shown in Table I. Also it is expected that, the smallerelongated Jahn-Teller distortion at sites, the stronger de-localization of electron occupying the orbitals of ionstoward the nearest ligands and also toward the ion,due to the advantage of coulomb repulsion energy. As a conse-quence, the smaller elongated Jahn-Teller distortion atsites, the stronger exchange coupling between the and

ions. A comparison between the molecules andconfirms this expectation, the molecule with smaller isalways accompanied with a stronger , as shown in Table I.

IV. CONCLUSION

By combining variations in the L and Z ligands, tennew high-spin [

] ( , ,

, , or ; or) molecules have been designed.

Our calculated results show that these ten modellingmolecules have and in the range

of ( 231.6, 147.4)K, in which the molecule withhas the highest

of 231.6 K corresponding to . This valueis over 3 times larger than that of synthesized SMMs.Our calculated results demonstrate combining variations in theL and Z ligands as an effective way to tailor intramolecularexchange coupling of the molecules. Also, these resultsdemonstrate the advantages of employing N-based ligandsinstead of oxygen to form exchange pathways between Mnatoms in distorted cubane molecules. The results shouldfacilitate the rational synthesis of new SMMs and, eventually,the preparation of technologically useful SMMs.

ACKNOWLEDGMENT

The authors thank the Vietnam’s National Foundation for Sci-ence and Technology Development (NAFOSTED) for fundingthis work within project 103.01.77.09. The computations pre-sented in this study were performed at the Information ScienceCenter of Japan Advanced Institute of Science and Technology,and the Center for Computational Science of the Faculty ofPhysics, Hanoi University of Science, Vietnam.

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