IEEE TRANSACTIONS ON MAGNETICS, VOL 47, NO 10, OCTOBER 2011 Ligand-Driven Exchange Coupling in Mn4 Single-Molecule Magnets 2429 Nguyen Anh Tuan1 , Ngo Thanh Tam1 , Nguyen Huy Sinh1 , and Dam Hieu Chi1;2 Faculty of Physics, Hanoi University of Science, Thanh Xuan, Hanoi, Vietnam School of Materials Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa 923-1292, Japan Distorted cubane dibenzoyl [Mn 4+ Mn3+ ( 3 L )3 ( X )(Z) (dbm)3 ] (L = O; X = various; Z = (OAc)3 ; dbmH = methane) single-molecule magnets (SMMs) have been studied by first-principles calculations Our earlier studies showed that the basic mechanism of antiferromagnetic Mn4+ Mn3+ coupling ( AB ) is determined by the type hybridization among the 3+ sites and the 4+ site through the orbitals at the ions This result allows L 2g orbitals at the Mn z orbitals at the Mn 3+ 4+ ) us to predict that ferrimagnetic structure of Mn4+ Mn3+ ( L Mn molecules will be the most stable with the Mn 4+ 3+ 4+ 3+ 90 , while synthesized Mn 95 One approach is suggested to design new Mn angle Mn molecules have Mn SMMs having a much more stable ferrimagnetic state This approach is controlling the Mn4+ ( L2 ) Mn3+ exchange pathways by rational variations in ligands to strengthen the hybridization between Mn ions In this paper, by combining variations in the ) ( (CH(CHO) ) ] (L = NCGeH , NGeCH , L F )3 (Z) L and Z ligands, ten new high-spin [Mn4+ Mn3+ 5 3 ( NGe2 H5 , NSiGeH5 , or NGeSiH5 ; Z = (OAc)3 or MeC(CH2 NCOMe)3 ) molecules have been designed Our calculated results 90 and AB show that these ten modelling Mn4 molecules have B in the range of ( 231.6, 147.4) K, in which the molecule with [L Z] = [NCGeH5 MeC(CH2 NCOMe)3 ] has the highest AB B of 231.6 K corresponding to = 89 23 This value is over times larger than that of synthesized Mn4 SMMs Our calculated results demonstrate combining variations in the L and Z ligands as an effective way to tailor intramolecular exchange coupling of the Mn4 molecules The results would give some hints for synthesizing new SMMs Index Terms—Computational materials design, exchange interaction, ferrimagnetic materials, single-molecule magnets I INTRODUCTION C LASSICAL magnets, e.g., metals, alloys, and metal oxides, play a significant role in the development of modern society, science, and technology, producing a multi-billion-dollar-per-year industry However, magnetic anisotropy of classical magnetic particles is disappeared when their size is reduced to several nanometers due to the superparamagnetic effect The development of molecule-based magnets gives us possibilities to design magnets at nanoscale As far as molecular nanomagnets are concerned, the past few years have withnessed an explosive growth of single-molecule magnets (SMMs) SMMs are individual molecules that can function as magnets below their blocking temperature They are being extensively studied due to their potential technological applications to molecular spintronics [1] They derive their properties 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 by ligands The challenge of SMMs consists in tailoring magnetic properties by specific modifications of the molecular units The results from local spin moments at magnetic ions and Moreover, has to exchange coupling between them be important to well separate the ground spin state from the Manuscript received February 21, 2011; accepted April 17, 2011 Date of current version September 23, 2011 Corresponding author: N A Tuan (e-mail: tuanna@hus.edu.vn) Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org Digital Object Identifier 10.1109/TMAG.2011.2152377 excited states [2]–[4] Therefore, seeking possibilities of the enhancement of will be a way to develop SMMs In the framework of computational materials design, distorted cubane [ ]( ; ; ; ) molecules [5], [6] is one of the most attractive SMM systems because their interesting geometric structure and important magnetic quantities can be well estimated by first-principles calculations [7]–[10] In our early studies [7], by using first-principles calculations within generalized gradient approximation, the basic mechanism of the antiferromagnetic (AFM) interaction between the ion and the three high-spin ions in molecules was analyzed The AFM coupling is determined by the type hybridization among the orbitals at the sites and the orbitals at site through the orbitals at the the ions This result allows us to predict that ferrimagnetic molecules will be the most structure of angle stable with the , while synthesized molecules have To design new SMMs having much more stable ferrimagnetic state, one approach is suggested: Controlling the exchange pathways by rational variations in ligands to strengthen the hybridization between Mn ions In our previous paper [8], by employing N-based ligands to form the exchange pathways between Mn atoms, new six high-spin ( , , , , , or ) of 9/2 have been designed The calculated molecules with tends to become results confirm the expectation that stronger 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 times SMMs larger than that of synthesized molecules with In this paper, to seek more new , new ten high-spin molecules have been designed by , combining variations in the L and Z ligands ( , , , or ; or Our calculated results show that all molecules have and these ten modelling in the range of ( 231.6, 147.4) K, in which the molecule with has the highest of 231.6 K corresponding to This value SMMs is over times larger than that of synthesized Our calculated results demonstrate combining variations in the L and Z ligands as an effective way to tailor intramolecular molecules The results provide exchange coupling of the some hints for synthesizing new SMMs Fig The schematic geometric structures of the molecules (a) and (b) The [Mn Mn ( L ) ( F )] is highlighted in the balls 0 III RESULTS AND DISCUSSION molecules have been New distorted cubane designed based on the synthesized [ ] ( and ) molecule [5], [6] Firstly, the molecule is reduced to II COMPUTATIONAL METHODS To compute the geometric structure, electronic structure and effective exchange coupling parameters of molecules, the same reliable computational method as in our previous paper [7] is adopted In this method, all calculations have been performed by using DMol [3] code with the double numerical basis sets plus polarization functional (DNP) [11] For the exchange correlation terms, the generalized gradient approximation (GGA) RPBE functional was used [12] All-electron scalar relativistic method was used to describe the interaction between the core and valence electrons [13] The real-space global cutoff radius was set to be 4.7 for all atoms The spin-unrestricted DFT was used to obtain all results presented in this study The atomic charge and magnetic moment were obtained by using the Mulliken population analysis [14], [18] The charge density in the self-consistent calculation is converged to In the optimization process, the energy, energy gradient, and , and atomic displacement are converged to , respectively The total energy difference method was adopted to calculate the exchange coupling parameters of molecules [7] To determine exactly the magnetic ground molecules, all possible spin configurations state of of molecules are probed, which are imposed as an initial condition of the structural optimization procedure The number of spin configurations should be considered depending on the charge state of manganese ions In terms of the ions could, in principle, have only the octahedral field, , in which three high-spin state with configuration electrons occupy three different orbitals The possible spin ion are the high-spin (HS) state with configurastates of tion and the low-spin (LS) state with configuration Additionally, the magnetic coupling between the ion 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 considered molecule, including: (i) AFM-HS, (ii) for each AFM-LS, (iii) FM-HS, and (iv) FM-LS ( and ) by replacing each ring of dbm groups with one H atom to improve the computational performance The schematic geometric structures and are displayed in Figs 1(a) and of molecules molecules have 1(b), respectively Then new been designed by variations in L and Z ligands of the mol To preserve the distorted cubane geometry of the ecule core of molecules and the formal charges of Mn ions, ligands subligand should satisfy following stituted for the core conditions: (i) To have the valence of 2; (ii) The ionic radius of ion these ligands should be not so different from that of , From these remarks, N based ligands, NR should be the best candidates Moreover, by variation in R group, the local electronic structure as well as electronegativity 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 to form 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 tends to become stronger when reaches to around 90 The molhas the highest of 174.47 ecule with This value is about 2.5 times K corresponding to larger than that of and molecules In this study, to seek more new , new ten high-spin molecules with have been designed by combining variations in the L and These ten molecules have a Z ligands of the molecule general chemical formula ( , , , , or ; or They are labeled from and , and their chemical formulas are tabulated and have in Table I It is noted that, the molecules TUAN et al.: LIGAND-DRIVEN EXCHANGE COUPLING IN SINGLE-MOLECULE MAGNETS THE CHEMICAL FORMULAS OF Z1 = (OAC) Z2 = MeC(CH NCOMe) Mn ( Mn Mn L Mn ( ) Mn ( ) 2431 TABLE I MOLECULES AND THEIR L LIGANDS Mn Mn Mn Mn O , Selected important magnetic and geometric parameters of molecules, the effective exchange and ions J =k , the magnetic moment at Mn sites (m and m ), the exchange coupling angle coupling parameter between the , the distance between the and ions d , the and bond lengths (d and d ),and the distortion factor of B sites f ) Mn ( ) Mn O Mn Mn molecules The (n), and by the N atoms in Fig Ligand configuration at the Mn sites of Q sites are located by the O atoms in the molecule the molecule n ( ) () ( ) Fig The typical geometric structures of molecules n and n Hydrogen atoms are removed for clarity This figure shows the difference in Z ligand between the molecules n and n () ( ) the same core L ligand but difference in the Z ligand The has the , while the molecules molecules have The typical geometric structures of molecules and are shown in Fig Our calculated results show that the most magnetic stable , , and state of all twelve molecules is the AFM-HS The three ions at the B sites exist in the HS state with configuration , and the ions and the exchange coupling between the three ion is AFM resulting in the ferrimagnetic structure in molecules with the large of 9/2 Note that, relates the HS state with configuration to the appearance of the elongated Jahn-Teller distortions at ions Our calculated results confirm that each of three sites is an elongated octahedron along the axis Here, the distortion factor of the B sites is measured by , where, is the interatomic and sites as labled in Fig distance between the is the average interatomic distance between the The site and the two O sites of the group as shown in Fig The values of , and is tabulated in Table I of molecules and is various in the The and range from 6.738% to 11.339% The molecules have the highest and smallest values of , respectively The HS spin state as well as the elongated Jahn-Teller distortions at ions is known as one of the origin of the axial anisotropy in Mn SMMs [15]–[17] These results demonstrate that all new molecules under consideration in this paper ten are expected to have axial anisotropy The geometric structures corresponding to the most stable states of these molecules are displayed in Figs and 2, of has been synthesized before [5], [6] The calcuwhich is in good agreement with lated geometric structure of the experimental data reported in [5] and [6] As displayed has symmetry, with the in Fig 1(a), the molecule axis passing through and ions The core can be simply viewed as a “distorted cubane” The Z ligand consists of three carboxylate (OAc) groups, forming three bridges between the ion and the three ions The molecule contains three dbm groups Each dbm group forms two coordinate bonds to complete the distorted octahedral geometry at each and show that their B site A comparison between skeletons are nearly the same For example, of these molecules are very small, the difference in and as shown in Table I Also their magnetic moments at Mn sites are nearly the same It is noted that the molecule and is obtained from the molecule by replacing each ring of dbm groups with one H atom These results demonstrate that variation in outer part of dbm groups is not so much influence molecules on magnetic properties of 2432 IEEE TRANSACTIONS ON MAGNETICS, VOL 47, NO 10, OCTOBER 2011 Our calculations show that the geometric structures of and are similar to , as molecules symmetry, with the shown in Fig They also have axis passing through and , even if their L and Z ligands are different Also the distorted cubane geometry core is preserved However, their bond angles of the , and interatomic distances are different from those of especially the exchange coupling angle The molecule has , while the molecules and have , as tabulated in Table I These results allow us of the to predict that the exchange coupling parameter molecules and is significant larger than Indeed, our calculated results show that the that of of molecules and is at least twice larger , as tabulated in Table I, in which the of than that of molecule is over times larger than that of the molecule Here it is noted that, the computational method adopted by a factor of about [7] in this study overestimate the of the molecules under Hence, the expected value of consideration should be a half of our calculated results and shows that A comparison between molecules of is larger than that of , while their and the are nearly the same, as shown in Table I It poses a question what causes the significant difference between the of and It is noted that, in molecules, each ion with the configuration has one orbital which can be delounpaired electron occupying the calized toward the nearest ligands and also toward the ion [7] This magnetic orbital may overlap strongly with orbitals of the ion resulting in the AFM half-filled and ions Therefore, it is coupling between the expected that the stronger delocalization of electron occupying orbitals, the smaller magnitude of the magnetic moments the of Mn ions, and the stronger AFM coupling between the and ions A comparison between the molecules and confirms this expectation, the molecule with and is always accompanied with a larger smaller , as shown in Table I Also it is expected that, the smaller sites, the stronger deelongated Jahn-Teller distortion at localization of electron occupying the orbitals of ions ligands and also toward the ion, toward the nearest due to the advantage of coulomb repulsion energy As a consequence, the smaller elongated Jahn-Teller distortion at sites, the stronger exchange coupling between the and ions A comparison between the molecules and confirms this expectation, the molecule with smaller is , as shown in Table I always accompanied with a stronger IV CONCLUSION By combining variations in the L and Z ligands, ten new high-spin [ ] ( , , , , or ; or ) molecules have been designed Our calculated results show that these ten modelling molecules have and in the range 147.4)K, in which the molecule with of ( 231.6, has the highest of 231.6 K corresponding to This value is over times larger than that of synthesized SMMs Our calculated results demonstrate combining variations in the L and Z ligands as an effective way to tailor intramolecular molecules Also, these results exchange coupling of the demonstrate the advantages of employing N-based ligands instead of oxygen to form exchange pathways between Mn molecules The results should atoms in distorted cubane facilitate the rational synthesis of new SMMs and, eventually, the preparation of technologically useful SMMs ACKNOWLEDGMENT The authors thank the Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) for funding this work within project 103.01.77.09 The computations presented in this study were performed at the Information Science Center of Japan Advanced Institute of Science and Technology, and the Center for Computational Science of the Faculty of Physics, Hanoi University of Science, Vietnam REFERENCES [1] L Bogani and W Wernsdorfer, Nature Mater., vol 7, p 179, 2008 [2] A Saitoh, H Miyasaka, M Yamashita, and R Clérac, J Mater Chem., vol 17, p 2002, 2007 [3] B J Milios, A Vinslava, W Wernsdorfer, S Moggach, S Parsons, S P Perlepes, G Christou, and E K Brechin, J Amer Chem Soc., vol 129, p 2754, 2007 [4] V Marvaud, J M Herrera, T Barilero, F Tuyeras, R Garde, A Scuiller, C Decroix, M Cantuel, and C Desplanches, Monatshefte für Chemie, vol 134, p 149, 2003 [5] H Andres, R Basler, H Güdel, G Aromí, G Christou, H Büttner, and B Rufflé, J Amer Chem Soc., vol 122, p 12469, 2000 [6] M W Wemple, D M Adarm, K Folting, D N Hendrickson, and G Christou, J Amer Chem Soc., vol 117, p 7275, 1995 [7] N A Tuan, S Katayama, 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formulas are tabulated and have in Table I It is noted that, the molecules TUAN et al.: LIGAND-DRIVEN EXCHANGE COUPLING IN SINGLE-MOLECULE MAGNETS THE CHEMICAL FORMULAS OF Z1... that the exchange coupling parameter molecules and is significant larger than Indeed, our calculated results show that the that of of molecules and is at least twice larger , as tabulated in. .. Our calculated results demonstrate combining variations in the L and Z ligands as an effective way to tailor intramolecular molecules Also, these results exchange coupling of the demonstrate the