DSpace at VNU: The role of ligands in controlling the electronic structure and magnetic properties of Mn-4 single-molecule magnets

Available online at www.sciencedirect.com Computational Materials Science 44 (2008) 111–116 www.elsevier.com/locate/commatsci The role of ligands in controlling the electronic structure and magnetic properties of Mn4 single-molecule magnets Nguyen Anh Tuan a,b, Shin-ichi Katayama a, Dam Hieu Chi a,b,* a School of Materials Science, Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa 923-1292, Japan b Faculty of Physics, Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam Available online 18 April 2008 Abstract single-molecule magnets (SMM), i.e, We present our studies of electronic structure and magnetic properties of Mn4ỵ Mn3ỵ 4ỵ 3ỵ ẵMn4ỵ Mn3ỵ O Cl OAcị pyị (py = pyridine) and ẵMn Mn O ClðOAcÞ ðdbmÞ Š (dbmH = dibenzoyl-methane) molecules by using 3 3 3 a first-principles all-electron relativistic method within spin-polarized density functional theory To investigate the possibility of ligands controlling the electronic structure and magnetic properties, we designed and calculated the geometric and electronic structures of twelve n+ other Mn4ỵ Mnnỵ ions, and the (n = 2, 3, 4) molecules with different peripheral-ligand congurations The electronic structure of Mn 4ỵ nỵ interatomic distances, electronic structure and magnetic properties of Mn Mn3 molecules display an interesting variation with n Ó 2008 Elsevier B.V All rights reserved PACS: 75.50.Xx; 75.75.+a; 31.15.Ar; 33.15.Àe; 33.15.Dj; 75.30.Wx Keywords: First-principles calculation; Single-molecule magnets; Mn clusters; Nano-piezomagnets; Molecular design Introduction Single-molecule magnets (SMM) have recently attracted much interest since they are collections of identical nanomagnets in which quantum phenomena such as step like hysteresis curves of magnetization are observed [1,2] Beyond being the actors of fundamental quantum phenomena, molecular magnets are widely studied because various present and future specialized applications of magnets require monodisperse, small magnetic particles Thestructure of each molecular magnet consists of the two components: the core which contains transition metal atoms, and the outer ligand complex Since each transition metal atom carries its own spin moment, the core of the SMM plays the primary role of determining the magnetic structure of the SMM, and the substitution of the transi* Corresponding author Address: School of Materials Science, Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa 923-1292, Japan Tel.: +81 76 151 1584; fax: +81 76 151 1535 E-mail address: dam@jaist.ac.jp (D.H Chi) 0927-0256/$ - see front matter Ó 2008 Elsevier B.V All rights reserved doi:10.1016/j.commatsci.2008.01.060 tion metal elements becomes an important way of controlling the magnetic character of the molecular magnet Of course, the outer ligand configuration around the core is another factor which controls the charge, i.e., valence of the metal ion and, thereby, its spin Indeed, rather different magnetic characteristics are observed in some SMM systems which have the same core structure [1,3–6] The only difference lies in their ligand components of the SMM system Moreover, the outer ligands govern the mutual spatial arrangement of the metal-oxide core, and thus play an important role in determining the intermolecular interaction [7] For example, Mn4O3Cl4(O2CEt)3(py)3, one of the tetrahedral Mn4 SMM system, forms a dimer structure in its crystal structure, and shows interesting magnetic behavior completely different from that of individual molecules [3,8,9] In other words, the difference in the spatial arrangement is the primary factor making various Mn4 molecules so different from each other, thereby contributing to the magnetism of the SMM system In this paper, we present our studies of the electronic structure and magnetic properties of trigonal-pyramid 112 N.A Tuan et al / Computational Materials Science 44 (2008) 111116 Mn4ỵ Mn3ỵ single-molecule magnets (SMM), i.e, ẵMn4ỵ 3ỵ Mn3 O3 ClOAcị3 dbmị3 (dbmH = dibenzoyl-methane) and ẵMn4ỵ Mn3ỵ O3 Cl4 ðOAcÞ3 ðpyÞ3 Š (py = pyridine) molecules by using a first-principles all-electron relativistic method within spin-polarized density functional theory To investigate the possibility of controlling the electronic structure and magnetic properties, we designed and calculated the geometric and electronic structures of the four(n = 2, 3, 4) molecules teen trigonal-pyramid Mn4ỵ Mn3ỵ Our calculations reveal an important role for the ligand complex in controlling electronic and magnetic properties of Mn4 SMM as well as in designing new SMM with new functions Methodology We performed cluster calculations using the program DMOL3 [10] in Materials Studio package, which is designed for the realization of large-scale density functional theory (DFT) calculations All-electron relativistic calculations were performed with the double numerical basis sets plus polarization functional (DNP) The DNP basis sets are of comparable quality to 6-31G** Gaussian basis sets [11] Delley et al showed that the DNP basis sets are more accurate than Gaussian basis sets of the same size [10] The RPBE functional [12] is so far the best exchange-correlation functional [13], based on the generalized gradient approximation (GGA), is employed to take account of the exchange and correlation effects of electrons The real-space global ˚ Spin-unrestricted DFT cutoff radius was set to be 7.0 A was used to obtain all results presented in this work For better accuracy, the octupole expansion scheme is adopted for resolving the charge density and Coulombic potential, and a fine grid is chosen for numerical integration The charge density is converged to  10À6 a.u in the self-consistent calculation In the optimization process, the energy, energy gradient, and atomic displacement are converged to  10À5,  10À4 and  10À3 a.u., respectively In order to explore the full freedom in the potential energy surface and avoid possible saddle points, the geometric optimization is performed without any symmetry restriction The atomic charge and magnetic moment are obtained by Mulliken population analysis A Fermi smearing of 0.005 hartree (Ha) (1Ha = 27.2114 eV) was used to improve computational performance Results and discussion OAc bridges, but differ in the peripheral-ligand L1 and L2 groups (Fig 1) Each of them is distinguished from the other by its peripheral ligands L1 and L2 L1 and L2 make two coordinations to complete the distorted octahedral geometry at each b-site (as shown in the inset of Fig 1a), and thus are crucial factor in controlling the charge of Mn ions at this site without breaking the distorted cubane geometry of the Mn4O3Cl core A naăve expectation of the formal charge state of metal ions in Mn4O3Cl core can be derived from the nominal charge of the connected ligands In the case that both L1 and L2 are neutral ligands, the obtained result is Mn4ỵ Mn2ỵ molecules In the case that L1 and L2 are a neutral ligand and a molecules are radical anion, respectively, Mn4ỵ Mn3ỵ obtained In the case that both L1 and L2 are radical anions, Mn4ỵ Mn4ỵ molecules are formed By this means, molecules, ve Mn4ỵ Mn3ỵ molecules, four Mn4ỵ Mn2ỵ 3 4ỵ 4ỵ and ve Mn Mn3 molecules have been designed Some of Mn4ỵ Mn3ỵ molecules have been synthesized [1,4] The molecules are labeled from (1) to fourteen Mn4ỵ Mnnỵ (14), being classied into the three groups by the formal charge of the manganese ions at the b-site (as shown in z a x O(OAc) L O(core) Mn y L O(core) Cl(1) O(6) O(5) O(4) OAc O(9) Mn(1) O(8) O(3) O(2) O(1) Mn(4) O(7) Mn(3) Mn(2) L1 Cl(1) L2 Mn4+, a-site b μ3-O2- 3-O2- 3-O2- Mnn+ Mnn+ Mnn+ 3.1 Designing trigonal-pyramid Mn4ỵ Mnnỵ molecules In this study, fourteen trigonal-pyramid Mn4ỵ Mnnỵ (n = 2, 3, 4) molecules have been designed or reconstructed They have the general chemical formula Mn4O3Cl(OAc)3L13L23 (L1 and L2 are ligand groups) These molecules consist of the same Mn4O3Cl core and three μ 3-Cl- b-site Fig (a) The geometric structure of Mn4O3Cl(OAc)3L13L23, with hydrogen removed for clarity, (b) The geometric structure of the core Mn4O3Cl N.A Tuan et al / Computational Materials Science 44 (2008) 111–116 Table The chemical formula and classification of Mn4 molecules by the formal charge of Mn ions at b-site Label (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) Ref [4] [1] L1 L2 n Group CH3CN NH3 py CH2O py py NH3 CH2O dbm CH3O CH3O Br Cl Cl CH3CN CH2O CH2O CH2O Cl Br Cl Cl I II III Br Cl Br Br Cl the Table 1) Group I consists of the four Mn4ỵ Mn2ỵ molecules labeled from (1) to (4) Group II consists of molecules labeled from (5) to (9) the ve Mn4ỵ Mn3ỵ Group III consists of the ve Mn4ỵ Mn4ỵ molecules from (10) to (14) 3.2 Equilibrium geometry, electronic and magnetic properties of Mn4ỵ Mnnỵ molecules To determine the ground-state atomic structure of each Mn4 SMM, we have carried out total-energy calculations with full geometry optimization allowing the relaxation of all atoms in the cluster In addition, to investigate the magnetic properties of the Mn4 SMMs, we probe several different spin configurations, which were imposed as an initial condition of the self-consistent calculation procedure Four possible spin configurations considered in this work include (i) AFM-HS, (ii) AFM-LS, (iii) FM-HS, and (iv) FM-LS, where FM and AFM denote the ferromagnetic and antiferromagnetic couplings between Mn4+ ion at the a-site with Mnn+ ions at the b-site, respectively HS and LS correspond to the high-spin (electrons are distributed so that all t2g and eg orbitals are singly occupied before any pairing occurs) and low-spin (electrons are distributed in t2g and eg orbitals so that they occupy the lowest possible energy levels) states of Mnn+ ions at the b-site We confirmed that the full geometry optimization calculation of all fourteen Mn4 molecules have a similarity in the arrangement of atoms in the core Mn4O3Cl and three bridging groups OAc (Fig 1a) Due to the surrounding oxygens and other ligand structures, one Mn ion at the a-site and three Mn ions at the b-site are correspondingly labeled as Mn(1), Mn(2), Mn(3) and Mn(4) to distinguish them 3.2.1 Equilibrium geometry and magnetic structure From four initial spin configurations, we obtained different geometric and magnetic structures of the Mn4 molecules in each group In the case of group I, we obtained four equilibrium geometric structures corresponding to four different 113 magnetic structures AFM-IS, AFM-LS, FM-IS and FMLS (IS denotes an intermediate-spin state between HS and LS of Mn ions at the b-site) of each Mn4 molecule Our calculations showed that there is no difference in atomic arrangement among the four geometric structures of each Mn4 molecule in group I Moreover, the geometric structures corresponding to the magnetic structures AFM-LS and FM-LS are nearly the same The geometric structures corresponding to the magnetic structures AFM-IS and FM-IS are also nearly the same Overall bond distances of the geometric structure corresponding to the magnetic structures AFM-IS and FM-IS are longer than those of the geometric structure corresponding to the magnetic structures AFM-LS and FM-LS Therefore, we call the geometric structure corresponding to the magnetic structures AFM-IS and FM-IS as the ‘‘long-structure”, and the geometric structure corresponding to the magnetic structures AFM-LS and FM-LS as the ‘‘short-structure” In the case of (1), the most stable state is the short-structure with the magnetic structure AFM-LS, while the most stable state of the three other Mn4 molecules (2)–(4) is the longstructure with the magnetic structure AFM-IS In the cases of groups II and III, we only obtained two equilibrium geometric structures of each Mn4 molecule from four initial spin configurations The two geometric structures of each Mn4 molecule in groups II and III are nearly the same They are only distinguished by difference in magnetic structure Their magnetic structures are AFM-HS and FM-HS The most stable state of Mn4 molecules of group II corresponds to the magnetic structure AFM-HS, while the most stable state of Mn4 molecules of group III corresponds to the magnetic structure FM-HS The geometric structures of the most stable state of (5) and (9) from our calculations are good in agreement with the experimental data reported in [1] and [4] Most differences of interatomic distances and bond angles are below 5% between our results and the experimental data Some selected interatomic distances of the 14 Mn4 molecules are shown in Fig They are quite similar within the same group, but some of them are considerably different between groups Previous experimental studies [1,4] reported that each of the three Mn3+ ions of (5) and (9) exhibit a Jahn–Teller distortion (elongation) along the Cl(1)–Mn3+–O(OAc) axis Our results also show the difference between bond distances from each Mn3+ ion to its six surrounding ligands for all five molecules of group II In each molecule of group II, Mn3+–O(OAc) and Mn3+–Cl(1) bond distances are considerably longer than the others The difference between Mn3+–O(OAc) bond distances with the other Mn3+–O bond distances is over 10% This is evidence of strongly elongated Jahn–Teller distortions along the Cl(1)–Mn3+– O(OAc) axes No Jahn–Teller distortion is observed in the five molecules of group III This result is also consistent with the HS state of all four Mn4+ ions in these molecules There is also no Jahn–Teller distortion observed in the short-structures of SMMs of group I But, each of the four 114 N.A Tuan et al / Computational Materials Science 44 (2008) 111–116 Table The detailed projections of magnetic moments at Mn sites of some selected Mn4 molecules Fig Some selected interatomic distances of the 14 Mn4 molecules long-structures of SMMs of this group displays three strongly elongated Jahn–Teller distortions along three Cl(1)–Mn(2)/Mn(3)/Mn(4)–O(OAc) axes The difference in interatomic distances between the short- and long-structures of each SMM of group I is a consequence of the Jahn–Teller distortions These elongated Jahn–Teller distortions are good evidence for the existence of an IS state of Mn2+ ions at the b-site in the long-structure of each SMM in group I, where four electrons occupy in three t2g states (dxy, dyz and dzx), one occupied in the higher energy state (dz2) We will discuss this in more detail in the next section 3.2.2 Electronic and magnetic properties Previous experimental studies [1,4] reported that (5) and (9) have the ground state spin ST of 9/2, where Mn(1) is antiferromagnetically coupled to Mn(2), Mn(3) and Mn(4), and assigned a formal valence charge +4 with corresponding magnetic moment À3 lB At the same time, Mn(2), Mn(3) and Mn(4) are ferromagnetically coupled to each other and have a formal valence of +3 with its magnetic moment lB From our calculations, the ground states of (5) and (9) are determined to have ST of 8.92/2 and 8.89/2, respectively, and the antiferromagnetic configuration, in good agreement with the experimental observation [1,4] Here, it should be noted that these calculated values are from a Mulliken analysis, so that the values not match exactly with the formal valence and spin but the relative magnitudes compare well The detailed projections of the calculated magnetic moments for each individual Mn site of Mn4 molecules, as listed in Table 2, also turn out to be consistent with the formal charges and magnetic moments of Mn In the case of (5), these results are also compared well with those of Han et al [14] In generally, Molecule Magnetic structure mMn(1) mMn(2) mMn(3) mMn(4) (1) AFM-IS FM-IS AFM-LS FM-LS À2.859 2.623 À2.949 2.789 3.098 3.179 1.072 1.135 3.095 3.180 1.064 1.119 3.103 3.184 1.070 1.125 (4) AFM-IS FM-IS AFM-LS FM-LS À2.758 2.485 À2.866 2.570 3.071 3.183 1.046 1.146 3.071 3.196 1.030 1.125 3.071 3.169 1.050 1.141 (5) AFM-HS FM-HS À2.708 2.905 3.879 3.897 3.873 3.889 3.872 3.888 (9) AFM-HS Han et al FM-HS À2.687 À2.540 2.894 3.862 3.690 3.874 3.853 3.710 3.862 3.863 3.680 3.876 (10) AFM-HS FM-HS À2.857 2.893 2.735 2.733 2.720 2.720 2.728 2.727 (14) AFM-HS FM-HS À2.903 2.921 2.778 2.805 2.765 2.793 2.773 2.802 the magnitude of magnetic moment of an Mn4+ ion at the a-site has a nearly constant value of lB, while the magnetic moment of Mnn+ ions at the b-site displays an interesting variation with n In the case of n = 4, the magnetic ground state of Mn4ỵ Mn4ỵ molecules are the FM-HS state with a magnetic moment nearly lB for all Mn ions These values of magnetic moment are consistent with the formal charge of Mn ions In the case of n = 3, the magnetic ground state of Mn4ỵ Mn3ỵ molecules are the AFM-HS state with a magnetic moment nearly À3 lB for Mn(1) and lB for Mn(2), Mn(3) and Mn(4) These values of magnetic moment are also in good agreement with the formal charge of Mn as well as the existence of the Jahn–Teller distortions at Mn(2), Mn(3) and Mn(4) sites In the case of n = within the long-structure, the magnitude of the magnetic moment of Mn(1) is nearly equal to lB, and the magnetic moment of Mn(2), Mn(3) and Mn(4) is nearly lB In the case of the short-structure, the magnetic moment of Mn(1) is also nearly equal to lB, but the magnetic moments of Mn(2), Mn(3) and Mn(4) are smaller by lB than those in the case of the long-structure The more detailed analyses show that the total number of down-spin electron of 3d states of Mn ions at the b-site in the long-structure and the short-structure is about and 2, respectively, as listed in Table These results show that the spin state of Mn2+ ions of molecules must be IS and LS corresponding Mn4ỵ Mn2ỵ to the long- and short-structures As presented in the previous section, the ground state of (1) is the short-structure with the magnetic structure AFMLS, and the ground state of (2)-(4) is the long-structure with the magnetic structure AFM-IS There is no ground state with the HS state of Mn2+ ions at the b-site of N.A Tuan et al / Computational Materials Science 44 (2008) 111–116 115 Table The calculated down-spin electron, nd; projected at 3d states of Mn ions at b-site of Mn4ỵ Mn2ỵ molecules Molecule (1) Equilibrium geometry Magnetic structure nd; Mn(2) Mn(3) Mn(4) Long-structure AFM-IS FM-IS AFM-LS FM-LS 1.258 1.213 2.299 2.268 1.257 1.211 2.303 2.375 1.255 1.210 2.299 2.273 AFM-IS FM-HS AFM-LS FM-LS 0.998 0.950 2.046 2.009 1.001 0.954 2.050 2.019 0.996 0.948 2.048 2.014 AFM-IS FM-IS AFM-LS FM-LS 1.019 0.965 2.098 2.055 1.019 0.968 2.105 2.062 1.018 0.950 2.094 2.052 AFM-IS FM-IS AFM-LS FM-LS 1.012 0.950 2.068 2.014 1.011 0.943 2.075 2.025 1.010 0.958 2.065 2.016 Short-structure (2) Long-structure Short-structure (3) Long-structure Short-structure (4) Long-structure Short-structure Mn3ỵ Mn2ỵ molecules, while the magnetic ground state of 4ỵ 4ỵ Mn4ỵ Mn3ỵ and Mn Mn3 molecules exhibits the HS state of Mn ions at the b-site Moreover, no compressed Jahn–Teller distortions are observed at the b-site of 4ỵ 3ỵ Mn4ỵ Mn2ỵ and Mn Mn3 molecules These results mean that the dx2-y2-orbital of Mn ions at the b-site of 4ỵ 3ỵ Mn4ỵ Mn2ỵ and Mn Mn3 molecules must be empty This can be explained in the term of the ligand field 3.2.3 Magneto-structural correlation in Mn4 molecules of group I In this section, we discuss about the relation between magnetic and geometric structures of Mn4 molecules The geometric structures of isomers of each Mn4 molecules of groups II and III are nearly the same Therefore, they are not mentioned further in this section In the case of group I, the considerable difference in some interatomic distances between the short- and long-structures of each Mn4ỵ Mn2ỵ molecules is found In each geometric structure of molecules, the total energy corresponding to Mn4ỵ Mn2ỵ the IS and LS states of Mn2+ ions has been calculated In the short-structure, the LS state of Mn2+ ions is more favourable than the IS state, while the IS state of Mn2+ ions is more favourable than the LS state in the longstructure To investigate the possibility of transitions between the IS and LS states of Mn2+ ions, we performed calculations of the total energy corresponding to the two magnetic structures AFM-IS and AFM-LS of the four linear transition structures from the long-structure to short-structure of each Mn4ỵ Mn2ỵ molecule The total energy corresponding to the IS state of Mn2+ ions increases on going from the long-structure to the short-structure, while the total energy corresponding to the LS state of Mn2+ ions is decreasing Fig displays the total energy corresponding to the two Fig The total energy corresponding to the two magnetic structures AFM-IS and AFM-LS of the linear transition structures from the longstructure to short-structure of Mn4ỵ Mn2ỵ molecules (1) and (4) magnetic structures AFM-IS and AFM-LS of the linear transition structures from the long-structure to short-strucmolecules (1) and (4) These ture of selected Mn4ỵ Mn2ỵ results show the existence of a transition structure in which the two magnetic structures AFM-IS and AFM-LS of each Mn4+Mn2+ molecules are equal in the total energy These results also show the existence of a low barrier about 0.5 eV between the long- and short-structures of each Mn4ỵ Mn2ỵ molecules, therefore the structure with higher total energy is considered as the meta-stable state Therefore, the magnetic transition between IS and LS states of Mn2+ ions accompanied by the transition between the long- and short-structures of Mn4ỵ Mn2ỵ molecules is more favourable than keeping their geometric structure By this particular behavior, Mn4+Mn2+ molecules can become potential candidates for nano-piezomagnets Conclusions We have performed studies of the structural, electronic and magnetic properties of fourteen Mn4 molecules using a first-principles method We found that the peripheral ligand groups play an important role in controlling charge and spin states of Mn ions, as well as type of Jahn–Teller distortion at the b-site octahedrons Changing peripheral ligands becomes an effective way to control the electronic structure and magnetic properties of Mn4 molecules The 116 N.A Tuan et al / Computational Materials Science 44 (2008) 111–116 geometric structure, electronic structure and magnetic molecules display an interesting properties of Mn4ỵ Mnnỵ variation with the charge state of Mnn+ ions at the b-site In these Mn4 molecules, the magnetic interaction between Mn ions is FM between ions in the same valence states, being AF between ions in difference valance states The strong magneto-structure correlation of Mn4ỵ Mn2ỵ molecules leads to the possibility of these molecules acting as a nano-piezomagnet Acknowledgments This work was supported by Special Coordination Funds for Promoting Science and Technology commissioned by MEXT, JAPAN References [1] S Wang, H.-L Tsai, E Libby, K Folting, W.E Streib, D.N Hendrickson, G Christou, Inorg Chem 35 (1996) 7578 [2] B Hammer et al., Phys Rev B 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