Tailoring magnetic properties in Mn4 molecules: A way to develop single-molecule magnets , Nguyen Anh Tuan , Nguyen Huy Sinh, and Dam Hieu Chi Citation: Journal of Applied Physics 109, 07B105 (2011); doi: 10.1063/1.3545812 View online: http://dx.doi.org/10.1063/1.3545812 View Table of Contents: http://aip.scitation.org/toc/jap/109/7 Published by the American Institute of Physics JOURNAL OF APPLIED PHYSICS 109, 07B105 (2011) Tailoring magnetic properties in Mn4 molecules: A way to develop single-molecule magnets Nguyen Anh Tuan,1,a) Nguyen Huy Sinh,1 and Dam Hieu Chi1,2 Faculty of Physics, Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi 10000, Vietnam School of Materials Science, Japan Advanced Institute of Science and Technologyn, 1-1, Asahidai, Nomi, Ishikawa, 923-1292, Japan (Presented 15 November 2010; received 24 September 2010; accepted November 2010; published online 21 March 2011) Distorted cubane Mn4ỵMn3ỵ3 single-molecule magnets (SMMs) having the general chemical formula [Mn4ỵMn3ỵ3(l3-L2)3(l3-X)(OAc)3(dbm)3] (L ẳ O; X ẳ various; dbmH ẳ dibenzoyl-methane), have been studied using first-principles calculations It was shown in our previous paper that the ferrimagnetic structure of Mn4ỵMn3ỵ3 SMMs is dominated by the p type hybridization between the dz2 orbitals at the three high-spin Mn3ỵ ions and the t2g orbitals at the Mn4ỵ ion This result allows us to predict that the ferrimagnetic structure of Mn4ỵMn3ỵ3 molecules will be the most stable with the Mn4ỵ-(l3-L2)-Mn3ỵ angle a % 90 , while synthesized Mn4ỵMn3ỵ3 molecules have a % 95 To design new Mn4ỵMn3ỵ3 molecules having a much more stable ferrimagnetic state, one following approach is suggested: Controlling the Mn4ỵ-(l3-L2)-Mn3ỵ exchange pathways by rational variations in ligands to strengthen the hybridization between Mn ions By employed N-based ligands to form the Mn4ỵ-(l3-L2)-Mn3ỵ exchange pathways, new distorted cubane Mn4ỵMn3ỵ3 molecules with a % 90 have been designed These molecules have the Mn4ỵ-Mn3ỵ exchange coupling of about 2.5 times stronger than that of the synthesized Mn4ỵMn3ỵ3 molecules These results should facilitate the rational C 2011 American Institute of Physics [doi:10.1063/1.3545812] synthesis of new SMMs V I INTRODUCTION Single-molecule magnets (SMMs) are molecules that can function as magnets below their blocking temperature (TB) They are being extensively studied due to their potential technological applications to molecular spintronics.1 Their behavior results from a high ground-state spin (ST) combined with a large and negative Ising type of magnetoanisotropy, as measured by the axial zero-field splitting parameter (D) 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 ST results from local spin moments at magnetic ions (Si) and exchange coupling between them (Jij) Moreover, Jij has to be significant to differentiate the ground spin state from the excited states.2–4 Therefore, seeking possibilities of the enhancement of Jij will be a way to develop SMMs In the framework of computational materials design, distorted cubane [Mn4ỵMn3ỵ3(l3-L2)3(l3-X)(OAc)3(dbm)3] (L ẳ O; X ¼ various; dbmH ¼ dibenzoyl-methane) molecules5,6 are one of the most attractive SMMs because their interesting geometric structure and important magnetic quantities can be well estimated by first-principles calculations.7–10 In our previous paper,7 by using first-principles calculations within generalized gradient approximation, the basic mechanism of the antiferromagnetic (AFM) interaction between the Mn4ỵ ion and the three high-spin Mn3ỵ ions in Mn4ỵMn3ỵ3 molecules was analyzed The AFM Mn4ỵMn3ỵ coupling (JAB) is determined a) Author to whom correspondence should be addressed Electronic addresses: tuanna@hus.edu.vn and tuanna@vnu.edu.vn 0021-8979/2011/109(7)/07B105/3/$30.00 by the p type hybridization among the dz2 orbitals at the Mn3ỵ sites and the t2g orbitals at the Mn4ỵ site through the p orbitals at the l3-L2À ions This result allows us to predict that ferrimagnetic structure of Mn4ỵMn3ỵ3 molecules will be the most stable with the Mn4ỵ-(l3-L2)-Mn3ỵ angle a % 90 , while synthesized Mn4ỵMn3ỵ3 molecules have a % 95 One approach has been suggested to design new Mn4ỵMn3ỵ3 SMMs having a much more stable ferrimagnetic state This approach is controlling the Mn4ỵ-(l3-L2)-Mn3ỵ exchange pathways by rational variation in l3-L ligands to strengthen the hybridization between Mn ions Our calculations show that JAB can be increased by a factor of 2.5 by using N-based ligands to form the exchange pathways between the Mn4ỵ and Mn3ỵ ions Our results should facilitate the rational synthesis of new SMMs II COMPUTATIONAL METHOD To compute the geometric structure, electronic structure, and effective exchange coupling parameters of Mn4 molecules, the same reliable computational method as in our previous paper7 is adopted In this method, all calculations have been performed by using DMol3 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 Allelectron relativistic was used to describe the interaction between the core and valence electrons.13 The real-space ˚ for all atoms The global cutoff radius was set to be 4.7 A spin-unrestricted discrete Fourier transform (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 The charge density is 109, 07B105-1 C 2011 American Institute of Physics V 07B105-2 Tuan, Sinh, and Chi J Appl Phys 109, 07B105 (2011) converged to  10–6 a.u in the self-consistent calculation In the optimization process, the energy, energy gradient, and atomic displacement are converged to  10–5,  10–4, and  10–3 a.u., respectively The total energy difference method was adopted to calculate the exchange coupling parameters of Mn4 molecules.7 To determine exactly the magnetic ground state of Mn4ỵMn3ỵ3 molecules, all possible spin configurations of Mn4ỵMn3ỵ3 molecules are investigated; they 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 octahedral field, Mn4ỵ ions could, in principle, have only the high-spin state with configuration d3(t2g3, eg0), in which three d electrons occupy three different t2g orbitals The possible spin states of Mn3ỵ ion are the highspin (HS) state with configuration d4(t2g3, eg1) and the lowspin (LS) state with configuration d4(t2g4, eg0) Additionally, the magnetic coupling between the Mn4ỵ ion at the A site and Mn3ỵ ions at the B site can be ferromagnetic (FM) or antiferromagnetic (AFM) Therefore, there are four spin configurations that should be considered for each Mn4ỵMn3ỵ3 molecule, including (i) AFMHS, (ii) AFM–LS, (iii) FM–HS, and (iv) FM–LS FIG (Color online) The schematic geometric structure of (1) The [Mn4(l3-L)3(l3-F)] core is highlighted in the balls pling between the three Mn3ỵ ions and the Mn4ỵ ion is AFM resulting in the ferrimagnetic structure in the molecules (1)– (8) with the large ST of 9/2 The calculated geometric structure of (1) is in good agreement with the experimental data reported in Refs and The geometric structures corresponding to the most stable states of the eight molecules (1)– (8) are displayed in Figs and of which (1) has been synthesized before.5,6 The geometric structure of (1) is depicted in Fig The molecule (1) has C3v symmetry with the C3 axis passing through Mn4ỵ and l3-F ions The [Mn4ỵMn3ỵ3(l3L2)3(l3-F)] core can be simply viewed as a “distorted cubane” in which the four Mn atoms are located at the corners of a trigonal pyramid with a l3-L2– ion bridging each of the vertical faces and a l3-F– ion bridging the basal face Three carboxylate (OAc) groups formed three bridges between the Mn4ỵ ion and the three Mn3ỵ ions The molecule (1) contains three dbm groups Each dbm group forms two coordinate bonds to complete the distorted octahedral geometry at each B site Our calculations show that the geometric structures of molecules (2)–(8) are similar to (1) as shown in Fig They also have C3v symmetry with the C3 axis passing through Mn4ỵ and l3-F even if their L ligand is different Also the III RESULTS AND DISCUSSION New distorted cubane Mn4ỵMn3ỵ3 molecules have been designed based on the synthesized [Mn4ỵMn3ỵ3(l3L2)3(l3-F)(OAc)3(dbm)3] (L ẳ O)1 molecule.5,6 First, the molecule (1) is reduced to [Mn4ỵMn3ỵ3(l3-L2)3(l3F)3(CH(CHO)2)3] (L ẳ O) (2) by replacing each C6H5 ring of dbm groups with one H atom to improve the computational performance, and then six different L ligands are employed to form the Mn4ỵ-(l3-L2)-Mn3ỵ exchange pathways to design new six Mn4ỵMn3ỵ3 molecules These six molecules have a general chemical formula [Mn4ỵMn3ỵ3(l3L2)3(l3-F)3(CH(CHO)2)3] with L ẳ N-H, N-CH3, N-C2H5, N-C2H3, N-C2H, or N-C6H5 They are labeled from (3) to (8), and their chemical formulas are tabulated in Table I Our calculated results show that the most magnetic stable state of all eight molecules (1)–(8) is the AFM–HS It means that the three Mn3ỵ ions at the B sites exist in the HS state with configuration d4(t2g3, eg1), and the exchange cou- TABLE I The chemical formulas of Mn4 molecules (1)–(8) and their L ligands.a (1) (2) (3) (4) (5) (6) (7) (8) a L Mn4 Molecules mA (lB) mB (lB) JAB/kB (K) a( ) ˚) dAB (A O O NH NCH3 NC2H5 NC2H3 NC2H NC6H5 Mn4O3F(OAc)3(dbm)3 Mn4O3F(OAc)3(CH(CHO)2)3 Mn4(NH)3F(OAc)3(CH(CHO)2)3 Mn4(NCH3)3F(OAc)3(CH(CHO)2)3 Mn4(NC2H5)3F(OAc)3(CH(CHO)2)3 Mn4(NC2H3)3F(OAc)3(CH(CHO)2)3 Mn4(NC2H)3F(OAc)3(CH(CHO)2)3 Mn4(NC6H5)3F(OAc)3(CH(CHO)2)3 À2.703 À2.692 À2.719 À2.566 À2.543 À2.615 À2.809 À2.469 3.896 3.907 3.919 3.917 3.909 3.990 4.018 3.966 À73.51 À75.15 À86.29 À161.40 À174.47 À108.46 À63.23 À163.25 95.037 95.060 94.35 91.24 89.77 91.30 93.05 88.84 2.834 2.840 2.876 2.820 2.798 2.860 2.944 2.831 Selected important magnetic and geometric parameters of (1)(8), the effective exchange coupling parameter between the Mn4ỵ and Mn3ỵ ions (JAB=kB), the magnetic moment at Mn sites (mA and mB), the exchange coupling angle Mn3ỵ-L-Mn4ỵ (a), and the distance between the Mn4ỵ and Mn3ỵ ions (dAB) 07B105-3 Tuan, Sinh, and Chi J Appl Phys 109, 07B105 (2011) FIG (Color online) The schematic geometric structures of (2)–(8) distorted cubane geometry of the Mn4L3F core is preserved However, their bond angles and interatomic distances vary; the exchange coupling angle (a) and the Mn3ỵ-Mn4ỵ interatomic distance (dAB) are changed to the ranges of 88.84– ˚ –2.944 A ˚ , respectively, as tabulated in 94.35 and 2.798 A Table I As expected, the exchange coupling parameter JAB also varies as shown in Table I The calculated results confirm the expectation that JAB tends to become stronger when the a reaches around 90 as demonstrated in Fig 3(a) The molecule (5) with L ¼ NC2H5 has the highest JAB=kB of À174.47 K corresponding to a ¼ 89.77 This value is about 2.5 times larger than that of (1) Also, as shown in Fig 3(b), the JAB tends to become stronger with decrease of dAB; this can be attributed to increase of direct overlap between 3d orbitals at the A and B sites The a and dAB dependence of JAB demonstrates that, ˚ , JAB of Mn4 in the space of 88 a 92 and dAB 2.850 A molecules studied is at least about two times stronger than that of (1) These results demonstrate the advantages of employing N-based ligands (NR, R ¼ various) instead of oxygen to form exchange pathways between Mn atoms in distorted cubane Mn4 molecules Variation in the R group is an effective way to tailor exchange couplings between Mn atoms A comparison between (1) and (2) shows that their Mn4L3F(OAc)3 skeletons are nearly the same For example, the difference in a and dAB in these molecules is very small as shown in Table I Also their magnetic moments at Mn sites and JAB are nearly the same It is noted that molecule (2) is obtained from molecule (1) by replacing each C6H5 ring of dbm groups with one H atom These results demonstrate that variation in the outer part of dbm groups is not as much of an influence on magnetic properties of Mn4 molecules FIG (a) the a dependence of JAB and (b) the dAB dependence of JAB IV CONCLUSION By employing N-based ligands to form the exchange pathways between Mn atoms, six new high-spin [Mn4ỵ Mn3ỵ3(l3-L2)3(l3-F)3(CH(CHO)2)3] (L ẳ NH, NCH3, NC2H5, NC2H3, NC2H, or NC6H5) molecules with ST of 9/2 have been designed The calculated results demonstrate that JAB tends to become stronger when a reaches around 90 Molecule (5) has the highest JAB=kB of À174.47 K corresponding to a ¼ 89.77 This value is about 2.5 times larger than that of synthesized Mn4 SMMs The results provide some hints for synthesizing new SMMs ACKNOWLEDGMENTS We thank the Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) for funding this work within Project No 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 We are especially thankful for financial support from TRIG project for presenting this work at the 55th Annual Conference on Magnetism and Magnetic Materials L Bogani and W Wernsdorfer, Nat Mater 7, 179 (2008) A Saitoh, H Miyasaka, M Yamashita, and R Cle´rac, J Mater Chem 17, 2002 (2007) C J Milios, A Vinslava, W Wernsdorfer, S Moggach, S Parsons, S P Perlepes, G Christou, and E K Brechin, J Am Chem Soc 129, 2754 (2007) V Marvaud, J M Herrera, T Barilero, F Tuyeras, R Garde, A Scuiller, C Decroix, M Cantuel, and C Desplanches, Monatsch Chem 134, 149 (2003) H Andres, R Basler, H Guădel, G Arom, G Christou, H Buăttner, and B Ruffle, J Am Chem Soc 122, 12469 (2000) M W Wemple, D M Adarm, K Folting, D N Hendrickson, and G Christou, J Am Chem Soc 117, 7275 (1995) N A Tuan, S Katayama, and D H Chi, Phys Chem Chem Phys 11, 717 (2009) N A Tuan, S Katayama, and D H Chi, Comput Mater Sci 44, 111 (2008) M J Han, T Ozaki, and J Yu, Phys Rev B, 70, 184421 (2004) 10 K Park, M R Pederson, and N Bernstein, J Phys Chem Solids 65, 805 (2004) 11 B Delley, J Chem Phys 92, 508 (1990) 12 B Hammer, L B Hansen, and J K Norskov, Phys Rev B, 59, 7413 (1999) 13 B Delley, Int J Quantum Chem 69, 423 (1998) 14 R S Mulliken, J Chem Phys 23, 1833 (1955); 23, 1841 (1955) ... presenting this work at the 55th Annual Conference on Magnetism and Magnetic Materials L Bogani and W Wernsdorfer, Nat Mater 7, 179 (2008) A Saitoh, H Miyasaka, M Yamashita, and R Cle´rac, J Mater... calculations show that JAB can be increased by a factor of 2.5 by using N-based ligands to form the exchange pathways between the Mn4 and Mn3ỵ ions Our results should facilitate the rational... SMMs having a much more stable ferrimagnetic state This approach is controlling the Mn4 -(l3-L2)-Mn3ỵ exchange pathways by rational variation in l3-L ligands to strengthen the hybridization between