Correlation between charge transfer and exchange coupling in carbon-based magnetic materials , Anh Tuan Nguyen , Van Thanh Nguyen, Thi Tuan Anh Pham, Viet Thang Do, Huy Sinh Nguyen, and Hieu Chi Dam Citation: AIP Advances 5, 107109 (2015); doi: 10.1063/1.4933076 View online: http://dx.doi.org/10.1063/1.4933076 View Table of Contents: http://aip.scitation.org/toc/adv/5/10 Published by the American Institute of Physics AIP ADVANCES 5, 107109 (2015) Correlation between charge transfer and exchange coupling in carbon-based magnetic materials Anh Tuan Nguyen,1,2,3,a Van Thanh Nguyen,1 Thi Tuan Anh Pham,1,4 Viet Thang Do,1,5 Huy Sinh Nguyen,1 and Hieu Chi Dam3 Faculty of Physics, VNU University of Science, 334 Nguyen Trai, Thanh Xuan, Ha Noi, Vietnam Science and Technology Department, Vietnam National University, Hanoi, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa, 923-1292 Japan Faculty of Science, College of Hai Duong, Nguyen Thi Due, Hai Duong, Viet Nam Faculty of Science, Haiphong University, 171 Phan Dang Luu, Kien An, Hai Phong, Vietnam (Received February 2015; accepted 29 September 2015; published online October 2015) Several forms of carbon-based magnetic materials, i.e single radicals, radical dimers, and alternating stacks of radicals and diamagnetic molecules, have been investigated using density-functional theory with dispersion correction and full geometry optimization Our calculated results demonstrate that the C31H15 (R4) radical has a spin of ½ However, in its [R4]2 dimer structure, the net spin becomes zero due to antiferromagnetic spin-exchange between radicals To avoid antiferromagnetic spin-exchange of identical face-to-face radicals, eight alternating stacks, R4/D2m/R4 (with m = 3-10), were designed Our calculated results show that charge transfer (∆n) between R4 radicals and the diamagnetic molecule D2m occurs with a mechanism of spin exchange (J) in stacks The more electrons that transfer from R4 to D2m, the stronger the ferromagnetic spin-exchange in stacks In addition, our calculated results show that ∆n can be tailored by adjusting the electron affinity (Ea) of D2m The correlation between ∆n, Ea, m, and J is discussed These results give some hints for the design of new ferromagnetic carbon-based materials C 2015 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License [http://dx.doi.org/10.1063/1.4933076] I INTRODUCTION Organic molecule-based magnets have received much interest in recent years, both theoretically and experimentally The reason behind this interest is ascribed to their small size and excellent electronic and magnetic properties.1–3 These properties may be used to prepare customized devices that are not possible with conventional materials.4 Hence, they are candidate materials for use in new spin-electronic technology The development of organic molecule-based magnets is accelerating as more scientists and engineers from various disciplines are brought together Understanding the magnetic interaction between unpaired electrons in organic molecule-based magnetic materials is one of the most fundamental and important topics in the field of molecular magnetism.2,5,6 The forces that bind molecules together in organic molecular crystals are intermolecular interactions The most important intermolecular interactions are hydrogen bonds, π–π stacking interactions, and van der Waals forces The intensity of intermolecular interactions strongly affects the magnetic properties and stability of these materials Much work has been done to build organic magnets at room temperature for applications in information storage and electronic devices Many carbon-based magnetic materials have been designed and synthesized.2,5–11 These materials show magnetic properties a Email: tuanna@hus.edu.vn 2158-3226/2015/5(10)/107109/8 5, 107109-1 © Author(s) 2015 107109-2 Nguyen et al AIP Advances 5, 107109 (2015) due to low dimension electron interactions However, the identification of room-temperature carbon-based ferromagnets still occurs by accident.2,12–15 The magnetic exchange interaction strongly depends on the contact area between molecules.2,9–11 Previous theoretical studies showed that planar radicals may be potential candidates for designing high-spin carbon-based magnetic materials,11 because ferromagnetic interactions can occur in alternating stacks of planar radicals and planar diamagnetic molecules However, in these studies11 the inter-plane spacing between radicals and diamagnetic molecules of stacks was fixed at 3.2 Å The molecular geometry was optimized for the isolated molecules, but structural relaxation caused by intermolecular interactions was neglected Therefore, the geometric structure, electronic structure, and magnetic properties of stacks reported in reference 11 can be significantly different from experimental data Full geometry optimization, allowing relaxation of all atoms in the stacks, is required6 to improve the reliability of calculated results In our previous study, several ferromagnetic carbon-based materials were designed.6 They were alternating stacks of radicals and diamagnetic molecules Our calculated results demonstrate that spin-exchange in stacks depends on electron transfer between radicals and diamagnetic molecules in stacks However, the nature of charge transfer between stacks remains unclear In this study, to shed light on the nature of charge transfer and exchange coupling in stacks, the geometric structure, electronic structure, and magnetic properties of eight alternating stacks of C31H15 radicals (hereafter R4), and diamagnetic molecules, C2(2m+m+2)H2(m+3) (hereafter D2m with m = 3–10), were investigated based on density-functional theory with dispersion correction These eight stacks have a general formula of R4/D2m/R4 Our calculated results show that spin-exchange in stacks as well as electron transfer from R4 to D2m increase as m increases As m increases, the size of D2m molecules increases as well, of course Moreover, to clarify the nature of charge transfer between stacked radicals and diamagnetic molecules, the molecular deformation electron density (MDED) of the stacks was computed Our calculated results show that the nature of charge transfer between radicals and diamagnetic molecules in stacks is determined by the relative electron affinity between them The formation energy of stacks also increases as the size of D2m molecules increases These results give some hints into how exchange coupling can be tailored in carbon-based magnetic materials II COMPUTATIONAL METHODS All calculations were performed using the DMol3 code16 with double numerical basis sets plus the polarization functional For the exchange correlation terms, the generalized gradient approximation (GGA) PBE functional was used.17 All electrons were included in our calculations Non-covalent forces such as van der Waals interactions, were described using the dispersion-corrected methods proposed by Grimme.18 For better accuracy, the hexadecapolar expansion scheme was adopted for resolving the charge density and Coulombic potential The slab dipole correction was employed to correct exchange energy The atomic charge and magnetic moment were obtained by using the Mulliken population analysis.19,20 The real-space global cutoff radius was set to 6.0 Å for all atoms The charge density converged to × 10−6 au in the self-consistency calculation In the optimization process, the energy, energy gradient, and atomic displacement converged to × 10−5, × 10−4, and × 10−3 au, respectively In order to determine the ground state magnetic structure of each stack, total-energy calculations were carried out using the full geometry optimization in the triplet and singlet states, allowing the relaxation of all atoms in stacks The geometric structure of the ground state was employed for calculating the spin-exchange interaction To evaluate the stability of the magnetic state for each molecular structure, the effective spinexchange, J, of the molecular structures was estimated by the singlet-triplet separation11,21,22 (See Eq (1)) 2J = ∆EST = ES − ET (1) where, ES and ET are the total electronic energy of the singlet and triplet states of a molecular structure, respectively The molecular deformation electron density (MDED) of stacks, ∆ ρ, was computed using Eq (2) to clarify the nature of spin-exchange coupling in stacks 107109-3 Nguyen et al AIP Advances 5, 107109 (2015) FIG (a) Schematic of the geometric structure of the C31H15 (R4) radical, (b) spin distribution in the R4 radical Density at the surface = 0.01 e/Å3 ∆ ρ = ρstack − (ρradical + ρdiamagnetic_molecule + ρradical) (2) where, ρstack, ρradical, and ρdiamagnetic_molecule are the electron density of a stack, an isolated radical, and an isolated diamagnetic molecule, respectively III RESULTS AND DISCUSSION A schematic of the geometric structure of the R4 radical is shown in Fig 1(a) R4 has a planar structure consisting of thirty-one C atoms forming nine aromatic rings with fifteen H atoms at the boundary Depending on the C and H sites, the C-C and C-H bond lengths in R4 vary slightly in the range of 1.366–1.443 Å and 1.074–1.092 Å, respectively Our calculated results show that R4 has one singly occupied molecular orbital (SOMO) resulting in a spin moment of µB (Bohr magneton unit), and its spin moment is distributed over nearly the entire radical, as shown in Fig 1(b) This feature is different from the magnetic moment distribution in 3d transition metals and their alloys, in which the magnetic moment is mainly localized on 3d atoms Our calculated results demonstrate that two R4 radicals combine to form a dimer with strong antiferromagnetic (AFM) couplings due to direct π–π stacking between their aromatic rings These results are consistent with previous theoretical studies for dimers of other radicals.6,10 Due to antiferromagnetic coupling between R4 radicals, the net spin of [R4]2 dimers becomes zero To avoid the typical AFM spin-exchange of identical face-to-face radicals, alternating stacks of R4 radicals, and diamagnetic molecules, C2(2m+m+2)H2(m+3) (hereafter D2m with m = 3–10) were designed These eight stacks have a general formula of R4/D2m/R4 (with m = 3–10) A schematic of the geometric structure of R4/D2m/R4 stacks is shown in Fig 2(a) In this study, each D2m is a planar diamagnetic molecule consisting of 2(2m + m + 2) C atoms forming 2m aromatic rings with 2(m + 3) H atoms at the boundary Figure 2(b) displays the geometric structure of D2m with m = 4, as an example The size of D2m increases as m increases Our calculated results show that the planar FIG (a) Schematic of the geometric structure of R4/D2m/R4 stacks, (b) schematic structure of the D2_4 diamagnetic molecule 107109-4 Nguyen et al AIP Advances 5, 107109 (2015) FIG (a) Schematic geometric structure of the R4/D2_5/R4 stack, (b) spin distribution in R4/D2_5/R4 Density at the surface = 0.03 e/Å3 structure of R4 radicals and D2m diamagnetic molecules is preserved in the stacks, as displayed in Fig 3(a) for stack R4/D2_5/R4 The intermolecular distance for R4-D2m (d) in the R4/D2m/R4 stacks tends to decrease from 3.259 Å for m = to 3.217 Å for m = 10, as shown in Table I This result is attributed to increased π–π stacking overlap between R4 radicals and D2m diamagnetic molecules as m increases Total energy calculations with full geometry optimization were carried out, allowing relaxation of all atoms in the stacks so that the ground state magnetic structure of each R4/D2m/R4 stack could be determined Our calculated results showed that the ground state of the R4/D2m/R4 stack is ferromagnetic (FM) with m = 5–10, while it is AFM with m = and To confirm this result, the spin polarization in a R4/D2m/R4 stack was computed The spin polarization in a R4/D2_3/R4 and R4/D2_10/R4 stack is shown in Fig As shown in Fig 4, the spin polarization for two R4 radicals is opposite from the R4/D2_3/R4 stack, being parallel for the R4/D2_10/R4 stack J for the stacks was estimated to evaluate the stability of the magnetic state of stacks The Js for different stacks are listed in Table I As show in Table I, J is negative for m = and 4, and positive for m = 5–10 It is easy to see that J increases as m increases J/k B increased from −38 K for m = to 832 K for m = 10 These results demonstrate that spin-exchange coupling in alternating stacks of radicals and diamagnetic molecules can be enhanced by using larger diamagnetic molecules We then computed the molecular deformation electron density (MDED) of stacks, ∆ρ, to shed light on the nature of spin-exchange coupling in stacks Pictures of ∆ρ for stacks R4/D2_3/R4, R4/D2_5/ R4, and R4/D2_10/R4 are shown in Fig A comparison between Fig 5(a), 5(b), and 5(c) shows that electron transfer to a diamagnetic molecule increases as m increases We computed the charge of D2m in stacks (∆n) to confirm our results Our results show that ∆n can be negative or positive, as tabulated in Table I This result means that electrons can be transferred from or to D2m A comparison between stacks shows that a relation exists between ∆n and J Stacks with m = and having positive or small negative ∆n result in a negative J, as shown in Table I, while stacks with m = 5–10 have a significant negative ∆n resulting in a positive J These results demonstrate that the direction of electron transfer in stacks plays a significant role in the spin-exchange coupling of the stacks The FM spin-exchange TABLE I Typical parameters for R4/D2m/R4 (m = 3–10) stacks: the inter-radical R4–R4 distance (d), the effective spinexchange coupling (J ), the charge transfer from radical R4 to diamagnetic molecule D2m( ∆ n), the spin polarization on the diamagnetic molecule D2m ( ∆ m), the electron affinity of D2m (E a ), and formation energy (E f ) m d (Å) J /k B (K) ∆n (e) ∆m(µB) E a (eV) E f (eV) 10 3.259 −38 0.034 0.078 −1.01 −2.25 3.239 −35 −0.024 0.142 −1.51 −2.59 3.231 103 −0.094 0.287 −1.87 −2.96 3.230 232 −0.124 0.387 −2.15 −3.20 3.226 345 −0.181 0.418 −2.33 −3.51 3.214 507 −0.186 0.454 −2.43 −3.59 3.217 689 −0.185 0.390 −2.48 −3.67 3.217 832 −0.182 0.392 −2.53 −3.52 107109-5 Nguyen et al AIP Advances 5, 107109 (2015) FIG Spin distribution in R4/D2m/R4 stacks for m = and m = 10 Density at the surface = 0.03e/Å3 Color code: dark/blue for spin up, light/yellow for spin down coupling in stacks can be enhanced by electron transfer from radicals to the diamagnetic molecules, while the electron transfer from diamagnetic molecules to radicals can weaken the FM spin-exchange coupling in stacks Moreover, our calculated results indicate that as more electrons are transferred from radicals to diamagnetic molecules, the stronger the FM spin-exchange coupling between radicals in stacks It is easy to see that the magnitude of ∆n increases with m Now we will investigate why ∆n increases as the size of the diamagnetic molecule D2m increases To elucidate this, we computed the electron affinity (Ea) of D2m using the formula in Eq (3) Ea = E − − E − (3) where, E and E are the total electronic energy in the neutral state and the anionic state of D2m, respectively Ea for D2m is tabulated in Table I Our calculated results show that Ea for D2m becomes more negative as m increases This means that the electron affinity of D2m increases as m increases This increasing electron affinity trend is why there is more electron transfer from R4 to D2m as m increases These results suggest that the FM spin-exchange coupling in stacks can be enhanced by using diamagnetic molecules having a strong electron affinity These correlations among J, ∆n, Ea, and m for R4/D2m/R4 stacks can be explained in terms of hybridizations between the HOMO (Highest Occupied Molecule Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) of the R4 radical and the D2m diamagnetic molecule Our calculated results show that the HOMO and LUMO of the aromatic molecules R4 and D2m are π-states resulting from hybridizations of the pz orbitals on carbon atoms, as shown in Fig The π-states can hybridize to form molecular orbitals for the R4/D2m/R4 stacks, as shown in Fig The hybridization between the HOMO of R4 and the HOMO of D2m leads to an AFM structure of the R4/D2m/R4 stacks, as displayed in Fig 7(a), while the hybridization between the HOMO of R4 and the LUMO of D2m leads to an FM FIG Pictures of ∆ρ of R4/D2m/R4 stacks: (a) m = 3, (b) m = 5, (c) m = 10 107109-6 Nguyen et al AIP Advances 5, 107109 (2015) FIG HOMOs and LUMOs for R4 radicals and D2_10 diamagnetic molecules Density at the surface = 0.03 e/Å3 structure of the R4/D2m/R4 stacks, as displayed in Fig 7(b) However, the strength of these hybridizations depends on the difference in their energy, the smaller the energy difference, the stronger the hybridization The calculated energies of HOMOs and LUMOs for R4 and D2m are listed in Table II Table II shows that the energy of the R4 HOMO is closer to the D2m HOMO than the D2m LUMO with m = and 4, while the energy of the R4 HOMO of is closer to the D2m LUMO than the D2m FIG Schematic AFM and FM configurations of R4/D2m/R4 stacks: (a) AFM configuration results from the hybridization between the R4 HOMO and the D2m HOMO, (b) FM configuration results from the hybridization between the R4 HOMO and the D2m LUMO Nguyen et al 107109-7 AIP Advances 5, 107109 (2015) TABLE II Calculated HOMO and LUMO energy of a single R4 radical and a single D2m diamagnetic molecule (m = 3–10) E LUMO (eV) E HOMO (eV) R4 D23 D24 D25 D26 D27 D28 D29 D2_10 −3.739 −4.269 −3.586 −4.858 −3.841 −4.683 −4.011 −4.572 −4.127 −4.502 −4.208 −4.458 −4.265 −4.431 −4.307 −4.414 −4.338 −4.404 FIG The energy difference between the R4 HOMO and the HOMO and LUMO of D2m (m = 3–10) HOMO with m = 5–10, as shown in Fig Hence, the hybridization between the R4 HOMO and the D2m HOMO dominates with m = and resulting in AFM spin-exchange coupling in R4/D2_3/R4 and R4/D2_4/R4 stacks, as shown in Fig 7(a) For stacks with m = 5–10, the hybridization between the R4 HOMO and the D2m LUMO dominates, leading to FM spin-exchange coupling of these stacks, as depicted in Fig 7(a) To evaluate the stability of R4/D2m/R4 stacks, their formation energy, E f , was calculated using Eq (4) E f = Estack − (2Eradical + Ediamagnetic_molecule) (4) where, Estack, Eradical, and Ediamagnetic_molecule are the total electronic energy of the stack, radical, and diamagnetic molecule, respectively The E f of R4/D2m/R4 stacks is tabulated in Table I E f is in the range of −2.25 eV to −2.67 eV The E f of the R4/D2m/R4 stacks becomes more negative as m increases This result means that stacks become more stable with increasing m This trend can be explained in terms of π − π stacking overlap between R4 and D2m These results demonstrate the advantage of using large diamagnetic molecules as building blocks when designing stacks IV CONCLUSION Eight alternating stacks of composition R4/D2m/R4 (R4 = C31H15, and D2m = C2(2m+m+2)H2(m+3) with m = 3–10) were designed and investigated using density-functional theory with dispersion correction and full geometry optimization, to explore ways to design ferromagnetic carbon-based materials Our calculated results show that J in alternating stacks of R4/D2m/R4 is antiferromagnetic with m = and 4, and ferromagnetic with m = 5–10 The mechanism of spin exchange in alternating stacks was determined by electron transfer (∆n) between R4 radicals and D2m diamagnetic molecules The ferromagnetic spin-exchange in stacks can be enhanced by electron transfer from R4 to D2m, while electron transfer from D2m to R4 can weaken the ferromagnetic spin-exchange in stacks Furthermore, ∆n depends on the electron affinity (Ea) of the D2m diamagnetic molecule The Ea for D2m tends to become stronger as m increases These results give interesting insight into the effects of 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(2015) Correlation between charge transfer and exchange coupling in carbon-based magnetic materials Anh Tuan Nguyen,1,2,3,a Van Thanh Nguyen,1 Thi Tuan Anh Pham,1,4 Viet Thang Do,1,5 Huy Sinh Nguyen,1... molecules increases These results give some hints into how exchange coupling can be tailored in carbon-based magnetic materials II COMPUTATIONAL METHODS All calculations were performed using the