Electronic Structure and Magnetic Properties of Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2 Based on First Principles

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1 Commun. Theor. Phys. (Beijing, China) 54 (2010) pp c Chinese Physical Society and IOP Publishing Ltd Vol. 54, No. 5, November 15, 2010 Electronic Structure and Magnetic Properties of Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2 Based on First Principles HUANG Hai-Ming (á ñ), 1, LUO Shi-Jun (î ), 1 and YAO Kai-Lun ( Ô ) 2,3 1 School of Science, Hubei University of Automotive Technology, Shiyan , China 2 School of Physics, Huazhong University of Science and Technology, Wuhan , China 3 International Center of Materials Physics, The Chinese Academy of Science, Shenyang , China (Received January 27, 2010; revised manuscript received April 6, 2010) Abstract The electronic structure and the magnetic properties of the molecule-based ferromagnets Cu[C(CN) 3] 2 and Mn[C(CN) 3] 2 are studied according to first principles within density-functional theory (DFT) and the full potential linearized augmented plane wave (FP-LAPW) method. The total energy, atomic spin magnetic moments, and density of states (DOS) of Cu[C(CN) 3] 2 and Mn[C(CN) 3] 2 are all calculated. The calculations reveal that the compounds have a stable ferromagnetic ground state and half-metallic properties. The total spin magnetic moment is 1.0µ B for Cu[C(CN) 3] 2 and 5.0µ B for Mn[C(CN) 3] 2 per molecule, the magnetic moment mainly comes from metal atoms, although there is a slight contribution from N and C atoms. PACS numbers: Xx, Mb, Rv Key words: first principles, magnetic properties, half-metallic properties 1 Introduction Over the past few years, with the rapid development of synthetical technology using organic-inorganic hybrid materials, and with the promising future of this technology, many one-, two-, and three-dimensional coordination polymers comprising paramagnetic transition metal cations and diamagnetic organic ligands exhibiting a wide variety of cooperative phenomena have been investigated, both theoretically and experimentally. [1 9] Recently, polymeric metal complexes containing the analogous organic anion [C(CN) 3 ] have attracted considerable attention because of their intriguing physical properties. [10 12] Such compounds are composed of transition metal ions (M = Mn, Fe, Co, Ni, and Cu) and organic [C(CN) 3 ] ligands. [C(CN) 3 ] is one of the simplest ligands with the ability to form infinite chain or sheet structures. In this paper, we report first principles calculations on the compounds Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2. Their crystal structures and magnetic properties have been determined experimentally in earlier studies. X-ray diffraction measurements at room temperature indicate that the single-crystal lattice parameters are a = Å, b = Å, c = Å for Cu[C(CN) 3 ] 2 and a = Å, b = Å, c = Å for Mn[C(CN) 3 ] 2. They crystallize in the space group Pmna, both salts are essentially isostructural. The metal atoms are bridged by two [C(CN) 3 ] anions to form an infinite double chain structure, the third CN end of the anion is weakly coordinated to the adjacent metal chain, making a three-dimensional network. The crystal is composed of two such interwoven networks. [13] The solid-state assembly of metal-organic polymers has potential applications in non-linear optics, magnetism, and molecular recognition. In order to understand the nature of these materials, it is necessary to study their electronic structure and magnetic properties, which is important in designing new materials. The main goals of our work are to investigate electronic structure and magnetic coupling, and analyze the interaction of magnetic properties via the density of states (DOS) and spontaneous magnetic moments. This provides new insights into the origin of the strong ferromagnetic coupling in this family of compounds, which should be useful for the design of novel ferromagnetic materials. 2 Computational Details First principles calculation based on density-functional theory (DFT) is one of the most powerful tools in studying the ground-state properties of materials. This can give us information about the electronic structures of complexes. In this paper, we use the first principles full potential linearized augmented plane wave (FP-LAPW) method based on DFT to calculate the electronic structures of Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2. The calculations have been carried out using WIEN2K [14] code. In the calculations, the generalized gradient approximation (GGA) [15] proposed in 1996 by Perdew, Burke, and Emzerhof is used to determine the exchange-correlation energy. The Supported by the National Natural Science Foundation of China under Grant No and the Excellent Middle Age and Youth People Science and Technology Creative Team Foundation of the Educational Department of the Hubei Province under Grant No. T smilehhm@163.com

2 No. 5 Electronic Structure and Magnetic Properties of Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2 Based on First Principles 939 atomic-sphere radii of Cu, Mn, C, and N have been chosen as 1.9, 2.0, 1.1, and 1.0 a.u., respectively. The cutoff parameter R mt K max, which limits the number of the plane waves, is equal to 5.0, where K max is the maximum value of the reciprocal lattice vector used in the plane wave expansion, and R mt is the smallest atomic-sphere radius of all the atomic spheres. The plane wave cutoff energy is set to 340 ev. We specify charge and energy as the convergence criterion, and set the charge and energy convergence at 0.1 mev. 3 Results and Discussion Before studying electronic structure and magnetic properties, we first fully optimize the structures of Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2. This optimization is crucial in reflecting the true structure of the crystal. In optimization, the volume and atoms positions have been automatically changed in order to get the minimization of the total energy. Figure 1 presents the calculated total energy versus cell volume for Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2. The total energy is changed with the volume increase or volume decrease. It is clear that the minimum energy of Cu[C(CN) 3 ] 2 is Ry and corresponding volume is a.u., 3 the minimum energy of Mn[C(CN) 3 ] 2 is Ry and corresponding volume is a.u. 3 It is well known that the lower the crystal total energy, the more stable. The energy versus volume data are each used in the murnaghan equation of state to obtain the equilibrium lattice constant. These values are listed in Table 1. The equilibrium lattice parameters in our calculations are in good agreement with experimental ones. We use the equilibrium lattice parameters in our calculations. Fig. 1 The calculated total energy versus volume for (a) Cu[C(CN) 3] 2 and (b) Mn[C(CN) 3] 2. Table 1 The calculated equilibrium lattice constants, the energy difference between the nonmagnetic states and the ferromagnetic states E 1, the energy difference between the antiferromagnetic states and the ferromagnetic states E 2. Compound a/å b/å c/å E 1 /mev E 2 /mev Cu[C(CN) 3 ] Mn[C(CN) 3 ] We perform total energy calculations corresponding to the ferromagnetic (FM), antiferromagnetic (AFM), and non-magnetic (NM) states for Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2. In the FM calculations, we let the two Cu, Mn, C, and N atoms have the same spin magnetic moment orientation. In the AFM state, the spin arrangement is such that the two atoms have the opposite orientation; thus, in these calculations, the two Cu, Mn, C, and N atoms have opposite spin magnetic moment orientations. In the NM calculations, we do not include spin polarization. The difference in energy between the nonmagnetic states and the ferromagnetic states (E 1 ), and between the antiferromagnetic states and the ferromagnetic states (E 2 ), are given in Table 1. It is clear that the ferromagnetic states for Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2 have lower energies than the antiferromagnetic states and nonmagnetic states, thus, the ferromagnetic states are more favorable in energy in these three states. In the following, we focus on the electronic structures and magnetic properties of Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2 in ferromagnetic states at the optimized equilibrium lattice constants. To study electronic structures and magnetic properties, the total density of states (DOS) of the compounds and the partial density of states (PDOS) for different atoms are calculated. The spin-dependent total and main partial density of states at the equilibrium lattice con-

3 940 HUANG Hai-Ming, LUO Shi-Jun, and YAO Kai-Lun Vol. 54 stants are presented in Fig. 2. Because the DOS distribution near the Fermi level determines the electronic properties, we concentrate our attention on the DOS in the vicinity of the Fermi level, which is set to zero and ranges from 6 to 4 ev. From Fig. 2(a), it is clear that for the spin-up channel of Cu[C(CN) 3 ] 2 there is an energy gap of 2.86 ev around the Fermi level, while the spin-down bands cut the Fermi level. Since the top of the spin-up valence bands are located at 0.15 ev and the bottom of the spin-up conduction bands are located at the 2.71 ev, the energy needed to create a spin-up hole at the top of the spin-up valence bands by exciting a spin-up electron into the conducting spin-down bands is 0.15 ev. In addition, the energy needed for a spin-up electron at the bottom of the spin-up conduction bands is 2.71 ev. Therefore, the energy needed to excite a spin or a spin flip gap is 0.15 ev. The non-zero spin flip gap shows that the Cu[C(CN) 3 ] 2 is a half-metallic ferromagnet. The same study is performed on Mn[C(CN) 3 ] 2. Figure 2(b) shows that the spin-down electrons are metallic while there is an energy gap of about 2.9 ev around the Fermi level for the spin-up electrons. Thus, the Mn[C(CN) 3 ] 2 is also a half-metallic ferromagnet, and the gap for creating a spin-up hole at the top of the spin-up valence bands by exciting a spin-up electron into the conducting bands is 1.7 ev. Moreover, the gap for a spin-up electron at the bottom of the spin-up conduction bands is 1.2 ev. This indicates the half-metallic gap of Mn[C(CN) 3 ] 2 is 1.2 ev. For Cu[C(CN) 3 ] 2, the spinup channel from 2.6 to 0.15 ev and spin-down channel from 2.3 to 0.1 ev mainly originate from the Cu 3d states. For Mn[C(CN) 3 ] 2, the spin-up channel from 4.0 to 1.7 ev and spin-down channel from 1.3 to 3.4 ev mainly originate from the Mn 3d states. Meanwhile, the N 2p and C 2p states contribute little to the compounds. We can surmise that the magnetic properties of Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2 mainly come from Cu and Mn atoms, respectively. Fig. 2 Calculated total and partial density of states for (a) Cu[C(CN) 3] 2 and (b) Mn[C(CN) 3] 2. In each panel, the positive and negative values correspond to the spin-up and spin-down states. The X-axis zero level corresponds to the Fermi level.

4 No. 5 Electronic Structure and Magnetic Properties of Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2 Based on First Principles 941 Table 2 Calculated magnetic moments for the atoms of Cu[C(CN) 3] 2 and Mn[C(CN) 3] 2. Cu[C(CN) 3 ] 2 Mn[C(CN) 3 ] 2 Atoms Magnetic moments (µ B) Atoms Magnetic moments (µ B) Cu Mn N N N N C C C C C C Total Total In Table 2, we list the spin magnetic moments of different atoms, these are defined as the difference of the average number of occupied ions with spin-up and spin-down in the muffin-tins sphere. It is found that the spin magnetic moments for different atoms are different, so their contributions to the magnetic properties are different. The spin magnetic moments for Cu atoms and Mn atoms are given by µ B and µ B in Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2, respectively. While the spin magnetic moments for N and C atoms in these two compounds are very small. These quantitative results reveal that most of the spin magnetic moments come from metal atoms, and the Cu and Mn atoms exist in a high spin state in the compounds. The total spin magnetic moment of Cu[C(CN) 3 ] 2 is 1.0 µ B per molecule and the total spin magnetic moment of Mn[C(CN) 3 ] 2 is 5.0 µ B per molecule, which is typical of half-metallic properties. Here we should mention that, in the compounds, the magnetic moment is not fully restricted to the atoms, but rather expands partially over the molecule. The cell has been divided into two kinds of region during the calculation: the non-overlapping atomic spheres surrounding each atom, and the interstitial regions. The values listed in Table 2 only include the spin populations confined in these atomic spheres, and do not include that distributed in the interstitial regions; thus, the magnetic moments of all atoms add up to a smaller value than the total calculated magnetic moment. We now discuss the origin of half-metallic properties. Cu atoms become divalent Cu 2+ cations because of the two lost electrons in Cu[C(CN) 3 ] 2. This means that nine electrons will occupy the Cu 3d states, which can accommodate ten electrons. Because of the spin splitting, the spin-up 3d states require less energy than the spin-down d states; as a result, the spin-up 3d states are fulfilled by five electrons and the spin-down 3d states are not filled, and a vacant site appears in the spin-down 3d states. Therefore, the total magnetic moment should be 1 µ B per formula unit. In Mn[C(CN) 3 ] 2, there are five electrons that will occupy the Mn 3d states for Mn 2+. According to the lowest energy principle, five electrons will occupy spin-up 3d states, so the spin-down 3d states are empty. Five vacant sites appear in the spin-down 3d states and the total magnetic moment should be 5 µ B per formula unit for Mn[C(CN) 3 ] 2. This analysis is consistent with our calculated result. In the Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2 compounds, the two metal atoms are bridged by two N1-C1-C2-C1-N1 linkages. From Table 2, we notice that the signs of the N1-C1-C2-C1-N1 spin population alternate as +/ /+/ /+ in Cu[C(CN) 3 ] 2, so that the ordered spin arrangement in the linkages is anti-parallel. This means that there is antiferromagnetic exchange interaction in Cu[C(CN) 3 ] 2. We also found that the ordered spin arrangement in the N1-C1-C2-C1-N1 linkages in Mn[C(CN) 3 ] 2 is parallel, so there is ferromagnetic exchange interaction in the N1-C1- C2-C1-N1 linkages. 4 Conclusion We have presented first principles study on the electronic structures and magnetic properties of the Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2 compounds using the FP- LAPW method within the framework of DFT. The results show that these two compounds have stable ferromagnetic ground states and half-metallic properties with spin magnetic moments of 1.0µ B and 5.0µ B per molecule for Cu[C(CN) 3 ] 2 and Mn[C(CN) 3 ] 2, respectively. The major part of the spin magnetic moment comes from metal atoms. We also found that there is antiferromagnetic exchange interaction in Cu[C(CN) 3 ] 2 and ferromagnetic exchange interaction in Mn[C(CN) 3 ] 2 that occurs through the N1-C1-C2-C1-N1 linkages. The half-metallic properties may have special applications in spintronics.

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