J. Phys. Chem. C 2009, 113, 18891–18896
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Theoretical Reinvestigation of the Electronic Structure of CuNCN: the Influence of Packing on the Magnetic Properties Hongping Xiang, Xiaohui Liu, and Richard Dronskowski* Institute of Inorganic Chemistry, RWTH Aachen UniVersity, Landoltweg 1, D-52056 Aachen, Germany ReceiVed: August 3, 2009; ReVised Manuscript ReceiVed: September 16, 2009
The electronic structure and magnetic properties of CuNCN have been reinvestigated by density-functional theory including explicit electronic correlation (GGA+U). The calculated results show that CuNCN is a semiconductor with a band gap of 0.1 eV and without any local magnetic moments, in practically quantitative agreement with experiment. The coupling constant (J1, J2, and J3) between the nearest-neighbor Cu(II) ions have been calculated as a function of the dihedral angle between the central CuN4 unit and its NdCdN carbodiimide ligands changing from 145° (experimental value) to 180° (hypothetical value). Only if the dihedral angle is close to 180°, CuNCN exhibits a local magnetic moment, characteristic for Cu2+, and adopts an antiferromagnetic structure (intralayer ferromagnetic, interlayer antiferro-magnetic). The former discrepancy between experiment and density functional theory appears to be solved. I. Introduction Two decades ago, the discovery of high-temperature superconducting compounds (HTSC) in perovskite-based cuprates initiated in-depth chemical and physical studies of these cuprates and chemically related compounds.1-5 If encapsulated in a crystalline environment, the orbital moment of the Cu2+ ion (L ) 2) is almost completely quenched, and the ion behaves similar to an isotropic “spin-only” system (S ) 1/2). Hence, the interactions often resemble those of antiferromagnetic Heisenberg systems, especially when the Cu2+ ions are coupled in one or two directions by means of superexchange interactions as a function of the intervening anions.6 For example, the magnetic superstructures of CuO can be viewed as ordered structures of the quasi-one-dimensional antiferromagnetic chains along the [101j] direction.7-9 An antiferromagnetic structure was also found in La2CuO4,10-12 which had encouraged speculation that magnetic interactions may be important for electron pairing in La2-xAxCuO4 (A ) Ba, Sr, Ca) high-temperature superconductors. Even today, a possible interplay between antiferromagnetism and HTSC remains one of the most interesting problems.3,5,13-17 Nonetheless, the origin of high-temperature superconductors is still far from being fully understood despite more than 20 years of intense research. Here, we will theoretically study the nonoxide carbodiimide CuNCN. This compound, which may be regarded as the nitrogen analogue of tenorite, CuO, because the doubly charged complex anion NCN2- replaces the oxide anion O2-, has been reported to show some similarities with CuO and also HTSC concerning the crystal structure although their magnetic properties are quite different. Both X-ray powder and neutron diffraction data manifest that CuNCN crystallizes in the orthorhombic system with space group Cmcm.18,19 The NCN2- unit adopts the carbodiimide shape with C-N ) 1.233(4) Å, that is, with two adjacent carbon-nitrogen double bonds (NdCdN). There is a distorted octahedral Cu2+ coordination due to a first-order Jahn-Teller effect, with interatomic distances of 4 × Cu-N ) 2.008(3) Å and 2 × Cu-N ) 2.592(4) Å (see Figure 1a), * To whom correspondence should be addressed. E-mail: drons@ hal9000.ac.rwth-aachen.de.
Figure 1. View into the (a, left) experimental and (b, right) hypothetical crystal structures of CuNCN approximately along the a axis; see also text.
and the difference between shorter and longer bonds is less pronounced than for the case of CuO (4 × Cu-O ) 1.96 Å, 2 × Cu-O ) 2.78 Å). The electrical resistivity data show that CuNCN is a semiconductor with a resistivity of about 1 kΩ · cm at room temperature, and the activation energy, on the basis of an Arrhenius plot, is about 0.1 eV. With respect to the magnetic properties, the heat capacity data evidence that there is no pronounced anomaly indicative of a magnetic phase transition in the temperature range of 4-100 K.18 In addition, the magnetic susceptibility data suggest that the material shows a very small and almost temperature-independent magnetic susceptibility, close to nonmagnetic behavior, on which a minute signal that probably goes back to a trace of a ferromagnetic impurity is superimposed.18,19 This experimental finding is difficult to understand, at first sight, because the oxidation state of Cu2+ and the Jahn-Teller distortion alludes to an electronic configuration of t2g6eg3, with one unpaired electron in the upmost 3dx2-y2 orbital directed at the N ligands. Since no local moment is found in the susceptibility data, however, the idea of a strongly coupled antiferromagnetic ground state immediately comes into play but such superstructure reflections were absent in the first neutron data.18 The absence of such magnetic reflections, however, might go back to a simple intensity problem because
10.1021/jp907458f CCC: $40.75 2009 American Chemical Society Published on Web 10/07/2009
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J. Phys. Chem. C, Vol. 113, No. 43, 2009
Xiang et al. study is targeted at theoretically redetermining the magnetic properties of the nonoxidic cuprate CuNCN. To do so, we will study the influences of the crystal packing on the electronic and magnetic properties of CuNCN by use of correlated density functional theory (DFT). As a final result it is found that the noncoplanar structure of the Cu-NdCdN-Cu structural motif due to more covalent Cu-N bonding destroys the Cu · · · Cu supersuperexchange coupling, resulting in the nonmagnetic properties of CuNCN. III. Theoretical Calculations
Figure 2. Diffractional signal of CuNCN measured with the DNS spectrometer using polarized neutrons at a temperature of 4.6 K.
magnetic reflections tend to be fairly small if compared with the nuclear onessunless one is able to exclusively collect the pure magnetic data, for example, using polarized neutrons. II. Theoretical and Experimental Status On the theoretical side, the first electronic-structure calculations by means of the generalized gradient approximation (GGA) and also of GGA+U type (U indicates an on-site Coulomb interaction) also yielded that CuNCN should be an antiferromagnetic semiconductor.18 In these calculations, the spinexchange interactions were dominated by two antiferromagnetic exchange paths within the ab plane. The coupling between the layers was suggested to be small enough to effectively decouple the layers and to support two-dimensional S ) 1/2 behavior of a frustrated triangular Heisenberg antiferromagnet. New experimental data based on polarized neutron diffraction, however, question this theoretical interpretation. Figure 2 shows the diffractional signal of CuNCN measured with the DNS spectrometer (located at the Munich high-flux FRM II neutron source) which operates with a beam of polarized neutrons and which allows the detection of the pure magnetic signal. For the present study, a temperature of 4.6 K and a neutron wavelength of 4.74 Å were chosen. In the figure, the nuclear coherent scattering (black) yields reflections at 2.154, 2.04, 1.34, and 0.57 Å-1, and the significant background goes back to isotope-incoherent scattering. The green curve shows the separated spin-incoherent scattering according to the chemical composition CuNCN, namely 2 × 0.5 b (14N) + 0.31 × 0.40 b (65Cu) ≈ 1.1 b per formula unit (with a negligible C contribution). The magnetic scattering (in red), however, is approximately zero over the entire range, with the only exception of Q ) 2.154 Å-1, but this phenomenon goes back to a systematic error in the separation process, also seen in the spinincoherent scattering but with opposite direction. Thus, magnetic scattering due to unpaired electrons can clearly be excluded for CuNCN. As it seems, experiment (nonmagnetic semiconductor) and GGA+U theory (frustrated antiferromagnet) are not in harmony with each other. Thus, a theoretical reinvestigation is necessary. We recall that CuNCN has some similarities with CuO and HTSC concerning their crystal structures such as the CuN4 plane (CuO4 plane in CuO and HTSC) and the CuN2 ribbon (CuO2 ribbon in CuO), but their magnetic properties are quite different: CuO and HTSC are antiferromagnets.3,5,11,13-17 Therefore, this
The calculations were based on DFT20,21 and performed by means of the plane-wave-pseudopotential Vienna ab initio simulation package (VASP).22-24 For the exchange-correlation functional, the generalized-gradient approximation as formulated by Perdew, Burke, and Ernzerhof (GGA-PBE)25 was employed. The projector-augmented wave (PAW) method proposed by Blo¨chl26 and implemented by Kresse and Joubert27 was used. 7 × 7 × 7 k-points were used to sample the complete Brillouin zone, and a 9 × 9 × 9 k-points grid to calculate the densitiesof-states. The Brillouin zone integration was carried out with the tetrahedron method and Blo¨chl’s correction to that.28 The PAW pseudopotentials considered in this study are 3d104s1 for Cu, 2s22p3 for N, and 2s22p2 for C. Electron-electron Coulomb interactions for Cu and the self-interaction correction are considered in the rotationally invariant way (GGA+U) with one effective Hubbard parameter Ueff ) U - J.29,30 In addition, the crystal structures were optimized by letting all lattice parameters and also the positions of Cu, C, and N relax simultaneously until self-consistency was achieved. The calculations were started with a nonmagnetic ground state, and then spin polarization was allowed for. Finally, a finite U value was employed. IV. Results and Discussion In CuNCN, each Cu2+ ion is coordinated by six nitrogen atoms with four short (≈2.0 Å) and two long (≈2.6 Å) Cu-N bonds, a first-order Jahn-Teller scenario. Thus, the Cu2+ ion can be approximatively considered as being coordinated by just four N atoms with short Cu-N bonds, thereby forming a CuN4 planar-rectangular unit (see Figure 1a). There are CuN2 ribbons along the a axis made up of edge-sharing CuN4 units which are connected by NdCdN units along the (vertical) c axis, and parallel to each other along the (horizontal) b axis, thereby forming a layered structure, clearly different from the case of tenorite, CuO. The CuN2 chains deViate from the ac plane, however, which results in Cu-NdCdN-Cu being not coplanar but with a dihedral angle of 145° between the CuN4 and NdCdN building blocks (Figure 1a); at the same time, the symmetry of CuN4 is lowered from an ideal square-planar D4h symmetry to a rectangular-planar shape with pseudo-D4h symmetry. By contrast, it is known that the three-dimensional lattice of CuO is constructed from CuO2 ribbons made up of edgesharing CuO4 square-planar units through sharing oxygen corners,7-9 and the CuO2 ribbons are oriented almost perpendicular to each other. In the high-temperature superconductors, the CuO2 chains made up of corner-sharing CuO4 square-planar units are almost parallel to the ab or ac planes, with the Cu-O-Cu angle being close to 180°.4,13 Although there are structural similarities between CuNCN and CuO or HTSC with respect to the coordination of the Cu atoms, the differences lie in the second coordination shell, e.g., in the dihedral angle. Upon iterating the electronic structure of CuNCN toward selfconsistency, it appears that we now arrived at an energetically lower nonmagnetic ground state than what was found before,18
Theoretical Reinvestigation of the Electronic Structure of CuNCN
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Figure 3. Ordered spin arrangements employed to extract the spin exchange parameters J1, J2, and J3 in the magnetic states designated as (a) FM, (b) AFM1, (c) AFM2, and (d) AFM3. Black and white spheres indicate different orientations of the spin moments residing on the Cu2+ ions, which are the only atoms shown.
even though we repeated the calculation of four different magnetic structures (see Figure 3) for which one may consider three spin-exchange interactions (J1, J2, and J3) between the nearest-neighbor Cu2+ ions. As done before,18 the ferromagnetic (FM) and three antiferromagnetic structures (AFM1, AFM2, and AFM3) were taken into account according to a Heisenberg spin Hamiltonian which reads
ˆ )H
∑
JijSˆi · Sˆj
i
