Article pubs.acs.org/JPCC
Theoretical Prediction of a Stable 2D Crystal of Vanadium Porphyrin: A Half-Metallic Ferromagnet Harish K. Singh, Pawan Kumar, and Umesh V. Waghmare* Theoretical Science Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560 064, India S Supporting Information *
ABSTRACT: We predict a 2D ferromagnetic half-metal based on vanadium porphyrin (V−PP) using first-principles density functional theoretical analysis. We establish the dynamical stability of its planar structure and magnetic ground state through determination of energetics and phonon dispersion. We find that the exchange interaction between spins of nearest neighbor V atoms is mediated by delocalized states of porphyrin and determine its strength from the relative energies of states with ferromagnetic and antiferromagnetic ordering. Using it in an Ising model, our estimate of its Curie temperature (Tc) is 197 K, which is higher than that of 2D manganese phthalocyanine (Mn−Pc) and 2D Cr−PP. With estimated work function of 4.9 eV, moderate in-plane stiffness, and a branch of very low energy flexural modes evident in its phonon dispersion, we find that 2D V−PP is quite suitable for use in flexible spintronic devices.
1. INTRODUCTION Spintronic devices operate making use of electronic spin as well as its charge and are useful in high density data storage and high speed data processing.1 Many spintronic devices can be made with half-metallic ferromagnetic (HMF) materials in which electric current is carried by completely (100%) spin polarized carriers.2 HMF materials are characterized by the coexistence of metallic gapless spectrum of electrons with one spin orientation, and a spectrum with semiconducting gap for electrons of the opposite spin. The concept of half-metallicity was first given by de Groot for NiMnSb based Heusler alloys occurring in the C1b crystal structure.3 While many of the reported half-metallic materials have been studied theoretically through determination of electronic structure, experimental evidence for half-metallic behavior is relatively scarce, and a relatively fewer of materials have been verified to be HM experimentally.4−7 Most of the reported half metals are ferromagnetic (FM), with some rare exceptions that are the half-metals with antiferromagnetic (AFM) ordering.8−11 Recently, half-metals based on graphene and organic materials have been studied with motivation to use them in flexible spintronic devices.12,13 Since properties of a material are greatly influenced by its dimensionality, it is fundamentally interesting to explore halfmetallic low dimensional structures that could also be used in nanoscale spintronic devices. Two-dimensional (2D) materials have been a subject of active research since the successful extraction of graphene from graphite.14 Graphene exhibits unique electronic properties with potential for applications in future nanoscale devices.15 However, most of the known 2D materials such as graphene, silicene, MoS2, and boron nitride are nonmagnetic in their pristine form and are not quite relevant to spintronic devices. To this end, organometallic © 2015 American Chemical Society
monolayered sheets (OMSs) are quite promising due to the flexibility in their synthesis and magnetic properties, which can be suitable for applications in flexible spintronics devices.16 Phthalocyanine and porphyrin based OMSs have an advantage that transition metal (TM) atoms are regularly distributed and separated from each other avoiding a direct d−d interaction and tendency of TM atoms to form clusters. Recently, Abel et al. synthesized a 2D monolayer of iron phthalocyanine (Fe− Pc) through a metal-directed polymerization of Fe−Pc molecules on an NaCl(100) thin film.17 Synthesis of other 3d TM based phthalocyanines can be achieved using a similar methodology. First-principles theoretical analysis of Mn−Pc sheet demonstrated its half-metallic ferromagnetic behavior with estimated Curie temperature (Tc) of 150 K.16 Recently, porphyrin based nanostructures have been shown to exhibit properties that facilitate various applications such as optoelectronic, hydrogen storage, conducting molecular wires, and spintronics.18−21 One dimensional (1D) zinc−porphyrin (Zn−PP) has been synthesized up to dodecamer units and UV spectra analysis revealed red-shifted absorption spectrum with increasing length (i.e., increasing the number of porphyrin units), suggesting that such a porphyrin array can be used as a conducting molecular wire.22 Synthesis of these OMSs17,22 stimulated further theoretical investigations of 2D TM−PP to predict their electronic and magnetic properties. Recently, Tan et al. determined the electronic and magnetic properties of 2D TM−PP (TM = Cr−Zn), and reported that the half-metallic properties can be achieved in 2D Cr−PP sheet after electron doping which exhibits ferromagnetic ordering below a Curie Received: October 6, 2015 Revised: October 21, 2015 Published: October 22, 2015 25657
DOI: 10.1021/acs.jpcc.5b09763 J. Phys. Chem. C 2015, 119, 25657−25662
Article
The Journal of Physical Chemistry C
Figure 1. (a) Optimized geometrical structure of 2D V−PP monolayer sheet (top view). (b) Phonon dispersion and density of states of 2D V−PP monolayer sheet (determined for the optimized structure) along the high symmetry q-points path in the Brillouin zone are Γ (0, 0) → X (1/2, 0) → M (1/2, 1/2) → Γ (0, 0).
temperature (Tc) of 187 K.23 Although an infinite sheet of 2D TM−PP has not been synthesized yet, Nakamura et al. fabricated a symmetric square zinc porphyrin sheet through oxidation of directly meso−meso-linked cyclic porphyrin tetramer.24,25 Such fabrication of 1D and 2D OMSs has opened up routes to synthesis of 2D TM−PP monolayer sheets. In fact, a monomer unit of vanadium porphyrin has been synthesized.26,27 As 1D V−PP has a ferromagnetic ground state,20 we undertake here a theoretical investigation to explore possible ferromagnetism in 2D V−PP monolayer and estimate its magnetic transition temperature. We use first-principles calculations to establish dynamical stability of 2D V−PP through determination of its phonon dispersion, and determine its electronic structure and magnetic properties. We find that the electronic structure of 2D V−PP is half-metallic, and its ground state exhibits a ferromagnetic ordering. Our estimate of its Curie temperature (Tc) is 197 K. Since the stability of 2D materials can be a limiting factor in their applications, we determined phonon spectrum of 2D V− PP and have established that it does not exhibit any structural instabilities and that its flat 2D structure is quite stable.
Å along z-axis to avoid the interactions between the adjacent periodic images. We relaxed the structure to minimum energy with respect to in-plane lattice parameters and atomic positions, until the stresses are less than 10 kbar and Hellmann−Feynman forces on each atom are less than 0.03 eVÅ−1 in magnitude. This resulted in a cell with in-plane lattice parameter of 8.40 Å. The primitive unit cell of 2D V−PP contains 20 carbon (C) atoms, four nitrogen (N) atoms, and one vanadium(V) atom. To find the lowest energy magnetic configuration we considered magnetic configurations with parallel (ferromagnetic) and antiparallel (antiferromagnetic) spins on neighboring V sites in a 2 × 2 supercell containing 100 atoms (four primitive cells) keeping structural parameters the same (used a 4 × 4 × 1 kmesh). Since strongly correlated systems with partially filled dsubshells may not be accurately described within GGA, we adopted GGA+U formalism for the 3d orbitals of the vanadium and included the onsite correlations with Hubbard parameter (U) of 3 and 6 eV.16,20,32,33 We find that the our results remain essentially unchanged with use of the DFT+U correction (see Figure S1, Supporting Information). To assess the dynamical stability of 2D V−PP monolayer, we determined its phonon spectrum within the framework of density functional perturbation theory (DFPT).34 To this end, we obtained phonon dispersion curves through interpolation of the dynamical matrices calculated at q-points on a 2 × 2 × 1 mess using DFPT.
2. COMPUTATIONAL METHODS Our first-principles calculations are based on spin-dependent density functional theory (DFT) and a plane wave pseudopotential approach as implemented in Quantum ESPRESSO package. 29 We use a generalized gradient approximation (GGA) with Perdew−Burke−Ernzerhof (PBE) parametrized form of the exchange-correlation energy functional.30 Valence electrons in configurations of C (2s22p2), N (2s22p3), and V (3d34s2) were treated using Vanderbilt ultrasoft pseudopotentials.31 Plane wave basis sets truncated with energy cutoffs of 36 and 216 Ry were used in representation of Kohn− Sham wave functions and charge densities, respectively. We used a uniform mesh of 8 × 8 × 1 k-points in sampling integrations of our Brillouin zones in calculations of total energy and structural relaxation, and smeared occupation numbers of electronic states employing Fermi−Dirac distribution with a smearing width of 0.003 Ry. We use periodic boundary conditions to simulate an infinite 2D V−PP monolayer sheet in the ab-plane introducing a vacuum of 10
3. RESULTS AND DISCUSSION Optimized structure of 2D V−PP obtained here is planar with no buckling (all atomic sites are in the same plane) and has a 4fold symmetry with lattice constant 8.40 Å (see Figure 1a). Before examining the electronic and magnetic properties of 2D V−PP monolayer sheet, we studied its dynamical stability. Any lattice dynamical instability of a system is evident in unstable modes (ω2 < 0) in its phonon dispersion: eigenvectors of unstable modes (if any) precisely give the atomic displacements that would distort the structure to lower energy. We obtained phonon dispersion curves at q-points along lines of high symmetry in the 2D Brillouin zone (see Figure 1b). It contains 75 phonon branches with real frequencies of all the vibrational modes throughout the Brillouin zone, indicating that the 25658
DOI: 10.1021/acs.jpcc.5b09763 J. Phys. Chem. C 2015, 119, 25657−25662
Article
The Journal of Physical Chemistry C
Figure 2. (a) Calculated spin-polarized electronic structure and density of states (DOS) of 2D V−PP Sheet. Partial density of states (PDOS) with projection on (b) s- and p-orbitals of C and N and (c) d-orbitals of V atom in 2D V−PP. Spin-up and spin-down electron densities are given by positive and negative values, and Fermi level is set to zero.
completely flat structure of 2D V−PP sheet is indeed dynamically stable (i.e., it corresponds to a minimum of energy). We note that frequencies of its acoustic modes go up to 200−300 cm−1, which indicates that their stiffness is comparable to other 2D materials. The lowest energy branch with quadratic dispersion corresponds to flexural modes, which is a universal feature reflecting the low cost of energy associated with rippling of 2D materials. Further, the PhDOS reveals quite a wide range of frequencies of various vibrational modes of the lattice. A subset of this information about a material, namely, the phonons close to Γ point in its vibrational spectrum (see Figure 1b), can be measured experimentally using infrared and Raman spectroscopies and constitutes its fingerprint. There is no experimental data available for vibrational modes of 2D V−PP as it has not been synthesized yet. Thus, our results will be useful in experimental characterization of 2D V−PP. Acoustic phonons of V−PP range from 0 to about 425 cm−1, which indicate that its in-plane stiffness is higher than that of silicene,28 but much less than that of graphene in which the hardest acoustic modes have frequencies of 1200 cm−1. More importantly, the flexural modes (acoustic modes with atomic out-of-plane displacements associated with the branch of modes of the lowest frequency see in Figure 1b) of 2D V−PP have very low frequencies (
