This project investigated magnetism in self-assembling metal-organic frameworks. To achieve this, we performed Density Functional Theory (DFT) calculations using the Vienna ab-initio Simulation package (VASP). All calculations used standard PBE_PAW potentials, accessible from VASP. These are not included in this repository.
MnPc was investigated due to the experimental synthesis of Fe-Phthalocyanine [1]. A spin-polarised DFT calculation using the generalised gradient approximation (GGA) and conjugate-gradient algorithm was used to minimise this system. This simulation employed the projector-augmented-wave (PAW) potential, using the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional. Since the standard GGA exchange function cannot properly describe strongly correlated systems with partially filled d subshells, the simulation used the GGA+U extension. By dividing the delocalised s and p electrons, and the localised d electrons into two separate groups, qualitative improvement for ground state properties such as exchange interaction was found. The chosen values for the Hubbard U and Hund J were 4 eV and 1 eV respectively. The Brillouin zone was sampled with a Gamma-centred, Monkhurst-Pack k-point grid of 9x9x1 with a z-axis separation of 15 A to minimise interaction between layers. The energy cut-off, convergence criteria and force was set to 400eV, 1e-5 eV and 0.01 eV/A. Using Fe as our transition metal, the lattice parameter was calculated to be 10.70 \AA which shows good agreement with Matthieu Abel et. al.. Using Mn, we attained a lattice parameter of 10.69 A.
To investigate the magnetic coupling, we used a 2x2 super-cell with a Monkhurst-Pack k-points grid of 5x5x1$. The spin moments were defined for the ferromagnetic (FM) and anti-ferromagnetic (AFM) symmetries were defined. Due to the magnetic moment arising from the d-orbitals, spin-orbit coupling parameters were defined. Using a non-self consistent calculation, the magnetic moment vector was varied from in-plane to out-of-plane ([100] -- [001]), to calculate the magnetic axis anisotropy energy.
The Hubbard U parameter and the Hund J parameter were required to properly describe the half-filled d-orbitals. This induced Jahn-Teller distortions through half-filling the d_{xz} and d_{yz} orbitals. Substantial spin-polarisation occurred, resulting in a half-metal DOS. A magnetic moment of 3 uB was found.
The Ta2S3 unit cell was created and periodic boundary conditions were implemented. We enforced a z-axis separation of 15 A to minimise inter-layer interactions. Using the PAW potentials and PBE functionals, a GGA+U approach was taken to describe the strongly correlated 4d electrons in Ta. The simplified, rotationally invariant approach by Dudarev et. al. was used and we chose 3.0 eV as our U-J parameter. Atomic positions and lattice parameters were fully relaxed using a sequential combination of quasi-Newton - Raphson integration of Newtonian mechanics (RMM-DIIS) and the conjugate-gradient algorithm. The Brillouin zone was sampled with an 11X11x1 Gamma-centred Monhurst-Pack grid. The energy cut-off, convergence criteria and force were set to 500eV, 1e-5 eV and 0.01 eV/A. Finally, the screened hybrid density functional by Heyd–Scuseria–Ernzerhof (HSE06) was used to check the electronic structure.
To investigate the magnetic exchange energies, the FM and AFM state were calculated using a self-consistent approach. Using a non-self consistent calculation, the magnetic moment was swept across [100] -- [001] to calculate the magnetic axis anisotropy energy.
Strong trigonal planar hybridisation was observed. Structure exhibited an insulator-like spin-down channel
We employed a 2D hexagonal unit cell with lattice parameter of 20.80 A and theta = 120* and enforced a z-axis distance of 15 A. Using PAW potentials and PBE functionals, a GGA approach was taken to minimise the system. The plane wave energy cut-off, convergence criteria and force was set to 550eV, 1e-5 eV and 0.01 eV/A respectively. The Brillouin zone was sampled with a 5x5x1 Gamma-centred Monkhurst-Pack grid. The lattice parameter and atomic positions were allowed to change.
The energies of the FM and AFM states were calculated using a self-consistent simulation, employing the spins from the unit cell. The magnetic axis anisotropy energy was calculated by sweeping the magnetic moment across [100] -- [001] with a non-self consistent approach.
