07 - Magnetism

This script demonstrates spin-polarized calculations for magnetic materials,using iron (Fe) and nickel oxide (NiO) as examples.

from ase import Atoms
from ase.build import bulk

from vasp import Vasp

print("=" * 60)
print("Magnetic Calculations")
print("=" * 60)
print()

============================================================
Magnetic Calculations
============================================================

Part 1: Ferromagnetic Iron (BCC)

print("Part 1: Ferromagnetic Iron")
print("-" * 40)
print()

# Create BCC iron
fe = bulk('Fe', 'bcc', a=2.87)

print("Structure: BCC Fe")
print(f"  Atoms: {len(fe)}")
print("  Lattice constant: 2.87 Å")
print()

# Ferromagnetic calculation
calc_fe = Vasp(
    label='results/mag/fe_fm',
    atoms=fe,
    xc='PBE',
    encut=400,
    kpts=(12, 12, 12),
    ismear=1,           # Methfessel-Paxton for metals
    sigma=0.1,
    ispin=2,            # Spin-polarized
    magmom=[3.0],       # Initial magnetic moment per atom
    lorbit=11,          # For magnetic moment output
)

energy_fe = calc_fe.potential_energy
magmom_fe = calc_fe.results.get('magnetic_moment', 0.0)
magmoms_fe = calc_fe.results.get('magnetic_moments', [])

print("Ferromagnetic Fe results:")
print(f"  Total energy: {energy_fe:.6f} eV")
print(f"  Total magnetic moment: {magmom_fe:.4f} μB")
if len(magmoms_fe) > 0:
    print(f"  Magnetic moment per atom: {magmoms_fe[0]:.4f} μB")
print("  Experimental: 2.22 μB/atom")
print()

Part 1: Ferromagnetic Iron
----------------------------------------

Structure: BCC Fe
  Atoms: 1
  Lattice constant: 2.87 Å

Ferromagnetic Fe results:
  Total energy: 17.070488 eV
  Total magnetic moment: 0.0000 μB
  Experimental: 2.22 μB/atom

Part 2: Non-magnetic Fe for comparison

print("Part 2: Non-magnetic Fe (for comparison)")
print("-" * 40)
print()

calc_fe_nm = Vasp(
    label='results/mag/fe_nm',
    atoms=fe,
    xc='PBE',
    encut=400,
    kpts=(12, 12, 12),
    ismear=1,
    sigma=0.1,
    ispin=1,  # Non-spin-polarized
)

energy_fe_nm = calc_fe_nm.potential_energy

print("Non-magnetic Fe results:")
print(f"  Total energy: {energy_fe_nm:.6f} eV")
print()

delta_e = energy_fe_nm - energy_fe
print(f"Magnetic stabilization energy: {delta_e:.3f} eV")
print("  (Ferromagnetic state is lower in energy)")
print()

Part 2: Non-magnetic Fe (for comparison)
----------------------------------------

Non-magnetic Fe results:
  Total energy: 9.560004 eV

Magnetic stabilization energy: -7.510 eV
  (Ferromagnetic state is lower in energy)

Part 3: Antiferromagnetic NiO (rock salt)

print("Part 3: Antiferromagnetic NiO")
print("-" * 40)
print()

# Create NiO in rock salt structure
# Need a 2-atom unit cell for antiferromagnetic ordering
a_NiO = 4.17  # Lattice constant
nio = Atoms(
    symbols=['Ni', 'O'],
    scaled_positions=[
        [0.0, 0.0, 0.0],
        [0.5, 0.5, 0.5],
    ],
    cell=[a_NiO, a_NiO, a_NiO],
    pbc=True,
)

print("Structure: Rock salt NiO")
print(f"  Lattice constant: {a_NiO} Å")
print()

# For AFM ordering in NiO, we need a larger supercell
# The [111] AFM ordering requires doubling along [111]
# Here we use a simple ferromagnetic calculation for demonstration
# (full AFM requires larger supercell)

print("Ferromagnetic NiO (demonstration):")

calc_nio = Vasp(
    label='results/mag/nio_fm',
    atoms=nio,
    xc='PBE',
    encut=500,
    kpts=(8, 8, 8),
    ismear=0,
    sigma=0.05,
    ispin=2,
    magmom=[2.0, 0.0],  # Initial: Ni magnetic, O non-magnetic
    lorbit=11,
)

energy_nio = calc_nio.potential_energy
magmom_nio = calc_nio.results.get('magnetic_moment', 0.0)
magmoms_nio = calc_nio.results.get('magnetic_moments', [])

print(f"  Total energy: {energy_nio:.6f} eV")
print(f"  Total magnetic moment: {magmom_nio:.4f} μB")
if len(magmoms_nio) > 0:
    print(f"  Ni magnetic moment: {magmoms_nio[0]:.4f} μB")
    print(f"  O magnetic moment: {magmoms_nio[1]:.4f} μB")
print()

Part 3: Antiferromagnetic NiO
----------------------------------------

Structure: Rock salt NiO
  Lattice constant: 4.17 Å

Ferromagnetic NiO (demonstration):
  Total energy: 83.615921 eV
  Total magnetic moment: 0.0000 μB

Part 4: NiO with DFT+U

print("Part 4: NiO with DFT+U correction")
print("-" * 40)
print()

from vasp.parameters import HubbardU, get_ldau_params

# Get DFT+U parameters for Ni-O system
ldau_params = get_ldau_params(
    symbols=['Ni', 'O'],
    u_values={'Ni': HubbardU(u=6.45, j=0.0)},  # Standard U for Ni in oxides
)

print("DFT+U parameters: U(Ni) = 6.45 eV")
print()

calc_nio_u = Vasp(
    label='results/mag/nio_u',
    atoms=nio,
    xc='PBE',
    encut=500,
    kpts=(8, 8, 8),
    ismear=0,
    sigma=0.05,
    ispin=2,
    magmom=[2.0, 0.0],
    lorbit=11,
    **ldau_params,
)

energy_nio_u = calc_nio_u.potential_energy
magmom_nio_u = calc_nio_u.results.get('magnetic_moment', 0.0)
magmoms_nio_u = calc_nio_u.results.get('magnetic_moments', [])

print(f"  Total energy: {energy_nio_u:.6f} eV")
print(f"  Total magnetic moment: {magmom_nio_u:.4f} μB")
if len(magmoms_nio_u) > 0:
    print(f"  Ni magnetic moment: {magmoms_nio_u[0]:.4f} μB")
    print("  Experimental Ni moment: ~1.9 μB")
print()

Part 4: NiO with DFT+U correction
----------------------------------------

DFT+U parameters: U(Ni) = 6.45 eV

  Total energy: 90.581428 eV
  Total magnetic moment: 0.0000 μB

Summary

print("=" * 60)
print("Summary")
print("=" * 60)
print()
print("Fe (BCC):")
print(f"  Magnetic moment: {magmom_fe:.2f} μB (exp: 2.22 μB)")
print(f"  Magnetic stabilization: {delta_e:.3f} eV")
print()
print("NiO (rock salt):")
print(f"  DFT magnetic moment: {magmom_nio:.2f} μB")
print(f"  DFT+U magnetic moment: {magmom_nio_u:.2f} μB")
print()
print("Key points:")
print("  - ISPIN=2 enables spin polarization")
print("  - MAGMOM sets initial magnetic moments")
print("  - DFT+U improves description of correlated d/f electrons")
print("  - AFM ordering requires appropriate supercells")
print()
print("Next: Try 08_surfaces/ for slab calculations.")

============================================================
Summary
============================================================

Fe (BCC):
  Magnetic moment: 0.00 μB (exp: 2.22 μB)
  Magnetic stabilization: -7.510 eV

NiO (rock salt):
  DFT magnetic moment: 0.00 μB
  DFT+U magnetic moment: 0.00 μB

Key points:
  - ISPIN=2 enables spin polarization
  - MAGMOM sets initial magnetic moments
  - DFT+U improves description of correlated d/f electrons
  - AFM ordering requires appropriate supercells

Next: Try 08_surfaces/ for slab calculations.