Spin FIRE

Syntax

For a Spin potential, use:

minimize spin_fire <tolerance> <maximal_number_of_steps> <variable_magnitude> [<fixed_atoms> [<box_change> [<hydrostatic_strain>]]]

  • variable_magnitude = 0 preserves each atom’s initial spin magnitude; 1 optimizes all three Cartesian spin components. Zero spins remain zero in mode 0 and can grow in mode 1.

  • fixed_atoms defaults to 1: atomic positions and the cell stay fixed, and only spins are optimized. Set it to 0 to enable atomic relaxation.

  • box_change defaults to 0 (fixed cell). Set it to 1 to jointly optimize atoms, spins, and the cell; this requires fixed_atoms = 0.

  • hydrostatic_strain defaults to 0 (all nine deformation components). Set it to 1 to apply only isotropic scaling, preserving the cell shape. It requires box_change = 1. The two cell flags have the same meanings as in ordinary FIRE, and follow the spin-magnitude and fixed-atom flags here.

  • Optional flags are positional: fixed_atoms, then box_change, then hydrostatic_strain. Supply preceding flags when setting a later one.

  • tolerance must be finite and positive. The maximum per-atom magnetic-force vector norm must be at most this value in eV/muB. Mode 0 tests only the component tangent to each constant-magnitude sphere; mode 1 tests the full magnetic force.

  • When atoms are optimized, their largest absolute force component must also be at most tolerance in eV/angstrom, as in ordinary FIRE. Thus one numeric tolerance is applied separately to atomic and magnetic forces, in their respective units.

  • When the cell is optimized, the largest absolute virial stress component must additionally be at most 1e-4 GPa, the same zero-pressure target as ordinary FIRE. With hydrostatic_strain = 1, only the mean normal stress is tested; shear and deviatoric stresses need not vanish.

  • maximal_number_of_steps is a positive iteration budget. All attempts count, including velocity resets and non-finite trial states.

Examples

Optimize only spin directions, keeping magnitudes, atoms, and the cell fixed:

minimize spin_fire 1.0e-4 10000 0

Optimize only spins, allowing their magnitudes to change:

minimize spin_fire 1.0e-4 10000 1

The same spin-only optimization with atoms explicitly fixed:

minimize spin_fire 1.0e-4 10000 1 1

Jointly optimize atoms and variable-magnitude spins at fixed cell:

minimize spin_fire 1.0e-4 20000 1 0

Jointly optimize atoms, variable-magnitude spins, and the cell:

minimize spin_fire 1.0e-4 20000 1 0 1

Keep spin magnitudes fixed during joint optimization:

minimize spin_fire 1.0e-4 20000 0 0 1

Allow only isotropic cell scaling during joint optimization:

minimize spin_fire 1.0e-4 20000 1 0 1 1

Write the optimized structure and magnetic moments using the same zero-time-step output procedure as ordinary FIRE:

potential nep.txt
minimize spin_fire 1.0e-4 20000 1 0 1
ensemble nve
time_step 0
dump_xyz 1 relaxed.xyz precision double force spin mforce virial
run 1

Caveats

  • A Spin potential and spin:R:3 in model.xyz are required. Ordinary minimize fire remains a lattice-only command and is not enabled for Spin potentials.

  • Cell optimization requires periodic boundaries in all three directions. Joint optimization does not support fix groups and rejects them; in spin-only mode, fix does not select frozen spins.

  • Atomic velocities and physical spin_vel are preserved. FIRE uses separate fictitious velocities. After joint optimization, positions, cell inverses, periodic images, and endpoint forces are updated for subsequent commands.

  • External magnetic fields do not participate in Spin FIRE minimization. add_mfield applies only to MD runs.

  • Output reports energy, maximum magnetic-force residual, and (for joint runs) maximum atomic force and virial stress in GPa (mean normal stress in the hydrostatic case). At fixed cell, stress is reported but is not a stopping criterion. Only converged means all active criteria have been met. maximum_steps and stalled do not indicate convergence.

  • Individual FIRE steps can increase the energy. Force convergence identifies a stationary point, not necessarily the global minimum or a particular phase. Variable-magnitude optimization requires a potential fitted over the relevant range of moments, atomic configurations, and cell deformations.

Algorithm and stagnation

The dot product of the generalized force and fictitious velocity controls FIRE’s step size and velocity resets. Energy is diagnostic; a constant energy offset does not change the optimization. Non-finite trials restore spins, positions, cell, and endpoint properties before retrying with a smaller step.

Fixed-magnitude spins use spherical updates with parallel transport of fictitious velocities; variable-magnitude spins use Cartesian updates. Each spin move is limited to 0.1 radians or 0.1 muB. Joint runs also limit each non-affine atomic move to 0.1 angstrom and the Frobenius norm of each cell deformation increment to 0.01. Cell coordinates use the initial cube-root volume as a length scale, as in ordinary cell FIRE. Cell deformation acts on both the cell and atomic positions; spins stay in laboratory Cartesian coordinates during this affine part of the update. The full virial transpose supplies the conjugate deformation force, including nonsymmetric components from spin-orbit interactions.

Stagnation is reported if the internal step drops below 1e-12, if 20 finite moves produce no resolved update (8 double epsilons relative to the component scale max(1, abs(old), abs(new))), or if 1000 attempts pass without a cumulative 1% improvement in the largest residual divided by its convergence tolerance. Joint runs include atomic, magnetic, and active stress residuals. The plateau detector may stop very slow relaxation; inspect the residuals before restarting. None of these conditions relaxes the requested convergence criteria. The internal FIRE step is an optimization parameter, not the MD time_step.