# min_style spin/lbfgs command¶

## Syntax¶

min_style spin
min_style spin/cg
min_style spin/lbfgs


## Examples¶

min_style  spin/lbfgs
min_modify line spin_cubic discrete_factor 10.0


## Description¶

Apply a minimization algorithm to use when a minimize command is performed.

Style spin defines a damped spin dynamics with an adaptive timestep, according to:

$\frac{d \vec{s}_{i}}{dt} = \lambda\, \vec{s}_{i} \times\left( \vec{\omega}_{i} \times\vec{s}_{i} \right)$

with $$\lambda$$ a damping coefficient (similar to a Gilbert damping). $$\lambda$$ can be defined by setting the alpha_damp keyword with the min_modify command.

The minimization procedure solves this equation using an adaptive timestep. The value of this timestep is defined by the largest precession frequency that has to be solved in the system:

${\Delta t}_{\rm max} = \frac{2\pi}{\kappa \left|\vec{\omega}_{\rm max} \right|}$

with $$\left|\vec{\omega}_{\rm max}\right|$$ the norm of the largest precession frequency in the system (across all processes, and across all replicas if a spin/neb calculation is performed).

$$\kappa$$ defines a discretization factor discrete_factor for the definition of this timestep. discrete_factor can be defined with the min_modify command.

Style spin/cg defines an orthogonal spin optimization (OSO) combined to a conjugate gradient (CG) algorithm. The min_modify command can be used to couple the spin/cg to a line search procedure, and to modify the discretization factor discrete_factor. By default, style spin/cg does not employ the line search procedure and uses the adaptive time-step technique in the same way as style spin.

Style spin/lbfgs defines an orthogonal spin optimization (OSO) combined to a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. By default, style spin/lbfgs does not employ line search procedure. If the line search procedure is not used then the discrete factor defines the maximum root mean squared rotation angle of spins by equation pi/(5*Kappa). The default value for Kappa is 10. The spin_cubic line search option can improve the convergence of the spin/lbfgs algorithm.

The min_modify command can be used to activate the line search procedure, and to modify the discretization factor discrete_factor.

Note

All the spin styles replace the force tolerance by a torque tolerance. See minimize for more explanation.

Note

The spin/cg and spin/lbfgs styles can be used for magnetic NEB calculations only if the line search procedure is deactivated. See neb/spin for more explanation.

## Restrictions¶

This minimization procedure is only applied to spin degrees of freedom for a frozen lattice configuration.

## Default¶

The option defaults are alpha_damp = 1.0, discrete_factor = 10.0, line = spin_none and norm = euclidean.

(Ivanov) Ivanov, Uzdin, Jonsson. arXiv preprint arXiv:1904.02669, (2019).