`ensemble` (SIB)

The semi-implicit B (SIB) integrator propagates the direction of each spin:R:3 vector with the stochastic Landau–Lifshitz–Gilbert equation. It preserves each vector’s initial magnitude and uses the public mforce:R:3 from a Spin potential as \(\boldsymbol H=-\partial E/\partial\boldsymbol S\).

Syntax

For spin-only dynamics with a fixed lattice, use:

ensemble nve_sib [alpha <value>] [gamma <value>] \
         [stemp <-1|value>] [seed <value>]

For fixed-cell dynamics, use:

ensemble nvt_sib <T_1> <T_2> <T_coup> \
         [lattice on|off] [alpha <value>] \
         [gamma <value>] [stemp <-1|0|value>] [seed <value>]

For pressure-controlled dynamics, use:

ensemble npt_sib temp <T_1> <T_2> <pressure_terms> \
         [tperiod <tau_temp>] [pperiod <tau_press>] \
         [alpha <value>] [gamma <value>] \
         [stemp <-1|0|value>] [seed <value>]

The MTTK portion of npt_sib has the same syntax as npt_mttk. SIB options must follow all MTTK options.

Examples

Propagate spins deterministically while keeping the lattice fixed:

ensemble nve_sib alpha 0.1 stemp -1 seed 12345

Propagate only spins at 300 K:

ensemble nvt_sib 300 300 100 lattice off alpha 0.1 seed 12345

Run coupled spin–lattice dynamics with the physical default gyromagnetic ratio:

ensemble nvt_sib 300 300 100 lattice on alpha 0.1

Run isotropic pressure-controlled spin–lattice dynamics:

ensemble npt_sib temp 300 300 iso 0 0 \
         tperiod 100 pperiod 1000 alpha 0.1 seed 12345

Parameters

T_1, T_2

Initial and final temperatures in K. SIB uses the linearly ramped target temperature for its thermal magnetic noise. With lattice dynamics enabled, the same target also controls the lattice thermostat.

T_coup

Nose–Hoover-chain coupling period in timesteps for the lattice. It remains required by nvt_sib when lattice off but then does not alter the spin equation.

lattice on|off

Available only for nvt_sib and defaults to on. off keeps atomic positions and velocities fixed while evaluating the Spin potential twice per timestep for the SIB midpoint and endpoint fields.

alpha <value>

Dimensionless Gilbert damping coefficient. It must be finite and non-negative. The default is 0; thermal noise is then also zero.

gamma <value>

Positive gyromagnetic factor \(\gamma/\hbar\) in \((\mathrm{eV\,ps})^{-1}\). The default is \(2/\hbar=3038.53\ (\mathrm{eV\,ps})^{-1}\) in GPUMD’s unit system.

stemp <-1|0|value>

Controls the thermal magnetic noise. -1 disables it while retaining deterministic damping, 0 follows the ensemble target temperature, and a positive value fixes the spin-noise temperature in K. The default is 0.

For nve_sib, the default is -1 because there is no lattice target temperature. A fixed positive spin temperature is accepted, while 0 is rejected. nve_sib always keeps lattice positions and velocities fixed, matching the DynSpin SIB/NVE separation between spin and lattice dynamics.

seed <value>

Positive integer for counter-based Gaussian noise. The default is 12345. A given atom, timestep, and seed always receive the same noise.

Algorithm

For a unit direction \(\boldsymbol e_n\), SIB forms

\[\boldsymbol\Omega = \frac{\gamma\Delta t}{1+\alpha^2} [\boldsymbol H+\alpha(\boldsymbol e\times\boldsymbol H)] +\boldsymbol\Omega_\mathrm{th}.\]

The predictor endpoint is an analytic Cayley rotation of \(\boldsymbol e_n\). GPUMD evaluates the second Spin-potential field at the unnormalized arithmetic chord midpoint \((\boldsymbol e_n+\boldsymbol e_\mathrm{pred})/2\), reuses the same thermal increment, and applies the corrected Cayley rotation from the original direction. A final force evaluation caches the endpoint energy, force, virial, and magnetic force for output and the next timestep. Thus SIB uses two Spin-potential evaluations per timestep after the initial force.

The angular-noise standard deviation for a spin magnitude \(\mu_s\) follows from matching its variance to the damping mobility \(\gamma\alpha/(1+\alpha^2)\) (fluctuation–dissipation):

\[\sigma_\Omega = \sqrt{\frac{2\alpha\gamma k_B T\Delta t}{\mu_s(1+\alpha^2)}}.\]

Restrictions

SIB requires one Spin potential, spin:R:3 on every atom, a positive timestep, positive target temperatures, alpha >= 0, gamma > 0, and a positive seed. Target temperatures are only required by the NVT/NPT forms. A zero spin vector remains zero. nve_sib always fixes the lattice and does not accept lattice; npt_sib always includes lattice and cell dynamics and therefore does not accept lattice off. SIB propagates nonzero moments of elements listed in spin_type. Moments of other elements are masked to zero, receive no magnetic noise, and remain zero. The initial magnitude of each active moment is conserved.

For variable-magnitude dynamics use the independent GLSD ensembles. SIB does not accept lsf, damping or mobility; its fixed-magnitude equation and Cayley integration are unchanged.

ensemble (SIB)