Introduce Magnetodynamics with thermal Stoner-Wohlfarth

[stekajack]

Magnetodynamics Overview

Magnetodynamics refers to the ability to evolve the degrees of freedom of a dipole moment using a defined set of rules (a model), such that magnetic relaxation is not strictly tied to the Brownian relaxation of a particle.

There are three relevant internal relaxation mechanisms for magnetic nanoparticles (on timescales typically interesting for MD simulations):

• Brownian relaxation ($\tau_B$)
• Néel relaxation ($\tau_N$)
• Rotational diffusion of the dipole moment ($\tau_D$)

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Thermal Stoner–Wohlfarth Model

The thermal Stoner–Wohlfarth (SW) model provides a state-of-the-art, scalable method for including Néel relaxation in simulations of single-domain magnetic nanoparticles.

Broadly speaking, the model:

1. Finds the critical points of the magnetic energy of a Stoner–Wohlfarth particle.
2. Based on the relative orientation of the local magnetic field and the particle’s director, determines the correct orientation for the dipole moment.
3. Computes the probability of the dipole moment flipping its orientation with respect to the easy axis (i.e. Néel relaxation), derived from the energy barrier between critical points.
4. Executes a kinetic Monte Carlo move according to that probability.

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Implementation Details

The feature is implemented under the compile-time flag:
THERMAL_STONER_WOHLFARTH

If enabled, the following particle properties become available:

/** Flag indicating if the particle is real and its director should be used */
bool sw_real = false;

/** Flag indicating if the particle is virtual and its dipole moment should be evolved */
bool sw_virt = false;

/** Angle between the director and dipole moment of a SW particle */
double phi0 = 0.0;

/** Saturation magnetization of the particle */
double sat_mag = 0.0;

/** 
 * Hk = 2 * K1 / (mu0 * Ms)
 *  -> anisotropy field [A/m], where K1 is the magnetic anisotropy constant [kg/(m·s²)].
 * On the particle, we store the inverse of Hk (Hkinv) in reduced units.
 */
double Hkinv = 0.0;

/** Energy units parameter for the kinetic MC step */
double kT_KVm_inv = 0.0;

/** Time units parameters for the kinetic MC step */
double tau0_inv = 0.0;
double tau_trans_inv = 0.0;

/** Time between kinetic MC steps */
double dt_incr = 0.0;

References
• Publication: Phys. Rev. B 111, 014438 (2025)
• Optimization Library: NLopt (used to find critical points in magnetic energy)

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Notes

This method relies on the DIPOLE_FIELD_TRACKING feature of ESPResSo to correctly incorporate dipole interactions.
For interacting systems, it should only be used with magnetostatic actors that support this feature.

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Tasks:

• replace marsenne-twister with philox
  • NOTE: now using rng state from thermostat
• replace sw_real/sw_virtual flags with single enable_magnetodynamics=true on virtual
• group magnetodynamics particle params in a typed enum magnetodynamics (similar to swimmers)
• enable access to RNG seed via script interface
  • NOTE: seed and step are taken directly from thermostat, so no need for extra interface
• sw_main refactor:
  • for_each loop over virtual particles
  • separate external field summation
  • separate main into smaler clearer steps
• improve docstrings:
  • write out SW abbreviations
  • annotate equation numbers from reference paper in code
  • docstrings for minimization helpers

[RudolfWeeber]

Thank you Deniz! @jngrad from my side, this PR is ready. Can you please take over for the merge?

[jngrad]

Overall, looks good to me and can go in the 5.0 release. I'll try to sort out the NLopt installation step as soon as possible.