Struct RandomAnisotropyModel 

pub struct RandomAnisotropyModel {
    pub num_grains: usize,
    pub grain_size: f64,
    pub bulk_anisotropy: f64,
    pub exchange_stiffness: f64,
    pub grain_axes: Vec<Vector3<f64>>,
    pub effective_anisotropy: f64,
}

Random anisotropy model (RAM) following the Herzer scaling theory.

In nanocrystalline materials the effective anisotropy is averaged over the exchange-correlated volume, leading to:

K_eff = K₁ / √N

where N = (L_ex / D)³ is the number of grains within the exchange length and L_ex = √(A / K₁) is the ferromagnetic exchange length.

Example

use spintronics::material::disorder::RandomAnisotropyModel;

let ram = RandomAnisotropyModel::new(
    100,     // 100 grains
    10.0e-9, // 10 nm grain size
    1.0e4,   // K₁ = 10 kJ/m³
    1.0e-11, // A = 10 pJ/m
    42,      // seed
).expect("valid parameters");

assert!(ram.effective_anisotropy < ram.bulk_anisotropy);

Fields

num_grains: usize

Number of grains in the model.

grain_size: f64

Average grain diameter [m].

bulk_anisotropy: f64

Bulk magnetocrystalline anisotropy constant K₁ [J/m³].

exchange_stiffness: f64

Exchange stiffness constant A [J/m].

grain_axes: Vec<Vector3<f64>>

Random easy axis direction for each grain (unit vectors).

effective_anisotropy: f64

Effective anisotropy K_eff from Herzer averaging [J/m³].

Implementations

impl RandomAnisotropyModel

pub fn new( num_grains: usize, grain_size: f64, bulk_anisotropy: f64, exchange_stiffness: f64, seed: u64, ) -> Result<Self>

Create a new random anisotropy model.

Arguments

• num_grains - Number of grains (must be > 0)
• grain_size - Average grain diameter D [m] (must be > 0)
• bulk_anisotropy - K₁ [J/m³] (must be > 0)
• exchange_stiffness - A [J/m] (must be > 0)
• seed - PRNG seed for reproducibility

Errors

Returns Error::InvalidParameter if any physical parameter is non-positive.

pub fn exchange_length(&self) -> f64

Compute the ferromagnetic exchange length L_ex = √(A / K₁) [m].

pub fn grains_in_exchange_volume(&self) -> f64

Number of grains within one exchange volume: N = (L_ex / D)³.

pub fn herzer_scaling_ratio(&self) -> f64

Herzer scaling exponent check: K_eff should scale as K₁⁴ D⁶ / A³.

Returns the ratio K_eff / (K₁⁴ D⁶ / A³) which should be of order unity in the regime where D << L_ex.

Trait Implementations

impl Clone for RandomAnisotropyModel

fn clone(&self) -> RandomAnisotropyModel

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for RandomAnisotropyModel

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.