AFMSingleIonCubicSixthAnisotropySC

Calculates a residual contribution for the magnetic anisotropy energy.

Overview

Consider the following sixth-order free energy contribution,

where is the normalized sublattice magnetization. The vector is the oxygen octahedral antiphase tilt vector (for the material). The suffix SC in this Kernel stands for strong-coupling where we treat as a MOOSE Variable. Therefore, we will need to compute additional off-diagonal jacobian entries. The effective field due to this term is,

The effective field is evaluated at every time step of the two sublattice LLG-LLB equation,

(1)

here is the electron gyromagnetic factor and the phenomenological Gilbert damping parameter. Ignoring the time derivative, moving over the RHS to the LHS, and multiplying by a test function , we have

Substituting the expression for and writing the above in index notation gives the residual contribution for the component,

The on- and off-diagonal jacobian entries are given by,

where is the shape function of the finite element method and if , we have the on-diagonal contributions and if we have the off-diagonal contributions. Note that also, since does not have cross-coupling between the sublattices (as is the case of other Kernels such as AFMHomogeneousSublatticeExchange), then further off-diagonal components () where are zeroed. As mentioned above, we have the SC suffix on this Kernel which means we are treating as a MOOSE Variable. Therefore, we have to compute

where only is nonzero.

Example Input File Syntax

Input Parameters

  • componentAn integer corresponding to the direction in order parameter space this kernel acts in (e.g. for unrotated functionals 0 for q_x, 1 for q_y, 2 for q_z).

    C++ Type:unsigned int

    Controllable:No

    Description:An integer corresponding to the direction in order parameter space this kernel acts in (e.g. for unrotated functionals 0 for q_x, 1 for q_y, 2 for q_z).

  • mag1_xThe x component of the constrained 1st sublattice magnetization vector

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The x component of the constrained 1st sublattice magnetization vector

  • mag1_yThe y component of the constrained 1st sublattice magnetization vector

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The y component of the constrained 1st sublattice magnetization vector

  • mag1_zThe z component of the constrained 1st sublattice magnetization vector

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The z component of the constrained 1st sublattice magnetization vector

  • mag_subAn integer corresponding to the sublattice this Kernel acts on

    C++ Type:unsigned int

    Controllable:No

    Description:An integer corresponding to the sublattice this Kernel acts on

  • variableThe name of the variable that this residual object operates on

    C++ Type:NonlinearVariableName

    Controllable:No

    Description:The name of the variable that this residual object operates on

Required Parameters

  • antiphase_A_xThe x component of the antiphase tilt vector

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The x component of the antiphase tilt vector

  • antiphase_A_yThe y component of the antiphase tilt vector

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The y component of the antiphase tilt vector

  • antiphase_A_zThe z component of the antiphase tilt vector

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The z component of the antiphase tilt vector

  • blockThe list of blocks (ids or names) that this object will be applied

    C++ Type:std::vector<SubdomainName>

    Controllable:No

    Description:The list of blocks (ids or names) that this object will be applied

  • displacementsThe displacements

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The displacements

  • mag2_xThe x component of the constrained 2nd sublattice magnetization vector

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The x component of the constrained 2nd sublattice magnetization vector

  • mag2_yThe y component of the constrained 2nd sublattice magnetization vector

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The y component of the constrained 2nd sublattice magnetization vector

  • mag2_zThe z component of the constrained 2nd sublattice magnetization vector

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The z component of the constrained 2nd sublattice magnetization vector

  • prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

Optional Parameters

  • absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution

    C++ Type:std::vector<TagName>

    Controllable:No

    Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution

  • extra_matrix_tagsThe extra tags for the matrices this Kernel should fill

    C++ Type:std::vector<TagName>

    Controllable:No

    Description:The extra tags for the matrices this Kernel should fill

  • extra_vector_tagsThe extra tags for the vectors this Kernel should fill

    C++ Type:std::vector<TagName>

    Controllable:No

    Description:The extra tags for the vectors this Kernel should fill

  • matrix_tagssystemThe tag for the matrices this Kernel should fill

    Default:system

    C++ Type:MultiMooseEnum

    Options:nontime, system

    Controllable:No

    Description:The tag for the matrices this Kernel should fill

  • vector_tagsnontimeThe tag for the vectors this Kernel should fill

    Default:nontime

    C++ Type:MultiMooseEnum

    Options:nontime, time

    Controllable:No

    Description:The tag for the vectors this Kernel should fill

Tagging Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

    C++ Type:std::vector<AuxVariableName>

    Controllable:No

    Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

  • implicitTrueDetermines whether this object is calculated using an implicit or explicit form

    Default:True

    C++ Type:bool

    Controllable:No

    Description:Determines whether this object is calculated using an implicit or explicit form

  • save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

    C++ Type:std::vector<AuxVariableName>

    Controllable:No

    Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Controllable:No

    Description:The seed for the master random number generator

  • use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

Input Files