def cubic_anisotropy(m, c1, c2, c3, Kc1, Kc2, Kc3):
""" Returns the cubic anisotropy part of the free energy in erg/cc
m: Reduced magnetization M/Ms (unit vector)
c1: In-plane orthogonal crystal direction 1 (unit vector)
c2: In-plane orthogonal crystal direction 2 (unit vector)
c3: In-plane orthogonal crystal direction 3 (unit vector)
Kc1: Cubic anisotropy energy 1 (erg/cc)
Kc2: Cubic anisotropy energy 2 (erg/cc)
Kc2: Cubic anisotropy energy 3 (erg/cc)
"""
if dot(c1, c2) != 0:
raise Exception("Crystal directions c1 and c2 must be orthogonal")
mc1 = dot(c1, m)
mc2 = dot(c2, m)
mc3 = dot(c3, m)
# First order term
Fc = Kc1 * ((mc1**2) * (mc2**2))
Fc += Kc1 * ((mc2**2) * (mc3**2))
Fc += Kc1 * ((mc1**2) * (mc3**2))
# Second order term
Fc += Kc2 * ((mc1**2) * (mc2**2) * (mc3**2))
# Third order term
Fc += Kc3 * ((mc1**4) * (mc2**4))
Fc += Kc3 * ((mc2**4) * (mc3**4))
Fc += Kc3 * ((mc1**4) * (mc3**4))
return Fc
def uniaxial_anisotropy(m, u, Ku1, Ku2):
""" Returns the uniaxial anisotropy part of the free energy in erg/cc
m: Reduced magnetization M/Ms (unit vector)
u: Uniaxial direction (unit vector)
Ku1: Uniaxial anisotropy energy 1 (erg/cc)
Ku2: Uniaxial anisotropy energy 2 (erg/cc)
"""
return -Ku1 * (dot(u, m)**2) - Ku2 * (dot(u, m)**4)
def zeeman(m, Ms, H):
""" Returns the Zeeman energy in erg/cc
m: Reduced magnetization M/Ms (unit vector)
Ms: Satuation magnetization (emu/cc)
H: Applied magnetic field (Oe)
"""
return Ms * dot(m, H)
def cubic_anisotropy(m, c1, c2, c3, hc1, hc2):
""" Returns the cubic anisotropy field
m: moment unit vector
c1, c2, c3: orthogonal cubic axis unit vectors
hc1: normalized cubic anisotropy field (1st order)
hc2: normalized cubic anisotropy field (2nd order)
"""
m_c1 = dot(m, c1)
m_c2 = dot(m, c2)
m_c3 = dot(m, c3)
h = hc1 * (m_c2 * m_c2 + m_c3 * m_c3) * (m_c1 * c1)
h += hc1 * (m_c1 * m_c1 + m_c3 * m_c3) * (m_c2 * c2)
h += hc1 * (m_c1 * m_c1 + m_c2 * m_c2) * (m_c3 * c3)
h += hc2 * (m_c2 * m_c2 * m_c3 * m_c3) * (m_c1 * c1)
h += hc2 * (m_c1 * m_c1 * m_c3 * m_c3) * (m_c2 * c2)
h += hc2 * (m_c1 * m_c1 * m_c2 * m_c2) * (m_c3 * c3)
return h
def uniaxial_anisotropy(m, u, hu1, hu2):
""" Returns the uniaxial anisotropy field
m: moment unit vector
u: uniaxial anisotropy unit vector
hu1: normalized uniaxial anisotropy field (1st order)
hu2: normalized uniaxial anisotropy field (2nd order)
"""
m_u = dot(m, u)
return u * (m_u * hu1) + u * (m_u * m_u * m_u * hu2)
def shape_anisotropy(m, Ms, Nxx, Nyy, Nzz):
""" Returns the shape anisotropy part of the free energy in erg/cc.
Assumes the demagnetization only requires diagonal elements of the
demagnetziation
m: Reduced magnetization M/Ms (unit vector)
Ms: Saturation magnetization (emu/cc)
Nxx: Demagnetization component along xx
Nyy: Demagnetization component along yy
Nzz: Demagnetization component along zz
Nxx + Nyy + Nzz = 4 pi
"""
return dot([Nxx, Nyy, Nzz], m) * (Ms**2)