Terminologies related to Multiferroics

Ferromagnets:
A ferromagnetic material is one that undergoes a phase transition from a high-temperature phase that does not have a macroscopic magnetic moment to a low-temperature phase that has a spontaneous magnetization even in the absence of an
applied magnetic field.

ferromanetic:
--> -->
--> -->

ferrimagnetic:

-> ->
<-- <--  

antiferromagnetic:
--> -->
<-- <-- 

Ferroelectric:
Ferroelectric materials is one that undergoes phase transition from a high-temperature phase that behaves as an ordinary dielectric (so that an applied electric filed induces an electric polarization, which goes to zero when the field is removed) to a low-termperature phase with a spontaneous electric polarization whose direction can be switched by an applied field.

d₃₃, charged constant:
One can use either the direct piezoelectric effect, i.e., applying a stress and measuring the induced charge (or voltage), or use the inverse piezoelectric effect, i.e., applying a voltage (field) and measuring the induced strain.
d₃₃=(∂S₃/∂E₃)_T
Or
d₃₃=(∂D₃/∂T₃)_E
S:strain
E:electric field
D: electric displacement
T: stress
x₃ axis is the poling direction. For thin film, usually it is the normal direction to the surface.

Tensors:
piezoelectric constatnt: third-rank tensor
electrostrictive constant and elastic constant: fourth-rank tensors.
Tensor notation/matrix notation: 11/1, 22/2, 33/3, 23(32)/4, 31(13)/5, 12(21)/6