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MPG 1

Properties:

1D Identification

  • P(x)
  • P(y)
  • P(z)
  • P'(x)
  • P'(y)
  • P'(z)
  • A(x)
  • A(y)
  • A(z)
  • A'(x)
  • A'(y)
  • A'(z)
  • C(x)
  • C(y)
  • C(z)
  • C'(x)
  • C'(y)
  • C'(z)
  • D'(x)
  • D'(y)
  • D'(z)

Odd-Order Property

Applied M1 Checked Description M2
E(x) ►
V(y)Transverse (Hall-type) voltage
V(z)
E(xy)
E(yx)
k(y)Anomalous Hall effect
k(z)
k(xy)
k(yx)
A(y)Transverse E-induced ferro-rotational vector
A(z)
A(xy)
A(yx)
M(y)
M(z)Transverse magnetoelectric effect
M(xy)
M(yx)
E(y) ►
V(x)
V(z)
E(xy)
E(yx)
k(x)
k(z)
k(xy)
k(yx)
A(x)
A(z)
A(xy)
A(yx)
M(x)
M(z)
M(xy)
M(yx)
E(z) ►
V(x)
V(y)
E(xy)
E(yx)
k(x)
k(y)
k(xy)
k(yx)
A(x)
A(y)
A(xy)
A(yx)
M(x)
M(y)
M(xy)
M(yx)
E(xy) ►
V(x)
V(y)
V(z)
E(yx)
k(x)
k(y)
k(z)
k(yx)
A(x)
A(y)
A(z)
A(yx)
M(x)
M(y)
M(z)
M(yx)
E(yx) ►
V(x)
V(y)
V(z)
E(xy)
k(x)
k(y)
k(z)
k(xy)
A(x)
A(y)
A(z)
A(xy)
M(x)
M(y)
M(z)
M(xy)
k(x) ►
V(y)Anomalous Hall effect
V(z)
E(xy)
E(yx)
k(y)Anisotropic conductivity.
k(z)
k(xy)
k(yx)
A(y)Transverse current-induced ferro-rotational vector
A(z)
A(xy)
A(yx)
M(y)
M(z)Transverse current-induced M, Transverse Edelstein effect
M(xy)
M(yx)
k(y) ►
V(x)
V(z)
E(xy)
E(yx)
k(x)
k(z)
k(xy)
k(yx)
A(x)
A(z)
A(xy)
A(yx)
M(x)
M(z)
M(xy)
M(yx)
k(z) ►
V(x)
V(y)
E(xy)
E(yx)
k(x)
k(y)
k(xy)
k(yx)
A(x)
A(y)
A(xy)
A(yx)
M(x)
M(y)
M(xy)
M(yx)
k(xy) ►
V(x)
V(y)
V(z)
E(yx)
k(x)
k(y)
k(z)
k(yx)
A(x)
A(y)
A(z)
A(yx)
M(x)
M(y)
M(z)
M(yx)
k(yx) ►
V(x)
V(y)
V(z)
E(xy)
k(x)
k(y)
k(z)
k(xy)
A(x)
A(y)
A(z)
A(xy)
M(x)
M(y)
M(z)
M(xy)
A(x) ►
V(y)
V(z)
E(xy)
E(yx)
k(y)
k(z)Shear-stress induced toroidicity (nonreciprocity) (piezotoroidic tensor)
k(xy)
k(yx)
A(y)Shear-stress induced ferro-rotational vector
A(z)
A(xy)
A(yx)
M(y)
M(z)Shear-stress induced M (piezomagnetic tensor)
M(xy)
M(yx)
A(y) ►
V(x)
V(z)
E(xy)
E(yx)
k(x)
k(z)
k(xy)
k(yx)
A(x)
A(z)
A(xy)
A(yx)
M(x)
M(z)
M(xy)
M(yx)
A(z) ►
V(x)
V(y)
E(xy)
E(yx)
k(x)
k(y)
k(xy)
k(yx)
A(x)
A(y)
A(xy)
A(yx)
M(x)
M(y)
M(xy)
M(yx)
A(xy) ►
V(x)
V(y)
V(z)
E(yx)
k(x)
k(y)
k(z)
k(yx)
A(x)
A(y)
A(z)
A(yx)
M(x)
M(y)
M(z)
M(yx)
A(yx) ►
V(x)
V(y)
V(z)
E(xy)
k(x)
k(y)
k(z)
k(xy)
A(x)
A(y)
A(z)
A(xy)
M(x)
M(y)
M(z)
M(xy)
H(x) ►
V(y)
V(z)
E(xy)
E(yx)
k(y)
k(z)Transverse magnetotoroidicity (magnetotoroidicity tensor)
k(xy)
k(yx)
A(y)Transverse H-induced ferro-rotational vector
A(z)
A(xy)
A(yx)
M(y)Transverse magnetic susceptibility
M(z)
M(xy)
M(yx)
H(y) ►
V(x)
V(z)
E(xy)
E(yx)
k(x)
k(z)
k(xy)
k(yx)
A(x)
A(z)
A(xy)
A(yx)
M(x)
M(z)
M(xy)
M(yx)
H(z) ►
V(x)
V(y)
E(xy)
E(yx)
k(x)
k(y)
k(xy)
k(yx)
A(x)
A(y)
A(xy)
A(yx)
M(x)
M(y)
M(xy)
M(yx)
H(xy) ►
V(x)
V(y)
V(z)
E(yx)
k(x)
k(y)
k(z)
k(yx)
A(x)
A(y)
A(z)
A(yx)
M(x)
M(y)
M(z)
M(yx)
H(yx) ►
V(x)
V(y)
V(z)
E(xy)
k(x)
k(y)
k(z)
k(xy)
A(x)
A(y)
A(z)
A(xy)
M(x)
M(y)
M(z)
M(xy)
C(x) ►
V(y)
V(z)
E(xy)
E(yx)
k(y)
k(z)Chiral light or torsional strain induced toroidicity
k(xy)
k(yx)
A(y)
A(z)
A(xy)
A(yx)
M(y)Chiral light or torsional strain induced M, inverse Faraday effect
M(z)
M(xy)
M(yx)
C(y) ►
V(x)
V(z)
E(xy)
E(yx)
k(x)
k(z)
k(xy)
k(yx)
A(x)
A(z)
A(xy)
A(yx)
M(x)
M(z)
M(xy)
M(yx)
C(z) ►
V(x)
V(y)
E(xy)
E(yx)
k(x)
k(y)
k(xy)
k(yx)
A(x)
A(y)
A(xy)
A(yx)
M(x)
M(y)
M(xy)
M(yx)
C(xy) ►
V(x)
V(y)
V(z)
E(yx)
k(x)
k(y)
k(z)
k(yx)
A(x)
A(y)
A(z)
A(yx)
M(x)
M(y)
M(z)
M(yx)
C(yx) ►
V(x)
V(y)
V(z)
E(xy)
k(x)
k(y)
k(z)
k(xy)
A(x)
A(y)
A(z)
A(xy)
M(x)
M(y)
M(z)
M(xy)
C'(x) ►
V(y)
V(z)
E(xy)
E(yx)
k(y)
k(z)
k(xy)
k(yx)
A(y)
A(z)
A(xy)
A(yx)
M(y)
M(z)
M(xy)
M(yx)
C'(y) ►
V(x)
V(z)
E(xy)
E(yx)
k(x)
k(z)
k(xy)
k(yx)
A(x)
A(z)
A(xy)
A(yx)
M(x)
M(z)
M(xy)
M(yx)
C'(z) ►
V(x)
V(y)
E(xy)
E(yx)
k(x)
k(y)
k(xy)
k(yx)
A(x)
A(y)
A(xy)
A(yx)
M(x)
M(y)
M(xy)
M(yx)
C'(xy) ►
V(x)
V(y)
V(z)
E(yx)
k(x)
k(y)
k(z)
k(yx)
A(x)
A(y)
A(z)
A(yx)
M(x)
M(y)
M(z)
M(yx)
C'(yx) ►
V(x)
V(y)
V(z)
E(xy)
k(x)
k(y)
k(z)
k(xy)
A(x)
A(y)
A(z)
A(xy)
M(x)
M(y)
M(z)
M(xy)
D'(x) ►
V(y)
V(z)
E(xy)
E(yx)
k(y)
k(z)
k(xy)
k(yx)
A(y)
A(z)
A(xy)
A(yx)
M(y)
M(z)
M(xy)
M(yx)
D'(y) ►
V(x)
V(z)
E(xy)
E(yx)
k(x)
k(z)
k(xy)
k(yx)
A(x)
A(z)
A(xy)
A(yx)
M(x)
M(z)
M(xy)
M(yx)
D'(z) ►
V(x)
V(y)
E(xy)
E(yx)
k(x)
k(y)
k(xy)
k(yx)
A(x)
A(y)
A(xy)
A(yx)
M(x)
M(y)
M(xy)
M(yx)
D'(xy) ►
V(x)
V(y)
V(z)
E(yx)
k(x)
k(y)
k(z)
k(yx)
A(x)
A(y)
A(z)
A(yx)
M(x)
M(y)
M(z)
M(yx)
D'(yx) ►
V(x)
V(y)
V(z)
E(xy)
k(x)
k(y)
k(z)
k(xy)
A(x)
A(y)
A(z)
A(xy)
M(x)
M(y)
M(z)
M(xy)

Longitudinal Property

Primary Secondary
P(x)P'(x), A(x), A'(x), C(x), C'(x), D'(x)
P(y)P'(y), A(y), A'(y), C(y), C'(y), D'(y)
P(z)P'(z), A(z), A'(z), C(z), C'(z), D'(z)
P'(x)A(x), A'(x), C(x), C'(x), D'(x)
P'(y)A(y), A'(y), C(y), C'(y), D'(y)
P'(z)A(z), A'(z), C(z), C'(z), D'(z)
A(x)A'(x), C(x), C'(x), D'(x)
A(y)A'(y), C(y), C'(y), D'(y)
A(z)A'(z), C(z), C'(z), D'(z)
A'(x)C(x), C'(x), D'(x)
A'(y)C(y), C'(y), D'(y)
A'(z)C(z), C'(z), D'(z)
C(x)C'(x), D'(x)
C(y)C'(y), D'(y)
C(z)C'(z), D'(z)
C'(x)D'(x)
C'(y)D'(y)
C'(z)D'(z)

Full Rank Property

Initial Subtracted
P(x)P'(x), A(x), A'(x), C(x), C'(x), D'(x)
P'(x)P(x), A(x), A'(x), C(x), C'(x), D'(x)
A(x)P(x), P'(x), A'(x), C(x), C'(x), D'(x)
A'(x)P(x), P'(x), A(x), C(x), C'(x), D'(x)
C(x)P(x), P'(x), A(x), A'(x), C'(x), D'(x)
C'(x)P(x), P'(x), A(x), A'(x), C(x), D'(x)
D'(x)P(x), P'(x), A(x), A'(x), C(x), C'(x)
P(y)P'(y), A(y), A'(y), C(y), C'(y), D'(y)
P'(y)P(y), A(y), A'(y), C(y), C'(y), D'(y)
A(y)P(y), P'(y), A'(y), C(y), C'(y), D'(y)
A'(y)P(y), P'(y), A(y), C(y), C'(y), D'(y)
C(y)P(y), P'(y), A(y), A'(y), C'(y), D'(y)
C'(y)P(y), P'(y), A(y), A'(y), C(y), D'(y)
D'(y)P(y), P'(y), A(y), A'(y), C(y), C'(y)
P(z)P'(z), A(z), A'(z), C(z), C'(z), D'(z)
P'(z)P(z), A(z), A'(z), C(z), C'(z), D'(z)
A(z)P(z), P'(z), A'(z), C(z), C'(z), D'(z)
A'(z)P(z), P'(z), A(z), C(z), C'(z), D'(z)
C(z)P(z), P'(z), A(z), A'(z), C'(z), D'(z)
C'(z)P(z), P'(z), A(z), A'(z), C(z), D'(z)
D'(z)P(z), P'(z), A(z), A'(z), C(z), C'(z)