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MPG 4'

Properties:

Rz, C4z⨂T

1D Identification

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

Odd-Order Property

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

Longitudinal Property

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