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MPG 2'y

Properties:

Ry⨂T

1D Identification

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

Odd-Order Property

Applied M1 Checked Description M2
E(x) ►
V(z)
k(y)Anomalous Hall effect
A(z)
M(y)
E(y) ►
E(xy)
E(yx)
k(x)
k(z)
k(xy)
k(yx)
A(xy)
A(yx)
M(x)
M(z)
M(xy)
M(yx)
E(z) ►
V(x)
k(y)
A(x)
M(y)
E(xy) ►
V(y)
E(yx)
k(x)
k(z)
k(yx)
A(y)
A(yx)
M(x)
M(z)
M(yx)
E(yx) ►
V(y)
E(xy)
k(x)
k(z)
k(xy)
A(y)
A(xy)
M(x)
M(z)
M(xy)
k(x) ►
V(y)Anomalous Hall effect
E(xy)
E(yx)
k(z)
k(xy)
k(yx)
A(y)Transverse current-induced ferro-rotational vector
A(xy)
A(yx)
M(z)Transverse current-induced M, Transverse Edelstein effect
M(xy)
M(yx)
k(y) ►
V(x)
V(z)
A(x)
A(z)
k(z) ►
V(y)
E(xy)
E(yx)
k(x)
k(xy)
k(yx)
A(y)
A(xy)
A(yx)
M(x)
M(xy)
M(yx)
k(xy) ►
V(y)
E(yx)
k(x)
k(z)
k(yx)
A(y)
A(yx)
M(x)
M(z)
M(yx)
k(yx) ►
V(y)
E(xy)
k(x)
k(z)
k(xy)
A(y)
A(xy)
M(x)
M(z)
M(xy)
A(x) ►
V(z)
k(y)
A(z)
M(y)
A(y) ►
E(xy)
E(yx)
k(x)
k(z)
k(xy)
k(yx)
A(xy)
A(yx)
M(x)
M(z)
M(xy)
M(yx)
A(z) ►
V(x)
k(y)
A(x)
M(y)
A(xy) ►
V(y)
E(yx)
k(x)
k(z)
k(yx)
A(y)
A(yx)
M(x)
M(z)
M(yx)
A(yx) ►
V(y)
E(xy)
k(x)
k(z)
k(xy)
A(y)
A(xy)
M(x)
M(z)
M(xy)
H(x) ►
V(y)
E(xy)
E(yx)
k(z)Transverse magnetotoroidicity (magnetotoroidicity tensor)
k(xy)
k(yx)
A(y)Transverse H-induced ferro-rotational vector
A(xy)
A(yx)
M(z)
M(xy)
M(yx)
H(y) ►
V(x)
V(z)
A(x)
A(z)
H(z) ►
V(y)
E(xy)
E(yx)
k(x)
k(xy)
k(yx)
A(y)
A(xy)
A(yx)
M(x)
M(xy)
M(yx)
H(xy) ►
V(y)
E(yx)
k(x)
k(z)
k(yx)
A(y)
A(yx)
M(x)
M(z)
M(yx)
H(yx) ►
V(y)
E(xy)
k(x)
k(z)
k(xy)
A(y)
A(xy)
M(x)
M(z)
M(xy)
C(x) ►
V(y)
E(xy)
E(yx)
k(z)Chiral light or torsional strain induced toroidicity
k(xy)
k(yx)
A(y)
A(xy)
A(yx)
M(z)
M(xy)
M(yx)
C(y) ►
E(xy)
E(yx)
k(x)
k(z)
k(xy)
k(yx)
A(xy)
A(yx)
M(x)
M(z)
M(xy)
M(yx)
C(z) ►
V(y)
E(xy)
E(yx)
k(x)
k(xy)
k(yx)
A(y)
A(xy)
A(yx)
M(x)
M(xy)
M(yx)
C(xy) ►
V(y)
E(yx)
k(x)
k(z)
k(yx)
A(y)
A(yx)
M(x)
M(z)
M(yx)
C(yx) ►
V(y)
E(xy)
k(x)
k(z)
k(xy)
A(y)
A(xy)
M(x)
M(z)
M(xy)
C'(x) ►
V(z)
k(y)
A(z)
M(y)
C'(y) ►
V(x)
V(z)
A(x)
A(z)
C'(z) ►
V(x)
k(y)
A(x)
M(y)
C'(xy) ►
V(y)
E(yx)
k(x)
k(z)
k(yx)
A(y)
A(yx)
M(x)
M(z)
M(yx)
C'(yx) ►
V(y)
E(xy)
k(x)
k(z)
k(xy)
A(y)
A(xy)
M(x)
M(z)
M(xy)
D'(x) ►
V(z)
k(y)
A(z)
M(y)
D'(y) ►
V(x)
V(z)
A(x)
A(z)
D'(z) ►
V(x)
k(y)
A(x)
M(y)
D'(xy) ►
V(y)
E(yx)
k(x)
k(z)
k(yx)
A(y)
A(yx)
M(x)
M(z)
M(yx)
D'(yx) ►
V(y)
E(xy)
k(x)
k(z)
k(xy)
A(y)
A(xy)
M(x)
M(z)
M(xy)

Longitudinal Property

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

Full Rank Property

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