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MPG 2'm'm

Properties:

Mz, Rx⨂T, My⨂T

1D Identification

  • P(x)
  • P'(y)
  • A'(z)

Odd-Order Property

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

Longitudinal Property

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

Full Rank Property

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