MPG 11

Properties:

I

1D Identification

A(x)
A(y)
A(z)
A'(x)
A'(y)
A'(z)
D'(x)
D'(y)
D'(z)

Odd-Order Property

Applied	M1	Checked
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)
E(y) ►
	V(x)
	V(z)
	E(xy)
	E(yx)
	k(x)
	k(z)
	k(xy)
	k(yx)
E(z) ►
	V(x)
	V(y)
	E(xy)
	E(yx)
	k(x)
	k(y)
	k(xy)
	k(yx)
E(xy) ►
	V(x)
	V(y)
	V(z)
	E(yx)
	k(x)
	k(y)
	k(z)
	k(yx)
E(yx) ►
	V(x)
	V(y)
	V(z)
	E(xy)
	k(x)
	k(y)
	k(z)
	k(xy)
k(x) ►
	V(y)	Anomalous Hall effect
	V(z)
	E(xy)
	E(yx)
	k(y)	Anisotropic conductivity.
	k(z)
	k(xy)
	k(yx)
k(y) ►
	V(x)
	V(z)
	E(xy)
	E(yx)
	k(x)
	k(z)
	k(xy)
	k(yx)
k(z) ►
	V(x)
	V(y)
	E(xy)
	E(yx)
	k(x)
	k(y)
	k(xy)
	k(yx)
k(xy) ►
	V(x)
	V(y)
	V(z)
	E(yx)
	k(x)
	k(y)
	k(z)
	k(yx)
k(yx) ►
	V(x)
	V(y)
	V(z)
	E(xy)
	k(x)
	k(y)
	k(z)
	k(xy)
A(x) ►
	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) ►
	A(x)
	A(z)
	A(xy)
	A(yx)
	M(x)
	M(z)
	M(xy)
	M(yx)
A(z) ►
	A(x)
	A(y)
	A(xy)
	A(yx)
	M(x)
	M(y)
	M(xy)
	M(yx)
A(xy) ►
	A(x)
	A(y)
	A(z)
	A(yx)
	M(x)
	M(y)
	M(z)
	M(yx)
A(yx) ►
	A(x)
	A(y)
	A(z)
	A(xy)
	M(x)
	M(y)
	M(z)
	M(xy)
H(x) ►
	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) ►
	A(x)
	A(z)
	A(xy)
	A(yx)
	M(x)
	M(z)
	M(xy)
	M(yx)
H(z) ►
	A(x)
	A(y)
	A(xy)
	A(yx)
	M(x)
	M(y)
	M(xy)
	M(yx)
H(xy) ►
	A(x)
	A(y)
	A(z)
	A(yx)
	M(x)
	M(y)
	M(z)
	M(yx)
H(yx) ►
	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)
C(y) ►
	V(x)
	V(z)
	E(xy)
	E(yx)
	k(x)
	k(z)
	k(xy)
	k(yx)
C(z) ►
	V(x)
	V(y)
	E(xy)
	E(yx)
	k(x)
	k(y)
	k(xy)
	k(yx)
C(xy) ►
	V(x)
	V(y)
	V(z)
	E(yx)
	k(x)
	k(y)
	k(z)
	k(yx)
C(yx) ►
	V(x)
	V(y)
	V(z)
	E(xy)
	k(x)
	k(y)
	k(z)
	k(xy)
C'(x) ►
	V(y)
	V(z)
	E(xy)
	E(yx)
	k(y)
	k(z)
	k(xy)
	k(yx)
C'(y) ►
	V(x)
	V(z)
	E(xy)
	E(yx)
	k(x)
	k(z)
	k(xy)
	k(yx)
C'(z) ►
	V(x)
	V(y)
	E(xy)
	E(yx)
	k(x)
	k(y)
	k(xy)
	k(yx)
C'(xy) ►
	V(x)
	V(y)
	V(z)
	E(yx)
	k(x)
	k(y)
	k(z)
	k(yx)
C'(yx) ►
	V(x)
	V(y)
	V(z)
	E(xy)
	k(x)
	k(y)
	k(z)
	k(xy)
D'(x) ►
	A(y)
	A(z)
	A(xy)
	A(yx)
	M(y)
	M(z)
	M(xy)
	M(yx)
D'(y) ►
	A(x)
	A(z)
	A(xy)
	A(yx)
	M(x)
	M(z)
	M(xy)
	M(yx)
D'(z) ►
	A(x)
	A(y)
	A(xy)
	A(yx)
	M(x)
	M(y)
	M(xy)
	M(yx)
D'(xy) ►
	A(x)
	A(y)
	A(z)
	A(yx)
	M(x)
	M(y)
	M(z)
	M(yx)
D'(yx) ►
	A(x)
	A(y)
	A(z)
	A(xy)
	M(x)
	M(y)
	M(z)
	M(xy)

Longitudinal Property

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

Full Rank Property

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