MPG 6

Properties:

C_3z, M_z, C_6z⨂I

1D Identification

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

Odd-Order Property

Applied	M1	Checked
E(x) ►
	V(y)	Transverse (Hall-type) voltage
	E(xy)
	E(yx)
	k(y)	Anomalous Hall effect
	k(xy)
	k(yx)
	A(z)
	M(z)	Transverse magnetoelectric effect
E(y) ►
	V(x)
	E(xy)
	E(yx)
	k(x)
	k(xy)
	k(yx)
	A(z)
	M(z)
E(z) ►
	A(x)
	A(y)
	A(xy)
	A(yx)
E(xy) ►
	V(x)
	V(y)
	E(yx)
	k(x)
	k(y)
	k(yx)
	A(z)
	M(z)
E(yx) ►
	V(x)
	V(y)
	E(xy)
	k(x)
	k(y)
	k(xy)
	A(z)
	M(z)
k(x) ►
	V(y)	Anomalous Hall effect
	E(xy)
	E(yx)
	k(y)	Anisotropic conductivity.
	k(xy)
	k(yx)
	A(z)
	M(z)	Transverse current-induced M, Transverse Edelstein effect
k(y) ►
	V(x)
	E(xy)
	E(yx)
	k(x)
	k(xy)
	k(yx)
	A(z)
	M(z)
k(z) ►
	A(x)
	A(y)
	A(xy)
	A(yx)
k(xy) ►
	V(x)
	V(y)
	E(yx)
	k(x)
	k(y)
	k(yx)
	A(z)
	M(z)
k(yx) ►
	V(x)
	V(y)
	E(xy)
	k(x)
	k(y)
	k(xy)
	A(z)
	M(z)
A(x) ►
	V(z)
	k(z)	Shear-stress induced toroidicity (nonreciprocity) (piezotoroidic tensor)
	M(y)
	M(xy)
	M(yx)
A(y) ►
	V(z)
	k(z)
	M(x)
	M(xy)
	M(yx)
A(xy) ►
	A(x)
	A(y)
	A(yx)
A(yx) ►
	A(x)
	A(y)
	A(xy)
H(x) ►
	V(z)
	k(z)	Transverse magnetotoroidicity (magnetotoroidicity tensor)
	M(y)	Transverse magnetic susceptibility
	M(xy)
	M(yx)
H(y) ►
	V(z)
	k(z)
	M(x)
	M(xy)
	M(yx)
H(xy) ►
	V(z)
	k(z)
	M(x)
	M(y)
	M(yx)
H(yx) ►
	V(z)
	k(z)
	M(x)
	M(y)
	M(xy)
C(x) ►
	A(y)
	A(xy)
	A(yx)
C(y) ►
	A(x)
	A(xy)
	A(yx)
C(z) ►
	A(x)
	A(y)
	A(xy)
	A(yx)
C(xy) ►
	V(z)
	k(z)
	M(x)
	M(y)
	M(yx)
C(yx) ►
	V(z)
	k(z)
	M(x)
	M(y)
	M(xy)
C'(x) ►
	V(z)
	k(z)
	M(y)
	M(xy)
	M(yx)
C'(y) ►
	V(z)
	k(z)
	M(x)
	M(xy)
	M(yx)
C'(z) ►
	M(x)
	M(y)
	M(xy)
	M(yx)
C'(xy) ►
	V(z)
	k(z)
	M(x)
	M(y)
	M(yx)
C'(yx) ►
	V(z)
	k(z)
	M(x)
	M(y)
	M(xy)
D'(x) ►
	V(y)
	E(xy)
	E(yx)
	k(y)
	k(xy)
	k(yx)
	A(z)
	M(z)
D'(y) ►
	V(x)
	E(xy)
	E(yx)
	k(x)
	k(xy)
	k(yx)
	A(z)
	M(z)
D'(z) ►
	V(x)
	V(y)
	E(xy)
	E(yx)
	k(x)
	k(y)
	k(xy)
	k(yx)
D'(xy) ►
	V(x)
	V(y)
	E(yx)
	k(x)
	k(y)
	k(yx)
	A(z)
	M(z)
D'(yx) ►
	V(x)
	V(y)
	E(xy)
	k(x)
	k(y)
	k(xy)
	A(z)
	M(z)

Longitudinal Property

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