Comparative study of the field-induced and spontaneous AF2′ multiferroic phases in MnWO₄ and Mn_0.90Co_0.10WO₄ within the magnetic symmetry framework

(Mn,Co)WO₄ compounds are regarded as reference spin-induced multiferroics. A comparative study is presented here, within the magnetic symmetry framework, of the incommensurate magnetic orders responsible for the ferroelectric phases of (i) MnWO₄ under a magnetic field (H || b) and (ii) Mn_0.90Co_0.10WO₄ in the absence of an external field. On the one hand, although these two ferroelectric phases are stabilized under different external physical conditions, both present the same Xc1′(α0γ)ss magnetic symmetry and practically the same modulation vector. The magnetic ordering in both phases is an elliptical helix with the magnetic moments (as the polarization vector, P) perpendicular to the b axis, although in most of the ferroelectric compositions of the (Mn,Co)WO₄ family the spins rotate in planes containing b (and have P || b). On the other hand, the anisotropy of the resulting magnetic modulations is extraordinarily different in the two phases. This is described and explained in the light of the different anisotropies of Co and Mn ions.

Computing details

(mnco_2K_magnetic)

Crystal data

Co0.1Mn0.9O4W	β = 90.912°
Mr = 303.7	V = 275.13 Å^3
Monoclinic, Xc.1(α0γ)ss	Z = 2
q = -0.222000a* + 0.472000c*	F(000) = 525
a = 4.8068 Å	Dx = 3.787 Mg m^−3
b = 11.488 Å	Neutrons radiation, λ = 1.2832 Å
c = 4.983 Å	T = 2 K

Data collection

649 measured reflections	θmax = 54.1°, θmin = 5.0°
367 independent reflections	h = −5→5
300 reflections with I > 3σ(I)	k = −13→13
Rint = 0.028	l = −2→1

Refinement

Refinement on F	0 restraints
R[F^2 > 2σ(F^2)] = 0.054	8 constraints
wR(F^2) = 0.063	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 2.98	(Δ/σ)max = 0.038
367 reflections	Absolute structure: 121 of Friedel pairs used in the refinement
4 parameters

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Mn1	0.5	0.3426	0.25	0*	0.906
Co1	0.5	0.3426	0.25	0*	0.094
W1	0	0.0909	0.25	0*
O1_1	0.2111	0.05105	0.941	0*
O1_2	−0.2111	−0.05105	−0.941	0*
O2_1	0.2512	0.1874	0.393	0*
O2_2	−0.2512	−0.1874	−0.393	0*

(mnco_9K_magnetic)

Crystal data

Co0.1Mn0.9O4W	β = 90.912°
Mr = 303.7	V = 275.13 Å^3
Monoclinic, Xc.1(α0γ)ss	Z = 2
q = -0.222000a* + 0.472000c*	F(000) = 525
a = 4.8068 Å	Dx = 3.787 Mg m^−3
b = 11.488 Å	Neutrons radiation, λ = 1.2832 Å
c = 4.983 Å	T = 9 K

Data collection

641 measured reflections	θmax = 55.0°, θmin = 5.0°
362 independent reflections	h = −5→5
280 reflections with I > 3σ(I)	k = −13→13
Rint = 0.033	l = −2→1

Refinement

Refinement on F	0 restraints
R[F^2 > 2σ(F^2)] = 0.061	8 constraints
wR(F^2) = 0.063	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 2.79	(Δ/σ)max = 0.045
362 reflections	Absolute structure: 116 of Friedel pairs used in the refinement
4 parameters

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Mn1	0.5	0.34233	0.25	0*	0.906
Co1	0.5	0.34233	0.25	0*	0.094
W1	0	0.0901	0.25	0*
O1_1	0.21142	0.05145	0.941	0*
O1_2	−0.21142	−0.05145	−0.941	0*
O2_1	0.2515	0.187535	0.3941	0*
O2_2	−0.2515	−0.187535	−0.3941	0*