Magnetic and dielectric properties in the langasite-type compounds: $A_{3}B{\text{Fe}}_3{D}_2{\text{O}}_{14}$ $\left(A=\text{Ba},\text{Sr},\text{Ca};B=\text{Ta},\text{Nb},\text{Sb};D=\text{Ge},\text{Si}\right)$

The Fe-based langasites are the only reported compounds presenting a magnetic ordering in this rich family, besides being well known for piezoelectric properties and optical activity. The structural, magnetic, and dielectric properties of the Fe-langasite compounds, with various substitution of nonmagnetic cations, have been studied with x-ray and neutron-diffraction, magnetostatic measurements, Mössbauer spectroscopy, and dielectric measurements. The title compounds (trigonal space group $P321$) display a helical magnetic order with signatures of frustration below $T_N\approx 24–35\text{K}$, where an anomaly of the dielectric permittivity is observed. The influence of the cationic substitutions and the nature of the magnetoelectric coupling are hereafter addressed.

Figure 1

Polyhedral representation of the langasite structure with its four different cation sites on two layers.

Figure 2

(Color online) Magnetic network of ${\text{Fe}}^{3+}$ cations projected along the $c$ axis (left), with the different intraplane (left) or interplane (right) exchange paths (dashed lines).

Figure 3

(Color online) Magnetization measurements on a ${\text{Ba}}_3{\text{NbFe}}_3{\text{Si}}_2{\text{O}}_{14}$ single crystal under a magnetic field applied parallel and perpendicular to the $c$ axis. Top: magnetic isotherms at 2 and 275 K. Bottom: thermal variation of the $M/H$ and its inverse under an applied magnetic field of 5 T. The continuous line represents the linear fit of $H/M$ in a Curie-Weiss model.

Figure 4

Thermal variation of the $M/H$ of a powder sample of ${\text{Ba}}_3{\text{SbFe}}_3{\text{Si}}_2{\text{O}}_{14}$ under an applied magnetic field of 0.1 T.

Figure 5

(Color online) Magnetic structure of the Fe langasites: within each triangle of the $\left(a,b\right)$ plane, the ${\text{Fe}}^{3+}$ magnetic moments are rotated by $2\pi /3$ from each other. The global phase factor, which cannot be determined by neutron diffraction, was arbitrary chosen equal to zero in this representation (one moment pointing toward the center of the triangles). Along the $c$ axis, the helix propagates with a period of $1/\tau$ in cell unit.

Figure 6

(Color online) Rietveld plot for ${\text{Ba}}_3{\text{NbFe}}_3{\text{Si}}_2{\text{O}}_{14}$ (top left), ${\text{Ba}}_3{\text{SbFe}}_3{\text{Si}}_2{\text{O}}_{14}$ (top right), ${\text{Sr}}_3{\text{NbFe}}_3{\text{Si}}_2{\text{O}}_{14}$ (bottom left), and ${\text{Sr}}_3{\text{SbFe}}_3{\text{Si}}_2{\text{O}}_{14}$ (bottom right) neutron powder data at 1.8 K (1.5 K for BNFS) from D1B, including nuclear and magnetic phases.

Figure 7

(Color online) Powder neutron-diffraction patterns of the compound ${\text{Ba}}_3{\text{NbFe}}_3{\text{Si}}_2{\text{O}}_{14}$, below the magnetic transition, at 1.5 K, and above the magnetic transition, at 30 K.

Figure 8

(Color online) ${}^{57}\text{F}\text{e}$ Mössbauer absorption spectra in ${\text{Ba}}_3{\text{NbFe}}_3{\text{Si}}_2{\text{O}}_{14}$ at selected temperatures. The spectra at 4.2, 23, and 26 K (circles) are fitted (black lines) to the helical magnetic structure model determined by neutron scattering. At 26 K, a quadrupolar subspectrum contribution (represented in red), overlapping the magnetic signal, suggests that the magnetic transition is first order.

Figure 9

(Color online) Rietveld plot for ${\text{Ba}}_3{\text{SbFe}}_3{\text{Si}}_2{\text{O}}_{14}$ x-ray powder data at 250 K from ID31; $R_{\text{Bragg}}=2.58$, $R_{\text{wp}}=23.4$, and ${\chi }^2=3.6$.

Figure 10

(Color online) Thermal variation in some refined parameters from ID31 x-ray powder-diffraction data on ${\text{Ba}}_3{\text{SbFe}}_3{\text{Si}}_2{\text{O}}_{14}$: (a) cell parameter $a$ $\left(\text{Å}\right)$; (b) cell parameter $c$ $\left(\text{Å}\right)$; (c) quadratic term $U$ of the Gaussian peak width function; (d) a.d.p.’s of ${\text{Ba}}^{2+}$, ${\text{Sb}}^{5+}$, and ${\text{Fe}}^{3+}$ cations.

Figure 11

Thermal variation in the electric capacity (proportional to the dielectric permittivity) of BNFS single crystal for an electric field applied perpendicular to the $c$ axis (left) and parallel to it (right).

Figure 12

(Color online) Thermal variation in the electric capacity (proportional to the dielectric permittivity) of a pellet of BSFS powder. The red line is a linear extrapolation of the data above 30 K shown to emphasize the cusp.

Figure 13

(Color online) Magnetic dependence of the relative variation in the dielectric permittivity of a BNFS single crystal for several temperatures. Both magnetic and electric fields are applied perpendicular to the $c$ axis. The lines are parabolic fits. The inset shows the quadratic coefficient of these fits versus temperature.