Figure 1: Ferroelectricity by magnon BEC in TlCuCl₃.

(a) Temperature dependence of the dielectric constant observed in AC electric fields E perpendicular to plane. The inset shows the experimental configuration of the measurement. (b) Temperature-field phase diagram. Closed circles shows the peak position of the dielectric constant. Open squares are the critical points, determined by the previous neutron diffraction measurements¹³. The light blue shedding area turns out to be a multiferroic state with both antiferromagnetic and ferroelectric orders. The magnetic field is normalized by the g-value g=2.06, evaluated by the ESR measurement¹⁰. (c) Temperature dependence of the electric polarization P⊥. (d) Field dependence of the electric polarization P⊥. A solid curve shows the experimental result. A dashed curve is field dependence of the calculated vector spin chirality <S₁ × S₂>, multiplied by a constant C=220 (μC m⁻²). The calculation is carried out in terms of the bond operator theory. Inset shows the field dependence of the vector spin chirality <S₁ × S₂> and the longitudinal spin component <S_z>, calculated up to 100 T.