Ferroelectricity by Bose-Einstein condensation in a quantum magnet

Abstract

The Bose-Einstein condensation is a fascinating phenomenon, which results from quantum statistics for identical particles with an integer spin. Surprising properties, such as superfluidity, vortex quantization or Josephson effect, appear owing to the macroscopic quantum coherence, which spontaneously develops in Bose-Einstein condensates. Realization of Bose-Einstein condensation is not restricted in fluids like liquid helium, a superconducting phase of paired electrons in a metal and laser-cooled dilute alkali atoms. Bosonic quasi-particles like exciton-polariton and magnon in solids-state systems can also undergo Bose-Einstein condensation in certain conditions. Here, we report that the quantum coherence in Bose-Einstein condensate of the magnon quasi particles yields spontaneous electric polarization in the quantum magnet TlCuCl₃, leading to remarkable magnetoelectric effect. Very soft ferroelectricity is realized as a consequence of the O(2) symmetry breaking by magnon Bose-Einstein condensation. The finding of this ferroelectricity will open a new window to explore multi-functionality of quantum magnets.

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 measurements. 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 measurement. (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.

Figure 2. Temperature dependence of the electric polarizations P//[010] and P⊥ for H//[010] at 18 T.

Inset shows the spin structure in the field-induced phase of TlCuCl₃ for H//[010], determined by the previous neutron diffraction measurements¹³. Grey shedding area shows a unit cell of TlCuCl₃. Bold solid and dashed lines show the dimer bonds, which are connected each other by the two-hold helical 2₁ or the glide symmetry transformations of the P2₁/c, which is the space group of TlCuCl₃. Arrows are spins of Cu²⁺ ion. The transverse components of the spins direct along the easy axis, which is inclined from [100] by 39° in (010) plane. The spin ordering breaks the space inversion I and the 2₁ symmetries, whereas the glide plane parallel to (010) remains. Therefore, the electric polarization, induced by the magnetic field for H//[010], should lie in (010) plane. The experimental result that almost no P//[010] is observed, agrees with the symmetry of the spin structure.

Figure 3. P-E hysteresis curve of P⊥ for H//[010].

Small electric coercive field for reversal of P indicates that 180° rotation of the antiferromagnetic domain easily occurs in TlCuCl₃. The insets show schematic pictures of the electric polarization on the dimer. The electric polarization reversal requires a reversal of the vector spin chirality S₁ × S₂.