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.
Highlights
The Bose–Einstein condensation is a fascinating phenomenon, which results from quantum statistics for identical particles with an integer spin
It is revealed that the spontaneous electric polarization proportional to an absolute value of the vector spin chirality in the ground state develops above Hc
The appearance of the spontaneous electric polarization by the magnon Bose–Einstein condensation (BEC) can be confirmed by the pyroelectric current measurements
Summary
The Bose–Einstein condensation is a fascinating phenomenon, which results from quantum statistics for identical particles with an integer spin. TlCuCl3 is the first material whose field-induced quantum phase transition was classified as a realization of Bose–Einstein condensation (BEC) in the quantum magnets[1] In this material, antiferromagnetic spin dimers, composed of a pair of Cu2 þ ions with spin S 1⁄4 1/2, are three-dimensionally coupled by interdimer Heisenberg exchange interactions, which are weaker than the intradimer one[2,3,4,5]. The quantum spin dimer has a finite matrix element of this vector spin chirality between its spin singlet and triplet states This property leads to the emergence of the ferroelectricity by the magnon BEC in the coupled dimer system. The observation of this ferroelectricity indicates that quantum magnets can be significant playgrounds for magnetoelectric coupling
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