Abstract
Magnetic-field-induced phase transitions are investigated in the frustrated gapped quantum paramagnet Rb$_{2}$Cu$_{2}$Mo$_3$O$_{12}$ through dielectric and calorimetric measurements on single-crystal samples. It is clarified that the previously reported dielectric anomaly at 8~K in powder samples is not due to a chiral spin liquid state as has been suggested, but rather to a tiny amount of a ferroelectric impurity phase. Two field-induced quantum phase transitions between paraelectric and paramagnetic and ferroelectric and magnetically ordered states are clearly observed. It is shown that the electric polarization is a secondary order parameter at the lower-field (gap closure) quantum critical point but a primary one at the saturation transition. Having clearly identified the magnetic Bose-Einstein condensation (BEC) nature of the latter, we use the dielectric channel to directly measure the critical divergence of BEC susceptibility. The observed power-law behavior is in very good agreement with theoretical expectations for three-dimensional BEC. Finally, dielectric data reveal magnetic presaturation phases in this compound that may feature exotic order with unconventional broken symmetries.
Highlights
Being the basis of superfluidity, superconductivity [1], and numerous other phenomena in systems ranging from cold atoms [2,3] to semiconductors [4,5] to ferromagnetic films [6], Bose-Einstein condensation (BEC) is arguably the most celebrated of all phase transitions
In an applied magnetic field, the capacitance of the sintered-powder sample develops a peak about 1.5 fF in the real part, as well as a distinct feature in the imaginary part at around T = 8 K [Fig. 2(a)]. This behavior is very similar to the dielectric anomaly reported in Refs. [31,33] and clearly corresponds to the same ferroelectric phase transition
With the purported high-temperature chiral spin liquid phase and sample-related issues out of the way, we focus on the low-temperature behavior across the field-induced magnon BEC transition using the pelletized sintered-powder and single-crystal samples
Summary
Being the basis of superfluidity, superconductivity [1], and numerous other phenomena in systems ranging from cold atoms [2,3] to semiconductors [4,5] to ferromagnetic films [6], Bose-Einstein condensation (BEC) is arguably the most celebrated of all phase transitions. BEC is a key example of a quantum phase transition (QPT) that can occur at zero temperature and is driven by quantum fluctuations [7]. For lattice gases it represents a transition from a gapless superfluid to a gapped Mott insulator state [8,9]. In BEC’s original formulation the order parameter, namely, the complex amplitude of the condensate wave function, has no physical field associated with it. The BEC order parameter is the spontaneous spatially modulated (often staggered) magnetization transverse to the applied field [10,13].
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