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By performing heat-capacity, magnetocaloric effect, torque magnetometry, and force magnetometry measurements up to 33 T, we have mapped out the T-H phase diagram of the S =1/ 2 spin dimer compound Ba 3 Cr 2 O 8 . We found evidence for field-induced magnetic order between H c1 = 12.52͑2͒ T and H c2 = 23.60͑5͒ T, with the maximum transition temperature T c ϳ 2.7 K at H ϳ 18 T. The lower transition can likely be described by Bose-Einstein condensation of triplons theory, and this is consistent with the absence of any magnetization plateaus in our magnetic torque and force measurements. In contrast, our measurements uncovered magnetic field irreversibility associated with a symmetric specific heat versus temperature near H c2 suggesting that the upper transition is first order. DOI: 10.1103/PhysRevB.79.100409 PACS number͑s͒: 75.30.Kz, 75.30.Sg, 75.40.Cx, 73.43.Nq Quantum phase transitions ͑QPT͒ can be achieved by varying a nonthermal control parameter, such as pressure or applied magnetic field, while at a temperature of absolute zero.1,2 These transitions are driven by quantum fluctuations resulting from the uncertainty principle, as opposed to the thermal fluctuations that drive classical phase transitions. A particular type of QPT is realized in a Heisenberg spin dimer system, which possesses a nonmagnetic spin-singlet ground state with a gap to the first triplet excited state. 3 The excited triplets ͑triplons͒ can be considered as bosons with a hardcore on-site repulsion. 4 The repulsion condition is necessary in order to prevent more than one triplon from lying on a single dimer.If one applies a magnetic field H to close the spin gap, a critical field H c1 is eventually reached which results in the generation of a macroscopic number of triplons. Above H c1 , the magnetic field can be varied to control the triplon density, and so it acts as a chemical potential. The system now consists of a series of interacting triplons with a ground state that critically depends on the balance between the kinetic energy and the repulsive interactions. Note that the kinetic energy of the interacting triplons arises from the xy component of the Heisenberg interdimer interaction, while the nearestneighbor repulsive interaction ͑different from the on-site repulsion͒ arises from the Ising or z component. The delicate balance between these two energies has led to interesting and diverse properties of QPTs in spin dimer systems.If the repulsive interactions dominate, it is most crucial to minimize this contribution to the microscopic Hamiltonian. The easiest way to do this is to ensure that the triplon density per dimer is a simple rational fraction as this allows the triplons to form a superlattice. These preferred fractional triplon densities result in plateaus in the magnetization as a function of field, and such behavior has been observed in SrCu 2 ͑BO 3 ͒ 2 . 5,6 When the kinetic energy terms dominate instead, this contribution will be minimized by allowing the triplons to have freedom to hop from dimer to dimer. The ground ...

Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors including thermal noise, frequency noise of the resonator and noise in the feedback circuitry. Increasing the vibration amplitude can mitigate some of these effects but the improvements are limited by nonlinearities that are particularly strong for miniaturized micro- and nano-mechanical systems. Here we design a micromechanical resonator with non-monotonic dependence of the eigenfrequency on energy. Near the extremum, where the dispersion of the eigenfrequency is zero, the system regains certain characteristics of a linear resonator, albeit at large amplitudes. The spectral peak undergoes narrowing when the noise intensity is increased. With the resonator serving as the frequency-selecting element in a feedback loop, the phase noise at the extremum amplitude is ~3 times smaller than the minimal noise in the conventional nonlinear regime.