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Ranjan et al. ͓Phys. Rev. B 65, 060102͑R͒ ͑2002͔͒ have recently presented results of a powder neutrondiffraction study of the high-temperature monoclinic (F M HT ) to low-temperature monoclinic (F M LT ) phase transition in Pb(Ti 1Ϫx Zr x )O 3 discovered by Ragini et al. ͓Phys. Rev. B 64, 054101 ͑2001͔͒. They attribute the presence of superlattice reflections in the diffraction data to tilting of oxygen octahedra and propose a monoclinic space group Pc for the F M LT phase. It is shown that for the model proposed by Ranjan et al., the correct space group of the F M LT phase should be Cc. This has also been corroborated by a group-theoretical approach to the problem. A different set of refined structural parameters for the Cc space group obtained from the Rietveld analysis of the powder neutron-diffraction data of Ranjan et al. is also presented.

Temperature dependent structural changes in a nearly pure monoclinic phase composition (x=0.525) of Pb(Zr x Ti 1-x )O 3 (PZT) have been investigated using Rietveld analysis of high-resolution synchrotron powder x-ray diffraction data and correlated with changes in the dielectric constant and planar electromechanical coupling coefficient. Our results show that the intrinsic piezoelectric response of the tetragonal phase of PZT is higher than that of the monoclinic phase. It is also shown that the high piezoelectric response of PZT may be linked with an anomalous softening of the elastic modulus (1/ E S 11 ) of the tetragonal compositions closest to the morphotropic phase boundary.

We study a quantum Otto engine operating on the basis of a helical spin-1/2 multiferroic chain with strongly coupled magnetic and ferroelectric order parameters. The presence of a finite spin chirality in the working substance enables steering of the cycle by an external electric field that couples to the electric polarization. We observe a direct connection between the chirality, the entanglement and the efficiency of the engine. An electric-field dependent threshold temperature is identified, above which the pair correlations in the system, as quantified by the thermal entanglement, diminish. In contrast to the pair correlations, the collective many-body thermal entanglement is less sensitive to the electric field, and in the high temperature limit converges to a constant value. We also discuss the correlations between the threshold temperature of the pair entanglement, the spin chirality and the minimum of the fidelities in relation to the electric and magnetic fields. The efficiency of the quantum Otto cycle shows a saturation plateau with increasing electric field amplitude.Keywords: quantum heat engine, quantum entanglement, frustrated spin chain, multiferroic system IntroductionWith the advances in nanotechnology enabling controlled miniaturization and functionalization of nanostructured materials, questions related to the thermodynamical properties are gaining increased attention. Several theoretical proposals were put forward for nanoscale Brownian motors [1], refrigerators [2] and quantum heat engines [3][4][5][6][7][8][9][10][11][12][13]. On the other hand, for finite systems, the application of the laws of thermodynamics is the subject of an ongoing debate [14]. One of the fundamental questions concerns the size limit to which the working substance might be scaled down. Recent studies point out that the quantum nature of a size-quantized working substance, e.g. a quantum heat engine, may lead to a close connection between the efficiency of the cycle and quantum correlations [15], which can be quantified in terms of the entanglement [16][17][18], behavior that is atypical for classical engines. According to the fundamental laws of thermodynamics, the efficiency of a classical engine is independent of its detail and is solely determined by the character of the cycle itself and the temperatures of the heat baths. The quantum nature of the working substance, however, has key consequences for the engine output power as well. Recently it was shown that purely quantum phenomena, such as noise-induced coherence, yield greater engine output power [19,20].In general, physical phenomena at the cross-over of quantum mechanics and thermodynamics are the subjects of the emergent field of quantum thermodynamics where, among other topics, questions are addressed as to what extent standard classical thermodynamic cycles, such as Carnot or Otto cycles, can be reformulated for quantum systems [4]. A key issue thereby is the difference between thermodynamic and quantum adiabatic processes. For example, a thermodynamical ...