QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation

The self-consistent mean field approximation of the two-flavor NJL model,with a free parameter a to reflect the competition between the "direct" channel and the "exchange" channel,is employed to study the QCD phase structure at finite iso spin chemical potential μ_I,finite bary on chemical potential μ_B and finite temperature T,and especially to study the location of the QCD critical point.Our results show that in order to match the corresponding lattice results of iso spin density and energy density,the contributions of the "exchange" channel need to be considered in the framework of the NJL model,and a weighting factor α=0.5 should be taken.It is also found that for fixed isospin chemical potentials,the lower temperature of the phase transition is obtained with increasing a in the T-μ_I plane,and the largest difference of the phase transition temperature with different a's appears at μ_I~1.5 mπ.At μ_I=0 the temperature of the QCD critical end point(CEP) decreases with increasing a,while the critical baryon chemical potential increases.At high isospin chemical potential(μ_I=500 MeV),the temperature of the QCD tricritical point(TCP) increases with increasing a,and in the low temperature regions the system will transition from the pion superfluidity phase to the normal phase as μ_B increases.At low density,the critical temperature of the QCD phase transition with different a's rapidly increases with μ_I at the beginning,and then increases smoothly around μ_I 300 MeV.In the high baryon density region,the increase of the iso spin chemical potential will raise the critical baryon chemical potential of the phase transition.     

Double spin-glass-like behavior and antiferromagnetic superexchange interaction between Fe~(3+) ions in α-Ga_(2-x)Fe_xO_3(0≤x≤0.4)

Single phase of Fe3+-doped α-Ga2-xFexO3(α-GF x O, x = 0.1, 0.2, 0.3, 0.4) is synthesized by treating the β-Ga2-x Fe x O3(β-GF x O) precursors at high temperatures and high pressures. Rietveld refinements of the X-ray diffraction data show that the lattice constants increase monotonically with the increase of Fe3+content. Calorimetric measurements show that the temperature of the phase transition from α-GF x O to β-GF x O increases, while the associated enthalpy change decreases upon increasing Fe3+content. The optical energy gap deduced from the reflectance measurement is found to decrease monotonically with the increase in Fe3+content. From the measurements of magnetic field-dependent magnetization and temperature-dependent inverse molar susceptibility, we find that the superexchange interaction between Fe3+ions is antiferromagnetic. Remnant magnetization is observed in the Fe3+-doped α-GF x O and is attributed to the spin glass in the magnetic sublattice. At high Fe3+doping level(x = 0.4), two evident peaks are observed in the image part of the AC susceptibility χ ac. The frequency dependence in intensity of these two peaks as well as two spin freezing temperatures observed in the DC magnetization measurements of α-GF0.4O is suggested to be the behavior of two spin glasses.     

Effect of Cu doping on the magnetic and electrical properties of n=2 Ruddlesden-Popper manganates

A series of polycrystalline Cu-doped n=2 Ruddlesden-Popper manganates La1.2Sr1.8CuzMn（2-x）O7 （x=0, 0.04, 0.13） were synthesized by the solid state reaction method. The effect of Cu doping on the magnetic and transport properties has been studied. It is found that Cu substitution for Mn greatly affects the magnetic and electrical properties of the parent phase La1.2Sr1.8Mn2O7. With the increase of Cu content, the system undergoes a transition from longrange ferromagnetic order to the spin glass state and further to an antiferromagnetic order. A little of Cu dopant can lead to the samples showing semiconductor or insulator behaviour in the whole observed temperature range while the parent phase has a metal-insulator transition. These samples show colossal magnetoresistance at low temperatures and the value of it decreases with increasing Cu content.     

Charge order and spin order in Nd0.5Sr0.5Mn1? x (Ga x , Ti x )O3 system

Magnetic properties of Nd0.5Sr0.5Mn1-x(Gax,Tix)O3 system (0.04≤x≤0.4) were investigated through magnetization and electron spin resonance (ESR) measurements. It was observed that a small amount of Ti substitution for Mn will destroy the charge-ordering (CO) phase completely and induce the cluster-spin-glass phase in the system, which displays a procedure of collapse of CO and of an enhancement of spin ordering (SO) phase. In contrast, the Ga substitution for Mn induces a melting of CO phase in the system. It was observed that with substitution the CO phase is suppressed gradually and the remanent CO phase is retained all the while, and withal, there is a co-existence of AFM CO phase and FM SO at low temperature. In addition, an abrupt rise of magnetization was observed in M-Tcurves. We attributed this abnormal phenomenon to a transition from canted AFM SO to FM SO in CO region.     

INVESTIGATION OF THE STRUCTURAL PHASE TRANSITION OF MnBi AND MnBiAl FILMS

Structural phase transition of MnBi and MnBiAl films has been investigated in the tem-perature range of 30-400℃. The transition from low-temperature phase to high-temperature phase occurs in both the films, but the phase transitions appear at different temperatures. According to the measurement of Kerr rotation as a function of thermal annealing and the phase transition process, it is shown that the transition is irreversible for MnBi film and reversible for MnBiAl film under our experimental condition. For this reason, we speculate that the aluminum added in MnBi makes the bonding force of Mn atoms with their neighbors stronger, which may be the cause for the difference of the phase transition between MnBi and MnBiAl films.     

Shock Compression and Phase Transitions of Magnesiowiistite （Mg,Fe）O up to Earth＇s Lowermost Mantle Conditions

We report new shock-compression data for polycrystalline （Mg,Fe）O up to 130 GPa shock pressures corresponding to Earth＇s lowermost mantle conditions. Our data together with the existing shock-wave data of （Mg, Fe）O and its end-members MgO and FeO reveal that the Hugoniot curves of （Mg,Fe）O does not change with varying FeO content for their B1 phase （NaCl-structure） in the pressure-relative-volume plane. The evidence of the volume change within 3% at around 120GPa along the Hugoniot of （Mgo.6, Feo.4）O is consistent with a structural transition from B1 phase （NaC1 cubic） to B8 phase （NiAs-type hexagonal）. Such a structural transition of （Mg, Fe）O, if indeed occurs, may in part contribute to the scattering of seismic waves and change in velocity gradient found in the lowermost mantle.     

The magnetic and dielectric properties of multiferroic Sr- substituted Zn2-Y hexagonal ferrites

The magnetic and dielectric properties of Sr-substituted Zn2-Y hexagonal ferrites （Ba2-x SrxZn2Fe12O22, 1.0 〈 x ≤ 1.5） are studied in this paper. Sr substitution will lead to the variation of cation occupation, which influences both the magnetic and electric properties. As Sr content x rises from 1.0 to 1.5, magnetic hysteresis loop gets wider gradually and the permeability drops rapidly due to the transformation from ferrimagnetic to antiferromagnetic phase. Moreover, permittivity rises with increasing Sr content. Under a certain external magnetic field, the phase transition of helical spin structure of Ba0.5Srl.5Zn2Fe12O22 at about 295 K seems to open a possibility for the room-temperature ferroelectricity induced by magnetic field. But its low resistivity prevents the observation of ferroelectric and magnetoelectric properties at room-temperature.     

Thermal expansion properties of Lu2-xFexMo3O12

The structures and thermal expansion properties of Lu2-xFexMo3O12 have been investigated by X-ray diffraction(XRD).XRD patterns at room temperature indicate that compounds Lu2-xFexMo3O12 with x≤1.3 exhibit an orthorhombic structure with space group Pnca;compounds with x=1.5 and 1.7 have a monoclinic structure with space group P21/a.Studies on thermal expansion properties show that the linear thermal expansion coefficients of orthorhombic phase vary from negative to positive with increasing Fe content.Attempts to make zero thermal expansion materials indicate that zero thermal expansion can be observed in Lu1.3Fe0.7Mo3O12 in the temperature range of 200-400℃.     

Peculiar Quantum Phase Transitions and Hidden Supersymmetry in a Lipkin-Meshkov-Glick Model

In this paper we theoretically report an unconventional quantum phase transition of a simple Lipkin- Meshkow-Glick model： an interacting collective spin system without external magnetic field. It is shown that this model with integer-spin can exhibit a flrst-order quantum phase transition between different disordered phases, and more intriguingly, possesses a hidden supersymmetry at the critical point. However, for half-integer spin we predict another flrst-order quantum phase transition between two different long-range-ordered phases with a vanishing energy gap, which is induced by the destructive topological quantum interference between the intanton and anti-instanton tunneling paths and accompanies spontaneously breaking of supersymmetry at the same critical point. We also show that, when the total spin-value varies from half-integer to integer this model can exhibit an abrupt variation of Berry phase from π to zero.     

Structures and magnetic behaviours of TiO2-Mn-TiO2 multilayers

The TiO2-Mn-TiO2 multilayers are successfully grown on glass and silicon substrates by alternately using radio frequency reactive magnetron sputtering and direct current magnetron sputtering. The structures and the magnetic behaviours of these films are characterised with x-ray diffraction, transmission electron microscope (TEM), vibrating sample magnetometer, and superconducting quantum interference device (SQUID). It is shown that the multi-film consists of a mixture of anatase and rutile TiO2 with an embedded Mn nano-film. It is found that there are two turning points from ferromagnetic phase to antiferromagnetic phase. One is at 42 K attributed to interface coupling between ferromagnetic Mn3O4 and antiferromagnetic Mn2O3, and the other is at 97 K owing to the interface coupling between ferromagnetic Mn and antiferromagnetic MnO. The samples are shown to have ferromagnetic behaviours at room temperature from hysteresis in the M-H loops, and their ferromagnetism is found to vary with the thickness of Mn nano-film. Moreover, the Mn nano-film has a critical thickness of about 18.5 nm, which makes the coercivity of the multi-film reach a maximum of about 3.965×10 2 T.     

Expanding the thermodynamical potential and analysis of the possible phase diagram of decon nement in the FL model

Decon nement phase transition is studied in the FL model at finite temperature and chemical potential. At MFT approximation, phase transition can only be first order in the whole μ-T phase plane. Using a Landau expansion, we further study the phase transition order and the possible phase diagram of decon nement. We discuss the possibilities of second order phase transitions in the FL model. From our analysis, if the cubic term in the Landau expansion could be cancelled by the higher order fluctuations, second order phase transition may occur. By an ansatz of the Landau parameters, we obtain a possible phase diagram with both the first and second order phase transitions, including the tri-critical point which is similar to that of the chiral phase transition.     

Expanding the thermodynamical potential and analysis of the possible phase diagram of deconfinement in the FL model

Deconfinement phase transition is studied in the FL model at finite temperature and chemical potential. At MFT approximation, phase transition can only be first order in the whole μ-T phase plane. Using a Landau expansion, we further study the phase transition order and the possible phase diagram of deconfinement. We discuss the possibilities of second order phase transitions in the FL model. From our analysis, if the cubic term in the Landau expansion could be cancelled by the higher order fluctuations, second order phase transition may occur. By an ansatz of the Landau parameters, we obtain a possible phase diagram with both the first and second order phase transitions, including the tri-critical point which is similar to that of the chiral phase transition.     

Phase transition and thermal expansion property of Cr_(2-x)Zr_(0.5x)Mg_(0.5x)Mo_3O_(12) solid solution

Compounds with the formula Cr2-xZr0.5xMg0.5xMo3O12（x = 0.0, 0.3, 0.5, 0.9, 1.3, 1.5, 1.7, 1.9） are synthesized, and the effects of Zr4＋ and Mg2＋ co-incorporation on the phase transition, thermal expansion, and Raman mode are investigated. It is found that Cr2-xZr0.5xMg0.5xMo3O12 crystallize into monoclinic structures for x 〈 1.3 and orthorhombic structures for x _〉 1.5 at room temperature. The phase transition temperature from a monoclinic to an orthorhombic structure of Cr2Mo3O12 can be reduced by the partial substitution of （ZrMg）6＋ for Cr3＋. The overall linear thermal expansion coefficient decreases with the increase of the （ZrMg）6＋ content in an orthorhombic structure sample. The co-incorporation of Zr4＋ and Mg2＋ in the lattice results in the occurrence of new Raman modes and the hardening of the symmetric vibrational modes, which are attributed to the MoO4 tetrahedra sharing comers with ZrO6/MgO6 octahedra and to the strengthening of Mo-O bonds due to less electronegativities of Zr4＋ and Mg2＋ than Cr3＋, respectively.     

Quantum Dissonance as an Indicator of Quantum Phase Transition in the XXZ Chain

We investigate the behavior of quantum dissonance in the anti-ferromagnetic XXZ spin S = 1/2 chain, which exhibits a quantum phase transition. Based on a unified view of quantum and classical correlations, quantum dissonance is analytically calculated and is compared with entanglement, discord, and classical correlations for the ground state of the system. It is found that the nearest-neighbor quantum dissonance achieves an extremum and exhibits the sharpest change at the critical point. Therefore, quantum dissonance may serve as a more efficient indicator of quantum phase transitions in the XXZ spin chain.     

Charge order and spin order in Nd_(0.5)Sr_(0.5)Mn_(1-x)(Ga_x, Ti_x)O_3 system

Magnetic properties of Nd_(0.5)Sr_(0.5)Mn_(1-x)(Ga_x, Ti_x)O_3 system (0.04≤x≤0.4) were inves- tigated through magnetization and electron spin resonance (ESR) measurements. It was observed that a small amount of Ti substitution for Mn will destroy the charge-ordering (CO) phase completely and induce the cluster-spin-glass phase in the system, which displays a procedure of collapse of CO and of an enhancement of spin ordering (SO) phase. In contrast, the Ga substitution for Mn induces a melt- ing of CO phase in the system. It was observed that with substitution the CO phase is suppressed gradually and the remanent CO phase is retained all the while, and withal, there is a co-existence of AFM CO phase and FM SO at low temperature. In addition, an abrupt rise of magnetization was observed in M-T curves. We attributed this abnormal phenomenon to a transition from canted AFM SO to FM SO in CO region.     

Structural properties of Bi1-xLaxFeO3 studied by micro-Raman scattering

This paper reports that La-doped BiFeO 3(Bi1-x La x FeO3,x = 0,0.1,0.2,0.3,0.6,0.8 and 1.0) were studied by using micro-Raman spectroscopy and x-ray diffraction(XRD).The XRD patterns indicate that the structure of Bi1-xLaxFeO 3 changes from rhombohedral BiFeO3 to orthorhombic LaFeO3.The results of Raman spectroscopy show good agreement with the XRD results.Strikingly,the phonon peak at around 610 cm-1 and the two-phonon peaks in the high frequency range exist in all compounds and enhance with increasing La substitution.The increasing intensity of the 610 cm-1 peak is attributed to the changes in the FeO 6 octahedron during the rhombohedral-orthorhombic phase transition.The enhancements of the two-phonon peaks are associated with the breakdown of the cycloid spin configuration with the appearance of the orthorhombic structure.These results indicate the existence of strong spin-phonon coupling in Bi1-xLax FeO3,which may provide useful information for understanding the effects of La content on the structural and magnetic properties of Bi1-xLaxFeO3.     

Cation distributions estimated using the magnetic moments of the spinel ferrites Co_(1-x)Cr_xFe_2O_4 at 10K

（A）[B]2O4 ferrite samples with the composition COl_xCrxFe204 （0.0 ≤ x ≤1.0） are prepared using a hydrothermal method, and subjected to calcining in a tube furnace with an argon-flow at 1673 K for 2 h. X-ray diffraction patterns indicate that each of all the samples has a single phase cubic spinel structure with a space group of Fd3m. Magnetic measurements show that the saturation magnetization decreases with as the Cr content x increases. The cation distribution of the samples is estimated by fitting the dependence of the magnetic moments on x at l 0 K, using the quantum mechanical model previously proposed by our group. The calculated sum of the content values of the Cr3＋ and Cr2＋ cations occupying the （A） sites increases as the value of x increases. In the fitting process, the magnetic moment directions of the Cr3＋ and Cr2＋ cations are assumed to be antiparallel to those of the Fe and Co cations, respectively, which is in accordance with Hund＇s rules.     

Pressure-induced changes in the magnetic properties of the single crystal of Mn3 single-molecule magnet

The magnetic measurements of the single crystal of Mn3 single-molecule magnet under high pressure at T=2 K have been performed.We find both the antiferromagnetic intermolecular coupling parameter J and the effective energy barrier to vary compared with the measurements at low pressure.The increase of|J|is estimated to be 12%at 0.7 GPa when compared with that of0 GPa,whereas the effective energy barrier becomes smaller with increasing pressure.Our results demonstrate that the intermolecular interaction of single-molecule magnet can be changed by pressure.Compared with the normal magnetic alloy,the effect of pressure on the magnetic properties of Mn3 is much more prominent,which implies that Mn3 may have great potential in magnetic multifunctional material.     

Near-zero thermal expansion of In_(2(1-x))(HfMg)_xMo_3O_(12) with tailored phase transition

Solid solutions of In_(2(1-x)(HfMg)_xMo_3O_(12) are synthesized by solid state reaction with the aim to reduce the phase transition temperature of In_2Mo_3O_(12) and improve its thermal expansion property.The effects of(HfMg)~(6+) incorporation on the phase transition and thermal expansion are investigated.It is shown that the monoclinic-to-orthorhombic phase transition temperature obviously decreases and the coefficient of thermal expansion(CTE) of the orthorhombic becomes less negative and approaches to zero with increasing the content of(HfMg)~(6+).A near zero thermal expansion covering the case at room temperature(RT) is achieved for the solid solutions with x ≥ 0.85,implying potential applications of this material in many fields.     

Structural,Magnetic and Magnetocaloric Properties of La-deficient La0.77-xSrxCa0.2MnO2 Perovskites

La-deficient La0.77-x Ca0.2SrxMnO3 （0 〈 x 〈 0.1） polycrystalline samples are synthesized using the sol-gel technique. The crystal structures of all the samples are single orthorhombic phase with Pbnm space group. Rietveld analysis of x-ray diffraction patterns shows that the Mn-O-Mn bond angle θUn-O-Mn increases whereas the Mn-O bond length dMn--o decreases monotonically with increasing Sr^2＋ content, which results in a rich overlap between Mn 3d and O2p orbitals and leads to a systematic increase of the Curie temperature in this compound. It is found that the magnetic entropy change has a maximum at x = 0.06 in La^3＋-deficient La0.77-xCa0.2SrxMnO3. This may result from competition between the super-exchange interactions （Mn 4＋-O2--Mn4＋） and double-exchange interactions （Mn^3＋-O^2- -Mn^4＋） originating from the appearance of superfluous Mn^4＋ ions by substitution of Sr^2＋ for La^3＋ in this series. Large magnetic entropy changes of 2.32 and 1.83Jkg^-1K^-1 in the x = 0.06 and x = 0.1 samples at their Tcs of 271 K and 303K upon a low magnetic field （10kOe） make these materials promising candidates at near room temperature.