• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Electron Correlations,Spin-Orbit Coupling,and Antiferromagnetic Anisotropy in Layered Perovskite Iridates Sr2IrO4?

    2018-07-09 06:46:42HaoZhou周浩YuanYuanXu徐園園andSenZhou周森1CASKeyLaboratoryofTheoreticalPhysicsInstituteofTheoreticalPhysicsChineseAcademyofSciencesBeijing100190China
    Communications in Theoretical Physics 2018年7期
    關(guān)鍵詞:周浩

    Hao Zhou(周浩),Yuan-Yuan Xu(徐園園),and Sen Zhou(周森),3,?1CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China

    2School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

    3CAS Center of Excellence in Topological Quantum Computation,University of Chinese Academy of Sciences,Beijing 100049,China

    1 Introduction

    Recently,the 5d transition metal oxides Sr2IrO4has been intensively studied because it exhibits several characteristics that are considered to be distinct and important for the high-temperature superconductivity.Sr2IrO4is isostructural to the cuprate La2CuO4,sharing the layered perovskite structure of K2NiF4.[1?2]Because of the interplay between spin-orbit coupling(SOC)and electron correlations,a novel Jeff=1/2 Mott insulating ground state[3?4]was proposed for the parent compound Sr2IrO4,which becomes a canted antiferromagnetic(AFM)insulator below a Néel temperature TN230 K.Carrier doping such an insulating AFM state is expected to achieve a 5d t2g-electron analog of the 3d eg-electron hightemperature cuprate superconductors.[5?10]Although no clear signature of superconductivity has been detected so far,angle-resolved photoemission[11?13]and scanning tunneling microscopy[14]have observed in electron-doped Sr2IrO4the Fermi arcs with a pseudogap behavior and V-shaped low-energy gap.Whether a superconducting state exists as in the cuprates requires detail understanding of the correlated spin-orbit entangled insulating canted AFM states of the parent Sr2IrO4.

    In the canted AFM state,the ordered in-plane magnetic moments track the θ11?staggered IrO6octahedra rotation about the z axis,[3?4,15?16]giving rise to a weak ferromagnetism(FM),which is believed to arise from the entanglement of structural distortion and SOC that introduces a strong anisotropy in the Jeff=1/2 isospin coupling.The nature of the canted AFM state in Sr2IrO4has been studied using the localized picture based on the Jeff= 1/2 pseudospin anisotropic Heisenberg model,[8,17?21]the three-orbital Hubbard model for the t2gelectrons with SOC,[22?25]and the microscopic correlated density functional theory such as the LDA+SOC+U and GGA+SOC+U.[3,26?27]Weather Sr2IrO4is an AFM Mott insulator or a Slater insulator is still under debate,[23,28?29]but it is now generally agreed that it is not deep in the Mott regime,where the localized picture is justified,since both characters have been observed experimentally.[22,30?31]This is partially the reason why the correlated density functional theory works so well in producing correctly the canted AFM as the ground state.Recent X-ray experiments[32?33]reveal that the nature of the magnetic moment deviates substantially from the ideal Jeff=1/2 picture,which cannot be accounted for by the redistribution of the orbital component within the t2gand points to the importance of egorbitals.[34]In addition,it is known that the rotation of IrO6octahedra induces a significant hybridization between the dxyof the t2gcomplex and the dx2?y2of the egcomplex.[24?26]Therefore,it is useful and desired to studythe canted AFM insulating Sr2IrO4based on microscopic model of the five 5d Ir orbitals,including both the t2gand egcomplex.

    In this paper,using a five-orbital Hubbard model proposed by Zhou et al.,[35]we study the electron correlations,the SOC,and their effects on the AFM anisotropy.We apply Hartree-Fock approximation to the electron correlations to obtain the ground state properties at various electron correlations and SOC,and demonstrate their effects on the AFM anisotropy.The rest of the paper is organized as follows.In Sec.2,we introduce the fiveorbital Hubbard model constructed for the five 5d Ir orbitals,consisting of the electron hopping,crystalline electric field(CEF),the SOC,and the on-site electron correlations.The inclusion of the egorbitals enables us to resolve both the in-plane and out-of-plane anisotropy.We describe briefly the Hartree-Fock approximation and numerical calculation method used to solve the five-orbital Hubbard model.The effects of electron correlations on the AFM anisotropy is presented in Sec.3 at a constant SOC of its physical value in Sr2IrO4.In the plane of U versus J/U,the five-orbital Hubbard model exhibits a rich magnetic phase structure consisting of paramagnetic(PM)phase,coplanar canted AFM phase,and collinear AFM phase with moments pointing along the z axis(hereafter referred to as z-AFM).A Variational calculation is introduced to study the in-plane and out-of-plane anisotropy.The effects of SOC is illustrated in Sec.4 by examining the behavior of the states as a function of SOC with fixed electron correlations.Though the values of anisotropy energies depends strongly on its strength,the SOC is shown to be ineffective in tuning the direction of the ordered AFM moment.Finally,we conclude our paper in Sec.5.

    2 Five-Orbital Hubbard Model

    We start with the two-dimensional five-orbital tightbinding model including SOC(TB+SOC)[35]of the five localized 5d Wannier orbitals centered at Ir site labeled by μ,ν =1(dYZ),2(dZX),3(dXY),4(d3Z2?R2),5(dX2?Y2),which captures faithfully the realistic low-energy electronic structure of Sr2IrO4obtained in the local-density approximation including SOC and the structural distortion.The TB+SOC Hamiltonian in the local coordinates that rotate with the IrO6octahedra has the form of

    wherecreates an electron with spin-σ in the μ-th orbital at site i,andis the hopping integrals between sites i and j of up to fifth nearest neighbors given in Ref.[35].Because of the staggered IrO6octahedral rotation along the z axis,the hopping integralsare complex and spin dependent,and the Ir sites are divided into two sublattices,IrAand IrBshown in the inset of Fig.1.The second term denotes the crystalline electric field(CEF)1,...,5=(0,0,202,3054,3831)meV,which produces correctly the hierarchy of CEF in the elongated octahedra IrO6.The separation between the t2gand egcomplexes due to the octahedral ligand field is?c≡10Dq3.4 eV.The last term in Eq.(1)describes the atomic SOC with the strength λSOC=357 meV.The matrix elements of the spin angular momentum in the spin spacewhere η =x,y,z and τηthe Pauli matrices,and the matrix elements of the orbital angular moment in the five d-orbital basis=?are given explicitly in Ref.[35].

    Fig.1 Magnetic phase diagram as a function of J/U and U for the five-orbital Hubbard model at n=5 with λSOC=357 meV.The grey-shaded regime corresponds to the PM phase,the green-shaded area denotes the collinear z-AFM phase,and the rest unshaded regime is for the in-plane canted AFM phase.The dashed line separating the light-green and dark-green shaded areas indicates a spin-state transition from low-spin state to high-spin state in the z-AFM phase,and the nearby dotted line corresponding to J=0.73 eV.The inset shows the schematics of the in-plane canted AFM moments on the Ir square lattice with a two-dimensional rendering of the staggered IrO6octahedral rotation.

    To study the interplay between electron correlations and SOC,and their effects on the magnetic anisotropy,we consider the five-orbital Hubbard model

    where the intra-atomic interaction HUis given by the standard multiorbital Hubbard model[36]

    which consists of the local Coulomb repulsion U(intraorbital)and U′(interorbital),and the Hund’s rule coupling J,with the relation U=U′+2J applied.Note that,in Eq.(3)for the complete set of five d orbitals,J should be understood as an average of the exchange interactions of the t2gand the egorbitals since the difference between them is usually small in cubic systems.[37?38]To investigate the ground state properties of the five-orbital Hubbard model,the Hartree-Fock approximation will be applied to the electron correlation in Eq.(3).In the presence of SOC,the Hartree and exchange self-energies induced by HUdepend on the full spin-orbital-dependent density matrixwhich are determined by minimizing the state energy via a numerical self-consistent iterative process.Local physical quantities in the ground state can be expressed in terms ofthe orbital occupation niμ= ∑,the spin density

    and the orbital angular momentum

    Here and after,we restrict the averaged density per site n=(1/N)∑iμniμ=5 for the undoped Sr2IrO4compound.

    In this paper,we focus on the anisotropy of the correlation-induced AFM moment in the presence of SOC.We thus restrict the local density matriceson lattice sites belongs to the same sublattice(A or B)to be identical,and perform a momentum-space calculation for the two-sublattice system.The ordered spin moment on each site thus can be expressed as Si=SFM+(?1)ix+iySAFM,and the(π,π)-ordered AFM and the(0,0)-ordered FM component are given by,respectively,

    where SA/Bdenotes the expectation values of the spin angular moment on sublattice A/B.Similarly,the orbit angular moment L and the total magnetic moment L+2S can be decomposed into AFM and FM components.In all numerical calculations presented in this paper,we discretize evenly the reduced Brillouin zone,corresponding to the enlarged unit cell containing one IrAand one IrBsites,into 400×400 k points.The criteria of convergence is set so that the sum of changes of all Hartree-Fock expectation values is less than 10?6.Under this criteria,the typical number of iterations needed for convergence is about 2000.At the end,calculations with different initials may converge to different states at one set of Hamiltonian parameters,and the one with the lowest energy should be chosen as the ground state.

    3 Effects of Electron Correlations

    3.1 Magnetic Phase Diagram

    We first fix the strength of SOC to be the physical value in Sr2IrO4,λ=357 meV,and study the effects of electron correlations,Hund’s rule coupling J and intraorbital repulsion U explicitly,on the anisotropy of the AFM moment.The main result is summarized in Fig.1,the Hartree-Fock phase diagram of the five-orbital Hubbard model shown in the plane of U versus J/U ratio,where U varying from 0 to 4 eV and J/U varying from 0 to 0.3 for the physical parameters relevant to 5d iridates.It shows clearly that,even at a constant SOC,the interplay between U and J leads to a very rich and interesting magnetic phase diagram.The phase diagram exhibits three phases,the PM,the in-plane canted AFM,and the collinear z-AFM phase.The inset shows the schematics of the canted AFM moments on the Ir square lattice with a two-dimensional rendering of the staggered IrO6octahedral rotation.In addition to an AFM component in the diagonal direction along the next-nearest-neighbor Ir-Ir bond(e.g.[1,1,0]),the ordered local moments on Ir sites in the canted AFM phase have an FM component perpendicular to the AFM component(e.g.[1,ˉ1,0]),originated from the staggered rotation of the IrO6octahedra.It is interesting to note that the critical intraorbital repulsion Umrequired for the emergence of AFM order is stronger for larger J/U ratio,in contrast to multiorbital systems without SOC.[39?41]This behavior is naturally understood since the Hund’s rule coupling competes with the SOC and works destructively for the formation of the quasiparticles of L+S character originated from SOC.[24,42]The AFM ordered phase is divided into three regimes in the phase diagram by two spin- flop transitions between the canted AFM and the z-AFM phases,Jsfin the small J/U regime beyond Um,and Usfin the regime with large J/U and large U.In the upper-right portion of the phase diagram,there is a spin-state transition from low-spin states to high-spin states in the z-AFM states.As we shall demonstrate later in this section,all phase transitions exhibited in the phase diagram are first-order.

    3.2 Antiferromagnetic Anisotropy

    In order to elaborate the anisotropy in the AFM ordered moment,we performed a variational calculation,which fixes the AFM moment into a specific direction.In practice,we restrict instead the direction of the AFM spin moment by adding a constraint term W(e0AFM?|SAFM|)to the Hamiltonian in Eq.(2),where e0is the unit vector along the desired direction and W is the corresponding Lagrange multiplier.Effectively,W acts as a staggered Zeeman field to pine SAFMalong the desired direction,and this term would not contribute to the state energy as long as the constraint is satisfied.Figure 2 plots the AFM state energy per Ir site as a function of the pinned direction of SAFMat six sets of electron correlations.For clarity,all energies are shown with respect to the[1,0,0]-ordered AFM state with SAFMalong the xaxis.Here and after,we use Ex,Exy,and Ezto denote the energy per site of the states with SAFMpointing along,respectively,[1,0,0],[1,1,0],and[0,0,1]direction.To describe the AFM anisotropy quantitatively,we introduce an out-of-plane anisotropy energy?Ez=Ez?Exand an in-plane anisotropy energy?Exy=Exy?Ex.

    Fig.2 The state energy per site as a function of the AFM moment direction at U=1.4 eV and U=3 eV with(a)J/U=0,(b)J/U=0.1,and(c)J/U=0.2.Insets focus on the in-plane magnetic anisotropy with the AFM moment rotating within the xy-plane.

    In the absence of the Hund’s rule coupling J=0,as shown in Fig.2(a)for both U=(1.4 and 3)eV,the state energy is independent of the AFM moment direction so long as it lies in the xy-plane,and it starts to decrease as the moment is tilted away from the plane,reaching a minimum at[0,0,1]direction.Quantitatively,?Exy=(0,0)and ?Ez=(?0.043,?0.035)meV at U=(1.4,3)eV,implying an easy-axis AFM along the z-axis with xy-plane rotational symmetry.The ground state is thus a z-AFM at both U=(1.4 and 3)eV.At J/U=0.1,one can see clearly from Fig.2(b)that the minimum at[0,0,1]becomes a maximum in the state energy,and a new shallow minimum is developed at[1,1,0].For U=(1.4,3)eV,the in-plane anisotropy energy?Exy=(?0.75,?0.91) μeV,and the out-of-plane anisotropy energy?Ez=(1.20,1.01)meV.It tells us that the system now prefers an easy-plane AFM moment and,in addition,the xy-plane rotational symmetry is broken into a C4symmetry,with the ground state of the lowest energy being the canted AFM along the[1,1,0]direction,giving rise to the canted AFM regime in the phase diagram shown in Fig.1.The C4symmetry of the xy-plane AFM moment is protected by the C4symmetry along principal z axis of the IrO6octahedra.When the J/U ratio reaches 0.2,the direction dependence of the state energy is pretty much unchanged at U=1.4 eV except for enlarged magnetic anisotropy with?Exy=?6.9μeV and?Ez=3.0 meV.On the other hand,its behavior is significantly different for U=3 eV.The state energy now has two minima located at[1,1,0]and[0,0,1],with?Exy=?213.4μeV and?Ez=?5.4 meV,leading to an easy-axis AFM along the z axis.

    In summary,the AFM moment has the xy-plane rotational symmetry in the absence of Hund’s rule coupling J,and the inclusion of J breaks the rotational symmetry to a C4symmetry with[1,1,0]being the preferred direction for in-plane AFM moment.In contrast,the out-of-plane anisotropy of the AFM moment is nonzero even in the absence of J,and the Hund’s rule coupling J has an interesting nonmonotonic effect on the out-ofplane anisotropy,allowing a reentrance behavior of the z-AFM state. In addition,the in-plane anisotropy is much weaker than the out-of-plane anisotropy,consistent with recent experiment.[43]It is important to note that a three-orbital Hubbard model of the t2gcomplex,with an effective orbital angular moment L=1,is invariant under continuous rotation along the z-axis and,as a result,they could not resolve the in-plane anisotropy.[22?25]Current localized picture based on the Jeff=1/2 pseudospin anisotropic Heisenberg model is derived from the three-orbital Hubbard model of t2gorbitals.[17]It would be interesting to investigate the changes in the exchange couplings,anisotropic ones in particular,if the exchange Hamiltonian is obtained from the five-orbital Hubbard model for all five 5d Ir orbitals.The magnetic ground state in the studied parameter regime is either the collinear z-AFM state or the coplanar canted AFM state with AFM ordered moment pointing along the[1,1,0]direction,we hence limit our discussion in the rest of the paper to these two states.

    3.3 Magnetic Moment and Phase Transitions

    To gain detail information of the phase transitions and the ordered moment,we next examine the behavior of the canted AFM and z-AFM states as a function of U(or J/U)while keeping the value of J/U(or U) fixed,and compare their energies to determine the ground state.In Fig.3,we fix J/U=0.25 and scan the intraorbital repulsion U.The energy difference between z-AFM and canted AFM,Ez?Exy,is plotted in Fig.3(a)as a function of U,with the evolutions of the local moments,spin moment|2S|and the total magnetic moment|L+2S|shown in Figs.3(b)and 3(c),respectively,for these two states.At small U,the electron correlation is not strong enough to induce any magnetic moment,and hence the ground state is a PM metal.With increasing U,the canted AFM moment develops at Um=1.2 eV.The magnetic transition from PM to canted AFM is weakly first order as evidenced by the discontinuity in the energy difference between the PM(the z-AFM is not developed yet,and thus Ezactually denotes the energy of the PM phase)and the canted AFM shown in Fig.3(a).

    Fig.3 (a)The intraorbital repulsion U dependence of the energy difference between the canted AFM and the z-AFM phase with fixed ratio J/U=0.25.The corresponding local spin moment|2S|and local magnetic moment|L+2S|are shown in(b)for the canted AFM phase and in(c)for the z-AFM phase.Insets in(c)show the schematics of the low-spin and high-spin states.The system undergoes a magnetic transition at Um=1.2 eV,a spin- flop transition at Usf=2.35 eV,and a spin-state transition at Usp=2.95 eV.The parameter regime is shaded with the color associated with the corresponding ground state,as used in Fig.1.

    The z-AFM moment emerges subsequently at a slightly stronger electron correlation with U=1.26 eV.But it is still higher in energy than the canted AFM,so the latter remains as the ground state.Further increasing U,the energy difference Ez?Exyfirst increases a little bit and then start to decrease,crossing zero at Usf=2.35 eV where the direction of the ordered AFM moments flops from[1,1,0]to[0,0,1].At this first-order spin- flop transition,the ground state changes from the coplanar canted AFM to the collinear z-AFM.It is interesting to notice the existence of another transition inside the z-AFM phase at Usp=2.95 eV,which we referred to as a spin-state transition.At this transition,the size of ordered local spin moment jumps from ~1.5μBto~ 5μBwhile keeping its direction along the z-axis unchanged.Below Usp,the spin S and orbital L are strongly coupled to each other due to SOC,and the quasiparticles carry an L+S character.As a result,the ordered magnetic moment has significant contributions from both S and L.In contrast,the spin S and orbital L are decoupled beyond Usp,as evidenced by the negligible L contribution to the total magnetic moment,and the system is in a high-spin S=5/2 state with one electron occupying each of the five orbitals,as depicted in the inset of Fig.3(c).

    The location of the spin-state transition can be roughly estimated by considering the atomic situation.Keeping the octahedral ligand field?cand ignoring the tetragonal crystal field for simplification,the energies of the low-spin S=1/2 and high-spin S=5/2 state are,respectively,E1/2=10(U?2J)and E5/2=10(U?3J)+2?c.When the difference E1/2?E5/2=2(5J??c)is larger than the SOC λSOC,i.e.J>(1/5)?c+(1/10)λSOC? 0.73 eV,the coupling between S and L is strongly suppressed and the system would rather stay in the high-spin state of pure S character.The dotted line in Fig.1 denotes J=0.73 eV and it is very close to the spin-state transition obtained for the itinerant electrons.

    The behaviors of these two AFM states are shown in Fig.4 as a function of J/U ratio with fixed U=3 eV.The intraorbital Coulomb repulsion U is so large that both the canted AFM and z-AFM are lower in energy than the PM phase in the whole J/U regime we investigated from 0 to 0.3.Zooming into the small J/U regime,the inset of Fig.4(a)shows that the energy difference between z-AFM and canted AFM(Ez?Exy)is negative at J/U=0 and crosses zero at Jsf/U=0.06,giving rise to the small z-AFM region in the bottom-right of the phase diagram in Fig.1 and a first-order spin- flop transition at Jsf.Further increasing J/U,Ez?Exyincreases and reaches a maximum value near J/U=0.14 and then starts to decrease,across zero again at J/U=0.173,i.e.Usf=3 eV at J/U=0.173.This leads to an interesting reentrance behavior of the z-AFM state through a second first-order spin- flop transition.At an even larger J/U=0.246,the system again undergoes a spin-state transition in the z-AFM phase.The competition between Hund’s rule coupling J and SOC is most pronounced in the canted AFM phase,as shown in Fig.4(b),where the local moments,both|2S|and|L+2S|,decrease with increasing J at small J,contradictory to the conventional behavior of moment in multiorbital systems without SOC.[39?41]At small J regime where SOC dominant,the latter couples the spin S and orbital L and imposes an L+S character to the quasiparticles,and thus the ordered moment have significant contributions from both S and L.At J=0,the ratio|L|/|S|to 3.6 in the canted AFM and 5 in the z-AFM state,which is close to the expected value 4 for the ideal Jeff=1/2 moment of a spin-orbit Mott insulator,but cannot be accounted for by the redistribution of orbital components within the t2gorbitals.[33]With the increasing of the Hund’s rule coupling,the coupling between S and L is suppressed and the S character of the quasiparticles is enhanced.As a result,the ratio|L|/|S|decreases as increasing J,and drops to negligible values after the spin-state transition.

    Fig.4 Same as Fig.3,but for the J/U ratio dependence with fixed U=3 eV.Inset in(a)zoom into the small J/U region,showing the spin- flop transition at Jsf.The system undergoes two spin- flop transitions at Jsf/U=0.06 and J/U=0.173(Usf=3 eV at this ratio),and a spinstate transition at J/U=0.246(Usp=3 eV at this ratio).

    In summary,due to the subtle interplay between the two electron correlations,intraorbital repulsion U and Hund’s rule coupling J,and the competition between J and SOC,the system undergoes multiple phase transitions as one varying one of the electron correlation parameters while keeping the other fixed.As a result,it leads to a very rich and interesting magnetic phase diagram for the five-orbital Hubbard model at constant SOC shown in Fig.1.

    4 Effects of Spin-Orbit Coupling

    For a better understanding of the effects of SOC,in this section,we fix the values of electron correlations(U and J),and study the state evolution as a function of λSOC.The behavior is relatively simple at U=3 eV and J/U=0.25(i.e.,J=0.75 eV),as shown in Fig.5.At λSOC=0,the spin S and orbital L are completely decoupled,and the moment has an SU(2)rotation symmetry in the absence of SOC.As a result,the z-AFM and canted AFM are degenerate with Ez?Exy=0 at λSOC=0.Because of the large value of J,the system is in the high-spin state with all moment coming from spin,|L+2S|=|2S|=4.68 μB.Switching on λSOC,the SOC tends to couple electrons with different spins from different orbitals,disfavoring the high-spin state with pure S character.Therefore,as λSOCincreasing,the spin moment and the total moment decrease and,at the same time,the contribution from orbital L increases.Note that the decreasing of moments here is very gradual and continuous,implying a crossover between the high-spin state and lowspin state as one increases SOC.It is very different from the situation when we fix λSOCand vary the electron correlations(the Hund’s rule coupling J in particular)presented in last section,where the ground state undergoes a first-order spin-state transition as it leaves the high-spin state.The energy difference Ez?Exydecreases with increasing λSOC,reaches a minimum at λSOC0.57 eV,and then starts to increase.But it never crosses zero up to the largest value we investigated,0.7 eV,which is twice of its physical value in Sr2IrO4,and the z-AFM is always the ground state.Therefore,the ordered AFM moment in the ground state never change its direction from the z axis as the SOC strength varying from 0 to 0.7 eV at(U,J)=(3,0.75)eV,though the anisotropy energy depends strongly on λSOC.

    In Fig.6,we scan λSOCwith fixed U=2 eV and J/U=0.1(i.e.,J=0.2 eV)where the ground state is in the canted AFM phase when the strength of SOC takes its physical value in Sr2IrO4,λSOC=357 meV.In the absence of SOC,λSOC=0,the magnetic moment has SU(2)rotation symmetry and all ordered moment comes from spin moment,|L+2S|=|2S|=1μB.The local moments in the canted AFM and z-AFM are plotted,respectively,in Figs.6(b)and 6(c).Switching on the SOC,the mixing of electrons with different spins suppresses the spin moment in both the canted AFM and z-AFM phase,but the behavior of the orbital L at a small but nonzero λSOCis quite different in these two AFM phases.In the z-AFM phase,the coupling between spin and orbit is very weak and the quasiparticles remains mostly S character,and thus the L contribution to the ordered moment is very small.On the other hand,the system in the canted AFM phase is found to be in a different state with lower energy,where the coupling between spin and orbital is already fully activated,despite at such a small λSOC.The orbital L contribution to the ordered moment is thus quite large.At the strongest SOC we studied,λSOC=0.7 eV,the ordered moment is 0.84 and 0.9μB,respectively,in the canted AFM and z-AFM phase,with a corresponding ratio|L|/|S|equal to 3.6 and 3.9,very close to the value of the ideal Jeff=1/2 moment.Reducing SOC from λSOC=0.7 eV,though the size of ordered moments changes very slowly in both AFM phases,it decreases in the canted AFM phase but increases in the z-AFM phase.Comparing the state energies of these two AFM phase,shown in Fig.6(a),one see clearly that the canted AFM is always lower in energy and thus being the ground state within the whole parameter regime of interest.

    Fig.5 The λSOCdependence of the energy difference between the canted AFM and the z-AFM phase with electron correlation U=3 eV and J/U=0.25.The corresponding local spin moment|2S|and local magnetic moment|L+2S|are shown in(b)for the canted AFM phase and in(c)for the z-AFM phase.

    From these two studies presented in Figs.5 and 6,we illustrate that the SOC,as the origin of magnetic anisotropy,is very ineffective in tuning the direction of the ordered AFM moment.This is very different from the situation in the strong coupling limit,[17]where the direction of the ordered AFM moment is sensitive to the strength of SOC relative to the tetragonal splitting of the t2gorbitals.

    Fig.6 Same as Fig.5,but for the λSOCdependence at U=2 eV and J/U=0.1.

    5 Conclusions

    Based on a five-orbital Hubbard model with SOC,in which the noninteracting part describes well the realistic band structure of Sr2IrO4,we study in this paper the electron correlations,the SOC,and their effects on the AFM anisotropy.The electron correlations are treated within the Hartree-Fock approximation to obtain the ground state properties of the multi-orbital Hubbard model,at various strengths of SOC and electron correlations.We demonstrate that,at a constant SOC,the interplay between Hund’s rule coupling J and intraorbital repulsion U leads to a rich magnetic phase diagram,including a canted AFM state with weak FM moment in a large area of the phase diagram,consistent with the ground state of Sr2IrO4identified in experiments.In contrast,the SOC is shown to be very ineffective in tuning the direction of the ordered AFM moment,despite the fact that it is the origin of magnetic anisotropy.While our result cannot be considered quantitatively accurate due to the intrinsic deficiencies of mean- field approximations,our weak-coupling study is still useful in understanding qualitatively the behaviors of spin-orbit coupled multi-orbital systems.The presence of magnetic anisotropy indicates the difference between the longitudinal(out-of-plane)and transverse(in-plane)spin susceptibilities,as expected for spin-orbit entangled systems where the spin SU(2)symmetry is broken.It would be very interesting to study the effects of such difference between spin susceptibilities on the spin fluctuation mediated superconductivity,which consists of both singlet and triplet pairing due to SOC.[5,44]

    Acknowledgments

    We thank Kun Jiang and Hua Chen for useful discussions.

    [1]G.Cao,J.Bolivar,S.McCall,et al.,Phys.Rev.B 57(1998)11039(R).

    [2]M.K.Crawford,et al.,Phys.Rev.B 49 9198(1994).

    [3]B.J.Kim,et al.,Phys.Rev.Lett.101(2008)076402.

    [4]B.J.Kim,et al.,323(2009)1329.

    [5]H.Watanabe,T.Shirakawa,and S.Yunoki,Phys.Rev.Lett.110(2013)027002.

    [6]Y.Yang,W.S.Wang,J.G.Liu,et al.,Phys.Rev.B 89(2014)094518.

    [7]Fa Wang and T.Senthil,Phys.Rev.Lett.106(2011)136402.

    [8]J.W.Kim,et al.,Phys.Rev.Lett.109(2012)037204.

    [9]Z.Y.Meng,Y.B.Kim,and H.Y.Kee,Phys.Rev.Lett.113(2014)177003.

    [10]S.Sumita,T.Nomoto,and Y.Yanase,Phys.Rev.Lett.119(2017)027001.

    [11]Y.K.Kim,et al.,Science 345(2014)187.

    [12]A.de la Torre,et al.,Phys.Rev.Lett.115(2015)176402.

    [13]Y.K.Kim,N.H.Sung,J.D.Denlinger,and B.J.Kim,Nat.Phys.12(2016)37.

    [14]Y.J.Yan,et al.,Phys.Rev.X 5(2015)041018.

    [15]Feng Ye,et al.,Phys.Rev.B 87(2013)140406(R).

    [16]Chetan Dhital,et al.,Phys.Rev.B 87(2013)144405.

    [17]G.Jackeli and G.Khaliullin,Phys.Rev.Lett.102(2009)017205.

    [18]S.Fujiyama,et al.,Phys.Rev.Lett.108(2012)247212.

    [19]N.B.Perkins,Y.Sizyuk,and P.W?lfle,Phys.Rev.B 89(2014)035143.

    [20]J.M.Carter,V.Shankar,and H.Y.Kee,Phys.Rev.B 88(2013)035111.

    [21]I.V.Solovyev,V.V.Mazurenko,and A.A.Katanin,Phys.Rev.B 92(2015)235109.

    [22]D.Hsieh,F.Mahmood,D.H.Torchinsky,et al.,Phys.Rev.B 86(2012)035128.

    [23]H.Watanabe,T.Shirakawa,and S.Yunoki,Phys.Rev.B 89(2014)165115.

    [24]H.Watanabe,T.Shirakawa,and S.Yunoki,Phys.Rev.Lett.105(2010)216410.

    [25]R.Arita,J.Kune? A.V.Kozhevnikov,et al.,Phys.Rev.Lett.108(2012)086403.

    [26]H.Jin,H.Jeong,T.Ozaki,and J.J.Yu,Phys.Rev.B 80(2009)075112.

    [27]P.T.Liu,et al.,Phys.Rev.B 92(2015)054428.

    [28]S.J.Moon,et al.,Phys.Rev.B 80(2009)195110.

    [29]Q.Li,et al.,Sci.Rep.3(2013)3073.

    [30]A.Yamasaki,et al.,Phys.Rev.B 89(2014)121111(R).

    [31]I.N.Bhatti and A.K.Pramanik,J.Magn.Magn.Mater.422(2017)141.

    [32]D.Haskel,G.Fabbris,M.Zhernenkov,et al.,Phys.Rev.Lett.109 027204(2012).

    [33]S.Fujiyama H.Ohsumi,K.Ohashi,et al.,Phys.Rev.Lett.112 016405(2014).

    [34]G.L.Stamokostas and G.A.Fiete,Phys.Rev.B 97(2018)085150.

    [35]S.Zhou,K.Jiang,H.Chen,and Z.Wang,Phys.Rev.X 7(2017)041018.

    [36]C.Castellani,C.R.Natoli,and J.Ranninger,Phys.Rev.B 18(1978)4945.

    [37]A.Georges,L.Medici,and J.Mravlje,Ann.Rev.Condens.Matter Phys.4(2013)137.

    [38]M.E.A.Coury,S.L.Dudarev,W.M.C.Foulkes,et al.,Phys.Rev.B 93(2016)075101.

    [39]S.Zhou and Z.Wang,Phys.Rev.Lett.105(2010)096401.

    [40]Y.M.Quan,L.J.Zou,D.Y.Liu,and H.Q.Lin,Eur.Phys.J.B 85(2012)55.

    [41]Q.Luo,K.Foyevtsova,G.D.Samolyuk,et al.,Phys.Rev.B 90 035128(2014).

    [42]A.J.Kim,H.O.Jeschke,P.Werner,and R.Valentí,Phys.Rev.Lett.118(2017)086401.

    [43]D.Pincini,et al.,Phys.Rev.B 96(2017)075162.

    [44]X.Wu,F.Yang,C.Le,et al.,Phys.Rev.B 92(2015)104511.

    猜你喜歡
    周浩
    大學(xué)生周浩:摩托騎行環(huán)游中國(guó)
    棄北大讀技校 自定別樣人生
    棄北大讀技校,自定別樣人生
    放棄北大讀技校
    認(rèn)真是成功的保證
    興趣是最好的老師
    放棄北大讀技校
    棄北大讀技校,自定別樣人生
    棄北大讀技校,這是鬧哪般?
    北大學(xué)生退學(xué)讀技校:專業(yè)沒興趣痛不欲生
    人生十六七(2015年6期)2015-01-11 03:19:01
    www.熟女人妻精品国产| 国产欧美日韩精品亚洲av| 99久久精品一区二区三区| 91麻豆av在线| 简卡轻食公司| 69av精品久久久久久| 有码 亚洲区| 国产精品av视频在线免费观看| 大型黄色视频在线免费观看| 小说图片视频综合网站| 9191精品国产免费久久| 久久精品国产亚洲av天美| 亚洲av免费高清在线观看| 亚洲欧美日韩卡通动漫| 国产主播在线观看一区二区| 国产高清视频在线播放一区| .国产精品久久| 看十八女毛片水多多多| 国产精品乱码一区二三区的特点| 欧美午夜高清在线| 精品国产亚洲在线| 欧美激情国产日韩精品一区| 国产在线精品亚洲第一网站| 日本在线视频免费播放| 成人鲁丝片一二三区免费| 免费看日本二区| 最近中文字幕高清免费大全6 | 桃红色精品国产亚洲av| 精品国产三级普通话版| 欧美绝顶高潮抽搐喷水| 亚洲av电影不卡..在线观看| 观看美女的网站| 国产老妇女一区| 丁香六月欧美| 国产单亲对白刺激| 好男人在线观看高清免费视频| 免费看a级黄色片| 欧美激情久久久久久爽电影| 亚洲av不卡在线观看| 亚洲成av人片免费观看| 亚洲狠狠婷婷综合久久图片| 亚洲av免费在线观看| 国产三级中文精品| 老熟妇乱子伦视频在线观看| 亚洲成人久久爱视频| 欧美性猛交黑人性爽| 黄色女人牲交| 国产主播在线观看一区二区| 欧美又色又爽又黄视频| 免费无遮挡裸体视频| 激情在线观看视频在线高清| 成人av一区二区三区在线看| 精品国内亚洲2022精品成人| 色av中文字幕| 成人亚洲精品av一区二区| 国产综合懂色| 国产精品一区二区免费欧美| 成年免费大片在线观看| 女人被狂操c到高潮| 男人狂女人下面高潮的视频| 最近最新中文字幕大全电影3| 久久精品国产亚洲av天美| 久久伊人香网站| 久久久久久久亚洲中文字幕 | 午夜福利在线在线| 国产精品一区二区性色av| 天天一区二区日本电影三级| 免费一级毛片在线播放高清视频| 国内精品久久久久精免费| 老司机午夜十八禁免费视频| www.www免费av| 免费大片18禁| 亚洲熟妇中文字幕五十中出| 精品国产三级普通话版| 久久欧美精品欧美久久欧美| 搡老岳熟女国产| 久久精品91蜜桃| 国产精品乱码一区二三区的特点| 美女被艹到高潮喷水动态| 乱码一卡2卡4卡精品| 一进一出抽搐动态| 97热精品久久久久久| 观看美女的网站| 综合色av麻豆| 亚洲精品粉嫩美女一区| 婷婷六月久久综合丁香| 亚洲国产精品999在线| 国产男靠女视频免费网站| 亚洲一区二区三区色噜噜| 少妇高潮的动态图| 国产伦精品一区二区三区四那| 99久久成人亚洲精品观看| 两人在一起打扑克的视频| 久久久国产成人免费| 日韩av在线大香蕉| 国产亚洲欧美在线一区二区| 最新中文字幕久久久久| 亚洲自拍偷在线| 亚洲av成人不卡在线观看播放网| 网址你懂的国产日韩在线| 国产成+人综合+亚洲专区| 国产精品野战在线观看| 日本三级黄在线观看| 亚洲成a人片在线一区二区| 青草久久国产| 欧美在线一区亚洲| 美女xxoo啪啪120秒动态图 | 国产麻豆成人av免费视频| 久9热在线精品视频| 亚洲欧美精品综合久久99| 午夜精品在线福利| 亚洲黑人精品在线| 日韩欧美免费精品| 69人妻影院| 中文字幕熟女人妻在线| 99国产精品一区二区蜜桃av| 国产高清有码在线观看视频| 女人十人毛片免费观看3o分钟| 少妇裸体淫交视频免费看高清| av在线天堂中文字幕| 美女xxoo啪啪120秒动态图 | 一个人免费在线观看的高清视频| 国产黄a三级三级三级人| 精品乱码久久久久久99久播| 九九热线精品视视频播放| 日韩欧美精品免费久久 | 久久精品91蜜桃| 亚洲成人中文字幕在线播放| 亚洲国产欧洲综合997久久,| 88av欧美| 亚洲熟妇熟女久久| 国产精品女同一区二区软件 | 色av中文字幕| 国产av麻豆久久久久久久| 熟妇人妻久久中文字幕3abv| 伦理电影大哥的女人| 99视频精品全部免费 在线| 欧美三级亚洲精品| 国产三级中文精品| 欧美在线黄色| 九色成人免费人妻av| 国产国拍精品亚洲av在线观看| 乱人视频在线观看| 欧美成人a在线观看| 免费在线观看亚洲国产| 亚洲欧美精品综合久久99| 精品久久久久久久久久免费视频| 亚洲无线观看免费| av福利片在线观看| 人人妻人人澡欧美一区二区| 99精品久久久久人妻精品| 18禁黄网站禁片午夜丰满| 亚洲男人的天堂狠狠| 一本综合久久免费| 国产精品人妻久久久久久| 亚洲精品一卡2卡三卡4卡5卡| 久久人人精品亚洲av| 国产一区二区三区在线臀色熟女| 一级毛片久久久久久久久女| 国产成人影院久久av| 女人被狂操c到高潮| 少妇的逼水好多| 国产一区二区三区视频了| 国内揄拍国产精品人妻在线| 乱人视频在线观看| 在现免费观看毛片| 色综合欧美亚洲国产小说| 日日夜夜操网爽| 欧美不卡视频在线免费观看| 人人妻,人人澡人人爽秒播| 国产三级黄色录像| 给我免费播放毛片高清在线观看| 简卡轻食公司| 精品无人区乱码1区二区| 蜜桃亚洲精品一区二区三区| 亚洲精品456在线播放app | 欧美丝袜亚洲另类 | 超碰av人人做人人爽久久| 欧美性猛交╳xxx乱大交人| 欧美在线一区亚洲| 欧美3d第一页| 又黄又爽又刺激的免费视频.| 看十八女毛片水多多多| 亚洲精品亚洲一区二区| 久久久久久久久久黄片| 亚洲aⅴ乱码一区二区在线播放| 欧美日韩福利视频一区二区| 亚洲成人久久爱视频| 国产单亲对白刺激| 免费观看精品视频网站| 欧美乱色亚洲激情| 999久久久精品免费观看国产| 午夜福利欧美成人| 露出奶头的视频| 久久久久国内视频| 国产成人欧美在线观看| 欧美潮喷喷水| 欧美最新免费一区二区三区 | 欧美激情在线99| 中文字幕免费在线视频6| 亚洲欧美日韩东京热| 国产高清激情床上av| 青草久久国产| 国产伦精品一区二区三区四那| 亚洲真实伦在线观看| 亚洲av电影在线进入| 少妇人妻精品综合一区二区 | 欧美成人免费av一区二区三区| 国产成人a区在线观看| 99久久九九国产精品国产免费| 精品一区二区免费观看| 一个人观看的视频www高清免费观看| 欧美高清性xxxxhd video| 婷婷精品国产亚洲av| 国内揄拍国产精品人妻在线| 亚洲七黄色美女视频| 老司机午夜福利在线观看视频| 好看av亚洲va欧美ⅴa在| 亚洲国产精品sss在线观看| 日日干狠狠操夜夜爽| 真实男女啪啪啪动态图| 午夜福利在线在线| 国产淫片久久久久久久久 | 亚洲精品色激情综合| 女人被狂操c到高潮| 不卡一级毛片| 最后的刺客免费高清国语| 亚洲无线观看免费| 亚洲精品粉嫩美女一区| 亚洲美女搞黄在线观看 | 日本撒尿小便嘘嘘汇集6| 69人妻影院| 亚洲人成电影免费在线| 精品国内亚洲2022精品成人| 久久久成人免费电影| 在线免费观看不下载黄p国产 | 午夜a级毛片| 午夜激情欧美在线| 三级国产精品欧美在线观看| 日本 欧美在线| 欧美日本视频| 国产欧美日韩精品亚洲av| 精品午夜福利视频在线观看一区| 人人妻人人澡欧美一区二区| 日韩 亚洲 欧美在线| 国语自产精品视频在线第100页| 午夜福利免费观看在线| av黄色大香蕉| 婷婷六月久久综合丁香| 亚洲av不卡在线观看| 国产精品一区二区性色av| 欧美激情在线99| 免费一级毛片在线播放高清视频| 亚洲国产欧洲综合997久久,| 中文字幕人妻熟人妻熟丝袜美| 午夜免费成人在线视频| 青草久久国产| 赤兔流量卡办理| 一级a爱片免费观看的视频| 欧美色视频一区免费| 757午夜福利合集在线观看| 色综合站精品国产| 夜夜躁狠狠躁天天躁| 久久亚洲精品不卡| 男人狂女人下面高潮的视频| 免费看a级黄色片| 毛片女人毛片| 一级黄色大片毛片| 天天躁日日操中文字幕| 久久久久免费精品人妻一区二区| 丰满乱子伦码专区| 免费在线观看日本一区| 男女床上黄色一级片免费看| 久久久久精品国产欧美久久久| 欧美日本亚洲视频在线播放| 国产美女午夜福利| 欧美一区二区精品小视频在线| 色精品久久人妻99蜜桃| 国产白丝娇喘喷水9色精品| 深爱激情五月婷婷| 中文字幕高清在线视频| 99在线人妻在线中文字幕| 级片在线观看| 一进一出好大好爽视频| 亚洲久久久久久中文字幕| 午夜福利在线在线| 午夜激情福利司机影院| 亚洲中文字幕一区二区三区有码在线看| 丰满乱子伦码专区| 人妻久久中文字幕网| 国产精品国产高清国产av| 一进一出好大好爽视频| av女优亚洲男人天堂| 久久久久免费精品人妻一区二区| 精华霜和精华液先用哪个| 久久久久国内视频| 波多野结衣巨乳人妻| 自拍偷自拍亚洲精品老妇| 一个人免费在线观看电影| 国产久久久一区二区三区| 亚洲一区二区三区色噜噜| 乱人视频在线观看| 国产久久久一区二区三区| 国语自产精品视频在线第100页| 国产高清视频在线观看网站| 国产麻豆成人av免费视频| 丁香六月欧美| av中文乱码字幕在线| 亚洲无线在线观看| 久久99热6这里只有精品| 国产在线男女| 日本与韩国留学比较| 日韩欧美免费精品| 亚洲久久久久久中文字幕| 成人特级黄色片久久久久久久| 国产精品一区二区三区四区久久| 午夜激情欧美在线| 757午夜福利合集在线观看| 久久久久久久久大av| 日韩欧美精品免费久久 | 午夜a级毛片| 欧美乱妇无乱码| 美女被艹到高潮喷水动态| 2021天堂中文幕一二区在线观| 男女视频在线观看网站免费| 久久久精品大字幕| 日本五十路高清| 一本久久中文字幕| 久久久久免费精品人妻一区二区| 精品国产三级普通话版| 亚洲成人久久爱视频| 欧美最黄视频在线播放免费| 亚洲熟妇中文字幕五十中出| 亚洲三级黄色毛片| 少妇的逼好多水| 亚洲在线观看片| 久久久成人免费电影| 亚洲人成网站在线播| 精华霜和精华液先用哪个| 性欧美人与动物交配| 欧美+亚洲+日韩+国产| 啪啪无遮挡十八禁网站| 欧美潮喷喷水| 午夜福利欧美成人| 亚洲成人久久爱视频| 久久久成人免费电影| 亚洲欧美日韩高清专用| 国产精品人妻久久久久久| av欧美777| 美女cb高潮喷水在线观看| 成人一区二区视频在线观看| 97人妻精品一区二区三区麻豆| 十八禁人妻一区二区| 9191精品国产免费久久| 精品一区二区免费观看| 很黄的视频免费| 三级男女做爰猛烈吃奶摸视频| 国产精品自产拍在线观看55亚洲| 亚洲第一电影网av| 亚洲成人精品中文字幕电影| 毛片女人毛片| 亚洲av五月六月丁香网| 香蕉av资源在线| 真人一进一出gif抽搐免费| 色5月婷婷丁香| 国产欧美日韩一区二区三| 三级毛片av免费| 白带黄色成豆腐渣| 国产精品日韩av在线免费观看| 精品久久久久久成人av| 欧美3d第一页| 国语自产精品视频在线第100页| 很黄的视频免费| 欧美一区二区精品小视频在线| 色综合站精品国产| 亚洲成av人片在线播放无| a级毛片a级免费在线| 日韩欧美在线乱码| 中文字幕熟女人妻在线| 老司机深夜福利视频在线观看| 日本免费a在线| 日韩国内少妇激情av| 日本免费a在线| 一个人看视频在线观看www免费| 嫩草影院新地址| 欧美精品啪啪一区二区三区| 嫩草影院入口| 小说图片视频综合网站| 日本一二三区视频观看| 色哟哟哟哟哟哟| 久久久国产成人免费| 老熟妇仑乱视频hdxx| 久久久国产成人免费| 国产高清视频在线播放一区| 国内精品久久久久久久电影| 亚洲国产精品999在线| 久久精品国产99精品国产亚洲性色| 搡老岳熟女国产| 一卡2卡三卡四卡精品乱码亚洲| 欧美bdsm另类| 乱码一卡2卡4卡精品| 亚洲av免费在线观看| 啦啦啦观看免费观看视频高清| 亚洲熟妇中文字幕五十中出| 久久久久久久久中文| or卡值多少钱| 少妇熟女aⅴ在线视频| 成人午夜高清在线视频| 国产老妇女一区| 久久九九热精品免费| 99久久久亚洲精品蜜臀av| 亚洲人与动物交配视频| 欧美日本亚洲视频在线播放| 欧美极品一区二区三区四区| 久久久成人免费电影| 真实男女啪啪啪动态图| 国产一区二区亚洲精品在线观看| 成人欧美大片| 亚洲av.av天堂| 精品久久久久久成人av| 麻豆av噜噜一区二区三区| 国产白丝娇喘喷水9色精品| 午夜两性在线视频| 欧美黑人巨大hd| 日韩精品中文字幕看吧| 国产成人福利小说| 天堂影院成人在线观看| 精品人妻视频免费看| 日本黄色片子视频| 91字幕亚洲| 久久性视频一级片| 又紧又爽又黄一区二区| 最近中文字幕高清免费大全6 | 一本久久中文字幕| 亚洲国产精品合色在线| 天堂√8在线中文| 又爽又黄a免费视频| 97人妻精品一区二区三区麻豆| 三级毛片av免费| 老熟妇仑乱视频hdxx| 成人性生交大片免费视频hd| 日韩欧美 国产精品| 亚洲av免费高清在线观看| 在线观看免费视频日本深夜| 国模一区二区三区四区视频| 精品福利观看| 深夜精品福利| aaaaa片日本免费| 麻豆久久精品国产亚洲av| 欧美一区二区亚洲| 啦啦啦韩国在线观看视频| 五月玫瑰六月丁香| 精品熟女少妇八av免费久了| 亚洲国产精品合色在线| 久久精品影院6| 99久久精品一区二区三区| 欧美日韩中文字幕国产精品一区二区三区| 午夜久久久久精精品| avwww免费| 精品人妻熟女av久视频| 亚洲中文字幕一区二区三区有码在线看| 久久天躁狠狠躁夜夜2o2o| 中文资源天堂在线| 成人av一区二区三区在线看| 97超视频在线观看视频| 丰满人妻熟妇乱又伦精品不卡| 精华霜和精华液先用哪个| 夜夜夜夜夜久久久久| 成人国产一区最新在线观看| 日韩亚洲欧美综合| 亚洲电影在线观看av| 51国产日韩欧美| 久久国产乱子伦精品免费另类| 亚洲久久久久久中文字幕| 亚洲自偷自拍三级| 9191精品国产免费久久| 亚洲精华国产精华精| 1000部很黄的大片| 一级av片app| 久久久久久久久大av| 国产欧美日韩精品一区二区| 亚洲七黄色美女视频| 全区人妻精品视频| 少妇人妻精品综合一区二区 | 热99re8久久精品国产| 中文字幕人成人乱码亚洲影| av在线老鸭窝| 18禁在线播放成人免费| 亚洲av五月六月丁香网| 成人av在线播放网站| 亚洲国产精品999在线| 乱码一卡2卡4卡精品| 丰满乱子伦码专区| 国产精品乱码一区二三区的特点| 给我免费播放毛片高清在线观看| 日本五十路高清| 久久精品国产亚洲av天美| 床上黄色一级片| 少妇熟女aⅴ在线视频| 给我免费播放毛片高清在线观看| 色在线成人网| 一本精品99久久精品77| 九九热线精品视视频播放| 伦理电影大哥的女人| 久久久国产成人免费| 成人三级黄色视频| 久久人妻av系列| 舔av片在线| 一级黄色大片毛片| 免费在线观看成人毛片| 亚洲av.av天堂| 9191精品国产免费久久| 最后的刺客免费高清国语| 日韩欧美国产一区二区入口| 丰满人妻熟妇乱又伦精品不卡| 久久精品综合一区二区三区| 欧美激情久久久久久爽电影| 成人av在线播放网站| 精品久久久久久久久亚洲 | 成人毛片a级毛片在线播放| 如何舔出高潮| 日本精品一区二区三区蜜桃| 欧美绝顶高潮抽搐喷水| 精品欧美国产一区二区三| 村上凉子中文字幕在线| 国产aⅴ精品一区二区三区波| 久久久久久大精品| 一级黄色大片毛片| 欧美色欧美亚洲另类二区| 久久婷婷人人爽人人干人人爱| 成人欧美大片| 欧美黑人巨大hd| 又粗又爽又猛毛片免费看| 亚洲人成网站在线播| 精品久久国产蜜桃| 亚洲经典国产精华液单 | 亚洲片人在线观看| 看片在线看免费视频| 亚洲国产精品成人综合色| 1000部很黄的大片| 亚洲人成网站在线播| 国产亚洲欧美在线一区二区| 波野结衣二区三区在线| aaaaa片日本免费| 国产私拍福利视频在线观看| 亚洲,欧美,日韩| 一本一本综合久久| 少妇被粗大猛烈的视频| 看片在线看免费视频| 最近最新免费中文字幕在线| 精品人妻1区二区| 一本精品99久久精品77| 免费观看人在逋| 国产一区二区三区视频了| 91麻豆av在线| 成年女人永久免费观看视频| 亚洲经典国产精华液单 | 99久久精品热视频| 韩国av一区二区三区四区| 国产精品野战在线观看| 美女xxoo啪啪120秒动态图 | 性欧美人与动物交配| 国产精品一区二区三区四区久久| 亚洲国产精品合色在线| 狂野欧美白嫩少妇大欣赏| 他把我摸到了高潮在线观看| 亚洲一区二区三区不卡视频| 亚洲欧美日韩高清专用| 最新中文字幕久久久久| 国产亚洲精品综合一区在线观看| 在线观看午夜福利视频| 日本与韩国留学比较| 国内精品久久久久精免费| 丝袜美腿在线中文| 日本黄色视频三级网站网址| 18禁黄网站禁片午夜丰满| 亚洲精品一区av在线观看| 熟女人妻精品中文字幕| 精品人妻1区二区| 精品99又大又爽又粗少妇毛片 | 中文字幕精品亚洲无线码一区| 色吧在线观看| 搞女人的毛片| 日韩有码中文字幕| 欧美午夜高清在线| 99精品在免费线老司机午夜| 欧美性感艳星| 日本成人三级电影网站| 亚洲人与动物交配视频| 国产精品,欧美在线| 欧美精品啪啪一区二区三区| 无人区码免费观看不卡| 欧美黄色片欧美黄色片| 免费看光身美女| 国产人妻一区二区三区在| 国产欧美日韩一区二区三| 久久精品国产亚洲av涩爱 | 国产不卡一卡二| 麻豆一二三区av精品| 俺也久久电影网| 3wmmmm亚洲av在线观看| 国产亚洲精品综合一区在线观看| 给我免费播放毛片高清在线观看| 国内揄拍国产精品人妻在线| 国产午夜精品论理片| 麻豆成人午夜福利视频| 丰满的人妻完整版| 亚洲,欧美,日韩| 国产美女午夜福利| 亚洲,欧美精品.| 伦理电影大哥的女人| 成年免费大片在线观看| 国产一区二区在线av高清观看| 成人高潮视频无遮挡免费网站| 嫩草影院入口|