Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

小尺寸正方形铁磁薄膜边界效应对磁化翻转过程的影响

用自旋动力学方法系统地研究磁偶极相互作用表现的边界效应对小尺寸正方形铁磁薄膜的磁化翻转过程的影响.在确定的磁偶极相互作用强度下,针对不同的单轴各向异性强度和不同的磁化角(外磁场与易轴间的夹角),具体给出矫顽场与磁化角及单轴各向异性强度之间的依赖关系和-些有代表性的磁滞回线,并给出磁化翻转过程中-些有代表性的微观磁结构.模拟结果表明:磁偶极相互作用表现的边界钉扎作用与单轴各向异性场之间的竞争决定磁滞回线的形状和矫顽场的大小,从而在不同磁化角情况下会导致不同的矫顽场机理.本文提出可有效地描述正方形铁磁性薄膜复杂微观磁畴结构的形成与演变的五磁畴模型.这种五磁畴模型既能直接揭示单轴各向异性正方形铁磁薄膜的几何特性和物理特性,也方便于磁化翻转过程的分析.     

Spin relaxation in the impurity band of a semiconductor in the external magnetic field

Spin relaxation in the impurity band of a 2D semiconductor with spin-split spectrum and hyperfine interaction in the external magnetic field is considered. Two contributions to the spin relaxation are shown to be relevant: the one given by optimal impurity configurations with the hop-waiting time inversely proportional to the external magnetic field and another one related to electron motion over large distances. The average spin relaxation rate is calculated. The article is published in the original.     

Analogue of a spin flop phase transition for an array of magnetic moments with dipole interaction

In a two-dimensional array of magnetic moments with planar magnetization and relatively weak anisotropy in the basal plane, a stepwise phase transition is induced by an external magnetic field parallel to the easy axis of the system. This transition is similar to the spin flop phase transition in weakly anisotropic Heisenberg antiferromagnets with the significant difference that it is accompanied by the rearrangement of the sublattice structure of the magnet; i.e., it can be interpreted as a topological transition. The transition should manifest itself for arrays of submicron magnetic particles (magnetic dots) on nonmagnetic substrates, which have recently become the object of intensive research.     

Effects of a longitudinal magnetic field on spin injection and detection in InAs/GaAs quantum dot structures

Effects of a longitudinal magnetic field on optical spin injection and detection in InAs/GaAs quantum dot (QD) structures are investigated by optical orientation spectroscopy. An increase in the optical and spin polarization of the QDs is observed with increasing magnetic field in the range 0-2?T, and is attributed to suppression of exciton spin depolarization within the QDs that is promoted by the hyperfine interaction and anisotropic electron-hole exchange interaction. This leads to a corresponding enhancement in spin detection efficiency of the QDs by a factor of up to 2.5. At higher magnetic fields, when these spin depolarization processes are quenched, the electron spin polarization in anisotropic QD structures (such as double QDs that are preferably aligned along a specific crystallographic axis) still exhibits a rather strong field dependence under non-resonant excitation. In contrast, such a field dependence is practically absent in more 'isotropic' QD structures (e.g.?single QDs). We attribute the observed effect to stronger electron spin relaxation in the spin injectors (i.e.?wetting layer and GaAs barriers) of the lower-symmetry QD structures, which also explains the lower spin injection efficiency observed in these structures.     

关于磁性物质的自旋位形的某些问题

本文用Lyons-Kaplan的方法,讨论了具有一种磁性离子组成的布拉维点阵的自旋位形在外磁场作用下的变化及磁晶各向异性时它的影响。存在有一个反铁磁-铁磁性结构转变的临界磁场,外磁场大于临界磁场时一切反铁磁结构都消失。磁场(小于临界磁场)和各向异性都使自旋位形的简并部分消失。最后还讨论了所得到的自旋位形的稳定性。     

Anisotropic Spin Splitting in Step Quantum Wells

By the method of finite difference, the anisotropic spin splitting of the AlxGa1-xAs/GaAs/Aly Ga1-yAs/AlxGal-xAs step quantum wells （QWs） are theoretically investigated considering the interplay of the bulk inversion asymmetry and structure inversion asymmetry induced by step quantum well structure and external electric field. We demonstrate that the anisotropy of the total spin splitting can be controlled by the shape of the QWs and the external electric field. The interface related Rashba effect plays an important effect on the anisotropic spin splitting by influencing the magnitude of the spin splitting and the direction of electron spin. The Rashba spin splitting presents in the step quantum wells due to the interface related Rashba effect even without external electric field or magnetic field.     

Anisotropy and magnetic field effects on the entanglement of a two qubit Heisenberg XY chain

We investigate the entanglement of a two-qubit anisotropic Heisenberg XY chain in thermal equilibrium at temperature T in the presence of an external magnetic field B along the z axis. By means of the combined influences of anisotropic interactions and a magnetic field B, one is able to produce entanglement for any finite T, by adjusting the magnetic field strength. This contrasts with the isotropic interaction or the B = 0 cases, for which there is no entanglement above a critical temperature T(c) that is independent of the external B field.     

Distribution of the local magnetic field of the vortex lattice near the surface of an anisotropic superconductor in oblique external magnetic fields

The distribution of the magnetic field in the unit cell of the Abrikosov vortex lattice near the surface of a uniaxial, anisotropic, type-II superconductor in an oblique external magnetic field is determined on the basis of the London model for the cases in which the symmetry axis is perpendicular and parallel to the boundary of the superconductor. The distribution of the local magnetic field is obtained as a function of the distance from the surface of the superconductor and the inclination angle of the external field. It is shown for an YBaCuO high-T _c superconductor that the investigation of the distribution function of the local magnetic field as a function of the angle of the external magnetic field relative to the symmetry axis and to the surface of the superconductor can yield important information about the anisotropic properties of the superconductor. Fiz. Tverd. Tela (St. Petersburg) 39, 1935–1939 (November 1997)     

Spin configurations in the absence of an external magnetic field in a magnetic bilayer with in-plane cubic or uniaxial anisotropies

The spin configurations in the absence of an external magnetic field have been systematically investigated for a magnetic bilayer system consisting of two ferromagnetic layers separated by a non-magnetic layer with interlayer exchange coupling. Based on a phenomenological model, the conditions for the existence of collinear and non-collinear spin structures were derived for three kinds of magnetic bilayers with different combinations of in-plane cubic and uniaxial anisotropies for the two ferromagnetic layers. The phase diagrams of the spin configurations at zero field were drawn, taking into account the lowest-order anisotropy parameters of both the ferromagnetic layers. The values of the canting angle have been derived analytically and then numerically plotted.     

The effects of electron–phonon interaction on anisotropic RKKY interaction in graphene nanoribbon

We study the Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction in doped armchair graphene nanoribbon. The effects of both external magnetic field and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a magnetic field along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain both transverse and longitudinal static spin susceptibilities of armchair graphene nanoribbon in the presence of electron-phonon coupling and magnetic field. The spin susceptibility components are calculated using the spin dependent Green’s function approach for Holstein model Hamiltonian. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of magnetic field on the spatial behavior of in-plane and longitudinal RKKY interactions are different in the presence of magnetic field.     

Anisotropy-induced quantum critical behavior of magnetite nanoparticles at low temperatures

The classical, thermally driven transition from ferrimagnets to superparamagnets in Fe₃O₄ nanoparticles can be converted into another quantum phase by a transverse microwave magnetic field or by a strong internal anisotropic field. These fields, perpendicular to the Ising axis, can destroy the magnetic long-range order to quantum paramagnets as the fields exceed some critical values. We have exploited the spin resonance spectrometer to determine the dynamic spin susceptibility and the critical exponent γ, which is a power-law dependent spanning of the quantum critical point. Quantum phase transition observed at low temperatures for small magnetite nanoparticles induced by strong surface anisotropic field illustrates the fascinating interplay between thermal and quantum fluctuations in the vicinity of a quantum critical point.     

Spin Squeezing and Quantum Fisher Information in the Lipkin-Meshkov-Glick Model

We investigate spin squeezing and quantum Fisher information in the Lipkin-Meshkov-Glick model. Approximate analytical expressions and the numerical analysis of spin squeezing and quantum Fisher information are derived. Spin squeezing and quantum Fisher information depend on the strength of the external transverse magnetic field and the anisotropic parameter     

Electromagnetic waves in a round rod in the presence of an arbitrarily directed external magnetic field or anisotropy axis

A rigorous theory of the propagation of electromagnetic waves in round anisotropic and semiconductor rods in the presence of an arbitrarily directed anisotropy axis or external magnetic field is developed. New types of independent waves are discovered. Exact dispersion equations are obtained for them, which define the dependence of their spectral characteristics on the parameters of the semiconductor or anisotropic crystal and on the magnitude and direction of the constant external magnetic field. The results of numerical investigations for rods made from a semiconductor or a uniaxial crystal are presented. Zh. Tekh. Fiz. 67, 86–91 (July 1997)     

Sudden Death, Birth and Stable Entanglement in a Two-Qubit Heisenberg XY Spin Chain

Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic field. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic field and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic field, and the coupling strength with their environment. In particular, we find that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence.     

Gate control of quantum dot-based electron spin–orbit qubits

We investigate theoretically the coherent spin dynamics of gate control of quantum dot-based electron spin–orbit qubits subjected to a tilted magnetic field under electric-dipole spin resonance (EDSR). Our results reveal that Rabi oscillation of qubit states can be manipulated electrically based on rapid gate control of SOC strength. The Rabi frequency is strongly dependent on the gate-induced electric field, the strength and orientation of the applied magnetic field. There are two major EDSR mechanisms. One arises from electric field-induced spin–orbit hybridization, and the other arises from magnetic field-induced energy-level crossing. The SOC introduced by the gate-induced electric field allows AC electric fields to drive coherent Rabi oscillations between spin-up and -down states. After the crossing of the energy-levels with the magnetic field, the spin-transfer crossing results in Rabi oscillation irrespective of whether or not the external electric field is present. The spin–orbit qubit is transferred into the orbit qubit. Rabi oscillation is anisotropic and periodic with respect to the tilted and in-plane orientation of the magnetic field originating from the interplay of the SOC, orbital, and Zeeman effects. The strong electrically-controlled SOC strength suggests the possibility for scalable applications of gate-controllable spin–orbit qubits.     

垂直自由层倾斜极化层自旋阀结构中的磁矩翻转和进动

在理论上研究了垂直自由层和倾斜极化层自旋阀结构中自旋转移矩驱动的磁矩翻转和进动.通过线性展开包括自旋转移矩项的Landau-Lifshitz-Gilbert方程并使用稳定性分析方法,得到了包括准平行稳定态、准反平行稳定态、伸出膜面进动态以及双稳态的磁性状态相图.发现通过调节电流密度和外磁场的大小可以实现磁矩从稳定态到进动态之间的转化以及在两个稳定态之间的翻转.翻转电流随外磁场的增加而增加,并且受自旋极化方向的影响.当自旋极化方向和自由层易磁化轴方向平行时,翻转电流最小;当自旋极化方向和自由层易磁化轴方向垂直时,翻转电流最大.通过数值求解微分方程,给出了不同磁性状态磁矩随时间的演化轨迹并验证了相图的正确性.     

Chirality of a forming spin spring and remagnetization features of a bilayer ferromagnetic system

Distribution of a magnetic moment in an exchange-coupled bilayer Fe/SmCo epitaxial structure grown on a (110) MgO substrate is visualized by the magnetooptic indicator film technique. The direction and the magnitude of the effective magnetization in this structure are determined both under external magnetic fields of variable magnitude and direction and after the removal of these fields. It is shown that such a heterostructure is remagnetized by a nonuniform rotation of a magnetic moment both along the thickness of a sample and in its plane. A field antiparallel to the axis of unidirectional anisotropy gives rise to spin springs with opposite chiralities in different regions of the magnetically soft ferromagnetic layer. The contributions of these springs to the net magnetization cancel out, thus decreasing the averaged magnetic moment and the remanent magnetization without their rotation. When the external field deviates from the easy axis, the balance is violated and the sample exhibits a quasi-uniform rotation of the magnetic moment. Asymmetry in the rotation of the magnetic moment is observed under the reversal of the field as well as under repeated remagnetization cycles. It is established that a monochiral spin spring is also formed in a rotating in-plane magnetic field when the magnitude of the field exceeds the critical value. Possible mechanisms of remagnetization in this system are discussed with regard to the original disordered orientation of magnetization of the magnetically soft layer with respect to the easy axis, which is defined by the variance of unidirectional anisotropy axes of this layer on the interface.     

Electrical control of valley and spin polarized current and tunneling magnetoresistance in a silicene-based magnetic tunnel junction

We investigate the electronic transport in a silicene-based ferromagnetic metal/ferromagnetic insulator/ferromagnetic metal tunnel junction. The results show that the valley and spin transports are strongly dependent on local application of a vertical electric field and effective magnetization configurations of the ferromagnetic layers. In particular, it is found that the fully valley and spin polarized currents can be realized by tuning the external electric field. Furthermore, we also demonstrate that the tunneling magnetoresistance ratio in such a full magnetic junction of silicene is very sensitive to the electric field modulation.     

Generation and control of electronic hybrid entanglement via a two-dimensional Rashba anisotropic nanodot

In the present article we report the dynamics of electronic spin–subbands, as well as subband–subband, hybrid entanglements in a two-dimensional anisotropic quantum dot. The dot is under the influence of Rashba effect and an external magnetic field. To study the hybrid entanglements, we partition the system into two categories in which either spatial degrees of freedom, subbands, entangle with the spin or the subbands become entangled amongst themselves. For the first case we calculate the von Neumann entropy, while for the latter the negativity is calculated. Our calculations show that for both cases information is periodically distributed between the corresponding subspaces. Effects of Rashba parameter and magnetic field on the characteristics of such oscillatory behavior are also discussed. For spin–subband entanglement the oscillations include dips, surrounded by plateaus of maximal entanglement. The subband–subband entanglement shows vanishingly small plateaus. The duration of plateaus is controlled by Rashba coupling and the external field.