Size dependence of phase transition temperatures of ferromagnetic, ferroelectric and superconductive nanocrystals

With the miniaturization of devices, size and interface effects become increasingly important for the properties and performances of nanomaterials. Here, we present a thermodynamic approach to the mechanism behind size-induced unusual behavior in the phase stabilities of ferromagnetic (FM), antiferromagnetic (AFM), ferroelectric (FE), and superconductive (SC) nanocrystals, which are different dramatically from their bulk counterparts. This method is based on the Lindemann criterion for melting, Mott’s expression for the vibrational melting entropy, and the Shi model for the size-dependent melting temperature. Simple and unified functions, without any adjustable parameter, are established for the size and interface dependences of thermal and phase stabilities of FM, AFM, FE and SC nanocrystals. According to these analytic functions, as the size of nanocrystals is reduced, the thermal and phase stabilities may strengthen or weaken, depending on the confluence of the surface/volume ratio of nanocrystals and the FM(AFM, FE or SC)/substrate interface situations. The validity of this model is confirmed by a large number of experimental results. This theory will be significant for the choice of materials and the design of devices for practical application.     

铁磁/反铁磁双层膜系统中的交换偏置及矫顽场的温度特性

提出了一个讨论铁磁／反铁磁双层膜中的交换偏置及矫顽场温度特性的物理模型，该模型，假设铁磁层为具有单畴各向异性的单畴膜而反铁磁层由许多相互独立具有多晶各向异性的颗粒组成，其温度依赖性主要来源于系统态的热不稳定，包括反铁磁颗粒易轴取向的热涨落和相关磁学量的温度依赖性等。计算结果表明其交换偏置随温度的增加非线性地减少而其矫顽场在体阻截温度处达极大值，且其体阻截温度随反铁磁颗粒粒径的增加而增加。我们的计算结果和相关实验结果一致，通过本的讨论，我们建议通过铁磁膜耦合上大粒径硬反铁磁颗粒膜可获得高交换偏置、低矫顽场且近独立于温度的相关磁学器件。     

The study of spin ordering in FM/AFM bilayers with a mixed interface

Monte Carlo simulation is adopted to study the spin ordering in ferromagnet(FM)/antiferromagnet(AFM) bilayers with a mixed interface. We introduce the time-dependent autocorrelation function to describe the thermal stability of the spin ordering for each plane, especially the interface, in FM/AFM bilayers with uncompensated and compensated AFM surfaces. It is found that the thermal decay of spin ordering depends on the plane, the interface coupling and the interface roughness. For the uncompensated AFM surfaces, when the interface coupling is small, the thermal decay of spin ordering is faster at the interface than other planes, while the large interfae coupling makes the spin ordering at the interface become relatively stable. In the case of compensated AFM surfaces, the spin ordering at the interface is thermally disordered much before that at other planes, and the thermal decay becomes slow gradually as the interface coupling increases.     

Exchange coupling mechanism for magnetization reversal and thermal stability of Co nanoparticles embedded in a CoO matrix

A model providing a semi-quantitative account of the magnetic behavior of Co nanoparticles embedded in a CoO matrix is presented. The results confirm that exchange coupling at the interface between ferromagnetic (FM) and antiferromagnetic (AFM) nanostructures could provide an extra source of magnetic anisotropy, leading to thermal stability of the FM nanoparticles. It is shown that perpendicular coupling between the AFM and FM moments may result in large coercivities. The energy barrier, which works against reversal is due to the AFM susceptibility anisotropy. The experimentally observed exchange bias is tentatively ascribed to pre-existing intrinsic canting of the AFM moments at the interface.     

The spin-1 Ising model on a two-layer Bethe lattice with FM/AFM interactions

Two-layer Bethe lattice with the Ising spins of the top layer having only ferromagnetic (FM) interactions and the bottom layer having only antiferromagnetic (AFM) interactions are allowed to interact with the interlayer interaction of either FM or AFM type. The model is studied by using the exact recursion relations in a pairwise approach for given coordination numbers q=3, 4 and 6 with equal external magnetic fields acting on the layers. The phase diagrams of the model are obtained on different planes for given system parameters by studying the ground state (GS) phase diagrams and the thermal variations of the order-parameters and the response functions, i.e. the susceptibility and the specific heat, in detail. The model presents second- and first-order phase transitions, and where their lines are combined is the tricritical point. The critical end points also exist. The reentrant behavior is also seen when the model presents two Néel temperatures.     

Exchange-coupling-induced fourfold magnetic anisotropy in CoFeB/FeRh bilayer grown on SrTiO3(001)

Exchange coupling across the interface between a ferromagnetic (FM) layer and an antiferromagnetic (AFM) or another FM layer may induce a unidirectional magnetic anisotropy and/or a uniaxial magnetic anisotropy, which has been extensively studied due to the important application in magnetic materials and devices. In this work, we observed a fourfold magnetic anisotropy in amorphous CoFeB layer when exchange coupling to an adjacent FeRh layer which is epitaxially grown on an SrTiO₃(001) substrate. As the temperature rises from 300 K to 400 K, FeRh film undergoes a phase transition from AFM to FM phase, the induced fourfold magnetic anisotropy in the CoFeB layer switches the orientation from the FeRh$\langle 110\rangle $ to FeRh$\langle 100\rangle $ directions and the strength is obviously reduced. In addition, the effective magnetic damping as well as the two-magnon scattering of the CoFeB/FeRh bilayer also remarkably increase with the occurrence of magnetic phase transition of FeRh. No exchange bias is observed in the bilayer even when FeRh is in the nominal AFM state, which is probably because the residual FM FeRh moments located at the interface can well separate the exchange coupling between the below pinned FeRh moments and the CoFeB moments.     

Interfacial roughness and temperature effects on exchange bias properties in coupled ferromagnetic/antiferromagnetic bilayers

Monte Carlo simulations have been used to study the relationship between the exchange bias properties and the interface roughness in coupled ferromagnetic/antiferromagnetic (FM/AFM) films of classical Heisenberg spins. It is shown that the variation of the exchange bias field versus the AFM anisotropy strongly depends on the FM/AFM interface. Unlike the flat interface, a non-monotonic dependence is observed for the roughest FM/AFM interface. This is explained by canted magnetic configurations at the FM/AFM interface, which appear after the first reversal due to the magnetic frustration. The temperature dependence of the exchange field is also dependent on the roughness. While the exchange field is roughly constant for the flat interface, a decrease is observed for the roughest interface as the temperature increases. This has been interpreted as a significant decrease of the effective coupling between the FM and the AFM due to the disordering of the moments at the FM/AFM interface because of the combination of magnetic frustration and temperature activation.     

Room temperature exchange bias in multiferroic BiFeO<Subscript>3</Subscript> nano- and microcrystals with antiferromagnetic core and two-dimensional diluted antiferromagnetic shell

Exchange bias (EB) of multiferroics presents many potential opportunities for magnetic devices. However, instead of using low-temperature field cooling in the hysteresis loop measurement, which usually shows an effective approach to obtain obvious EB phenomenon, there are few room temperature EB. In this article, extensive studies on room temperature EB without field cooling were observed in BiFeO₃ nano- and microcrystals. Moreover, with increasing size the hysteresis loops shift from horizontal negative exchange bias (NEB) to positive exchange bias (PEB). In order to explain the tunable EB behaviors with size dependence, a phenomenological qualitative model based on the framework of antiferromagnetic (AFM) core-two-dimensional diluted antiferromagnet in a field (2D-DAFF) shell structure was proposed. The training effect (TE) ascertained the validity of model and the presence of unstable magnetic structure using Binek’s model. Experimental results show that the tunable EB effect can be explained by the competition of ferromagnetic (FM) exchange coupling and AFM exchange coupling interaction between AFM core and 2D-DAFF shell. Additionally, the local distortion of lattice fringes was observed in hexagonal-shaped BiFeO₃ nanocrystals with well-dispersed behavior. The electrical conduction properties agreed well with the space charge-limited conduction mechanism.     

Relative-thickness dependence of exchange bias in bilayers and trilayers

We consider the models of ferromagnetic (FM)/antiferromagnetic (AFM) bilayers and trilayers and perform a modified Monte Carlo method to study their exchange bias (EB) properties at low temperature after field cooling on increasing one component thickness at the expense of the other one. The results indicate that EB is insensitive to the thickness variations as the FM layer is thicker than the AFM one. Otherwise, it has a steep increase with the decrease of FM thickness, but the purely inverse proportion is no longer valid due to the dual influences of FM and AFM thicknesses. EB in trilayers should be approximately twice larger than that in bilayers because there is a double interfacial area in the trilayers compared with the bilayers, but the dispersed FM/AFM distributions may break this relation as a result of thermal destabilization. Moreover, EB is independent of FM/AFM stacking sequences probably because of the ideal interface between them. It has been clarified unambiguously that such control of EB through varying the FM/AFM dimensions in heterostructures is attractive for spintronics applications.     

Magnetic structures of exchange bias Ni/FeF2(1 1 0) interface

Electronic and magnetic structures of ferromagnetic (FM)/antiferromagnetic (AFM), Ni/FeF₂(1 1 0), with a compensated AFM interface are investigated by using the full-potential linearized augmented plane-wave method. We find that magnetic structures at the AFM interface are perturbed by a contact with the FM material, where the superexchange interaction through the interface F excites and induces a small net moment at the AFM interface. These results predicted may play an important role for explaining the exchange bias in this system, and rule out the exchange bias mechanisms with the spin-flop coupling and the magnetic moment reorientation.     

Half-metallic exchange bias ferromagnetic/antiferromagnetic interfaces in transition-metal chalcogenides

To investigate half-metallic exchange bias interfaces, magnetic structures at ferromagnetic (FM)/antiferromagnetic (AFM) interfaces in the zinc blende transition-metal chalcogenides, and with compensated and uncompensated AFM interfaces, were determined by the full-potential linearized augmented plane-wave method. With the uncompensated AFM interface, an antiparallel alignment of the Cr and Mn moments induces an excellent half-metallicity. More striking still, in the compensated AFM interface the Cr moments in the FM layer lie perpendicular to the Mn moments in the AFM layer but the Mn moments strongly cant to induce a net moment so as to retain the half-metallicity. These findings may offer a key ingredient for exchange biased spintronic devices with 100% spin polarization, having a unidirectional anisotropy to control and manipulate spins at the nanoscale.     

Phase diagram of superconductivity and antiferromagnetism in high-Tc hole-doped cuprates

A phase diagram of superconductivity (SC) and antiferromagnetism (AFM) for hole-doped cuprate superconductors in presence of chemical potential (μ) by using a model Hamiltonian is reported here. The Hamiltonian of the system is a mean field one and has been solved by writing equations of motion for the single particle Green functions. The expressions for appropriate single particle correlation function are derived. It is assumed that SC arises due to BCS pairing mechanism and AFM order is simulated by staggered magnetic field in lattices of Cu–O planes. The expressions for SC order parameter, AFM order parameter and dopant concentration are calculated analytically by using Green function technique of D.N. Zubarev. The value of SC gap (z), AFM gap (h) and chemical potential (μ) are solved self consistently for different dopant concentrations (x) by changing model parameters. It is found that a disordered phase appears after antiferromagnetism is destroyed in the range of very small doping. On further increase of the doping, the SC critical temperature first increases, attains a maximum value (?39 K) and then decreases which agrees well with experimental observations for hole-doped cuprates. Our theoretical findings suggest that the AFM coupling plays the vital role of the glue for the Cooper pairs.     

Dynamic magnetic behavior of the mixed spin （2, 5/2） Ising system with antiferromagnetic/antiferromagnetic interactions on a bilayer square lattice

Using the mean-field theory and Glauber-type stochastic dynamics, we study the dynamic magnetic properties of the mixed spin （2, 5/2） Ising system for the antiferromagnetic/antiferromagnetic （AFM/AFM） interactions on the bilayer square lattice under a time varying （sinusoidal） magnetic field. The time dependence of average magnetizations and the thermal variation of the dynamic magnetizations are examined to calculate the dynamic phase diagrams. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and the effects of interlayer coupling interaction on the critical behavior of the system are investigated. We also investigate the influence of the frequency and find that the system displays richer dynamic critical behavior for higher values of frequency than that of the lower values of it. We perform a comparison with the ferromagnetic/ferromagnetic （FM/FM） and AFM/FM interactions in order to see the effects of AFM/AFM interaction and observe that the system displays richer and more interesting dynamic critical behaviors for the AFM/AFM interaction than those for the FM/FM and AFM/FM interactions.     

The exchange bias phenomenon in uncompensated interfaces: theory and Monte Carlo simulations

We performed Monte Carlo simulations of a bilayer system composed of two thin films, one ferromagnetic (FM) and the other antiferromagnetic (AFM). Two lattice structures for the films were considered: simple cubic and body centered cubic (bcc). We imposed an uncompensated interfacial spin structure in both lattice structures; in particular we emulated an FeF2-FM system in the case of the bcc lattice. Our analysis focused on the incidence of the interfacial strength interactions between the films, J(eb), and the effect of thermal fluctuations on the bias field, H(EB). We first performed Monte Carlo simulations on a microscopic model based on classical Heisenberg spin variables. To analyze the simulation results we also introduced a simplified model that assumes coherent rotation of spins located on the same layer parallel to the interface. We found that, depending on the AFM film anisotropy to exchange ratio, the bias field is controlled either by the intrinsic pinning of a domain wall parallel to the interface or by the stability of the first AFM layer (quasi-domain wall) near the interface.     

Can we explain the coexistence of ferromagnetism and superconductivity based on two parameters model?

A possible explanation about the coexistence of ferromagnetism (FM) and superconductivity (SC) based on a two parameters mean field model in a two-dimensional system is discussed. The key feature of this model is that there are two independent parameters which are responsible for ferromagnetism and superconductivity, respectively. We point out that the coexisting FM and s-wave pairing SC state is energetically not favorable among all possible state. We generalize the two parameter model to include the coexistence of FM with p-wave SC. We find that the phase diagram is not consistent with what experimentally discovered in UGe₂.     

Temperature dependence of exchange bias and coercivity in ferromagnetic/antiferromagnetic bilayers

A model for the temperature dependence of exchange bias and coercivity in epitaxial ferromagnetic (FM)/ antiferromagnetic (AFM) bilayers is developed. In this model, the interface coupling includes two contributions, the direct coupling and the spin-flop coupling. The temperature dependence arises from the thermal disturbance to the system, involved in the thermal fluctuations of magnetization of AFM grains and the temperature modulation of the relevant magnetic parameters. In addition, the randomness of original orientations of easy axes of AFM grains after field cooling is taken into account. A self-consistent calculation scheme is proposed and numerical treatment is carried out. The results show that the temperature dependence of exchange bias and coercivity is closely related to the sizes of AFM grains and the interface exchange coupling constants. Especially, the exchange bias will have a peak and the blocking temperature will increase if the spin-flop coupling plays a role. On the other hand, the original orientation distribution of easy axes of AFM grains will affect exchange bias and coercivity prominently. The prediction has been well supported by experiments.Received: 12 May 2004, Published online: 31 August 2004PACS: 75.30.Et Exchange and superexchange interactions - 75.50.Ee Antiferromagnetics - 75.30.Gw Magnetic anisotropy     

Electroluminescence from hybrid organic–inorganic LEDs based on thermally evaporated CdS thin films

Hybrid organic–inorganic light emitting devices combine the color purity and durability of inorganic light emitting diodes (LEDs) with high efficiency, flexibility and low processing cost of organic LEDs (OLEDs). A significant challenge is to incorporate inorganic nanocrystals inside the OLED structure. In the present work, thin films of CdS were successfully incorporated inside standard OLED structure using vacuum thermal evaporation technique. For the characterization of these films, they were deposited on plain glass plates at room temperature and studied using structural (XRD and TEM), morphological (SEM and AFM) and optical (UV and PL) techniques. The films were found to be composed of nanocrystals of CdS in which the size of the crystals increased with the increase in film thickness. The hybrid organic–inorganic LEDs showed improved luminance and efficiency as compared to the organic LED without CdS layers.     

纳米多晶体的热力学函数及其在相变热力学中的应用

以往关于纳米材料热力学的研究，绝大多数以界面的热力学函数表征整体纳米材料的热力学性质，这种近似处理，对于尺寸超过几十纳米的较粗纳米材料，在相变热力学中对特征转变温度和临界尺寸等重要参量的预测，将导致很大误差. 应用“界面膨胀模型”和普适状态方程，研究了纳米晶界的热力学特性，进一步发展了纳米晶整体材料热力学函数的计算模型，给出了单相纳米多晶体的焓、熵和吉布斯自由能随界面过剩体积、温度，以及晶粒尺寸发生变化的明确表达式. 以Co纳米晶为例，分析了界面与整体纳米多晶体热力学函数的差异，确定了相变温度与晶粒尺寸的依赖关系，以及一定温度下可能发生相变的临界尺寸. 关键词： 纳米多晶体 热力学函数 相变热力学     

Melting of nanocrystals embedded in a crystal matrix heated by nanosecond laser pulses

The kinetics of phase transformations of nanocrystals in a crystal matrix is considered upon non-stationary heating by laser pulses. The melting and crystallization kinetics of nanocrystals is described taking into account their size, shape, elemental composition, and elastic deformations appearing due to the mismatch of the lattice constants for nanocrystals and the matrix. The possibility of decreasing the dispersion of nanocrystals over their size in heterostructures with quantum dots is predicted. As an example, melting of Ge nanocrystals in a Si matrix is considered.     

Simulating a perpendicular exchange-biased structure with a partially covering nonmagnetic insertion at the FM/AFM interface

The existence of minority spins, opposite to the perpendicular exchange bias, and majority spins aligned with this bias, and the dependence of the perpendicular exchange-bias field on the imprint effect, caused by the partially covering spacer at the ferromagnetic/antiferromagnetic (FM/AFM) interface, have been studied using Ising-type simulations. The present investigation suggests that the main factors influencing this phenomenon were dependent on the FM/AFM interface morphology, the balance between FM/AFM coupling and the FM-spins coupling, and the numerical balance between minority and majority spins. It was also determined that the imprint phenomenon can be used to enhance the perpendicular exchange-bias for small partial insertions at the FM/AFM interface. An erratum to this article is available at.