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.     

The influence of magnetic impurities in the vortex core dynamics in magnetic nano-disks

In this work we have used spin dynamics simulations to study the gyrotropic frequency behavior in nano-disks of Permalloy with magnetic impurities. We consider the effect of attractive impurity and repulsive impurity placed near the vortex core gyrotropic trajectory. We observed that the gyrotropic frequency is affected by the presence of impurity. The gyrotropic frequency shift depends on the relative position between the impurity and the vortex core gyrotropic trajectory and if impurity is attractive or repulsive. Our results agree with the analytical model and with experimental behavior for the gyrotropic frequency shown in the literature.     

Dependence of exchange bias on core/shell relative dimension in ferromagnetic/antiferromagnetic nanoparticles

We employ a modified Metropolis Monte Carlo simulation to study the effect of bimagnetic core/shell relative dimension on exchange bias in ferromagnetic/antiferromagnetic nanoparticles. The exchange bias field is inversely proportional to the ferromagnetic shell thickness in the antiferromagnetic (core)/ferromagnetic (shell) nanoparticles, while in the nanoparticles with an opposite core/shell structure the exchange bias behavior is complex and distinguished in different ranges of the ferromagnetic core radius. The work elucidates unambiguously how the core and shell dimensions optimize the exchange bias in nanoparticles.     

Numerical study of exchange bias in antiferromagnetic/ferromagnetic core/shell nanoparticles with non-magnetic defects

We perform Monte Carlo simulations for an antiferromagnetic/ferromagnetic core/shell nanoparticle with a doubly inverted structure. We investigate the dependence of the exchange bias field and coercivity on the magnetic dilution of the shell-interface and shell part. It is demonstrated that exchange bias and coercivity can exhibit monotonic or non-monotonic behavior depending on the location of the non-magnetic components. Also, temperature dependence of the exchange bias and coercivity of the system are studied for a particular defect concentration value. Our results provide an alternative way for tunning the magnetic properties of doubly inverted nanoparticles.     

Resultant exchange bias and coercivity on rotatable antiferromagnetic anisotropy in ellipsoidal core/shell nanoparticles

A special consideration has been conducted on the dependencies of exchange bias and coercivity on rotatable antiferromagnetic anisotropy with respect to the collinear ferromagnetic anisotropy and field-cooling directions in ellipsoidal core/shell nanoparticles. With increasing the angle between antiferromagnetic and ferromagnetic easy axes, exchange bias field and coercivity both exhibit biaxial symmetries about the ferromagnetic easy and hard axes. Moreover, the variations of the antiferromagnetic anisotropy constant cannot change the trends of these novel behaviors, but only control their occurrences by dominating the coercive field behaviors. This new exchange-biased feature obtained by means of the special nanoparticle shape and the relative angle between anisotropies is of technological importance for maximizing exchange bias, in order to optimize the designs of the involved devices.     

Tunning exchange bias in inverted antiferromagnetic/ferromagnetic core/shell nanoparticles by binary alloy shells

A detailed investigation of exchange bias properties of an inverted nanoparticle with an antiferromagnetic core and a ferromagnetic binary alloy shell of the type $B_x{C}_{1?x}$ is presented by benefiting from Monte Carlo simulations. Exchange bias displays a non-monotonic behavior with the varying value of the concentration the type-B magnetic components, x. Coercivity exhibits a monotonic or a non-monotonic variation with x depending on the relative strength between unlike magnetic components in the shell. Particular attention has also been given to determine the effects of the cooling field process on the magnetic properties of the nanoparticle. Numerical results obtained in this work present a different physical mechanism and an alternative way for tuning the exchange bias and coercivity of bimagnetic core/shell nanoparticles.     

Modeling of exchange bias in the antiferromagnetic (core)/ferromagnetic (shell) nanoparticles with specialized shapes

Zero-field-cooled (ZFC) and field-cooled (FC) hysteresis loops of egg- and ellipsoid-shaped nanoparticles with inverted ferromagnetic (FM)-antiferromagnetic (AFM) core-shell morphologies are simulated using a modified Monte Carlo method, which takes into account both the thermal fluctuations and energy barriers during the rotation of spin. Pronounced exchange bias (EB) fields and reduced coercivities are obtained in the FC hysteresis loops. The analysis of the microscopic spin configurations allows us to conclude that the magnetization reversal occurs by means of the nucleation process during both the ZFC and FC hysteresis branches. The nucleation takes place in the form of “sparks” resulting from the energy competition and the morphology of the nanoparticle. The appearance of EB in the FC hysteresis loops is only dependent on that the movements of “sparks” driven by magnetic field at both branches of hysteresis loops are not along the same axis, which is independent of the strength of AFM anisotropy. The tilt of “spark” movement with respect to the symmetric axis implies the existence of additional unidirectional anisotropy at the AFM/FM interfaces as a consequence of the surplus magnetization in the AFM core, which is the commonly accepted origin of EB. Our simulations allow us to clarify the microscopic mechanisms of the observed EB behavior, not accessible in experiments.     

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.     

磁性纳米颗粒系统偶极相互作用的Monte Carlo研究

采用局域Monte Carlo方法模拟不同易轴分布的简单立方排列单分散单畴Fe纳米颗粒系统的ZFC-FC曲线及磁滞回线.结果表明：随着偶极相互作用的增强，系统的阻塞温度T_B逐渐增大，且ZFC曲线的峰变宽.说明偶极相互作用使得系统的有效能垒提高，分布宽度增加.研究FC曲线磁化强度的倒数与温度关系，发现偶极相互作用系统中存在反铁磁有序.系统的阻塞态及超顺磁态的磁滞回线表明，极低低温下，随着偶极相互作用的增强，系统的矫顽力和剩磁减小，偶极相互作用阻碍系统的磁化；系统处于超顺磁态，各向异性作用及偶极相互作用使得系统的磁化曲线偏离Langevin曲线且偶极相互作用展现出退磁相互作用效应.偶极相互作用增强，系统磁化曲线与Langevin曲线偏差量的最大值向低场移动.在偶极相互作用下，易轴与外场夹角为45°的磁性纳米颗粒系统的平均有效能垒和有效能垒分布宽度较易轴随机分布系统的大.     

Exchange bias mechanism in FM/FM/AF spin valve systems in the presence of random unidirectional anisotropy field at the AF interface: The role played by the interface roughness due to randomness

We propose an atomistic model and present Monte Carlo simulation results regarding the influence of FM/AF interface structure on the hysteresis mechanism and exchange bias behavior for a spin valve type FM/FM/AF magnetic junction. We simulate perfectly flat and roughened interface structures both with uncompensated interfacial AF moments. In order to simulate rough interface effect, we introduce the concept of random exchange anisotropy field induced at the interface, and acting on the interface AF spins. Our results yield that different types of the random field distributions of anisotropy field may lead to different behavior of exchange bias.     

Magnetic properties of nanoscale crystalline maghemite obtained by a new synthetic route

In this work we describe the synthesis and characterization of maghemite nanoparticles obtained by a new synthetic route. The material was synthesized using triethylamine as a coprecipitation agent in the presence of the organic ligand N,N′-bis(3,5-di-tert-butyl-catechol)-2,4-diaminotoluene (LCH₃). Mössbauer spectrum at 4 K shows typical hyperfine parameters of maghemite and Transmission Electron Microscopy images reveal that the nanoparticles have a mean diameter of 3.9 nm and a narrow size distribution. AC magnetic susceptibility in zero field presents an Arrhenius behavior with unreasonable relaxation parameters due to the strong influence of dipolar interaction. In contrast when the measurements are performed in a 1 kOe field, the effect of dipolar interactions becomes negligible and the obtained parameters are in good agreement with the static magnetic properties. The dynamic energy barrier obtained from the AC susceptibility results is larger than the expected from the average size observed by HRTEM results, evidencing the strong influence of the surface contribution to the anisotropy.     

Non-Arrhenius relaxation of the Heisenberg model with dipolar and anisotropic interactions

The dynamical properties of a 2D Heisenberg model with dipolar interactions and perpendicular anisotropy are studied using Monte Carlo simulations in two different ordered regions of the equilibrium phase diagram. We find a temperature defining a dynamical transition below which the relaxation suddenly slows down and the system apart from the typical Arrhenius relaxation to a Vogel-Fulcher-Tamann law. This anomalous behavior is observed in the scaling of the magnetic relaxation and may eventually lead to a freezing of the system. Through the analysis of the domain structures we explain this behavior in terms of the domains dynamics. Moreover, we calculate the energy barriers distribution obtained from the data of the magnetic viscosity. Its shape supports our comprehension of both, the Vogel-Fulcher-Tamann dynamical slowing down and the freezing mechanism.     

Ferromagnetism of Pd(001) substrate induced by antiferromagnetic CoO

Our first-principles study has revealed unexpected spin polarization of the Pd(001) substrate in contact with antiferromagnetic CoO overlayers. We give an evidence that the ferromagnetism of Pd is caused by the zigzag positions of Co atoms with respect to the Pd interface, resulted from the lattice-mismatch driven structural relaxation. Because of the itinerant nature of its 4d electrons, we see that the ferromagnetic properties of Pd are highly sensitive to the local environment and can be enhanced further by increasing the thickness of CoO overlayer film or/and by applying an additional uniaxial pressure along c-axis exerted externally on the bottom layers of the Pd substrate. Our finding provides new functionality for the interfacial moments of the CoO/Pd system, which can be accessed experimentally, e.g., by the magneto-optical Kerr effect (MOKE) or/and by element-resolved X-ray magnetic circular dichroism (XMCD) measurement.     

Effects of component ratio and easy axes distribution on the exchange bias in ferromagnetic-antiferromagnetic random alloys

For a ferromagnetic (FM)-antiferromagnetic (AFM) system with composition x(FM)+(AFM)_1−x, a modified Monte Carlo Metropolis method is performed to study the effects of x and easy axes distribution at the FM/AFM nearest neighbors on exchange bias field H_E, coercivity H_C, and vertical magnetization shift M_E after cooling under different magnetic fields h_CF. When the orientations of easy axes are uniform, the x dependence of H_E and M_E undergo a non-monotonous to monotonous process with the increase of h_CF, whereas H_C shows a more complex behavior. On the other hand, for the case of the random orientation, H_C has a peak around x=0.5, while M_E decreases with the increase of x. H_E exhibits negative extrema at small x and disappears for larger x. However, abnormal positive H_E observed depends on the frustration and the distinct trends of two coercive fields with x in such a special model.     

铁磁/反铁磁双层膜中的磁锻炼效应

采用Monte Carlo 方法,研究铁磁/反铁磁双层膜中的磁锻炼效应.结果表明,反铁磁层中冷场诱发的界面净磁化(钉扎效应)的磁弛豫可导致系统中的交换偏置场的磁锻炼效应.进一步研究表明,反铁磁层中掺杂可调控交换偏置场的磁锻炼效应,原因在于反铁磁层中掺杂能有效地改变冷场诱发的净磁化的磁弛豫过程.     

Coupling of ferromagnetic nanoparticles through dipolar interactions

We consider two ferromagnetic nanoparticles coupled via long-range dipolar interactions. We model each particle by a three-dimensional array of classical spin vectors, with a central spin surrounded by a variable number of shells. Within each particle only ferromagnetic coupling between nearest neighbor spins is considered. The interaction between particles is of the dipolar type and the magnetic properties of the system is studied as a function of temperature and distance between the centers of the particles. We perform Monte Carlo simulations for particles with different number of shells, and the magnetic properties are calculated via two routes concerning the dipolar contribution: one assuming a mean-field like coupling between effective magnetic moments at the center of the particles, and other one, where we take into account interactions among all the pairs of spins, one in each particle. We show that the dipolar coupling between the particles enhances the critical temperature of the system relative to the case in which the particles are very far apart. The dipolar energy between the particles is smaller when the assumption of effective magnetic moment of the particles is used in the calculations.     

Blocking temperature in nanocrystalline systems with “alloy-like” ferromagnetic-antiferromagnetic heterogeneous morphology

A modified Monte Carlo Metropolis method is performed to simulate the blocking temperature (T_B) in an “alloy-like” heterogeneous system with geometrical frustration. It is found that the blocking temperature, at which the field-cooled (FC) and zero-field-cooled (ZFC) magnetization curves are splitting, changes little for x≤0.5 initially, then decreases obviously with the increase in x. Some discrete error bars emerge for large x owing to the superparamagnetic or agglomerate behavior of the small antiferromagnet. Using a thermal fluctuation model, an analytic expression for T_B as a function of x is obtained. By calculating the curves of temperature derivative of the difference between FC and ZFC magnetizations and analyzing the distribution of energy barriers, we interpret the dependence of T_B on different proportions of ferromagnetic phase in detail.     

Interface induced exchange bias effect in La0.67Sr0.33MnO3/SrIrO3 multilayer

Epitaxial superlattices of ferromagnetic/paramagnetic La_0.67Sr_0.33MnO₃/SrIrO₃ materials have been prepared on SrTiO₃ (100) substrate using pulse laser deposition technique. An unexpected onset of interface magnetic interaction has been observed around 40 K. Interestingly, magnetic exchange bias effect has been observed in both field cooled and zero field cooled magnetization loops, however, the shifting of loop is opposite in both measurements. Exchange bias field vanishes as temperature increases to interface magnetic ordering temperature. Moreover, exchange bias field is found to decrease with increasing cooling field. We believe that tuning of magnetic exchange at interface during field cooling induces this evolution in nature of exchange bias field.     

Effect of dipolar and exchange interactions on magnetic blocking of maghemite nanoparticles

Magnetic interparticle interactions compete with the magnetic blocking of ultrafine magnetic nanoparticles. We have prepared maghemite (γ-Fe₂O₃) nanoparticles by microwave plasma synthesis as a loose powder and in compacted form. In ZFC/FC measurements, blocking temperature of the compacted sample C is larger than that of the powder sample P. The frequency dependence of AC susceptibility of the sample C shows a large shift of blocking temperature with increasing frequency. Vogel-Fulcher law gives a large value of T₀ for the sample C. To get evidence of a possible spin-glass freezing in both samples, scaling law fitting is applied to the AC susceptibility data. The value of the exponent (zv) of the critical slowing down dynamics fits to the spin-glass regime for both samples. For the sample P, spin-glass freezing occurs on the surface of individual nanoparticles, while in the sample C surface spin-glass freezing is concomitant with a superspin-glass formation as a consequence of coupling between particles. The sample C also shows an enhancement of coercivity due to dipolar interactions among the nanoparticles. Exchange interactions are attributed only to touching nanoparticles across their interfaces. All these measurements indicate the presence of strong interparticle dipolar interactions in the compacted sample C.