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 Otherwise, it has a steep increase with the decrease of FM thickness, but the purely inverse proportion is no longer valid due to the dual influences of FM and AFM thicknesses.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.     

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.     

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.     

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.     

Temperature and set field dependence of exchange bias training effects in Co/NiO/[Co/Pt] heterostructures with orthogonal easy axes

Training effects in a new class of exchange biased ferromagnet/antiferromagnet/ferromagnet trilayers (Co/NiO/[Co/Pt]₃) with mutually orthogonal easy axes have been measured and successfully modeled. Previous experiments have demonstrated an enhanced blocking temperature as well as the ability to isothermally field tune the magnitude of the room temperature in-plane exchange bias. These effects have been attributed to the presence of the [Co/Pt] multilayer with perpendicular magnetic anisotropy, which variably pins the backside NiO domains. Here we show that the tuning of the exchange bias and the blocking temperature enhancement are highly dependent on both the temperature and the in-plane remanence of the normally out-of-plane [Co/Pt] multilayer, achieved using modest in-plane set fields. Training effects and their dependence on temperature and in-plane remanence are modeled using a thermodynamic approach. The in-plane remanence of the [Co/Pt] acts only to set the equilibrium exchange bias value and sets the scale for the blocking temperature; it has no effect on the training. We conclude that training effects occur only at the Co/NiO interface and that the relaxation towards equilibrium is confined to this interface. The field enhanced blocking temperature and isothermal tuning of exchange bias in these magnetic heterostructures with mutually orthogonal easy axes could play a role in the enhancement of exchange bias effects in future spin-valve devices. A thorough knowledge of the training effects is essential to account for the fundamental relaxation mechanisms that occur with repeated field cycling.     

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.     

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.     

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.     

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.     

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.     

Polarized current changes the exchange bias in a current-in-plane spin valve

A spin-polarized current changes the strength and direction of the exchange bias in spin valves with a current-in-plane geometry. The exchange bias can be manipulated and systematically changed by applying current pulses. The changes are nonmonotonic and asymmetric with respect to the directions of the applied field and current pulses. For different current pulses, different exchange-bias fields can be achieved in the same sample. Furthermore, for samples with different exchange bias, the bias field exhibits a dependence on the applied pulse. Since the strength of exchange bias is highly correlated to the micromagnetic state distribution of the antiferromagnet, we explain our observations by the spin torque exerted on the interfacial antiferromagnetic moments, excluding Joule heating and training effects.     

The effects of Co-metal clusters on exchange bias for Co-doped NiO/FeNi bilayers

Co-doped NiO inhomogeneous films were synthesized by sputtering metallic Co chips and NiO together and the exchange bias of bilayers Co-doped NiO/FeNi was investigated. When Co content was up to 25.2%, the exchange bias field H_E at the room temperature increased to the maximum which was about three times compared to the undoped-bilayers. With further increase of Co content, the exchange bias field H_E and blocking temperature T_B decreased. Analysis suggests that the configuration of nanometer-sized Co-metal clusters enchased into NiO matrix played an important role in the change of magnetic behavior for the bilayers.     

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.     

Cooling-field dependence of exchange bias in Mg-diluted Ni1−xMgxO/Ni granular systems

The exchange-bias (EB) properties of Mg-diluted Ni_1−xMg_xO/Ni (0?x?0.3) granular systems have been investigated. Magnetic dilution with Mg greatly affects the EB field and the coercivity. The temperature dependence of the EB field and the coercivity can be explained in terms of formation of domain states. The value of the EB field increases and shows a maximum value with increasing cooling field, which can be explained by the competition between the field-dependent Zeeman energy and the exchange interaction at the interface.     

Influence of the roughness on the exchange bias effect of NiFe/FeMn/NiFe trilayers

We have studied the effect of roughness on the exchanged biased NiFe/FeMn/NiFe trilayers system. The samples were prepared under three different argon working pressures (2, 5 and 10 mTorr) to obtain different roughness degrees. The root mean square roughness of the NiFe/FeMn interfaces enhances as the argon working pressure during the deposition increases from 2 to 10 mTorr. High-angle X-ray diffraction reveals that the samples have 1 1 1 texture and besides, possible changes in grain size could be an extra contribution to the interfacial roughness. Magnetometry measurements have shown that the coervive field enhances as the root mean square roughness of the NiFe/FeMn interfaces increases, while the dependence of the exchange bias field runs in the opposite way.     

A new paradigm for exchange bias in polycrystalline thin films

In this paper we provide a review and overview of a series of works generated in our laboratory over the last 5 years. These works have described the development and evolution of a new paradigm for exchange bias in polycrystalline thin films with grain sizes in the range 5-15 nm. We have shown that the individual grains in the antiferromagnetic (AF) layer of exchange bias systems contain a single AF domain and reverse over an energy barrier which is grain volume dependent. We show that the AF grains are not coupled to each other and behave independently. Understanding this process and using designed measurement protocols has enabled us to determine unambiguously the blocking temperature distribution of the AF grains, the anisotropy constant (K_AF) of the AF, understand the AF grain-setting process, and predict its magnetic viscosity. We can explain and predict the grain size and film thickness dependence of the exchange field H_ex. We have also studied interfacial effects and shown that there are processes at the interface, which can occur independently of the bulk of the AF grains. We have seen these effects via studies of trilayers and also via the field dependence of the setting process which does not affect the blocking. From separate experiments we have shown that the disordered interfacial spins exist as spin clusters analogous to a spin glass. These clusters can order spontaneously at low temperatures or can be ordered by the setting field. We believe it is the degree of order of the interfacial spins that gives rise to the coercivity in exchange bias systems. Based on this new understanding of the behaviour of the bulk of the grains in the antiferromagnet and the interfacial spins we believe that we have now a new paradigm for the phenomenon of exchange bias in sputtered polycrystalline thin films. We emphasize that the phenomenological model does not apply to core-shell particles, epitaxial single-crystal films and large grain polycrystalline films.     

Dependence of exchange bias on the field-cooled remanent magnetic state in Ni/NiO nanogranular samples

The magnitude of the exchange bias (EB) effect in nanogranular Ni/NiO samples (with Ni content between about 4 and 69 wt% and mean size of the Ni crystallites of the order of 10 nm) has been found to be strictly related to the increase in the remanent magnetization measured after field-cooling, with respect to the value after zero-field-cooling, normalized to the saturation magnetization. This allows describing the EB mechanism in terms of the fraction of the magnetic moments of the Ni nanocrystallites that irreversibly has aligned in the field direction during field-cooling, due to the exchange anisotropy, and that is effectively involved in the loop shift. Hence, the possibility of tuning EB by controlling the field-cooled remanent magnetic state is shown.     

Zero-field cooled exchange bias and magnetization reversal in La1.5Sr0.5Co0.4Fe0.6MnO6

The polycrystalline sample La_1.5Sr_0.5Co_0.4Fe_0.6MnO₆ (LSCFMO) was prepared by sol-gel method and its magnetic properties were studied. The interesting magnetization reversal phenomenon and the zero-field cooled exchange bias (ZEB) effect were simultaneously observed in LSCFMO. ZEB effect can exist in a wider temperature range (0–200 K) compared with La_1.5Sr_0.5CoMnO₆ (0–10 K), which is very important in the potential applications. A schematic diagram based on the coupling between the Fe³⁺ spins, Mn³⁺ spins and Co²⁺ or Co³⁺ spins is used to understand the ZEB and the reversal behaviors. Due to the doping of 60% Fe ion, the magnetic microstructure of LSCMFO is more complex than that of LSCMO, resulting in the meta-stable spin structure and more interesting magnetic phenomenon.     

Thickness dependence of positive exchange bias in ferromagnetic/antiferromagnetic bilayers

For the ferromagnetic (FM)/antiferromagnetic (AFM) bilayers, both negative and positive exchange bias H_E have been observed for low and high cooling field H_CF, respectively. The thickness dependence of H_E and coercivity H_C have been investigated for the cases of negative and positive H_E. It is found that the negative H_E and the positive one have similar FM thickness dependence that is attributed to the interfacial nature of exchange bias. However, the AFM thickness dependence of positive H_E is completely contrary to that of the negative one, which clearly demonstrates that the AFM spins play different roles for the cases of positive and negative H_E. In particular, the AFM thickness of positive H_E was first highlighted by an AFM spin canting model. These results should be attributed to the interfacial spin configuration after field cooling procedure.