Search

We have studied the effect of the interface structure on the exchange bias in the ${\mathrm{FeF}}_{2}\ensuremath{-}\mathrm{Fe}$ system, for ${\mathrm{FeF}}_{2}$ bulk single crystals or thin films. The exchange bias depends very strongly on the crystalline orientation of the antiferromagnet for both films and crystals. However, the interface roughness seems to have a strong effect mainly on the film systems. These results indicate that the exchange bias depends strongly on the spin structure at the interface, especially on the angle between the ferromagnetic and antiferromagnetic spins. We have also found a strong dependence of the hysteresis loops shape on the cooling field direction with respect to the antiferromagnetic anisotropy axis, induced by a rotation of the ferromagnetic easy axis as the sample is cooled through ${T}_{N}.$ For the single crystal systems the results imply the existence of a perpendicular coupling between the antiferromagnetic and ferromagnetic spins at low temperatures.

The temperature dependence of the exchange bias (H{sub E}) near the FeF{sub 2} N{acute e}el temperature ({approximately} 78.4 K) was correlated with structural measurements in FeF{sub 2}-Fe bilayers. Low-angle x-ray diffraction and atomic force microscopy show that samples with larger height fluctuations have larger lateral grain sizes. Samples with larger lateral grain sizes exhibit a surface critical exponent ({beta}{sub S}{approximately}0.8) while samples with smaller grains and smaller height fluctuations have a decreased {beta}{sub S}, indicating a more three-dimensional-like phase transition or an increase in the FeF{sub 2} surface exchange interaction. {copyright} {ital 1997} {ital The American Physical Society}

The induced moment in antiferromagnetic (AFM)--ferromagnetic (FM) $({\mathrm{FeF}}_{2}\ensuremath{-}\mathrm{Fe}$ and ${\mathrm{MnF}}_{2}\ensuremath{-}\mathrm{Fe})$ bilayers has been studied from the shift along the magnetization axis of the exchange-biased hysteresis loops. The magnetization shift depends strongly on the cooling field and microstructure of the AFM layer. The shift for small cooling fields can be opposite to the cooling field, indicating that, in some cases, the presence of the FM layer induces an antiferromagnetic coupling at the interface. Samples with negative magnetization shifts (antiferromagnetic coupling) exhibit large changes in exchange bias ${H}_{E}$ as a function of cooling field and positive exchange bias. Samples with positive magnetization shifts (ferromagnetic coupling) show almost no change in ${H}_{E}$ with cooling field and the exchange bias field remains always negative. These results confirm the theoretical assumption that an antiferromagnetic interface coupling is necessary to observe positive exchange bias.

The magnetic properties of $ϵ{\text{-Fe}}_{2}{\text{O}}_{3}$ nanoparticles are investigated by x-ray magnetic circular dichroism. Sum rules relating the orbital and spin moment in the $\text{Fe}\text{ }3d$ band to the $\text{Fe}\text{ }{L}_{2,3}$ absorption cross sections show that the Fe orbital moment $({m}_{\text{orb}})$ is considerably high, explaining the origin of the large coercivity of this material at room temperature. Moreover, at $T\ensuremath{\sim}110\text{ }\text{K}$, the collapse of the coercivity $({H}_{c})$ and the magnetocrystalline anisotropy coincides with a strong reduction of the spin-orbit coupling evidenced by a drastic drop of ${m}_{\text{orb}}$. The decrease in ${m}_{\text{orb}}$ originates from changes in the electron transfer between Fe and O ions accompanied by significant modifications of some of the Fe-O bond distances. Similarly, the recovery of ${m}_{\text{orb}}$ at lower temperatures mimics the behavior of the Fe-O bond lengths.

We investigate the reversal behavior of circularly exchange-biased micron-sized bilayer disks of Permalloy (Py)/IrMn and CoFe/IrMn. A circular exchange bias is induced by imprinting the vortex configuration of the ferromagnetic layer into the IrMn when the disks are cooled in zero external field through the blocking temperature of IrMn. The resulting circular exchange bias has a profound effect on the reversal behavior of the ferromagnetic magnetization. In Py/IrMn disks the reversal takes place via vortex motion only, and the behavior is controlled by the exchange bias; it is reversible over a range of small fields and the vortex maintains a single chirality throughout reversal, determined by the chirality of the exchange bias. In CoFe/IrMn disks the non-negligible magnetocrystalline anisotropy causes a reversal via both vortices and domain walls resulting in a finite coercivity, and the behavior is controlled by microstructure. We verify that circular exchange bias does not give rise to a hysteresis loop shift. It lowers coercivity with respect to the field-cooled case, and in Py/IrMn disks it even causes completely reversible magnetic behavior. In both Py/IrMn and CoFe/IrMn disks, circular exchange bias removes the randomness (i.e., stochastic processes due to thermal activation) inherent in single-layer ferromagnetic disks and causes the magnetic behavior to be reproducible over time.

We measured directly the depth-dependent Fe spin rotation upon magnetization reversal in exchange-coupled $\text{Fe}/{\text{MnF}}_{2}$ bilayers using nuclear resonant scattering of synchrotron radiation from an $^{57}\text{F}\text{e}$-probe layer buried at different depths within the Fe film. Our results show that the exchange-biased ferromagnetic layer develops a noncollinear spin structure along the film normal direction, reminiscent of a partial domain wall parallel to the $\text{Fe}/{\text{MnF}}_{2}$ interface. This is contrary to most theoretical models of exchange bias which assume a collinear spin structure in the ferromagnetic layer.

Ion irradiation of ${\text{Fe}}_{60}{\text{Al}}_{40}$ alloys results in the phase transformation from the paramagnetic, chemically ordered B2 phase to the ferromagnetic, chemically disordered A2 phase. The magnetic phase transformation is related to the number of displacements per atom (dpa) during the irradiation. For heavy ions (${\text{Ar}}^{+}$, ${\text{Kr}}^{+}$, and ${\text{Xe}}^{+}$), a universal curve is observed with a steep increase in the fraction of the ferromagnetic phase that reaches saturation, i.e., a complete phase transformation, at about 0.5 dpa. This proves the purely ballistic nature of the disordering process. If light ions are used (${\text{He}}^{+}$ and ${\text{Ne}}^{+}$), a pronounced deviation from the universal curve is observed. This is attributed to bulk vacancy diffusion from the dilute collision cascades, which leads to a partial recovery of the thermodynamically favored B2 phase. Comparing different noble gas ion irradiation experiments allows us to assess the corresponding counteracting contributions. In addition, the potential to create local ferromagnetic areas embedded in a paramagnetic matrix is demonstrated.

Exchange bias effects are investigated in antiferromagnetic- $({\mathrm{AF}}_{1}\text{\ensuremath{-}})$ ferromagnetic- (F-) antiferromagnetic $({\mathrm{AF}}_{2})$ structures, where the F consists of a $[\mathrm{Pt}∕\mathrm{Co}]$ multilayer with perpendicular anisotropy and the two AF layers are composed of IrMn. The ${\mathrm{AF}}_{1}$ and ${\mathrm{AF}}_{2}$ thicknesses are varied so that the two IrMn layers exhibit different blocking temperatures. After field cooling, enhancements of the coercivity ${H}_{C}$ and exchange bias field ${H}_{E}$ are observed in the ${\mathrm{AF}}_{1}\text{\ensuremath{-}}\mathrm{F}\text{\ensuremath{-}}{\mathrm{AF}}_{2}$ structures with respect to the two subsystems with a single AF layer (i.e., ${\mathrm{AF}}_{1}\text{\ensuremath{-}}\mathrm{F}$ and $\mathrm{F}\text{\ensuremath{-}}{\mathrm{AF}}_{2}$). For all systems, the magnitude and sign of ${H}_{E}$ can be subsequently tailored by field cooling processes under fields of different sign while ${H}_{C}$ remains constant. The net effect of having two AF-F interfaces is roughly the sum of each individual interface contribution.

Depth-dependent Fe spin structures of the remanent state in exchange-coupled Fe/$\mathrm{Mn}{\mathrm{F}}_{2}$ films have been probed using $^{57}\mathrm{Fe}$ conversion electron M\"ossbauer spectroscopy, both above and well below the $\mathrm{Mn}{\mathrm{F}}_{2}$ N\'eel temperature. $^{57}\mathrm{Fe}$ probe layers were embedded either at the Fe/$\mathrm{Mn}{\mathrm{F}}_{2}$ interface or in the center of the Fe film. Remarkably, exchange bias induces a significant change of the in-plane angular distribution of the Fe magnetic moments at the interface and inside the Fe film, away from the saturation magnetization direction. Results from vector magnetometry support these conclusions.

An analytical model of exchange anisotropy in epitaxial ferromagnetic/antiferromagnetic bilayers was developed. The model demonstrates that the high symmetry exchange anisotropy terms in ferromagnetic/ antiferromagnetic bilayers originate from a partial domain wall in the antiferromagnetic layer. Application of the model to the experimental data analysis enables one to separately determine the fraction of uncompensated interfacial spins in the antiferromagnetic layer and the interfacial exchange coupling energy between spins in the ferromagnet and in the antiferromagnet. The model provides a quantitative description of complex exchange anisotropy recently observed in Fe/MnF 2 bilayers.

Stacking faults are found to play a crucial role in the evolution of the structural and magnetic properties of cobalt subjected to ball milling. This has been evidenced by using complementary techniques, i.e., magnetometry and torque measurements, nuclear magnetic resonance (NMR) and x-ray diffraction (XRD). After short milling times a stacking-fault driven transformation from fcc to hcp cobalt is observed, which is accompanied by an increase of the effective magnetic anisotropy, the NMR restoring field and the coercivity. The results suggest that small amounts of stacking faults can be beneficial to enhance the coercivity in hexagonal Co. For longer milling times, both XRD and NMR results show that the hcp phase becomes heavily distorted because of the large amount of stacking faults accumulated. This induces a decrease of the magnetic anisotropy, which leads to the overall softening of the material.

The magnetic behavior of Fe lines on top of a continuous FeF${}_{2}$ antiferromagnetic layer was investigated as a function of the orientation of the lines with respect to the applied magnetic field and a unidirectional anisotropy established by field cooling. The orientational dependence of the asymmetric loop shift, called exchange bias, shows that the competition between shape and unidirectional anisotropies modifies the exchange bias and the coercivity. Remarkably, in certain cases, exchange bias can be observed even when the applied field is perpendicular to the unidirectional anisotropy. Numerical simulations with a coherent rotation model illustrate a rich phase diagram, which originates from the noncollinearity of the involved anisotropies. Using this phase diagram, exchange bias and coercivity can be predictably tailored. In particular, different preferred magnetization directions can be designed in separately patterned structures of the same sample with identical preparation and magnetic history.

The effect of antisite (AS) defects and electron doping on the ferromagnetic-paramagnetic (FM-PM) transition of Sr 2 FeMoO 6 (SFMO) double perovskite has been studied. From a detailed analysis of the magnetization curves across the FM-PM transition we conclude that AS defects decrease the average strength of the magnetic interactions, although, remarkably enough, some of them are actually enhanced. It follows that the mean-field Curie temperature lowers whereas the onset of magnetization occurs at somewhat higher temperatures. The FM-PM transition has also been analyzed in electron-doped La x Sr 2 - x FeMoO 6 , where the AS defects concentration has been found to increase upon La doping. It turns out that in spite of the presence of AS, the mean-field Curie temperature significantly rises upon La and electron doping. This experimental finding contrasts with some recent predictions and emphasizes the role of itinerant electrons in the ferromagnetic coupling in these oxides. Moreover, our results indicate that disordered (i.e., with AS) double perovskite materials should be described as systems with random magnetic anisotropy.

The dependence of exchange bias on antiferromagnet thickness has been measured in FeF 2 /Fe and MnF 2 /Fe bilayers. The two fluoride systems have identical crystal structures, similar lattice constants, but anisotropy fields that differ by a factor of 20. Hence, by comparing the antiferromagnetic layer thickness dependence of the exchange bias in the two systems we are able to directly establish the effect of the antiferromagnet anisotropy. We find that the critical antiferromagnet thickness for the onset of exchange biasing is an order of magnitude smaller for the more anisotropic fluoride, confirming the often-used assumption that the anisotropy dictates the critical thickness. By measuring the temperature dependence of the exchange bias and the structural morphology of the layers we are able to prove that the effects we observe are not due to the blocking-temperature thickness dependence or the onset of discontinuity in thin antiferromagnet lavers.

A route toward enhancing the energy product $(\mathrm{BH}{)}_{\mathrm{max}}$ of permanent magnetic materials, at room temperature, based on ferromagnetic-(FM-) antiferromagnetic (AFM) exchange interactions has been developed. The exchange coupling, which is induced by ball milling hard magnetic ${\mathrm{SmCo}}_{5}$ with AFM NiO powders, results in an enhancement of coercivity ${H}_{C}$ and squareness ratio ${M}_{R}{/M}_{S}$ (remnant-saturation magnetizations), which depends on the FM:AFM ratio and the processing conditions. However, the presence of the AFM in the composite results also in a competing effect, i.e., reduction of the overall saturation magnetization, which decreases $(\mathrm{BH}{)}_{\mathrm{max}}.$ Nevertheless, it has been found that after an optimization of the FM:AFM ratio and the milling conditions it is possible to achieve an improvement of $(\mathrm{BH}{)}_{\mathrm{max}}.$

The angular dependence of the magnetic anisotropy of exchange biased Fe/MnF 2 bilayers was measured. Below the Neel temperature of the antiferromagnetic MnF 2 layer, an exchange anisotropy is observed which consists of unidirectional, uniaxial, threefold and fourfold symmetry components. The threefold exchange anisotropy term is responsible for the asymmetric magnetization reversal process recently observed in this system.

Exchange-biased ${\mathrm{MnF}}_{2}/\mathrm{F}\mathrm{e}$ bilayers, examined by variable angle and temperature ferromagnetic resonance (FMR), exhibit a sudden onset of a unidirectional and fourfold anisotropy below the ${\mathrm{MnF}}_{2}$ N\'eel temperature. This unexpected fourfold symmetry arises from frustrated perpendicular coupling between the ${\mathrm{MnF}}_{2}$ and the Fe overlayer in the presence of twinning in the antiferromagnet layer. These data are consistent with earlier polarized-neutron-reflectometry results. The FMR data show a clear reversal in the direction of the unidirectional anisotropy as a function of cooling field, switching sign at ${H}_{\mathrm{FC}}=13\mathrm{kOe},$ which is consistent with the onset of positive exchange bias observed in conventional magnetometry experiments. The low-temperature FMR linewidth reflects the in-plane symmetry of the resonance itself, exhibiting surprising divergence in the hard directions. Temperature-dependent FMR measurements reveal a sharp reduction in the resonance field below the N\'eel point due to the ferromagnetic/antiferromagnetic coupling.

Polarized neutron reflectometry is used to measure the thermal response of the net-magnetization vector of polycrystalline ferromagnetic (F) Fe films exchange coupled to twinned $(110){\mathrm{MnF}}_{2}$ antiferromagnetic (AF) layers. We observe a strong correlation between the temperature dependencies of the net sample magnetization perpendicular to the applied field at coercivity and exchange bias. For cooling field and measurement conditions involving magnetization reversal via rotation, we find a range of temperature dependencies. For the smoothest F-AF interface, the temperature dependence of exchange bias compares well to a $S=\frac{5}{2}$ Brillouin function---an observation predicted by some theoretical models. This temperature dependence is expected for the sublattice magnetization and the square root of the anisotropy constant $\sqrt{{K}_{1}}$ of bulk ${\mathrm{MnF}}_{2}.$ In contrast, for a rough F-AF interface the magnetization reversal process (and exchange bias) showed little temperature dependence up to temperatures approaching the AF N\'eel point---a clear consequence of increasing interfacial disorder in a F-AF epitaxial system.

Bean's, Kim's, and the exponential-law critical-state models have been used to calculate the magnetization curves M(H) of hard superconductors assumed to have an infinitely long geometry with rectangular cross section of 2a\ifmmode\times\else\texttimes\fi{}2b. Some computed M(H) curves are given to illustrate our analytical results for different b/a and other relevant parameters. These results can be satisfactorily applied to many experimental data, particularly in the study of high-${\mathit{T}}_{\mathit{c}}$ superconductors. A brief analysis on this is also given.