Discriminating the microscopic origin of positive exchange bias near the blocking temperature: atomistic interfacial spins versus whole-grain antiferromagnetic reversal versus training-induced reorganization

Exchange bias — the shift of a ferromagnet's hysteresis loop produced by exchange coupling to an antiferromagnet — occasionally reverses sign, shifting the loop along the cooling-field direction (positive exchange bias) instead of opposite to it. Positive exchange bias frequently appears in a narrow window just below the blocking temperature $T_B$, and at least three distinct microscopic origins have been proposed: antiferromagnetic coupling of atomistic interfacial spins, reversal of whole antiferromagnetic grains in granular antiferromagnets, and training-induced reorganization of metastable interfacial spin configurations. Dobrynin, Warin, Vorobiev and Givord (J. Magn. Magn. Mater. 520, 166707, 2021) resolved the Co/CoO case in favor of reversible antiferromagnetic entities being individual spins, inferred from the identical positive-EB behavior of two samples whose CoO grain sizes — and hence blocking temperatures — differ; the same inference implies that whole-grain reversal, where it operates, should imprint a strong grain-size dependence on $H_{eb}(T)$. The unresolved problem is to establish, for exchange-biased systems in general, validated criteria — experimental signatures and/or model-based discriminants — that identify which mechanism produces positive exchange bias close to $T_B$ in a given system, including the predicted grain-size signature of whole-grain reversal and the accompanying coercivity enhancement, and to determine how far the temperature-dependent granular model transfers to systems with different interfacial coupling strengths, antiferromagnetic anisotropy landscapes, and more complex reversal pathways.

Background

When a ferromagnet (FM) is exchange-coupled to an antiferromagnet (AFM) and the bilayer is cooled in a magnetic field through the temperature at which the AFM becomes magnetically rigid, the FM hysteresis loop shifts horizontally by the exchange-bias field $H_{eb}$ — the exchange bias (EB) effect, first reported for Co particles embedded in CoO by Meiklejohn and Bean (1956). In polycrystalline films the AFM layer consists of grains, each with an anisotropy energy barrier $K(T)V$ set by its anisotropy constant $K$ and volume $V$; EB disappears above the blocking temperature $T_B$, the temperature at which thermal fluctuations overcome these barriers on the measurement timescale, and the modern granular description of EB relates the loop shift and its temperature dependence to the distribution of AFM grain sizes and energy barriers (O'Grady, Fernandez-Outon and Vallejo-Fernandez, 2010). Repeated magnetization cycling (the training effect) gradually relaxes $H_{eb}$, reflecting metastable configurations of interfacial AFM spins. EB is conventionally negative ($H_{eb}$ opposite to the cooling-field direction). In some systems, however, the loop shifts along the cooling-field direction — positive exchange bias — first observed in FeF$_2$/Fe bilayers cooled in large fields (Nogués, Lederman, Moran and Schuller, 1996). In that family of systems the sign reversal was tied to antiferromagnetic (rather than ferromagnetic) exchange coupling across the FM/AFM interface, which favors an FM antiparallel to its field-cooled direction (Hong, 1998; Nogués, Leighton and Schuller, 2000; Kiwi, Mejía-López, Portugal and Ramírez, 2000). Two further established routes to positive EB are training-induced metastable disorder at the frustrated interface, reported in NiFe/IrMn just below $T_B$ (Mishra, Radu, Dürr and Eberhardt, 2009), and a crystallography-driven, cooling-field-independent rotation of the effective anisotropy and EB axis in epitaxial Co/CoO (Suszka, Idigoras, Nikulina, Chuvilin and Berger, 2012). Positive EB is typically accompanied by enhanced coercivity, which in Co/CoO has been shown to have a unidirectional component (Gredig, Krivorotov, Eames and Dahlberg, 2002). Against this backdrop, Dobrynin, Warin, Vorobiev and Givord (2021) analyzed two oxidized Co films, sputtered by different techniques, whose CoO layers have different grain sizes and consequently blocking temperatures differing by 50 K. Both samples show the same sign change of EB from negative to positive in proximity to $T_B$, accompanied by coercivity enhancement. A computational granular model incorporating the measured temperature dependence of the CoO magnetocrystalline anisotropy and sublattice magnetisation reproduces positive EB when a significant fraction of antiferromagnetic entities becomes involved in magnetization reversal and these entities are mutually coupled antiferromagnetically; the accompanying coercivity enhancement arises because the anisotropy energies of the reversible AFM entities add to the ferromagnetic layer's energy barrier. Because the positive-EB behavior is quantitatively identical in the two samples with different grain sizes, the authors conclude that, in these samples, the reversible antiferromagnetic entities must be individual (atomistic) interfacial spins rather than whole grains; by the same inference, a system in which positive EB instead arises from whole-grain AFM reversal should exhibit a strong grain-size dependence of $H_{eb}(T)$. Reviews of the field (Blachowicz and Ehrmann, 2021; Blachowicz, Ehrmann and Wortmann, 2023) list the growing family of positive-EB systems — nanostructured FeMn/Co/FeMn networks, perovskites, core-shell nanoparticles, van der Waals magnets, noncollinear antiferromagnets — but no general criterion exists for deciding, in an arbitrary exchange-biased system, which microscopic mechanism is operating.

Problem Statement

For an exchange-biased system exhibiting positive exchange bias in proximity to the blocking temperature $T_B$, establish how to determine which microscopic mechanism produces the positive bias — antiferromagnetically coupled atomistic interfacial spins participating in magnetization reversal, reversal of whole antiferromagnetic grains in a granular antiferromagnet, or training-related reorganization of metastable interfacial configurations. (This trichotomy covers the mechanisms proposed for positive EB near $T_B$; the cooling-field-independent, crystallography-driven rotation of the effective anisotropy and EB axis reported in epitaxial Co/CoO (Suszka et al., 2012) is a distinct established route outside it, and a mechanism assignment must not misclassify systems of that kind as one of the three.) Concretely: (i) establish experimentally measurable signatures and/or model-based discriminants that distinguish these mechanisms — for example the grain-size dependence of $H_{eb}(T)$ expected for whole-grain reversal versus its absence for atomistic reversible entities, the temperature window and sign behavior relative to $T_B$, the accompanying coercivity enhancement, and the response to cooling field and training cycles — such that they can be applied to the experimental data of a given system to identify which mechanism, or which superposition of coexisting mechanisms, produces its positive bias; and (ii) determine how far the temperature-dependent granular framework of Dobrynin et al. (2021), formulated for a single-domain ferromagnet coupled to a binary-spin antiferromagnet, transfers to systems with different interfacial coupling strengths, different antiferromagnetic anisotropy landscapes, and more complex reversal pathways, delimiting the parameter regimes in which each mechanism dominates.

References

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