Cobalt ferrites exhibit widely varied magnetic behaviour due to the presence of a miscibility gap leading to the formation of periodic self-assembled nanostructures via spinodal decomposition. Periodicity and amplitude of the compositional fluctuations can be controlled by thermodynamic and kinetic processing parameters which allows for careful tuning of the magnetic properties. Although reports have shown evidence of spinodal decomposition, there is a lack of detailed characterization of the magnetic interactions and reversal mechanisms in these materials. In this work we use high-resolution first order reversal curves (FORC) measurements to understand the underlying magnetic processes occurring in a cobalt ferrite with a nominal composition of Co1.8Fe1.2O4 before (calcined) and after spinodal decomposition (annealed). Additionally, FORC measurements with preconditioning fields were conducted to separate the interaction signatures at low coercive fields by biasing the sample in positive and negative mean fields. Microstructural characterization using TEM combined with EDS showed uniform chemistry in the calcined sample and the presence of Fe rich and Co rich regions in the annealed sample, due to spinodal decomposition. Signs of positive exchange interactions were observed in both calcined and annealed samples. This work presents the first detailed magnetic characterization of magnetic interactions in a nanostructured cobalt ferrite, and provides an example of magnetic characterization of nanostructured ferrites using FORC.
Spinel ferrites are a class of ceramic oxides given by the formula AB2O4 with A and B being the divalent cation and trivalent cation respectively. In cubic spinel ferrites, oxygen forms a face-centred lattice, and cations occupy 1/8 of the tetrahedral and ½ of the octahedral voids. Magnetism in ferrites is governed by the A-A, B-B and A-B super-exchange interactions mediated via oxygen anions.1 Depending on cation chemistry and distribution, high saturation moments, low coercivities and high resistivities can be achieved.2 Therefore, these materials are used in diverse soft magnetic applications such as magnetic hyperthermia, magnetic resonance imaging, and power electronics.3–5 In comparison to Mn, Ni, or Mn-Zn ferrites, Co-ferrites exhibit larger coercivities, making them suitable for semi-hard magnetic material applications.6 Higher coercivities originate from large anisotropy caused by spin orbit coupling of the unquenched orbital moment of the Co+2 ion.7
From the fundamental perspective, magnetic behaviour of cobalt ferrites is of particular interest due to a tendency to undergo spinodal decomposition, yielding periodic nanostructured regions.8 The ability to achieve tailored microstructures with nanoscale chemical heterogeneities provides a unique opportunity to study magnetization processes in complex nanostructured magnetic ceramics, as cation chemistry will also yield variations of intrinsic magnetic properties. Preliminary investigation by Takahashi and Fine8 reported large increase in coercivity both at 297 and 77 K for samples aged inside the coherent spinodal. These samples showed periodic compositional variations along the ⟨100⟩ direction with wavelengths ranging from 60 to 150 Å. Upon long term annealing (>100 hrs) inside the spinodal, ferrimagnetic Fe rich regions surrounded by paramagnetic Co rich regions were observed.9 Chemical segregation due to decomposition was also hypothesized to be present in samples quenched rapidly from the single-phase region thereby leading to the presence of regions with fully compensated moments on A and B sites, yielding net zero magnetization locally. These regions were claimed to impede domain wall motion causing relatively large coercivities at 77 K.10
Although changes in average magnetic properties upon decomposition have been extensively reported, detailed studies of magnetic interactions and reversal mechanisms have yet to be investigated. Major hysteresis loop (MHL) measurements provide only limited information about microscopic mechanisms, as only bulk magnetic response is measured. First order reversal curve (FORC) distributions allow for characterization of magnetic interactions and irreversible contributions to bulk magnetization.11 FORC distributions are generated by first saturating the sample in a positive field, decreasing to a reversal field Br, and recording magnetization with applied field Ba increasing back to saturation in equal increments.12 This process is repeated in equal decrements of Br, until the reversal field reaches negative saturation. The FORC distribution is generated by a negative mixed derivative of magnetization with respect to Br and Ba obtained from local polynomial fitting. Typically, the FORC distribution is plotted as a function of the bias (Bu) and coercive (Bc) fields, defined as Bc = (Br − Ba)/2 and Bu = (Br + Ba)/2. Bc and Bu represent the half-width and horizontal bias of ideal rectangular hysteresis loops, called hysterons, whose superposition yields measured results.
In case of random assemblages of interacting single-domain (SD) particles, Bc and Bu correspond roughly to the switching field of each particle and the internal field caused by magnetic interactions with neighbour particles, respectively. In this so-called Preisach-Néel model,13 the vertical spread represents a distribution of interaction fields. Positive (magnetizing) and negative (demagnetizing) mean field interactions, where the internal field is proportional to bulk magnetization, and produces specific deformations of intrinsic FORC signatures13 taking the form of a wishbone14 (negative interactions dominate) or boomerang15 (positive interactions dominate). In case of non-SD particles, Bu no longer represents a real internal field. Particles with few magnetic states are characterized by discrete peaks above and below the Bu = 0 axis, produced by state transitions such as the symmetric pair of positive peaks and butterfly feature around the central ridge of particles with SD-like and vortex-like states.16 The number of magnetic states generally increases with particle size, adding more contributions that fill a triangular region limited by Bc ≤ Bs and |Bu| ≤ Bs, where Bs is the field in which the major hysteresis loop becomes closed.13 Finally, nucleation of weakly pinned domains decreases maximum Bc until FORC diagrams converge to a vertical ridge centred near Bc = 0.17
In previous work, we used hysteresis measurements combined with preliminary FORC to explore magnetic responses before and after spinodal decomposition.18 FORC distributions of calcined samples for which spinodal decomposition should be minimized, showed two peaks centred near Bu = 0, surrounded by diverging contour lines typical of particles with flux closure. The FORC distribution includes a large tail stretching up to 80 mT along the Bc axis. Annealed samples treated to intentionally induce significant spinodal decomposition displayed a distinct wasp-waisted hysteresis loop resulting from a bimodal coercivity distribution. The corresponding FORC distribution features a single maximum near the origin, and a downward-bended tail with weakly negative amplitudes below. Here we use high resolution FORC measurements to further clarify the nature of magnetic interactions in calcined and annealed samples. In addition, FORC measurements with preconditioned fields are carried out to delineate from the effect of interactions on different magnetic entities. Microstructural characterization at the nm scale is carried out using TEM. This, combined with FORC data, is used to propose a basic model that explains the magnetic behaviour of these materials.
Cobalt ferrite samples were synthesized using powder processing, the details of which can be found in our previous publication.18 The sample air quenched from the single phase region to minimize spinodal decomposition and the sample heat treated within the miscibility gap to induce significant decomposition, will be referred to as calcined and annealed respectively. FORC measurements were carried out using a Lakeshore Cryotronics 8607 VSM at room temperature. To increase signal-to-noise ratio in critical regions of the FORC space, measurements of calcined sample in steps of 1 mT were repeated 15 times. The larger coercivity range of annealed sample was covered by 4 repeated measurement series in steps of 1.5 mT up to Bc = 150 mT, and 5 repeated measurement series in steps of 2 mT up to Bc = 400 mT. Measurements were processed using VARIFORC19 with a minimum smoothing factor of 2, yielding a maximum resolution of ∼2 mT (calcined) and ∼3 mT (annealed), over critical regions of FORC space. Samples for TEM were prepared dispersing powders in acetone and drop casting onto a carbon grid. Samples were characterized using a Thermo Scientific Titan Themis probe Cs-corrected G2 200 TEM in TEM mode for acquisition of TEM images and diffraction and in STEM mode for EDS elemental mapping using SuperX EDS spectroscopy.
RESULTS AND DISCUSSION
TEM combined with EDS in STEM was carried out to investigate microstructure at nm length scales, results are shown in Fig. 1. The calcined particle showed uniform chemistry. Upon annealing, Fe-rich and Co-rich regions within a single particle are observed, consistent with spinodal decomposition occurring within particles.20 Fe-rich and Co-rich regions are isostructural but are expected to have distinct intrinsic magnetic properties.21 For example, the strength of exchange interaction between A and B site cations decrease with increasing Co3+ content as reflected by the Curie temperature decrease associated with increasing Co/(Co + Fe) ratios.10 Compositions for Fe rich and Co rich regions are estimated from EDS (supplementary material) to be approximately Co1.3Fe1.7O4 and Co0.38Fe2.62O4 respectively. Fe rich and Co rich regions are therefore expected to exhibit ferrimagnetic and paramagnetic behavior, respectively, with a coherent, spatially distributed interface between.
The processed low-noise, high-resolution FORC diagrams for the calcined and annealed sample are shown in Fig. 2. Typically, FORC plots represent the amplitude of the mixed double derivative as a function of Bc and Bu and for a better quantitative assessment, the FORC distribution is plotted using quantile contours.13 A q-quantile contour encloses a part of the FORC function which contributes to a fraction 1 − q of the total magnetization. Conventional FORC measurements and processing yield significant results for amplitudes >10% of the central maximum. These amplitudes, however, account for only ∼60% (calcined) and ∼30% (annealed) of the total magnetization, due to their limited extension in the FORC space.
The FORC plot of the calcined sample is characterized by a central maximum centred at (Bc, Bu) = (13, 0) mT surrounded by contours whose shape evolves from oval for q > 0.8 to divergent towards Bc = 0 at lower amplitudes. The central maximum occurs near the origin for the annealed sample, and in this case all contours diverge towards Bc = 0. In both diagrams, a broadened ridge departs from the central maximum towards higher coercivities (Feature 1, dotted lines). A sharp, straight ridge running along Bu = 0, known as the central ridge, arises in systems with field-reversal memory, such as non-interacting SD particles13 and certain spin glasses.22 This ridge is broadened and shifted vertically by random and mean components of magnetic interactions.13,23 The low-amplitude negative region below the descending diagonal (Feature 2) is typical of reversible rotations of magnetization vector in proximity of the reversal field in SD and single-vortex particles.13,16 They are also typical for particle assemblages collectively behaving as SD and single-to multi-vortex magnetization states.13,24
In addition to these features, a vertical ridge extending along Bc = 0 over Bu < 0 (Feature 3) is associated with a viscous magnetization decay occurring at negative reversal fields.25 Both FORC plots contain two pairs of positive-negative ridges extending along the descending diagonal (Feature 4) and just above (Feature 5). These ridges correspond to processes occurring around Ba = 0 (Feature 4) or in small positive fields Ba = 0–50 mT (Feature 5). The negative ridge of Feature 4 peaks at Bc = 40–50 mT for both samples and overlaps with the positive contributions of the FORC function below the central maximum, creating a characteristic indentation of the contour lines. Feature 5, on the other hand, covers different coercivity ranges, peaking at Bc ≈ 50 mT in the calcined sample, and at Bc ≈ 160 mT in the annealed sample. In the latter case, the positive and negative ridges are almost perfectly symmetric. A similar pair of ridges along the descending diagonal (Feature 4) has been interpreted as the result of magnetic interactions between hard and soft regions within the samples,26,27 where the soft region switches in a small biasing field created by the hard region. As the hard region is progressively switched in negative reversal fields of increasing amplitudes, the mean biasing field Bi increases or decreases depending on whether the two regions are positively or negatively coupled. As a result, the switching field of the soft regions depend on Br, and the mixed derivative of the soft phase magnetization with respect to Br and B yields a positive-negative pair of peaks in the case of positive coupling [Bi = α Mhard with α > 0, Fig. 2(c)], or a negative-positive pair of peaks in case of negative coupling (α < 0). The presence of a negative central ridge offset in Bc > 110 mT and Feature 5 indicate the presence of interactions between the magnetically hard regions of the annealed sample. Both these features point towards interactions characterized by α > 0, which, given the random arrangement of the particles, can only be explained by a positive exchange coupling between hard regions (central ridge offset) and between hard and soft regions (features 4 and 5), which is not surprising given the coherent nature of the spinodal decomposed microstructure. The central peak of the FORC function, which is controlled by the soft region, is located very close to Bu = 0. The lack of a significant central peak offset indicates the main FORC contribution, which, in our case, is carried by soft regions, is not affected by net positive or negative mean field interactions, unlike the case of more ordered structures such as films where the interaction or exchange field takes a preferred direction.26 This does not exclude exchange interactions effects near the interfaces with hard regions, as indicated by features 4 and 5. Although calcined sample quenched from the single phase showed no evidence of chemical segregation through EDS [Figs. 1(a1)–1(f1)], phase separation has been claimed at very fine length scales by previous authors because of the absence of an energy barrier for phase separation via spinodal decomposition.28 Presence of diagonal ridges and shearing of the central ridge as in the annealed sample may be consistent with possibility of local chemical segregation at fine length scales unresolved in TEM/EDS.
Magnetic interaction effects masked by the broadness of the FORC function, particularly diagonal ridges on the descending diagonal (Feature 4) in the calcined and annealed FORC distribution, have been highlighted by a modified FORC protocol where a preconditioning field Bpre = ±1 T has been used to saturate the hard regions in the positive or negative direction. FORC measurements have been subsequently performed over a range of fields not exceeding +100 mT, using a field Bs = +120 mT (calcined) or +135 mT (annealed) to reset the soft region prior to the acquisition of each curve. This ensures that hard regions with Bc > Bs maintain the polarity imparted by Bpre during the whole measurement sequence, producing a constant biasing field that acts on coupled regions with lower coercivity. Technically, measurements obtained with Bpre = −1 T are not FORC, as they do not branch from the major hysteresis loop. The difference between the same FORC measurements obtained with Bpre = +1 T and Bpre = −1 T highlights effects of a magnetic coupling between hard and soft regions. In the case of the calcined sample shown in Fig. 3, measurements are practically identical, except for a small vertical shift of the central maximum (from Bu = +0.46 mT for Bpre = +1 T to Bu = −0.54 mT for Bpre = −1 T) and a slight decrease of the amplitude of the negative ridge along the B = 0 diagonal for Bpre = −1 T. The difference between FORC functions is dominated by features expected from a vertical offset of the whole FORC function, with maximum amplitudes just above and below the central maximum, where the flanks of the FORC function are steeper [Fig. 3(c)]. This offset is compatible with a fixed internal field with opposite polarity relative to the magnetization of the hard regions (α < 0). Exchange interactions are slightly affected by Bpre, as seen by the slightly smaller negative offset of the central ridge at higher coercivities for Bpre = −1 T. The smaller offset can be explained by the fact that part of the high-coercivity region that was negatively saturated by Bpre = −1 T is switched back to positive saturation by Bs. The same effect on the central ridge is visible also for the annealed sample (Fig. 4). In this case, the much stronger offset difference creates the positive Feature 1 in the FORC function difference [Fig. 4(c)]. The weakening of exchange interactions with Bpre = −1 T is also visible when comparing the amplitude of negative ridges along the B = 0 diagonal (Feature 4). Comparison of this feature in Figs. 4(a) and 4(b) is made difficult by overlap with the soft region contribution to the FORC function, also sensitive to Bpre. Changes in soft region signature from Bpre = +1 T to Bpre = −1 T can be described by an overall compression of FORC function towards Bc = 0, which moves the central maximum towards the origin and makes contour lines steeper. Differences are most evident for Bu > 0, resulting in the vertical ridge labelled as Feature 6 in Fig. 4(c).
Using detailed FORC analyses we can conclude that the magnetic properties of the calcined and annealed cobalt ferrite samples are strongly affected by presence of interactions. Positive exchange interactions occur between soft and the hard magnetic regions and also within the hard magnetic regions. The pair of diagonal ridges at low and high coercive fields and a downward bending central ridge are signatures of such interactions. In addition, the calcined sample also shows negative interactions.
The phase end members Co0.38Fe2.62O4 and Co1.3Fe1.7O4 created by spinodal decomposition support the existence of compositional transition interfaces between ferrimagnetic, Fe-rich regions and paramagnetic Co-rich regions, with an estimated thickness of ∼25 nm [estimate from line scan in supplementary material Fig. S1(c).]. Similar interfaces have been observed in the hemoilmenite system29 upon exsolution of canted antiferromagnetic hematite lamellae in a paramagnetic ilmenite matrix. These intergrowths have been found to be several times more magnetic than can be explained by the canted antiferromagnetism moment of the hematite contained within them. The excess magnetization of these fine-scale intergrowths comes from the interfaces, which effectively behave as a hard magnetic phase exchange coupled with hematite. The existence of a hard interfacial phase in our samples is supported by the fact that the maximum switching field deduced from the FORC measurements (∼400 mT for the annealed sample) largely exceeds the maximum switching field predicted for the Fe-rich phase (i.e., Bsw = K/Ms ≈ 120 mT for magnetocrystalline anisotropy and Bsw = µ0Ms/2 ≈ 190 mT for shape anisotropy, using the data of Jalili et al.30). We therefore propose a model for spinodally decomposed samples where Fe-rich regions are separated from the paramagnetic Co-rich phase by a magnetically hard interface layer (Fig. 5). Furthermore, we assume that a positive exchange coupling occurs between the Fe-rich regions and the interface layer, as well within the interface layer or at contact points between two such layers.
At the beginning of each FORC measurement, magnetizations of all regions are aligned with the applied saturation field (State 1 in Fig. 5). In the case of smaller reversal fields, only the soft regions are reversed at Br [State 2 in Fig. 5(a)], while larger negative reversal fields can also switch the hard interface [State 2 in Fig. 5(b)]. During FORC measurements, the soft regions are switched back to positive saturation, followed by the hard regions (States 2–4 in Fig. 5). Parts of the soft regions close to the hard interface will be affected by a bias field from exchange interactions, so that their effective switching field depends on the proportion of interface regions that have been negatively switched at Br. Exchange interactions between hard interfaces are also affected by Br. These phenomena make the difference between state 2–3 in the two examples of Fig. 5, creating the diagonal ridges (Feature 4 and 5) in the FORC diagram, as well as the central ridge offset at higher coercivities.
In this work we systematically investigated the magnetic behaviour of a cobalt ferrite before and after spinodal decomposition using high resolution FORC measurements. In addition to standard FORC measurements, FORC measurements were carried by subjecting the sample to prior preconditioning fields which saturated the hard regions. This allowed for investigation of exchange interactions and magnetic states at low Bc fields selectively. FORC measurements combined with microstructural characterization using TEM was used to propose a model for magnetic interactions in the annealed sample. The calcined sample showed uniform distribution of Co and Fe across the particles in the elemental maps obtained using EDS, while clear compositional variations leading to distinct Co- and Fe-rich regions occur after annealing. On the other hand, FORC measurements of both the calcinated and the annealed sample show peculiar signatures that can be attributed to exchange interactions between two magnetic phases with distinct coercivities. We associate the magnetically soft phase with ferrimagnetic Fe-rich regions that are sufficiently large to display inhomogeneous magnetization states but small enough to be fully single-domain across the width. The magnetically hard phase, whose coercivity is too large to be explained by the magnetocrystalline or shape anisotropy of homogeneous cobalt ferrite particles, is identified with interfaces between Fe-rich regions and a paramagnetic Co-rich matrix, in analogy with exsolved hemoilmenite systems where an emergent interfacial magnetic phase with high coercivity has been documented. Annealing leads to the development of larger Fe-rich regions, as seen from the apparent shift of the FORC signature towards the multidomain endmember. FORC signatures related to the exchange interaction between Fe-rich regions and their interface with the paramagnetic matrix are also more pronounced in annealed samples. These observations lead to the conclusion that Fe-rich regions and corresponding interfaces with a Co-rich matrix grow during the annealing process.
Future work will seek to further understand magnetic behaviour of nanostructured materials with different characteristic length scales. Furthermore, low temperature magnetometry and FORC will be used to measure the temperature dependent interactions and the corresponding magnetic states. This will be combined with micromagnetic simulations with an objective to delineate magnetization processes occurring in spinodal decomposed cobalt ferrites, also providing an example for applying similar tools in future nanostructured ferrites.
The supplementary material contains a line scan of the annealed particle shown in Figs. 1(b2)–1(f2) showing the composition variation along a line from a Co rich region to the Fe rich region.
The authors acknowledge financial support from the University of Pittsburgh Dean's Office, the Office of Naval Research (ONR GRANT No. N000142112498). This work was supported in part by the Advanced Magnetics for Power and Energy Development (AMPED) consortium industry participant funding. M.V.S. acknowledges Noah A. Sargent (University of Pittsburgh) for the technical discussions.
Conflict of Interest
The authors have no conflicts to disclose.
Suraj V. Mullurkara: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Ramon Egli: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). B.C. Dodrill: Data curation (equal); Methodology (equal); Resources (equal); Validation (equal); Writing – review & editing (equal). Susheng Tan: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal). P.R. Ohodnicki, Jr.: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Writing – review & editing (equal).
The data that support the findings of this study are available from the corresponding author upon reasonable request.