Beatriz Rivas-Murias

Martín Testa-Anta

Alexander S Skorikov

Miguel Comesaña-Hermo

Sara Bals

Verónica Salgueiriño

Interfaceless Exchange Bias in CoFe 2 O 4 Nanocrystals

Keywords: Exchange bias, spinel ferrite nanocrystals, pinned and unpinned uncompensated moments, Raman spectroscopy

Oxidized cobalt ferrite nanocrystals with a modified distribution of the magnetic cations in their spinel structure give place to an unusual exchange-coupled system with a double reversal of the magnetization, exchange bias and increased coercivity, but without the presence of a clear physical interface that delimits two well-differentiated magnetic phases. More specifically, the partial oxidation of cobalt cations and the formation of Fe vacancies at the surface region entail the formation of a cobalt-rich mixed ferrite spinel which is strongly pinned by the ferrimagnetic background from the cobalt ferrite lattice. This particular configuration of exchange-biased magnetic behavior, involving two different magnetic phases but without the occurrence of a 2 crystallographically coherent interface, revolutionizes the established concept of the exchange bias phenomenology.

The exchange bias (EB) effect, also referred to as unidirectional or exchange anisotropy, describes a magnetic coupling observed in core-shell nanocrystals (NCs) or thin films, generally between an antiferromagnet (AFM) and a ferro-or ferrimagnet (FM and FiM, respectively) separated by a physical interface. 1 The EB effect with FM/FM, FiM/FiM, AFM/AFM or FM/spin glass exchange interactions has also been reported, [START_REF] Schubert | Interfacial Exchange Coupling in Fe-Tb/[Co/Pt] Heterostructures[END_REF][START_REF] Hebler | Double Exchange Bias in Ferrimagnetic Heterostructures[END_REF][START_REF] Romer | Temperature Dependence of Large Exchange-Bias in TbFe-Co/Pt[END_REF][START_REF] Borchers | Spatially Modulated Antiferromagnetic Order in CoO/NiO Superlattices[END_REF][START_REF] Ali | Exchange Bias Using a Spin Glass[END_REF] as well as more exotic systems stemming from interfacial spin configurations (that is, non-collinear or frustrated interface spins) [START_REF] Ali | Exchange Bias Using a Spin Glass[END_REF][START_REF] Testa-Anta | Spin Frustration Drives Exchange Bias Sign Crossover in CoFe2O4-Cr2O3 Nanocomposites[END_REF][START_REF] Zhang | Realization of Exchange Bias Control with Manipulation of Interfacial Frustration in Magnetic Complex Oxide Heterostructures[END_REF] or even in magnetic NCs holding antiphase boundaries due to their strained crystalline structure. [START_REF] Levy | Correlating Magneto-Structural Properties to Hyperthermia Performance of Highly Monodisperse Iron Oxide Nanoparticles Prepared by a Seeded-Growth Route[END_REF][START_REF] Wetterskog | Anomalous Magnetic Properties of Nanoparticles Arising from Defect Structures: Topotaxial Oxidation of Fe1-XO|Fe3-ΔO4 Core|Shell Nanocubes to Single-Phase Particles[END_REF] Such coupling produces a horizontal shift in the hysteresis loop after cooling under an applied magnetic field, and is often accompanied by an increase in its coercive field (HC), endorsing these systems with a huge relevance in many technological applications related to permanent magnets [START_REF] Lottini | Strongly Exchange Coupled Core|Shell Nanoparticles with High Magnetic Anisotropy: A Strategy toward Rare-Earth-Free Permanent Magnets[END_REF] or magnetic recording media. [START_REF] Skumryev | Beating the Superparamagnetic Limit with Exchange Bias[END_REF][START_REF] Allibe | Room Temperature Electrical Manipulation of Giant Magnetoresistance in Spin Valves Exchange-Biased with BiFeO3[END_REF] Given that EB is by definition an interfacial phenomenon dependent on a physical boundary between two well-differentiated magnetic components, 1,[START_REF] López-Ortega | Applications of Exchange Coupled Bi-Magnetic Hard/Soft and Soft/Hard Magnetic Core/Shell Nanoparticles[END_REF] fine tuning of the dimensions, nature and overall quality of such interface is needed in order to control the magnetic coupling. [START_REF] Liu | Effect of Interface Roughness on the Exchange Bias for NiFe/FeMn[END_REF][START_REF] Wang | Influence of Interface Roughness on the Exchange Bias of Co/CoO Multilayers[END_REF] In this context, thin interfacial layers with FM or AFM properties generated at film-substrate interfaces, driven by a structural [START_REF] Gilbert | Controllable Positive Exchange Bias via Redox-Driven Oxygen Migration[END_REF] or magnetic reconstruction, [START_REF] Chen | Hidden Interface Driven Exchange Coupling in Oxide Heterostructures[END_REF] as well as spin disorder, [START_REF] Zhang | Magnetic Transition and the Associated Exchange Bias[END_REF] can add new degrees of freedom for its engineering across heterointerfaces.

The origin of EB is known to lie on pinned uncompensated interfacial spins, [START_REF] Ohldag | Correlation between Exchange Bias and Pinned Interfacial Spins[END_REF] but a crucial influence of the inner (bulk) pinned uncompensated spins from the AFM component was recently demonstrated. [START_REF] Schuller | Role of the Antiferromagnetic Bulk Spins in Exchange Bias[END_REF] In fact, the interfacial spin distribution can be modified by the bulk AFM magnetic landscape, for instance via non-magnetic impurities or crystallographic defects, both of them conducive to AFM order dilution and the consequent AFM domain formation. [START_REF] Schuller | Role of the Antiferromagnetic Bulk Spins in Exchange Bias[END_REF][START_REF] Wee | Rotatable Anisotropy and Mixed Interfaces: Exchange Bias in Fe / KNiF 3[END_REF] These phenomena have been mostly investigated in AFM materials, but the underlying physical mechanism can be considered for their FiM counterparts.

Among the FiM candidates for the development of EB systems, combinations of different spinel ferrites stand out given their potential in spintronics. [START_REF] Emori | Ultralow Damping in Nanometer-Thick Epitaxial Spinel Ferrite Thin Films[END_REF][START_REF] Li | Ultrathin Epitaxial Ferromagnetic γ-Fe2O3 Layer as High Efficiency Spin Filtering Materials for Spintronics Device Based on Semiconductors[END_REF] These spinel-type oxides are prone to disorder and exchange processes on the cation sublattices, with the normal and inverse spinel as the two limiting cases under an ordered sublattice occupation. The disorder, if controlled, can perturb the ideal local coordination, for instance by inducing charge imbalances and ion vacancies, all of this having a huge impact on the heterostructure behavior. Consequently, the electrical and magnetic properties of these ferrites and, in general, of the transition metal oxide heterostructures, [START_REF] Sulpizio | Nanoscale Phenomena in Oxide Heterostructures[END_REF][START_REF] Goodenough | Magnetism and the Chemical Bond[END_REF][START_REF] Ndione | Control of the Electrical Properties in Spinel Oxides by Manipulating the Cation Disorder[END_REF] can be modified when tailoring the interfacial and lattice characteristics through ionic motion. [START_REF] Maier | Pushing Nanoionics to the Limits: Charge Carrier Chemistry in Extremely Small Systems[END_REF] Along these lines, a systematic tuning of the atomic distribution at the tetrahedral and octahedral sites of these spinel ferrites has opened new pathways for generating emergent phenomena in heterostructures due to ion migration. [START_REF] Fontaiña-Troitiño | Exchange Bias Effect in CoO@Fe3O4 Core-Shell Octahedron-Shaped Nanoparticles[END_REF][START_REF] Fontaiña-Troitiño | Room-Temperature Ferromagnetism in Antiferromagnetic Cobalt Oxide Nanooctahedra[END_REF][START_REF] López-Ortega | Topotaxial Phase Transformation in Cobalt Doped Iron Oxide Core/Shell Hard Magnetic Nanoparticles[END_REF] Nevertheless, some control in the ion migration is required, to avoid the otherwise deleterious effects degrading the EB. [START_REF] Lentijo-Mozo | Unexpected Insights about Cation-Exchange on Metal Oxide Nanoparticles and Its Effect on Their Magnetic Behavior[END_REF] Still, despite the important advances made in understanding the EB effect, [START_REF] Lottini | Strongly Exchange Coupled Core|Shell Nanoparticles with High Magnetic Anisotropy: A Strategy toward Rare-Earth-Free Permanent Magnets[END_REF][START_REF] López-Ortega | Topotaxial Phase Transformation in Cobalt Doped Iron Oxide Core/Shell Hard Magnetic Nanoparticles[END_REF] its analysis in singlephase objects lacking a core-shell or a layered structure, that is, lacking of a physical interface between two magnetic phases, has been reported scarcely. [START_REF] Wetterskog | Anomalous Magnetic Properties of Nanoparticles Arising from Defect Structures: Topotaxial Oxidation of Fe1-XO|Fe3-ΔO4 Core|Shell Nanocubes to Single-Phase Particles[END_REF][START_REF] Lottini | Strongly Exchange Coupled Core|Shell Nanoparticles with High Magnetic Anisotropy: A Strategy toward Rare-Earth-Free Permanent Magnets[END_REF] Herein, we present a confined chemical treatment at the surface of single-crystallite CoFe2O4 NCs by which a change in the spinel crystalline structure is not appreciated but an ionic rearrangement in the subsurface and surface regions of the spherical NCs is induced. This situation offers a unique exchange coupling interaction within the same NC, without establishing a physical or coherent crystallographic interface. Yet, the magnetization reversal of the modified NCs is observed to occur in two steps and to come along with an increase in coercivity and an EB shift, suggesting the existence of a strong exchange interaction between two magnetic components. The chemical changes registered, associated to the cation rearrangement in the spinel structure, help understand the magnetism displayed and underline the possibilities of this new chemical route for the engineering of EBrelated functionalities for final device applications.

CoFe2O4 NCs with spherical shape and narrow size distribution (10.6 */1.3 nm average diameter (95.5%), log-normal fit) were synthesized by a seed-mediated growth (experimental details and Figure S1 in the Supporting Information (SI)). Figure 1a includes a TEM image of the NCs and Figure 1b shows its powder XRD pattern at room temperature, which is indexed to a cubic spinel structure (Fd-3m symmetry group) and allows to discard secondary phases. The cell parameter obtained from the Le Bail analysis is 0.8394 nm (see Table S1.1 in the SI), in good agreement with bulk cobalt ferrite (JCPDS card 22-1086). [START_REF] Wohlfarth | Ferromagnetic Materials : A Handbook on the Properties of Magnetically Ordered Substances[END_REF][START_REF] Pereira | Superparamagnetic MFe2O4 (M = Fe, Co, Mn) Nanoparticles: Tuning the Particle Size and Magnetic Properties through a Novel One-Step Coprecipitation Route[END_REF][START_REF] Deepak | A Systematic Study of the Structural and Magnetic Properties of Mn-, Co-, and Ni-Doped Colloidal Magnetite Nanoparticles[END_REF] Elementary analysis using ICP-OES indicates an average Co0.95Fe2.05O4 stoichiometry (from now on referred to as CoFe2O4). A fraction of the same batch of these CoFe2O4 NCs was subsequently immersed and confined in a basic aqueous medium using a water-in-oil (W/O) reverse microemulsion, that is, stabilizing them by a nonionic surfactant (Igepal CA-520) in water droplets in a hydrophobic continuous phase. [START_REF] Koole | On the Incorporation Mechanism of Hydrophobic Quantum Dots in Silica Spheres by a Reverse Microemulsion Method[END_REF] Besides the surfactant, these water droplets of very small volume exposed the NCs to a high pH, promoting an oxidation process at their surface. [START_REF] Koole | On the Incorporation Mechanism of Hydrophobic Quantum Dots in Silica Spheres by a Reverse Microemulsion Method[END_REF][START_REF] Lee | Synthesis and Magnetic Properties of Silica-Coated FePt Nanocrystals[END_REF] This sample is hereafter labelled as CoFe2O4@Ox. (g) and CoFe2O4@Ox (h) NCs. Hysteresis loops measured at 10 K of CoFe2O4 (blue) and CoFe2O4@Ox (red) samples (i) and comparison of their derivatives, with 0HS1 and 0HS2 magnetic fields at which two events of magnetization switching occur (j). ZFC and FC curves measured at 10 mT (k) and distribution of energy barriers f(TB) calculated from the ZFC-FC curves and derivatives (l) of CoFe2O4 (blue dots) and CoFe2O4@Ox (red dots) samples. Hysteresis loops measured at 10 K of the CoFe2O4@Ox sample after ZFC (red) and FC at 5 T (gray) (m).

To shed light on the effect these conditions exert on the CoFe2O4 spinel structure, a high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) study of the assynthesized (Figure 1c andd and Figure S2a andc, CoFe2O4 sample) and the chemically-treated (Figure 1e and f and Figure S2b andd, CoFe2O4@Ox sample) NCs was performed. These images show no clear differences in the crystalline structure of these representative NCs, lacking in both cases the core-shell structure expected from a superficial oxidation. Indeed, the spinel crystalline lattice highlighted at these high resolution images has not defects, dislocations or twin boundaries up to the surface. The higher resolution image included in Figure 1e, obtained along the [110] zone axis, permits to appreciate distinct contrast associated to the positions of the atomic columns, offering an enlarged view of the defect-free spinel structure in the whole nanocrystal from the CoFe2O4@Ox sample. Interestingly, we can appreciate neither Moiré fringes nor grain or antiphase boundaries. [START_REF] Fontaiña-Troitiño | Antiphase Boundaries in Truncated Octahedron-Shaped Zn-Doped Magnetite Nanocrystals[END_REF] Moreover, the size histogram of the samples (fitted to log-normal function) does not show apparent modifications either (Figures 1g and1h), and the analysis of atomic column positions in a 2D projection of a CoFe2O4@Ox NC shows the absence of systematic strain fields (Figure S3), thus excluding the presence of interfacial strain between two crystalline phases.

Yet, the magnetic behavior of the two CoFe2O4 and CoFe2O4@Ox samples points to an important change in the configuration of the magnetic cations in the spinel structure. Figure 1i includes the comparison of the magnetic properties displayed by the as-synthesized CoFe2O4 sample (blue curve) and by the CoFe2O4@Ox sample (red curve) at 10 K. The value of maximum magnetization registered for the CoFe2O4 sample is ~87 Am 2 /kg when applying the maximum field (7 T), close to that of the bulk cobalt ferrite saturation magnetization (MS(bulk) ~90 Am 2 /kg) [START_REF] Cullity | Introduction to Magnetic Materials[END_REF] and similar to others values reported for NCs. [START_REF] Peddis | Beyond the Effect of Particle Size: Influence of CoFe2O4 Nanoparticle Arrangements on Magnetic Properties[END_REF][START_REF] Gomide | Nanoparticle Size Distribution and Surface Effects on the Thermal Dependence of Magnetic Anisotropy[END_REF] This is in agreement with the very good crystallinity of the NCs observed by HAADF-STEM and the stoichiometry registered. Anyhow, different effects related to a canted surface spin structure, [START_REF] Peddis | Magnetic Properties of Spinel Ferrite Nanoparticles: Influence of the Magnetic Structure[END_REF] a gradient in the magnetic cations ratio moving outwards from the core to the surface, [START_REF] Sathya | CoxFe3-XO4 Nanocubes for Theranostic Applications: Effect of Cobalt Content and Particle Size[END_REF][START_REF] Ijiri | Correlated Spin Canting in Ordered Core-Shell Fe3O4/MnxFe3-XO4 Nanoparticle Assemblies[END_REF][START_REF] Yan | Manganese and Cobalt Substituted Ferrite Nanoparticles Synthesized via a Seed-Mediated Drip Method[END_REF] or a cationic disorder in the crystalline structure at the surface can explain the slight difference. While this value of MS when applying the maximum 7 T field drops to ~45 Am 2 /kg for the CoFe2O4@Ox sample, the coercive field value increases (0HC = 1.06 T and 0HC = 1.26 T for CoFe2O4 and CoFe2O4@Ox samples, respectively). In both cases, these high values of 0HC are related to the high magnetostriction of CoFe2O4, due to the strong spin-orbit coupling from the Co 2+ ions in the crystalline lattice. [START_REF] Sathya | CoxFe3-XO4 Nanocubes for Theranostic Applications: Effect of Cobalt Content and Particle Size[END_REF][START_REF] Zhou | Correlation between Structure and Intervalence Charge-Transfer Transitions in Nanocrystalline CoFe2-XMxO4 (M=Mn, Al, Sc) Thin Films[END_REF] In addition, the shape of the hysteresis loop has evolved after the chemical microemulsion-based treatment, with two reversals of magnetization (one of them much larger), seen as two inflection points (0HS1 and 0HS2 magnetic fields) around 5 and 10 mT and 1.14 and 1.55 T when comparing the derivatives (dM/dH), shown in Figure 1j. The significantly larger reversal contribution at low field in the CoFe2O4@Ox sample clearly hints that a cationic modification took place. Similar contributions at low field were reported in samples of CoFe2O4 NCs synthesized by a co-precipitation method under alkaline conditions, [START_REF] Pereira | Superparamagnetic MFe2O4 (M = Fe, Co, Mn) Nanoparticles: Tuning the Particle Size and Magnetic Properties through a Novel One-Step Coprecipitation Route[END_REF][START_REF] Zeb | Surface Effects in Uncoated and Amorphous SiO2 Coated Cobalt Ferrite Nanoparticles[END_REF][START_REF] Gyergyek | Influence of Synthesis Method on Structural and Magnetic Properties of Cobalt Ferrite Nanoparticles[END_REF] where phase segregation (due to Co3O4 and/or Fe2O3) or a phase with a reduced crystallinity was formed, both cases not possible here according to the STEM analysis. Figure 1k displays the temperature dependent magnetization curves, measured under ZFC (zero-field cooled) and FC (field cooled) conditions and recorded applying a field of 10 mT.

Whereas the mass magnetization value of the CoFe2O4@Ox has decreased notably in comparison to that of the initial sample (in line with the hysteresis loops), the shape of the ZFC and FC curves is very similar. Based on these ZFC-FC curves, it is possible to estimate the energy barrier distribution (in terms of the blocking temperature, TB: [START_REF] Micha | Estimation of the Co Nanoparticles Size by Magnetic Measurements in Co/SiO2 Discontinuous Multilayers[END_REF][START_REF] Mamiya | Extraction of Blocking Temperature Distribution from Zero-Field-Cooled and Field-Cooled Magnetization Curves[END_REF][START_REF] Bruvera | Determination of the Blocking Temperature of Magnetic Nanoparticles: The Good, the Bad, and the Ugly[END_REF] fitted to a log-normal function in agreement with the size distribution, see Figures 1g, 1h and1l). The average TB values obtained are very similar, 265 and 262 K for CoFe2O4 and CoFe2O4@Ox samples, respectively, and comparable to other values of the literature. [START_REF] Peddis | Beyond the Effect of Particle Size: Influence of CoFe2O4 Nanoparticle Arrangements on Magnetic Properties[END_REF][START_REF] López-Ortega | Exploring the Magnetic Properties of Cobalt-Ferrite Nanoparticles for the Development of a Rare-Earth-Free Permanent Magnet[END_REF][START_REF] Gu | Facile Synthesis and Characterization of Cobalt Ferrite Nanocrystals via a Simple Reduction-Oxidation Route[END_REF][START_REF] Torres | Magnetic Properties and Energy Absorption of CoFe2O4 Nanoparticles for Magnetic Hyperthermia[END_REF] This match in the blocking temperature reflects the very similar magnetically coherent volumes of FiM material in both samples, [START_REF] Knobel | Superparamagnetism and Other Magnetic Features in Granular Materials: A Review on Ideal and Real Systems[END_REF] despite the fact of observing two reversals of magnetization. Such finding is in line with the absence of an interface or any other crystalline defect in the crystalline structure, and the absence of byproducts (smaller nanoparticles or low anisotropy magnetic phases).

f(TB)  (1/T) [d(MZFC-MFC)/dT],
In order to further analyze the switching behavior in the CoFe2O4@Ox sample in terms of exchange-coupling properties, we measured the hysteresis loops in ZFC and FC conditions applying an external magnetic field of 5 T (Figure 1m). Though there is a decrease in coercivity, the FC hysteresis loop shows a negative field shift (0HE= -56.9 mT) associated to an EB effect. Such coupling, usually attributed to a FM/AFM interaction, is strong enough to produce a unidirectional anisotropy that causes the observed shift. The reduced coercivity registered for the CoFe2O4@Ox sample under FC conditions (compared to the ZFC loop) also unveils a reduction of the effective magnetic anisotropy, likely induced by the large cooling field. Similar trends have been reported in previous studies and ascribed to AFM order frustration. [START_REF] Leighton | Coercivity Enhancement in Exchange Biased Systems Driven by Interfacial Magnetic Frustration[END_REF][START_REF] Perzanowski | Magnetization Reversal Mechanism in Exchange-Biased Spring-like Thin-Film Composite[END_REF][START_REF] Rostamnejadi | Cooling-Field Dependence of Exchange Bias Effect in La0.45Sr0.55MnO3 Nanoparticles[END_REF] In our case, this observation can be understood considering the presence of pinned uncompensated spins, which align with the sufficiently large cooling field employed and induce frustration of the FiM exchange coupling. The presence of this hypothesized larger number of pinned uncompensated moments is supported experimentally by the large drop in the saturation magnetization but increased coercivity. Overall, these results point to a crucial influence of the synthetic conditions on the magnetic behavior of the CoFe2O4@Ox sample with respect to the as-synthesized one, and despite the absence of crystallographic modifications in the spinel structure.

Aiming to corroborate the idea of the confined chemical effect in the micelles as the origin of the change in the magnetic behavior observed for the CoFe2O4@Ox sample, we performed an additional mapping of Fe and Co distribution and investigated their electronic configuration using electron energy loss spectroscopy (EELS). Figure 2a shows elemental mapping for CoFe2O4 and CoFe2O4@Ox samples, which indicates a similar increasing concentration of Co towards the surface of the nanocrystal in both cases. Although we cannot completely exclude an effect of electron beam irradiation, the results of different experimental techniques corroborate that CoFe2O4 or MnFe2O4 NCs synthesized via thermal decomposition typically have an increased content of Co or Mn at their surface, owing to the different decomposition temperature of the metallic precursors. [START_REF] Sathya | CoxFe3-XO4 Nanocubes for Theranostic Applications: Effect of Cobalt Content and Particle Size[END_REF][START_REF] Ijiri | Correlated Spin Canting in Ordered Core-Shell Fe3O4/MnxFe3-XO4 Nanoparticle Assemblies[END_REF][START_REF] Yan | Manganese and Cobalt Substituted Ferrite Nanoparticles Synthesized via a Seed-Mediated Drip Method[END_REF][START_REF] Hoene | Thermal Decomposition of Metal Acetylacetonates: Mass Spectrometer Studies[END_REF] In this regard, the hysteresis loops of the initial sample show a very small reversal of magnetization at low field which can stem from the cobalt patches observed at the surface, and present in both native and oxidized samples. Anyway, the very large value of coercivity registered at low temperature can only be associated to the CoxFe3-xO4 stoichiometry, even with increasing values of x as moving outwards. Additionally, EELS spectra of L edges for Fe and Co in CoFe2O4 and CoFe2O4@Ox samples (Figure 2b) reveal that: a) the L edge of Co in CoFe2O4@Ox is shifted by ca. +1.0 eV in comparison to CoFe2O4, indicating an increase in the oxidation state of Co, resulting from the chemical treatment, [START_REF] Wang | Valence State Mapping of Cobalt and Manganese Using Near-Edge Fine Structures[END_REF][START_REF] Bazin | Genesis of Co/SiO2 Catalysts: XAS Study at the Cobalt LIII,II Absorption Edges[END_REF] and b) the ratio between the Fe L3 and Co L3 edges decreases from 2.95 in the CoFe2O4 sample to 2.59 in the CoFe2O4@Ox sample, indicating an average decrease in the iron content. These experimental results point to a partial oxidation of cobalt cations and the formation of Fe vacancies in the spinel structure at the subsurface region, providing an explanation for the presence of pinned uncompensated moments associated to the changes in the magnetic behavior of the CoFe2O4@Ox sample and, particularly, to the EB effect. To further confirm this relationship, we performed a Raman analysis of the as-synthesized CoFe2O4 and CoFe2O4@Ox samples in order to investigate the chemical/structural origin of the peculiar magnetic features observed. [START_REF] Testa-Anta | Raman Spectroscopy to Unravel the Magnetic Properties of Iron Oxide Nanocrystals for Bio-Related Applications[END_REF] This technique can register six Raman active modes from the spinel structure, namely 2A1g, Eg, and 3T2g, characteristic of spinels with two different types of cations occupying the octahedral or tetrahedral sites, such as CoFe2O4 (see Figure S4 in the SI). [START_REF] White | Interpretation of the Vibrational Spectra of Spinels[END_REF] In general, the ferrite A1g modes appear above 600 cm -1 and are usually assigned to the motion of oxygen in the tetrahedral AO4 group along the 111 direction, involving a symmetric stretching of the oxygen atoms with respect to the metal ion at the tetrahedral void (T), [START_REF] Shebanova | Raman Spectroscopic Study of Magnetite (FeFe2O4): A New Assignment for the Vibrational Spectrum[END_REF] as well as the deformation of the three octahedral sites (O) nearest to each oxygen. [START_REF] Laguna-Bercero | Raman Spectroscopic Study of Cation Disorder in Poly-and Single Crystals of the Nickel Aluminate Spinel[END_REF] Figure 2c includes the Raman spectra registered. In the as-synthesized sample (blue spectrum) the expected modes for the spinel lattice are observed, [START_REF] Chandramohan | Cation Distribution and Particle Size Effect on Raman Spectrum of CoFe2O4[END_REF] with the most intense peak at 679 cm -1 (A1g(2)) and a small shoulder at 620 cm -1 (A1g(1)), which stem from the presence of Fe 3+ and Co 2+ ions at the tetrahedral sites, respectively. [START_REF] Laguna-Bercero | Raman Spectroscopic Study of Cation Disorder in Poly-and Single Crystals of the Nickel Aluminate Spinel[END_REF][START_REF] Bahlawane | Tailoring the Properties and the Reactivity of the Spinel Cobalt Oxide[END_REF] Note that the A1g(1)) mode intensity is much lower than that of A1g (2), meaning that the primary contribution to the AO4 vibrations originates from the Fe 3+ ions.

There is less consensus regarding the origin of the other low-frequency modes (Eg and T2g), typically assigned to the tetrahedral unit in the Fe3O4 material, [START_REF] Shebanova | Raman Spectroscopic Study of Magnetite (FeFe2O4): A New Assignment for the Vibrational Spectrum[END_REF][START_REF] Verble | Temperature-Dependent Light-Scattering Studies of the Verwey Transition and Electronic Disorder in Magnetite[END_REF] or to the octahedral unit when considering mixed spinel ferrites such as CoFe2O4 or ZnFe2O4. [START_REF] Liao | Temperature Dependent Phonon Raman Scattering of Highly A-Axis Oriented CoFe2O4 Inverse Spinel Ferromagnetic Films Grown by Pulsed Laser Deposition[END_REF][START_REF] Wang | High Pressure Raman Spectroscopy of Spinel-Type Ferrite ZnFe2O4[END_REF] In the latter case, the Eg vibrational mode has been assigned to the symmetric bending of oxygen with respect to Fe in the octahedral BO6 void [START_REF] Shebanova | Raman Spectroscopic Study of Magnetite (FeFe2O4): A New Assignment for the Vibrational Spectrum[END_REF] and is usually absent in nanocrystals. [START_REF] Singh | Micro-Raman Investigation of Nanosized Zinc Ferrite Effect of Crystallite Size and Fluence of Irradiation[END_REF] The fact that this mode can be ascertained in our spectrum underlines once again the optimal crystallinity of the CoFe2O4 NCs.

On the other hand, the T2g(2) mode has been reported to account solely for the Co 2+ ions occupying the octahedral sites. [START_REF] Shemer | Tuning a Colloidal Synthesis to Control Co 2+ Doping in Ferrite Nanocrystals[END_REF] Hence, the higher intensity of the T2g(2) and the A1g(2) modes compared to the A1g(1) mode confirms the predominant inverse spinel configuration anticipated for the cobalt ferrite.

The characteristic features of the spinel crystalline structure are still present in the CoFe2O4@Ox spectrum (red curve). However, the relative intensities of the A1g and T2g vibration modes have notably changed; being the T2g( 2) mode (at ~470 cm -1 ) the most prominent feature in the Raman spectrum. Interestingly, the vibrational modes T2g(3) and A1g (1) begin to merge into one broad band owing to the pronounced red-shift of the A1g(1) mode, now located at 600 cm -1 (see also Figure S4). This shift is usually associated to structural distortions and/or the presence of a different set of cations at the tetrahedral/octahedral sites. Taking into account the absence of strain fields (Figure S3) and the ca. +1.0 eV shift observed in the Co L edge from the CoFe2O4@Ox sample (compared to CoFe2O4) (Figure 2b), the red-shift of the A1g(1) mode is consistent with the presence of Co 3+ cations within the spinel structure, in addition to Fe 3+ and Co 2+ . [START_REF] Bahlawane | Tailoring the Properties and the Reactivity of the Spinel Cobalt Oxide[END_REF] The resultant charge compensation of the crystalline structure may proceed via Fe vacancies [START_REF] Pratt | Enhanced Oxidation of Nanoparticles through Strain-Mediated Ionic Transport[END_REF] or a partial Fe 3+ /Fe 2+ reduction. While the presence of Fe 3+ vacancies is supported by the decrease in the Fe/Co L3 ratio registered, which indicates a reduced iron content in the CoFe2O4@Ox sample with respect to the pristine sample, the partial Fe 3+ /Fe 2+ reduction seems less probable, given the absence of observable changes in the L edge of the Fe spectrum in the EELS analysis. The fact that we have not registered the vacancies in the HAADF-STEM analysis suggests that their content must be rather small. Along these lines, the decrease in the A1g(2) mode intensity can be explained by this chemical and local modification promoted by the Fe 3+ vacancies created. The oxidation of some of the Co 2+ ions to Co 3+ and the changes associated to the Fe 3+ ions raise the question whether a non-stoichiometric Co II Co III Fe III •O4 spinel is formed at the subsurface region, but since the HAADF-STEM analysis reveals no evidence of two crystallographic phases at the core and the surface shell, the as-formed mixed ferrite spinel must be highly disordered in terms of the metallic cation distribution. This disorder is also hinted by the presence of additional features in the Raman spectrum of the CoFe2O4@Ox sample, displaying new modes of low intensity at 420 and 760 cm - 1 , for instance.

An additional experiment registering the evolution of the Raman spectra as a function of the incident laser power was also performed for the two CoFe2O4 and CoFe2O4@Ox systems (Figure S5). The Raman spectrum of the as-synthesized sample evolves into the same signature observed for CoFe2O4@Ox when treated under a laser power of 5.82 mW (Figure S5a), which can be associated to a partial oxidation of Co 2+ cations reported above. [START_REF] Rivas-Murias | Thermodynamic CoO-Co3O4 Crossover Using Raman Spectroscopy in Magnetic Octahedron-Shaped Nanocrystals[END_REF] Furthermore, the very similar spectra recorded at 0.42 mW, after subjecting both samples to the highest laser power (21 mW) (Figure S5a andb), exhibit a remarked increase in the T2g(2) mode intensity compared to the A1g (2) mode, in agreement with a reduced iron content due to Fe 3+ vacancy formation. The presence of these vacancies can be understood as a preliminary step prior to the transformation toward maghemite (-Fe2O3), and is also corroborated by the blue-shift of the A1g(2) mode to 690 cm -1 (note that the A1g mode characteristic from maghemite occurs at 700 cm -1 ).

Conclusively, to explain the coupling mechanism and the local magnetic configuration given the chemical changes registered by EELS and Raman spectroscopy and given the fact that there is no crystallographically coherent interface, we take the coercivity of the initial CoFe2O4 NCs as reference (0HC = 1.06 T). With this large value into account, the fraction of CoFe2O4 phase at the outer shell of the as-synthesized NCs switches readily (0HS1 = 5 mT) (Figure 1j). However, for the CoFe2O4@Ox sample, while the magnetic phase at the subsurface region now switches with a value of 0HS1 = 10 mT, the CoFe2O4 phase at the core follows an even larger switching field (0HS2 = 1.55 T). This can be explained considering the presence of unpinned uncompensated moments in the cation disordered subsurface region of the CoFe2O4@Ox sample, which couple to the external field and rotate along with the FiM CoFe2O4 core, resulting in a coercivity enhancement. [START_REF] Schuller | Role of the Antiferromagnetic Bulk Spins in Exchange Bias[END_REF][START_REF] Wee | Rotatable Anisotropy and Mixed Interfaces: Exchange Bias in Fe / KNiF 3[END_REF] On the other hand, the rather strong negative 0HE field (-56.9 mT) indicates the presence of pinned uncompensated moments that strongly couple to the FiM lattice but do not rotate even at the maximum field (7 T). The presence of these pinned and unpinned magnetic moments can be understood as the outcome of competing interactions within the parental spinel structure, where the Co 2+ oxidation has the Fe-O-Fe and Co-O-Fe superexchange interactions disrupted, leading to a highly frustrated subsurface region. This increased magnetic frustration, boosted by the assumed cation disorder, is reflected not only in the drop in the value of magnetization down to 45 Am 2 /kg (which can be explained by the presence of low-spin Co 3+ on octahedral sites [START_REF] Eskandari | Magnetization and Anisotropy of Cobalt Ferrite Thin Films[END_REF] ), but also in the low-anisotropy component detected during the reversal of the CoFe2O4@Ox sample. This fact hints that, besides inducing magnetic disorder, some short-range correlated spin disorder occurs. This situation, particularly in terms of the effects stemming from the presence of Co 3+ and the iron vacancies, inducing a charge reorganization, with local modifications of the valence charge states and possible creation of defect gap states, can explain the changes not only in the magnetization, but also in the electronic, ionic and tunnel conductivities. [START_REF] Sharma | Influence of the Cation Distribution, Atomic Substitution, and Atomic Vacancies on the Physical Properties of CoFe2O4 and NiFe2O4 Spinel Ferrites[END_REF] Such effects require a more in-depth investigation that falls out of the scope of the present study. Alternative scenarios in the attained cation distribution at the subsurface, such as a change from an inverse to a normal spinel configuration, [START_REF] Rivas-Murias | Structural and Magnetic Implications of Transition Metal Migration within Octahedral Core-Shell Nanocrystals[END_REF][START_REF] Ferreiro-Vila | Apparent Auxetic to Non-Auxetic Crossover Driven by Co 2+ Redistribution in CoFe2O4 Thin Films[END_REF] would lead to a magnetization enhancement and can be therefore discarded.

Figure 1 .

 1 Figure 1. TEM image with general particle overview and X-ray diffraction pattern with Le Bail

Figure 2 .

 2 Figure 2. (a) Mapping of Fe and Co distribution in CoFe2O4 and CoFe2O4@Ox NCs based on

Acknowledgments 17 V. S. acknowledges the financial support from the Spanish Ministerio de Ciencia e Innovación under project PID2020-119242-I00 and from the European Union under project H2020-MSCA-RISE-2019 PEPSA-MATE (project number 872233). S. B. acknowledges funding from the European Research Council under the European Union's Horizon 2020 research and innovation program (ERC Consolidator Grant Nº 815128 REALNANO).

Summarizing, whereas the HAADF-STEM images show NCs with a uniform crystalline structure up to the surface and without the presence of defects or strain, both EELS and Raman spectroscopy, jointly with the magnetic properties, point to the presence of a pseudo core-shell structure with no physical interface. Such unusual characteristics render the system particularly fascinating, pointing to a interfaceless exchange coupling between two different distributions of magnetic cations within the parent spinel structure.

Additional information

The Supporting Information is available free of charge on the ACS Publications website at DOI: XXXX. Experimental methods; supplementary Le Bail refinement data, HAADF-STEM data, strain analysis; supplementary magnetic data and supplementary Raman spectroscopy analysis.

Author information

Corresponding authors *E-mail: vsalgue@uvigo.es ORCID Beatriz Rivas-Murias: 0000-0002-8048-5364 Martín Testa-Anta: 0000-0003-4437-2589 Alexander S. Skorikov: 0000-0001-8870-5344 Miguel Comesaña-Hermo: 0000-0001-8471-5510 Sara Bals: 0000-0002-4249-8017 Verónica Salgueiriño: 0000-0002-9396-468X

Notes

The authors declare no competing financial interest.