RESEARCH ARTICLE www.small-methods.com Elucidating Individual Magnetic Contributions in Bi-Magnetic Fe3O4/Mn3O4 Core/Shell Nanoparticles by Polarized Powder Neutron Diffraction I. V. Golosovsky, I. A. Kibalin, A. Gukasov, A. G. Roca, A. López-Ortega, M. Estrader, M. Vasilakaki, K. N. Trohidou, T. C. Hansen, I. Puente-Orench, E. Lelièvre-Berna, and J. Nogués* 1. Introduction Heterogeneous bi-magnetic nanostructured systems have had a sustained interest during the last decades owing to their unique magnetic properties During the last decades magnetic nanos- tructured materials composed of two or and the wide range of derived potential applications. However, elucidating the more magnetic phases (e.g., compos- details of their magnetic properties can be rather complex. Here, a ite nanoparticle assemblies, nanoparti- comprehensive study of Fe3 O4 /Mn3 O4 core/shell nanoparticles using cles in matrices or core/shell nanopar- polarized neutron powder diffraction, which allows disentangling the ticles) have been extensively studied magnetic contributions of each of the components, is presented. The results both from fundamental and applied show that while at low fields the Fe3 O4 and Mn3 O4 magnetic moments viewpoints.[1–16] From a basic science per- spective, issues like dipolar and exchange averaged over the unit cell are antiferromagnetically coupled, at high fields, interactions, collective behavior, mag- they orient parallel to each other. This magnetic reorientation of the Mn3 O4 netic graded interfaces, proximity effects, shell moments is associated with a gradual evolution with the applied field of among many others, have been investi- the local magnetic susceptibility from anisotropic to isotropic. Additionally, gated. Additionally, bi-magnetic materi- the magnetic coherence length of the Fe3 O4 cores shows some unusual field als are being studied for countless appli- cations, like biomedical uses (e.g., mag- dependence due to the competition between the antiferromagnetic interface netic hyperthermia and magnetic res- interaction and the Zeeman energies. The results demonstrate the great onance imaging), permanent magnets, potential of the quantitative analysis of polarized neutron powder diffraction magnetic recording, magnetic refrigera- for the study of complex multiphase magnetic materials. tion, or microwave absorption.[1–16] The most common technique to study these materials is magnetometry. How- ever, magnetization measurements usu- ally cannot discern between the different I. V. Golosovsky A. G. Roca, J. Nogués National Research Center “Kurchatov Institute” Catalan Institute of Nanoscience and Nanotechnology (ICN2) B. P. Konstantinov Petersburg Nuclear Physics Institute CSIC and BIST Gatchina 188300, Russia Campus UAB, Bellaterra, Barcelona 08193, Spain I. A. Kibalin, A. Gukasov E-mail: josep.nogues@icn2.cat Laboratoire Léon Brillouin A. López-Ortega CEA-CNRS Departamento de Ciencias CE-Saclay Universidad Pública de Navarra Gif-sur-Yvette 91191, France Pamplona 31006, Spain A. López-Ortega Institute for Advanced Materials and Mathematics INAMAT2 Universidad Pública de Navarra Pamplona 31006, Spain The ORCID identification number(s) for the author(s) of this article M. Estrader can be found under https://doi.org/10.1002/smtd.202201725 Departament de Química Inorgànica i Orgànica © 2023 The Authors. Small Methods published by Wiley-VCH GmbH. carrer Martí i Franqués 1–11 This is an open access article under the terms of the Creative Commons Universitat de Barcelona Attribution-NonCommercial License, which permits use, distribution and Barcelona 08028, Spain reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes. DOI: 10.1002/smtd.202201725 Small Methods 2023, 7, 2201725 2201725 (1 of 10) © 2023 The Authors. Small Methods published by Wiley-VCH GmbH 23669608, 2023, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202201725 by Readcube (Labtiva Inc.), Wiley Online Library on [30/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-methods.com contributions of the diverse magnetic components, although in no software to properly analyze the data. The weak diffraction some cases, indirect information about the magnetic phases can signal is exacerbated in nanostructured systems since the broad- be obtained using more advanced analyses like Henkel plots or ening of the diffraction peaks reduces even further the signal- first-order reversal curves.[14,17] to-background ratio. However, improvements made in neutron To obtain some information about the contribution of each instrumentation[32] (focusing monochromators, 3 He spin filters, magnetic phase a number of techniques can be used, like neutron high field magnets, position sensitive detectors) and the event of diffraction,[12,18–20] X-ray magnetic circular dichroism (XMCD), a new software,[43] which has already been successfully applied to and derived methods such as X-ray photoemission electron mi- data treatment of different compounds,[44,45] make PNPD much croscopy or X-ray microscopy,[21–23] small angle neutron scat- more attractive. tering (SANS),[24–26] electron magnetic circular dichroism (e- MCD),[27,28] Mössbauer spectroscopy,[20,29,30] among others. Each 2. Results and Discussion of these methods has its advantages and drawbacks. For example, although XMCD or SANS can provide quantitative information Two different Fe3 O4 /Mn3 O4 core/shell nanoparticles have been about the magnetic moment, they bear only limited structural in- studied (with different core sizes and shell thickness; see Exper- formation (e.g., crystallographic phases) about the components, imental Section). The transmission electron microscopy (TEM) e-MCD can only be used on very thin samples or Mössbauer spec- images (Figure 1a–h) show that the particles have a somewhat troscopy is basically restricted to Fe-based materials. Hence, the irregular shape with average sizes of 14.8 ± 2.3 nm (sample 1) interpretation of the magnetic behavior of multicomponent mag- and 13.0 ± 1.5 nm (sample 2), respectively. The electron energy netic materials is often challenging and frequently a combination loss spectroscopy (EELS; Figure 1d,h) analysis of the samples evi- of different techniques is necessary to understand the insights of dences that the particles have a roughly spherical Fe3 O4 core with their magnetic properties. In this framework, novel approaches a diameter of ≈13 nm (sample 1) and ≈10 nm (sample 2), re- can be very valuable to help in the understanding of the complex spectively. On the other hand, the Mn3 O4 shell is rather inhomo- magnetic properties of composite nanostructured magnetic sys- geneous with thicknesses of ≈0.4–1.5 nm (sample 1) and ≈0.7– tems. 2.1 nm (sample 2). Here, we demonstrate that polarized neutron powder diffrac- To disentangle the contributions of Fe3 O4 and Mn3 O4 on the tion (PNPD) is a valuable tool to acquire unique information, dif- magnetic properties of the samples, a detailed PNPD study at 5 ficult or impossible to retrieve with other techniques, from bi- K in different applied fields was carried out. As a first step, to magnetic nanostructured systems (i.e., Fe3 O4 /Mn3 O4 core/shell determine the nuclear structure data (lattice parameters, site oc- nanoparticles). In particular, the results demonstrate that distinct cupancies, and so on) two different approaches were carried out. magnetic features of the two different counterparts can easily be For sample 1, the sum of the spin-up and spin-down polariza- obtained using with PNPD. tion patterns (equivalent to unpolarized powder diffraction mea- Polarized neutron diffraction consists in measuring neutron surements) was used (Figure 2a,b) (refined using CrysPy, see Ex- structure factors using an incident neutron beam polarized par- perimental section). For sample 2 (for which the polarized sum allel (spin-up) and anti-parallel (spin-down) to a vertically applied profile cannot be refined reliably), the conventional neutron pow- magnetic field.[19,31,32] Unlike neutron diffraction with an unpo- der diffraction was analyzed by a usual Rietveld procedure (using larized beam, this method is sensitive at determining a magne- FullProf; see Experimental Section). As expected, the Fe3 O4 cores tization distribution within a unit cell, as well as the local sus- ̄ i.e., present an inverse cubic spinel structure (space group Fd3m; ceptibility tensor at each magnetic site,[19,31,32] and has been ex- stoichiometric magnetite for sample 1 and close to stoichiomet- tensively used with single crystals.[19,31–35] However, PNPD has ric maghemite for sample 2), whereas the Mn3 O4 shells have a been only seldom used in polycrystalline structures,[31,32,36–42] be- normal tetragonal spinel structure (space group I41 /amd). cause of the weak diffraction signal and there was until recently The refined core sizes (from the peak broadening; see Table 1) are consistent with the ones obtained from TEM. Concern- ing the shell size, it is difficult to obtain a reliable value from M. Estrader diffraction data because of the overlapping of the peaks from the Institut de Nanociència i Nanotecnologia IN2UB shell and the core, and the small contribution of a shell to the carrer Martí i Franqués 1–11 pattern, which is further complicated by the anisotropic (platelet- Universitat de Barcelona like) shape of the shell particles. Thus, in order to estimate ap- Barcelona 08028, Spain proximately the “average thickness” of the shell, the volume frac- M. Vasilakaki, K. N. Trohidou tion of the two phases obtained from the refinement was used as- Institute of Nanoscience and Nanotechnology NCSR “Demokritos” suming a uniform shell on a spherical core. The thicknesses ob- 153 10, Agia Paraskevi, Attiki 15310, Greece tained from this approach give only indicative trends and cannot T. C. Hansen, I. Puente-Orench, E. Lelièvre-Berna be readily compared with the estimates obtained from the TEM- Institut Laue Langevin EELS study. Although the estimated thicknesses are exceedingly 71 avenue des Martyrs, Grenoble 38000, France small, what is clearly illustrated is that the sample 1 has a thin- I. Puente-Orench ner shell than sample 2 (Table 1), in agreement with the EELS Instituto de NanoCiencia y Materiales de Aragón Zaragoza 50009, Spain analysis of the samples (Figure 1d,h). J. Nogués In our case, the diffraction signal of the difference pattern ICREA (spin up − spin down) has a rather weak signal due to the Barcelona 08010, Spain small amount of sample (see Figure 2 and Figure S1, Supporting Small Methods 2023, 7, 2201725 2201725 (2 of 10) © 2023 The Authors. Small Methods published by Wiley-VCH GmbH 23669608, 2023, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202201725 by Readcube (Labtiva Inc.), Wiley Online Library on [30/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-methods.com Figure 1. Low-resolution TEM images, particle size distribution, high-resolution TEM image and Fe (red) and (green) Mn L-edge EELS mapping for a–d) sample 1 and e–h) sample 2. Figure 2. Refinement of the sum (spin up + spin down; top curves) and difference (spin up − spin down; bottom curves) of the spin-up and spin-down pattern for sample 1 at a) 5 kOe and b) 50 kOe. The bars indicate the position of diffraction reflections for Mn3 O4 (top row) and Fe3 O4 (bottom row) (see Supporting Information). Information) and, consequently, the Rietveld profile analysis (us- the diffraction and the one obtained from SQUID measurements ing CrysPy; see Experimental Section) does not provide univocal are similar (see Experimental Section for details). results. Therefore, to simplify the fitting procedure (i.e., intro- Notably, the fit of the patterns allows to separate the field ducing some constraints in the magnetic structure to reduce the dependence of the magnetic moments of the two phases in a number of fitting parameters), a novel approach combining the straightforward way. Note that the small differences in the mag- PNPD refinement and magnetization measurements has been netic moments averaged over the unit cell for the two iron oxide used. Namely, to check the consistency of the model used in the cores originate from the different iron oxide phases of the cores fitting procedure (i.e., a simplified model of the magnetic struc- (sample 1—magnetite versus sample 2—maghemite). As can be ture; see Experimental Section), the refined moment averaged seen in Figure 3a,b, the refined magnetic moments averaged over over the whole system (mFe3O4 + mMn3O4 ) was compared to su- the unit cell (i.e., the projection of the moment onto the applied perconducting quantum interference device (SQUID) magneti- field direction) unambiguously demonstrate that the moments zation measurements. When the appropriate refined model is averaged over the unit cells of the Fe3 O4 and its Mn3 O4 coun- defined, the field evolution of the magnetization calculated from terpart are antiferromagnetically coupled at low fields for both Small Methods 2023, 7, 2201725 2201725 (3 of 10) © 2023 The Authors. Small Methods published by Wiley-VCH GmbH 23669608, 2023, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202201725 by Readcube (Labtiva Inc.), Wiley Online Library on [30/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-methods.com Table 1. Refined parameters from the neutron powder diffraction of samples 1 and 2 at 5 K in zero field. The errors given in brackets are standard deviations obtained using the FullProf and CrysPy programs. Name Core Shell a [Å] Size [nm] Volume fraction (%) a [Å] c [Å] Volume fraction [%] Average thickness [nm] Sample 1 8.354(1) 10.5(5) 87(2) 5.698(4) 9.23(2) 12(2) 0.2 Sample 2 8.336(1) 7.7(5) 73 (3) 5.723(6) 9.48(3) 27(2) 0.4 Figure 3. a,b) Dependence of the Fe3 O4 (red symbols) and Mn3 O4 (green symbols) moments averaged over the unit cell for a) sample 1 and b) sample 2 on the applied magnetic field. The green and red arrows indicate the orientations of the averaged moments of the Mn3 O4 and Fe3 O4 counterparts, respectively. c,d) Evolution of the difference of the magnetizations at 5 and 50 K (i.e., slightly above the bulk TC of Mn3 O4 , TC = 43 K) [M(5K)–M(50K)] for diverse applied fields for c) sample 1 and d) sample 2. The lines are guides to the eye. Shown in the inset is an example of the calculation of M(5K)– M(50K) for sample 2 at 10 kOe, where the arrow shows the difference M(5K)–M(50K). The error bars (about ±0.7 μB ) in panels (a) and (b), that is, estimates standard deviation from the CrysPy refinement, do not exceed the symbol size. samples. This behavior is indicative of an antiferromagnetic in- netization, MS , low anisotropy) and hard Mn3 O4 (low MS , high terface coupling between the Fe3 O4 and Mn3 O4 moments at low anisotropy).[1,23] Namely, sample 2 with a larger amount of fields, typical for Fe3 O4 /Mn3 O4 .[23] However, at increased fields, Mn3 O4 exhibits a somewhat lower MS but a considerably larger the averaged moment of Mn3 O4 changes sign with respect to the coercivity, HC , and higfield susceptibility, 𝜒 HF (Figure 4a,b). How- one of Fe3 O4 . This is due to the fact that the antiferromagnetic ever, it is important to emphasize that the hysteresis loops of both coupling is overcome, leading to the parallel arrangement of the samples are rather homogeneous without any obvious differen- Fe3 O4 and Mn3 O4 moments at high fields. This reorientation is tiated contribution of each of the two phases (Figure 4a,b). illustrated schematically by arrows in Figure 3a,b. However, as it Interestingly, given the large difference between the Néel tem- will be discussed later, one can note that the magnetic order of the perature of Mn3 O4 [TC (Mn3 O4 ) = 43 K] and the blocking tem- Mn3 O4 phase is more complex than this schematic illustration. perature of the Fe3 O4 cores [TB (Fe3 O4 ) ≈ 250–300 K], the tem- Additionally, the field needed to overcome the antiferromag- perature dependence of the zero-field cooled (ZFC) magnetiza- netic interface coupling is larger for sample 2 than for sample 1, tion provides some useful information. For both samples, at low which should probably be ascribed to dissimilar strengths of the fields, the magnetization increases as the temperature is raised interface coupling in the two samples.[23] from low temperatures to above TC (Mn3 O4 ) (Figure 4c,d). This To illustrate the magnetic configuration obtained from PNPD, behavior is consistent with the low field antiparallel arrangement magnetization measurements were carried out. The overall mag- observed with PNPD. On the other hand, for large fields, the netic behavior of the samples (Figure 4a,b) is consistent with ex- magnetization decreases as the temperature is increased from change coupled magnetically soft Fe3 O4 (high saturation mag- low temperatures to above TC (Mn3 O4 ) (Figure 4c,d), indicating a Small Methods 2023, 7, 2201725 2201725 (4 of 10) © 2023 The Authors. Small Methods published by Wiley-VCH GmbH 23669608, 2023, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202201725 by Readcube (Labtiva Inc.), Wiley Online Library on [30/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-methods.com Figure 4. a) Magnetization hysteresis loops at 5 K for samples 1 and 2. b) Enlargement of the hysteresis loops at low fields. c,d) Temperature dependence of the ZFC magnetization for c) sample 1 and d) sample 2 in different applied fields. The bulk Néel temperature of Mn3 O4 (TC = 43 K) is highlighted by a dashed vertical line. The green and red arrows in (d) indicate the orientation of the moments of the averaged Fe3 O4 and Mn3 O4 counterparts, respectively. reorientation of the averaged Mn3 O4 moments from antiparal- lel to parallel to the averaged Fe3 O4 moments, also in agreement with PNPD. The difference in the field required to induce the Mn3 O4 mo- ment reorientation in the two samples observed with PNPD can also be clearly seen in the ZFC magnetization (Figure 4c,d). In fact, the evolution of the difference of the magnetizations mea- sured at 5 and 50 K (see inset in Figure 3d; somewhat indicative of the relative orientation of the moments of the two phases) is comparable to the changes in the Mn3 O4 moment observed with PNPD (Figure 3c,d). Nevertheless, it is important to emphasize that magnetization measurements cannot alone confirm the antiferromagnetic in- terface coupling since other magnetic effects (such as the pres- ence of a spin glass phase) might give rise to a similar behavior. In this regard, the evolution of the averaged moments of the Fe3 O4 Figure 5. Dependence of the core size of the Fe3 O4 counterpart of sam- and Mn3 O4 phases with field observed with PNPD is also consis- ples 1 and 2 on the applied magnetic field. The error bars (about ±0.5 nm tent with the evolution deduced from element selective XMCD for sample 1 and ±2 nm for sample 2), that is, estimates standard devia- tion from the CrysPy refinement, do not exceed the symbol size. in similar samples, where the Fe-edge signal saturates at rather low fields, while the Mn-edge signal changes sign at intermediate fields.[23] sentially identical to the crystallite size (Table 1) obtained from a Another appealing parameter that can be directly obtained separate refinement of the nuclear and magnetic contributions. from the PNPD refinement, is the magnetic coherence length. This indicates that at low fields the core is magnetically homo- From the peak broadening of the polarized neutron patterns, this geneous. This contrasts with single phase nanoparticles, which length can be estimated even if, due to the reduced statistical ac- typically show a magnetically disordered surface layer.[46,47] Ad- curacy, we simultaneously refined the sum and difference pat- ditionally, for sample 1 (with a thin shell and a large core) the terns with CrysPy, by assuming the magnetic size (i.e., magnetic coherence length does not significantly change as the field in- coherence length) is the same as the nuclear size (i.e., crystallite creases (Figure 5). size). Indeed, since the crystallite size should not change with On the other hand, the magnetic size of the core of sample 2 field, any changes in the refined size should be related to the (at H = 10 kOe; Figure 5) is slightly smaller than its magnetic evolution of the magnetic coherence length. As can be seen in coherence length at H = 0 (deduced from the unpolarized beam Figure 5, at low fields, the magnetic size of sample 1 remains es- pattern). Additionally, the magnetic coherence length of sample Small Methods 2023, 7, 2201725 2201725 (5 of 10) © 2023 The Authors. Small Methods published by Wiley-VCH GmbH 23669608, 2023, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202201725 by Readcube (Labtiva Inc.), Wiley Online Library on [30/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-methods.com Figure 6. Evolution of the a) local susceptibility ellipsoids (top row) and b) magnetic moments (bottom row) versus applied magnetic field in the Mn3 O4 shell for sample 2. Tetrahedral A-sites (green) and octahedral B-sites (red). The black arrows show the magnetic moments, calculated according the standard formulas.[53,54] 2 seems to further decrease at large fields (Figure 5). This effect the particles with a larger core and thinner shell, in concordance is opposite to the one usually observed in single phase nanopar- with the experimental results. ticles, for example, by SANS or Mössbauer spectroscopy, where From the refinement of the PNPD profiles, the local anisotropy the coherence length increases at large fields due to the mag- of all sublattices can also be inferred. While unpolarized pow- netic ordering of the disordered surface layer.[48,49] The decrease der diffraction data deals with ground state magnetic structures of the coherence length of sample 2 is probably a consequence in the absence of magnetic field, PNPD gives information about of the competition between the antiferromagnetic interface cou- the local magnetic moments under magnetic field and allows to pling and the effect of the applied field (Zeeman energy).[50] The estimate the local susceptibility tensor.[19,31,32,43] lower energy state of the Fe3 O4 /Mn3 O4 interface corresponds to Figures 6a and 6b show respectively the evolution with the ap- the spins antiferromagnetically coupled. However, as the field in- plied field of the local susceptibility tensor and the magnetic mo- creases the Mn3 O4 moments start to rotate toward an alignment ments of the Mn3 O4 shell of sample 2 for a crystallite with the with the applied magnetic field. Consequently, the Fe3 O4 mo- field applied along its [1 2 0] direction. ments located at the interface suffer a competition between keep- The refinement indicates that the Mn2+ (s-state, L = 0) ions ing the antiferromagnetic interface coupling and aligning with in the tetrahedral A-sites of the Mn3 O4 lattice are rather insensi- the applied field, which inevitably leads to some interface mag- tive to the magnetic field, that is, the local susceptibility remains netic disorder and, hence, a decrease in the coherence length. In roughly constant with the applied field. On the other hand, the sample 1, while a similar effect should occur, the shell is too thin moments in the octahedral B-positions rotate to align toward the to exert a sufficient torque on the large Fe3 O4 core to result in magnetic field. This implies that while at low fields the magnetic any detectable effect within our experimental accuracy. To con- arrangement of the Mn3 O4 lattice is canted, it evolves toward a firm these effects, Monte Carlo simulations[51,52] on two different collinear arrangement as the field increases. Note, that the in- particles analogous to the experiment ones were carried out (see duced magnetic moment of each crystallite depends on its orien- Supporting Information). The simulations confirm that at inter- tation with respect to the applied field. This rearrangement of the mediate fields, where the shell moments are rotating, the spins of octahedral moments is at the origin of the evolution of the mag- the core close to the interface tilt more than the inner spins of the netic properties of these core/shell particles at high fields (i.e., an- core (Figures S5 and S6, Supporting Information), implying a re- tiparallel versus parallel average moment arrangement between duced coherence length. Interestingly, the effects are weaker for the core and the shell as the field increases). Small Methods 2023, 7, 2201725 2201725 (6 of 10) © 2023 The Authors. Small Methods published by Wiley-VCH GmbH 23669608, 2023, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202201725 by Readcube (Labtiva Inc.), Wiley Online Library on [30/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-methods.com Remarkably, the local magnetic susceptibility tensor in the interactions in magnetite and maghemite, with a Néel temperatures above octahedral B-site (ellipsoids in Figure 6) changes as the field 850 K, dominated over the magnetic anisotropy. is increased. This variation from ellipsoids (i.e., anisotropic) (ii) For Mn2+ (A-site of Mn3 O4 ), an anisotropic model due to symmetry limitations had only two refined parameters: 𝜒 xx = 𝜒 yy and 𝜒 zz . Preliminary to spheres (i.e., isotropic) indicates the evolution of the local calculations show that it was not possible to refine them individually due anisotropy, that is, how the different magnetic ions respond to to the strong correlation. Therefore, an isotopic model with fixed 𝜒 xx = 𝜒 yy the applied field. It is worth mentioning that apart from the = 𝜒 zz = 5 μB /B was used. single ion anisotropy the inter (and intra) sublattice exchange (iii) For Mn3+ (B-site of Mn3 O4 ) an anisotropic model can have vari- interactions might be also at the origin of the anisotropy. In par- able parameters 𝜒 xx , 𝜒 yy , 𝜒 zz , and 𝜒 yz (the latter defines the inclination ticular, the B-site ions, arranged in a frustrated pyrocholore-like of the ellipsoid). The refinement shows that 𝜒 xx and 𝜒 yy are indistinguish- able, and the parameter 𝜒 yz cannot be refined reliably (i.e., it diverges). lattice,[55,56] could also be the source of the observed ellipsoid The parameters 𝜒 yy (or 𝜒 xx ) and 𝜒 zz are strongly correlated and cannot be evolution. refined individually. (iv) Obviously, the moment in any direction of the applied field can- not exceed the free-ion value. More importantly, there was a magnetic ex- 3. Conclusions perimental constraint. Namely, the calculated overall moment should be consistent with the experimental magnetization data with only a scalable To summarize, we have systematically explored the use of polar- parameter. ized powder neutron diffraction to unravel the contribution of (v) For the sample 2, to reduce the number of variable parameters fur- the two magnetic phases in bi-magnetic Fe3 O4 /Mn3 O4 core/shell ther it was assumed that the diagonal terms in the susceptibility tensor nanoparticles by using the newly developed CrysPy software. De- of the Fe3 O4 core to be 5 𝜇 B /B independent of the applied field. This cor- responded to a Néel-type magnetic structure with a constant magnetic spite the very challenging experimental conditions, quantitative moment of 5 𝜇 B . information on both Fe3 O4 and Mn3 O4 magnetic phases has (vi) For the sample 2, the parasitic reflections due to the cryostat were been obtained. The evolution of the Fe3 O4 and Mn3 O4 signals exceedingly large and disallowed the simultaneous fit of the sum and dif- with the applied field shows that while the moment of the Fe3 O4 ference patterns. Thus, only the difference pattern (where the parasitic core remains roughly constant, the moment averaged over the reflections are absent) was fitted using CrysPy. For this sample, the ba- unit cell of the Mn3 O4 shell reorients form antiparallel to parallel sic parameters of the particles (e.g., lattice parameters, crystallite size, to the Fe3 O4 as the field increases. This reorientation is evidenced core/shell volume ratio) were obtained from non-polarized powder diffrac- tion measurements performed at the D1B diffractometer of the ILL and also in the changes in the local susceptibility of Mn3 O4 . In addi- analyzed with the FullProf package.[59] tion, the coherence length of the Fe3 O4 core has been found to (vii) The diffraction peaks from a shell were strongly broadened and, decrease at large fields due to the interface disorder induced by consequently, had only a weak effect on the refinement. As a result, the the rotation of the averaged moment of the Mn3 O4 shell. These magnetic structure of the shell, despite the above constrains, cannot be results open new avenues to obtain valuable information on the inferred with sufficient accuracy only from the refinement of PNPD data. individual magnetic properties of each phase in multi-magnetic In order to distinguish between the various models (i.e., different terms of the local susceptibility tensors to be refined by CrysPy; including diverse nanostructured materials by the quantitative refinement of polar- structures that could potentially lead to the effects observed in the magne- ized powder neutron diffraction. tization data), an integral overall local susceptibility ellipsoids in the sys- tem was calculated, which was proportional to the bulk magnetization of the system. Then the calculated overall magnetization was compared to the magnetization measured using a SQUID (see Figures 7 and 8). Note 4. Experimental Section that the values of M obtained from the CrysPy refinement were scaled by Polarized Neutron Powder Diffraction Measurements and Data Analysis: a factor ≈0.4 to match the ones obtained from SQUID measurements. The PNPD experiments were carried out at the D20 diffractometer (𝜆 = As can be seen in Figures S7 and S8, Supporting Information, even 2.4 Å) of the Institut Laue Langevin (ILL) (sample 1) and at the 6T2 diffrac- small changes in the applied model can have substantial effect on the over- tometer (𝜆 = 1.4 Å) of the Laboratoire Léon Brillouin (LLB) (sample 2). all moment (i.e., integrated over all local susceptibility ellipsoids) obtained The beam was polarized with a 3 He spin filter at D20[57,58] and a pyrolytic from the refinement. In the specific case of Figures S7 and S8, Supporting graphite monochromator combined with a supermirror bender at 6T2. Information, whereas using 𝜒 yy = −1.8 the overall moment agrees with the Both experiments were performed in magnetic fields up to 50 kOe after magnetization data, using 𝜒 yy = −1.4 led to an exceedingly large moment zero field cooling from 300 to 10 K. To avoid any rotation of the powders, at low fields. the experiments were carried out on tightly packed samples. Note that the It was also important to emphasize that for less challenging samples refinements did not show any preferred orientation. the number of constraints applied to the refinements should be far lower, The polarized neutrons patterns were fitted using the new software if any at all. However, the experiment demonstrated that the flipping ratio package CrysPy,[43] specially developed for polarized neutron diffraction method can be very enlightening, even in very unfavorable conditions. data analysis.[53,54] The definition of different parameters refined by CrysPy Sample Preparation: The Fe3 O4 /Mn3 O4 core/shell nanoparticles were can be found in ref.[43 ] Note that in PNPD experiments the sum and the synthesized in two steps using the seeded growth technique following a difference of the spin-up and spin-down patterns can be refined simultane- previously reported synthesis.[23] In the first step, Fe3 O4 nanoparticles ously. It is important to highlight that the difference pattern was free from were synthesized through thermal decomposition and in the second step, the contribution of any parasitic reflections (e.g., due to the cryostat). a Mn3 O4 layer is grown on top of the Fe3 O4 nanoparticles. Importantly, the demanding experimental conditions, that is, few tens The Fe3 O4 seeds were synthesized by thermal decomposition of of mg of sample and heterostructured nanometric system with very thin iron(III) oleate.[60] The growth of the Mn3 O4 layer onto Fe3 O4 seeds was Mn3 O4 shells, make the analysis of the results particularly challenging. performed by injecting a certain amount of Mn acetylacetonate previously Thus, certain constraints were used to guarantee the convergence of the heated with oleylamine, oleic acid, 1,2-hexadecanediol, and dibenzyl ether. fitting procedure: The main difference between both samples was in (i) the size of the (i) It was assumed that the local susceptibilities at the A- and B-sites of Fe3 O4 seeds, which were synthesized in different conditions of precursor Fe3 O4 core were isotropic, which implied that the susceptibility tensor[43] concentration and heating rate and (ii) the amount of Mn precursor which had diagonal terms only. This approach was justified because the exchange in sample 2 was the double of that in sample 1. Small Methods 2023, 7, 2201725 2201725 (7 of 10) © 2023 The Authors. Small Methods published by Wiley-VCH GmbH 23669608, 2023, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202201725 by Readcube (Labtiva Inc.), Wiley Online Library on [30/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-methods.com Figure 7. Initial magnetization (solid line; measured by SQUID) and the averaged total magnetic moment (symbols; obtained from the Cryspy refinement ×0.4) for the samples 1 (left) and 2 (right). The error bars, that is, estimates standard deviation from the CrysPy refinement, do not exceed the symbol size. Figure 8. Temperature dependence of the ZFC magnetization for a) sample 1 and b) sample 2 in different applied fields (lines). The symbols correspond to the refined total average magnetic moment. The error bars, that is, estimates standard deviation from the CrysPy refinement, do not exceed the symbol size. All the particles were purified several times by centrifuging at Magnetization Measurements: The magnetization measurements 10 000 rpm mixing with hexane and acetone. were carried out on either manually packed powdered samples (samples Nanoparticles of sample 1 were dispersed in n-eicosane to minimize 1 and 2) or on dispersed nanoparticles in n-eicosane (sample 1) using a dipolar interactions. 50 mL suspension of nanoparticles in toluene were SQUID magnetometer (Quantum Design) with a 70 kOe maximum field. sonicated for 5 min to prevent any possible sample aggregation. Mean- The temperature dependence of the magnetization was recorded while while, 5 g of n-eicosane were heated using a heat gun until it became liq- warming after ZFC from 300 to 5 K at different fields. The hysteresis loops uid, and then 200 mL were rapidly added to the nanoparticle suspension. were carried out at 5 K (using a maximum field of 70 kOe) after ZFC from The homogeneous suspension was solidified by placing it in iced water. 300 K. Note that magnetite (Fe3 O4 ) nanoparticles were susceptible to surface To properly correlate the PNPD and magnetometry data, both ex- oxidation to maghemite (𝛾-Fe2 O3 ). This effect increases with time, espe- periments were carried out under the same conditions, that is, using cially for small sizes. This is why the core of sample 2, which was smaller tightly packed powders. However, for completeness, some magnetome- in size and was synthesized 7 years ago, oxidized to 𝛾-Fe2 O3 . try experiments on powders dispersed in n-eicosane (to minimize dipolar Transmission Electron Microcopy Characterization: The morphology of interactions)[10,17,63] were also carried out for sample 1 (see Supporting the nanoparticles was characterized by TEM, using a JEOL JEM-1400, oper- Information). ating at 120 kV, and a FEI Tecnai G2 F20 HR(S)TEM microscope (operated X-Ray Diffraction: Powder X-ray diffraction patterns were measured at 80 kV to avoid any beam induced damage[61] ). The EELS studies were with a wavelength of 0.4131 Å at the BL04-beamline of the ALBA Syn- performed in the latter microscope, equipped with a Quantum GIF EELS chrotron and with a Panalytical X’Pert Pro diffractometer with CuK𝛼 ra- spectrometer. Note that only a few nanoparticles were analyzed during the diation. EELS mapping study. Thus, the core sizes and shell thicknesses obtained Statistical Analysis √ from this study should be taken as approximate. Note that the data presentation is given as mean ± variance for TEM Since the particle size distributions were slightly asymmetric, they were particle sizes, and average (estimated standard deviation) for other pa- fitted using a log-normal distribution. Fits using Gaussian distributions led rameters. The errors for the particle size distribution were obtained by to comparable particle sizes with similar 𝜒 2 values, thereby confirming the means of non-linear fits using Origin 8.5, using at least 200 particles. The very slight asymmetry of the distribution. errors related to the neutron diffraction refinements were obtained from Note that previous high-resolution TEM studies on analogous particles the estimated standard deviation calculated by the FullProf and CrysPy pro- have shown the Mn3 O4 shell grew coherently on the Fe3 O4 core with rather grams, which corresponded to one sigma error in a normal distribution sharp interfaces.[23,61,62] with a 68% confidence interval. Small Methods 2023, 7, 2201725 2201725 (8 of 10) © 2023 The Authors. Small Methods published by Wiley-VCH GmbH 23669608, 2023, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202201725 by Readcube (Labtiva Inc.), Wiley Online Library on [30/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-methods.com Supporting Information [9] A. Omelyanchik, S. Villa, M. Vasilakaki, G. Singh, A. M. Ferretti, A. Ponti, F. Canepa, G. Margaris, K. N. Trohidou, D. Peddis, Nanoscale Supporting Information is available from the Wiley Online Library or from Adv 2021, 3, 6912. the author. [10] E. H. Sanchez, M. Vasilakaki, S. S. Lee, P. S. Normile, G. Muscas, M. Murgia, M. S. Andersson, G. Singh, R. Mathieu, P. Nordblad, P. C. Ricci, D. Peddis, K. N. Trohidou, J. Nogues, J. A. De Toro, Chem. Acknowledgements Mater. 2020, 32, 969. [11] P. Gorria, D. Martínez-Blanco, J. A. Blanco, M. J. Pérez, A. Hernando, I.V.G. acknowledges financial support from the Russian Foundation for L. Fernández Barquín, R. I. Smith, Phys. Rev. B 2005, 72, 01440. Basic Research under Grant No 20-02-00109. A.G.R. and J.N. acknowl- [12] I. V. Golosovsky, G. Salazar-Alvarez, A. Lopez-Ortega, M. A. edge financial support from the grants PID2019-106229RB-I0 funded Gonzalez, J. Sort, M. Estrader, S. Suriñach, M. D. Baro, J. Nogues, by MCIN/AEI/10.13039/50110001103 and 2021-SGR-00651 from Gener- Phys. Rev. Lett. 2009, 102, 247201. alitat de Catalunya. I.K. and A.G. acknowledge the European Union’s [13] M. Yuan, B. Zhao, C. Yang, K. Pei, L. Wang, R. Zhang, W. You, X. Liu, H2020 reserach and innovation program, Grant agreement No 871072. X. Zhang, R. Che, Adv. Funct. Mater. 2022, 32, 2203161. A.G.R. acknowledges financial support from RYC2019-027449-I funded [14] A. López-Ortega, M. Estrader, G. Salazar-Alvarez, S. Estradé, I. by MCIN/AEI/10.13039/501100011033. ICN2 is funded by the CERCA V. Golosovsky, R. K. Dumas, D. J. Keavney, M. Vasilakaki, K. N. programme/Generalitat de Catalunya. The ICN2 is supported by the Trohidou, J. Sort, F. Peiró, S. Suriñach, M. D. Baró, J. Nogues, CEX2021–001214–S grant funded by MCIN/AEI/10.13039/501100011033. Nanoscale 2012, 4, 5138. M.E. acknowledges the grants RYC2018-024396-I and PID2019-106165GB- C22 funded by MCIN/AEI/ 10.13039/501100011033 and by “ESF Investing [15] C. Romero-Muñiz, V. Franco, A. Conde, Appl. Phys. Lett. 2013, 102, in your future.” A.L.O. acknowledges financial support from the grants 082402. PID2021-122613OB-I00 funded by MCIN/AEI/ 10.13039/501100011033 [16] E. Lottini, A. López-Ortega, G. Bertoni, S. Turner, M. Meledina, G. and PJUPNA2020 from Universidad Pública de Navarra. The authors Van Tendeloo, C. de Julián Fernández, C. Sangregorio, Chem. Mater. thank ILL (D1B https://doi.org/10.5291/ILL-DATA.5-31-2650, D20 https: 2016, 28, 4214. //doi.org/10.5291/ILL-DATA.5-32-932), LLB and ALBA for the provision of [17] J. A. De Toro, M. Vasilakaki, S. S. Lee, M. S. Andersson, P. S. Normile, beam-time. N. Yaacoub, P. Murray, E. H. Sánchez, P. Muñiz, D. Peddis, R. Mathieu, K. Liu, J. Geshev, K. N. Trohidou, J. Nogués, Chem. Mater. 2017, 29, 8258. Conflict of Interest [18] S. M. Yusuf, A. Kumar, Appl. Phys. Rev. 2017, 4, 031303. [19] R. J. Harrison, Rev. Miner. Geochem. 2006, 63, 113. The authors declare no conflict of interest. [20] M. Estrader, A. López-Ortega, I. V. Golosovsky, S. Estradé, A. G. Roca, G. Salazar-Alvarez, L. López-Conesa, D. Tobia, E. Winkler, J. D. Ardisson, W. A. A. Macedo, A. Morphis, M. Vasilakaki, K. N. Trohidou, Data Availability Statement A. Gukasov, I. Mirebeau, O. L. Makarova, R. D. Zysler, F. Peiró, M. D. Baró, L. Bergström, J. Nogues, Nanoscale 2015, 7, 3002. The data that support the findings of this study are available from the cor- [21] G. van der Laan, A. I. Figueroa, Coord. Chem. Rev. 2014, 277–278, 95. responding author upon reasonable request. [22] X. M. Cheng, D. J. Keavney, Rep Prog Phys 2012, 75, 026501. [23] M. Estrader, A. López-Ortega, S. Estradé, I. V. Golosovsky, G. Salazar- Alvarez, M. Vasilakaki, K. N. Trohidou, M. Varela, D. C. Stanley, M. Keywords Sinko, M. J. Pechan, D. J. Keavney, F. Peiró, S. Suriñach, M. D. Baró, J. Nogues, Nat. Commun. 2013, 4, 2960. antiferromagnetic coupling, core/shell nanoparticles, Fe3 O4 , magnetic [24] D. Honecker, M. Bersweiler, S. Erokhin, D. Berkov, K. Chesnel, D. coherence length, Mn3 O4 , polarized neutron powder diffraction A. Venero, A. Qdemat, S. Disch, J. K. Jochum, A. Michels, P. Bender, Nanoscale Adv 2022, 4, 1026. Received: December 31, 2022 [25] K. L. Krycka, J. A. Borchers, M. Laver, G. Salazar-Alvarez, A. Lopez- Revised: May 10, 2023 Ortega, M. Estrader, S. Suriñach, M. D. Baro, J. Sort, J. Nogues, J. Published online: June 30, 2023 Appl. Phys. 2013, 113, 17B531. [26] S. D. Oberdick, A. Abdelgawad, C. Moya, S. Mesbahi-Vasey, D. Kepaptsoglou, V. K. Lazarov, R. F. Evans, D. Meilak, E. Skoropata, J. Van Lierop, I. Hunt-Isaak, H. Pan, Y. Ijiri, K. L. Krycka, J. A. Borchers, [1] A. Lopez-Ortega, M. Estrader, G. Salazar-Alvarez, A. G. Roca, J. S. A. Majetich, Sci. Rep. 2018, 8, 3425. Nogues, Phys. Rep. 2015, 553, 1. [27] D. S. Song, Z. Q. Wang, X. Y. Zhong, J. Zhu, Chin. Phys. B 2018, 27, [2] F. Liu, Y. Hou, S. Gao, Chem. Soc. Rev. 2014, 43, 8098. 056801. [3] O. Gutfleisch, J. Phys. D: Appl. Phys. 2000, 33, R157. [28] D. del-Pozo-Bueno, M. Varela, M. Estrader, A. López-Ortega, A. G. [4] G. W. Qin, Y. P. Ren, N. Xiao, B. Yang, L. Zuo, K. Oikawa, Int. Mater. Roca, J. Nogues, F. Peiró, S. Estradé, Nano Lett. 2021, 21, 6923. Rev. 2009, 54, 157. [29] C. L. Bianchi, R. Djellabi, A. Ponti, G. S. Patience, E. Falletta, Can. J. [5] L. Fallarino, B. J. Kirby, E. E. Fullerton, J. Phys. D: Appl. Phys. 2021, 54, Chem. Eng. 2021, 99, 2105. 303002. [30] A. S. Kamzin, I. M. Obaidat, A. A. Valliulin, V. G. Semenov, I. A. Al- [6] J. A. De Toro, D. P. Marques, P. Muñiz, V. Skumryev, J. Sort, D. Givord, Omari, Phys. Solid State 2020, 62, 1933. J. Nogues, Phys. Rev. Lett. 2015, 115, 057201. [31] O. Rivin, H. Shaked, A. Gukasov, E. N. Caspi, J. Neutron Res. 2015, [7] F. Fabris, E. Lima Jr., C. Quinteros, L. Neñer, M. Granada, M. Sirena, 18, 13. R. D. Zysler, H. E. Troiani, V. Leborán, F. Rivadulla, E. L. Winkler, Phys. [32] E. Lelièvre-Berna, A. S. Wills, E. Bourgeat-Lami, A. Dee, T. Hansen, Rev. Appl. 2019, 11, 054089. P. F. Henry, A. Poole, M. Thomas, X. Tonon, J. Torregrossa, K. [8] J. Sort, V. Langlais, S. Doppiu, B. Dieny, S. Suriñach, J. S. Muñoz, M. H. Andersen, F. Bordenave, D. Jullien, P. Mouveau, B. Guéard, G. D. Baró, C. Laurent, J. Nogues, Nanotechnology 2004, 15, S211. Manzin, Meas. Sci. Technol. 2010, 21, 055106. Small Methods 2023, 7, 2201725 2201725 (9 of 10) © 2023 The Authors. Small Methods published by Wiley-VCH GmbH 23669608, 2023, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202201725 by Readcube (Labtiva Inc.), Wiley Online Library on [30/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-methods.com [33] D. Luneau, B. Gillon, Magnetochemistry 2021, 7, 158. [48] D. Zákutná, D. Nižňanský, L. C. Barnsley, E. Babcock, Z. Salhi, A. [34] A. Borta, B. Gillon, A. Gukasov, A. Cousson, D. Luneau, E. Jeanneau, Feoktystov, D. Honecker, S. Disch, Phys. Rev. X 2020, 10, 031019. I. Ciumacov, H. Sakiyama, K. Tone, M. Mikuriya, Phys. Rev. B 2011, [49] H. R. Rechenberg, E. C. Sousa, J. Depeyrot, M. H. Sousa, R. Aquino, 83, 184429. F. A. Tourinho, R. Perzynski, Hyperfine Interact. 2008, 184, 9. [35] K. Ridier, A. Mondal, C. Boilleau, O. Cador, B. Gillon, G. Chaboussant, [50] C. Leighton, J. Nogues, H. Suhl, I. K. Schuller, Phys. Rev. B 1999, 60, B. Le Guennic, K. Costuas, R. Lescouëzec, Angew. Chem., Int. Ed. 12837. 2016, 55, 3963. [51] E. Eftaxias, M. Vasilakaki, K. N. Trohidou, Mod. Phys. Lett. B 2007, 21, [36] O. Rivin, E. N. Caspi, H. Ettedgui, H. Shaked, A. Gukasov, Phys. Rev. 1169. B 2013, 88, 054430. [52] K. Trohidou, M. Vasilakaki, in Applications of Monte Carlo Method in [37] E. Brok, K. Lefmann, P. P. Deen, B. Lebech, H. Jacobsen, G. J. Nilsen, Science and Engineering (Ed.: S. Mordechai), InTechOpen, London L. Keller, C. Frandsen, Phys. Rev. B 2015, 91, 014431. 2011, pp. 513–538. [38] D. Lin, A. C. Nunes, C. F. Majkrzak, A. E. Berkowitz, J. Magn. Magn. [53] A. Gukasov, P. J. Brown, J. Phys.: Condens. Matter 2002, 14, 8831. Mater. 1995, 145, 343. [54] A. Gukasov, P. J. Brown, J. Phys.: Condens. Matter 2010, 22, 502201. [39] S. Sabyasachi, M. Patra, S. Majumdar, S. Giri, S. Das, V. S. Amaral, [55] A. Kuriki, Y. Moritomo, S. Xu, K. Ohoyama, K. Kato, A. Nakamura, J. O. Iglesias, W. Borghols, T. Chatterji, Phys. Rev. B 2012, 86, 104416. Phys. Soc. Jpn. 2003, 72, 458. [40] H. Hiraka, K. Ohoyama, Y. Ogata, T. Ogawa, R. Gallage, N. Kobayashi, [56] S. Pal, S. Lal, Phys. Rev. B 2017, 96, 075139. M. Takahashi, B. Gillon, A. Gukasov, K. Yamada, Phys. Rev. B 2014, 90, [57] E. Lelièvre-Berna, A. Ioffe, J. Neutron Res. 2009, 20, 30. 134427. [58] J. Dreyer, L. P. Regnault, E. Bourgeat-Lami, E. Lelièvre-Berna, S. Pujol, [41] C. H. Wang, S. N. Baker, M. D. Lumsden, S. E. Nagler, W. T. Heller, F. Thomas, M. Thomas, F. Tasset, Nucl. Instrum. Methods Phys. Res., G. A. Baker, P. D. Deen, L. M. D. Cranswick, Y. Su, A. D. Christianson, Sect. A 2000, 449, 638. Phys. Rev. B 2011, 83, 214418. [59] J. Rodríguez-Carvajal, Phys. B: Condens. Matter 1993, 192, 55. [42] L. Chang, B. D. Rainford, J. R. Stewart, C. Ritter, A. P. Roberts, Y. Tang, [60] J. Park, K. An, Y. Hwang, J. G. Park, H. J. Noh, J. Y. Kim, J. H. Park, N. Q. Chen, J. Geophys. Res. 2009, 114, B07101. M. Hwang, T. Hyeon, Nat. Mater. 2004, 3, 891. [43] I. A. Kibalin, A. Gukasov, Phys. Rev. Res. 2019, 1, 033100. [61] M. A. Roldan, A. Mayence, A. López-Ortega, R. Ishikawa, J. [44] E. A. Klahn, C. Gao, B. Gillon, A. Gukasov, X. Fabrèges, R. O. Piltz, S. Salafranca, M. Estrader, G. Salazar-Alvarez, M. D. Baró, J. Nogues, D. Jiang, J. Overgaard, Chem. - Eur. J. 2018, 24, 16576. S. J. Pennycook, M. Varela, Chem. Eng. J. 2021, 405, 126820. [45] I. A. Kibalin, F. Damay, X. Fabrèges, A. Gukassov, Phys. Rev. Res. 2020, [62] P. Torruella, A. Ruiz-Caridad, M. Walls, A. G. Roca, A. Lopez-Ortega, 2, 033509. J. Blanco-Portals, L. Lopez-Conesa, J. Nogués, F. Peiro, S. Estrade, [46] S. Disch, E. Wetterskog, R. P. Hermann, A. Wiedenmann, U. Vainio, Nano Lett. 2018, 18, 5854. G. Salazar-Alvarez, L. Bergström, T. Brückel, New J Phys 2012, 14, [63] E. H. Sanchez, M. Vasilakaki, S. S. Lee, P. S. Normile, M. S. 013025. Andersson, R. Mathieu, A. Lopez-Ortega, B. P. Pichon, D. Peddis, C. [47] R. H. Kodama, A. E. Berkowitz, E. J. McNiff Jr, S. Foner, Phys. Rev. Binns, P. Nordblad, P. C. Ricci, K. N. Trohidou, J. Nogues, J. A. De Lett. 1996, 77, 394. Toro, Small 2022, 18, 2106762. Small Methods 2023, 7, 2201725 2201725 (10 of 10) © 2023 The Authors. Small Methods published by Wiley-VCH GmbH