Research Article www.small-journal.com Crossover From Individual to Collective Magnetism in Dense Nanoparticle Systems: Local Anisotropy Versus Dipolar Interactions Elena H. Sánchez,* Marianna Vasilakaki, Su Seong Lee, Peter S. Normile, Mikael S. Andersson, Roland Mathieu, Alberto López-Ortega, Benoit P. Pichon, Davide Peddis, Chris Binns, Per Nordblad, Kalliopi Trohidou, Josep Nogués,* and José A. De Toro* 1. Introduction Dense systems of magnetic nanoparticles may exhibit dipolar collective behavior. However, two fundamental questions remain unsolved: i) whether Dense assemblies of magnetic nano­ particles continue to attract high interest, the transition temperature may be affected by the particle anisotropy or it both from the technological[1–4] and basic is essentially determined by the intensity of the interparticle dipolar interac- science (e.g., superspin-glass dynamics, tions, and ii) what is the minimum ratio of dipole–dipole interaction (Edd) collective vs individual behavior)[5–11] view­ to nanoparticle anisotropy (KefV, anisotropy⋅volume) energies necessary to points. The magnetic properties of the crossover from individual to collective behavior. A series of particle assem- assembly depend markedly on the con­ blies with similarly intense dipolar interactions but widely varying anisotropy centration. While dilute systems show magnetic properties similar to those of is studied. The Kef is tuned through different degrees of cobalt-doping the individual particles, sufficiently con­ in maghemite nanoparticles, resulting in a variation of nearly an order of centrated assemblies may exhibit col­ magnitude. All the bare particle compacts display collective behavior, lective behavior, with properties (e.g., except the one made with the highest anisotropy particles, which presents transition temperature or coercivity) “marginal” features. Thus, a threshold of KefV/Edd ≈ 130 to suppress collective distinctly different from those of their constituent particles. Dipolar collective behavior is derived, in good agreement with Monte Carlo simulations. This behavior in magnetic nanoparticle sys­ translates into a crossover value of ≈1.7 for the easily accessible parameter tems can be beneficial in applications TMAX(interacting)/TMAX(non-interacting) (ratio of the peak temperatures of such as magnetic resonance imaging and the zero-field-cooled magnetization curves of interacting and dilute particle hyperthermia,[12,13] and detrimental to the systems), which is successfully tested against the literature to predict the performance of others (such as magnetic individual-like/collective behavior of any given interacting particle assembly storage, permanent magnets, or magne­ toresistive sensors).[14–16] In addition, in comprising relatively uniform particles. the recently discovered “liquid permanent E. H. Sánchez, P. S. Normile, A. López-Ortega, C. Binns, J. A. De Toro S. S. Lee Instituto Regional de Investigación Científica Aplicada (IRICA) and NanoBio Lab, Institute of Materials Research and Engineering Departamento de Física Aplicada 31 Biopolis Way, #09-01, The Nanos, Singapore 138669, Singapore Universidad de Castilla-La Mancha M. S. Andersson Ciudad Real 13071, Spain Department of Chemistry E-mail: elena.hsanchez@uclm.es; joseangel.toro@uclm.es Ångström Laboratory M. Vasilakaki, K. Trohidou Uppsala University Institute of Nanoscience and Nanotechnology NCSR “Demokritos” Uppsala 75121, Sweden Agia Paraskevi 153 10, Greece M. S. Andersson Department of Chemistry and Chemical Engineering The ORCID identification number(s) for the author(s) of this article Chalmers University of Technology can be found under https://doi.org/10.1002/smll.202106762. Göteborg SE-412 96, Sweden © 2022 The Authors. Small published by Wiley-VCH GmbH. This R. Mathieu, P. Nordblad is an open access article under the terms of the Creative Commons Department of Materials Science and Engineering Attribution License, which permits use, distribution and reproduction in Uppsala University any medium, provided the original work is properly cited. Box 35, Uppsala 751 03, Sweden DOI: 10.1002/smll.202106762 Small 2022, 18, 2106762 2106762 (1 of 11) © 2022 The Authors. Small published by Wiley-VCH GmbH 16136829, 2022, 28, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202106762 by Readcube (Labtiva Inc.), Wiley Online Library on [10/05/2023]. 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-journal.com magnets” dipolar interactions may play a role in the magnetic been studied experimentally.[11] The abundant experimental lit­ stabilization of the particles jammed at the interface of immis­ erature on strongly interacting particle systems has delved into cible liquids.[17] Yet, the fundamental question as to the relative the effects of dipolar interactions by varying the concentration importance of the local anisotropy and the interparticle interac­ of the magnetic nanoparticles, first in frozen ferrofluids[21,27–29] tions in the blocking/freezing temperature and other magnetic and nanogranular alloys in thin film or powder form,[30–32] and properties of nanoparticle assemblies remains an open ques­ more recently by controlling the thickness of non-magnetic tion, despite the relevance of this issue in many applications spacers (such as silica or dendrimer coatings)[20,22,24,33–35] or the and the fundamental incentive provided by the contrasting degree of powder compaction.[36] theoretical descriptions of the effect. Namely, Mørup proposed Here, our experimental design takes on the opposite in his seminal phase diagram that the freezing temperature approach; namely, the packing fraction has been fixed (≈ 60%, (peak temperature in zero-field-cooled (ZFC) magnetization close to the theoretical maximum of random-close-packing curves of systems exhibiting collective behavior) is simply pro­ of hard spheres,[37] in order to procure the strongest possible portional to the dipole–dipole interaction strength,[18] whereas dipolar interactions), and the particle anisotropy systemati­ the anisotropy energy barrier of the individual nanoparticles is cally varied across an order of magnitude (by using maghemite explicitly considered in the Vogel–Fulcher approach, also used nanoparticles doped with different amounts of Co).[38,39] Con­ to describe interacting nanoparticles.[19–21] sequently, this shifts the focus from interparticle interactions It is important to emphasize that while the behavior of par­ to the importance of nanoparticle magnetic anisotropy. This ticle systems with weak dipolar interactions can be simply strategy has allowed us to tackle the unsolved issue of the role accounted for by a modified Néel–Brown model, where the of the local anisotropy barrier on the collective characteristics anisotropy of the particles still plays the main role in deter­ of dense assemblies of nanoparticles. The results, backed by mining the blocking temperature,[22] dense random systems of Monte Carlo simulations and a literature review, show that dipolar-interacting nanoparticles have far more complex char­ sufficiently large local anisotropies will suppress the collective acteristics. In particular, they have been extensively reported to behavior of the assembly. In addition, they offer an estimate of exhibit a collective (superspin glass) transition similar to that the ratio of the relevant energies (anisotropy barrier and dipole– in conventional (atomic) spin-glass freezing.[6,22–26] However, dipole interaction) that yields a crossover from individual to col­ a fundamental difference between superspin- and classical lective dynamics. spin-glass systems is the existence in the former of random (nanoparticle) anisotropy barriers (KefV) yielding strongly temperature-dependent local relaxation times. Their effect on 2. Results and Discussion the overall magnetic properties of dense assemblies has rarely 2.1. Preparation of Dense Nanoparticle Systems A. López-Ortega Departamento de Ciencias Four batches of highly monodisperse nanoparticles were syn­ Universidad Pública de Navarra thesized through thermal decomposition using oleic acid (OA) Pamplona 31006, Spain as surfactant:[8,40] pure maghemite (γ-Fe2O3) nanoparticles with A. López-Ortega a mean diameter of 6.9 ± 0.6 nm and three types of cobalt- Institute for Advanced Materials and Mathematics (INAMAT2) doped maghemite particles with similar sizes (6.7 ± 0.6 nm) Universidad Pública de Navarra Pamplona 31006, Spain and different fCo = Co/(Co+Fe) ratio, namely fCo = 0.11, 0.19, B. P. Pichon and 0.23. Figure 1 shows the transmission electron microscopy Université de Strasbourg (TEM) images and particle size histograms, confirming the CNRS almost identical nanoparticle diameter independently of the Co- Institut de Physique et Chimie des Matériaux de Strasbourg doping. The narrow size distribution shown is representative UMR 7504, Strasbourg F-67000, France of all the particles, with a polydispersity lower than 4%. Elec­ B. P. Pichon Institut Universitaire de France tron energy-loss spectroscopy (EELS) mapping analysis was Paris Cedex 05 75231, France performed to discard cation segregation during the synthesis. D. Peddis The images (see Figure S1, Supporting Information) reveal a Dipartimento di Chimica e Chimica Industriale homogeneous distribution of the cobalt and iron ions across Università degli Studi di, Genova the whole nanoparticle, ruling out phase separation. Via Dodecaneso 31, Genova 1–16146, Italy After the chemical synthesis, a fraction of the particles was D. Peddis washed with acetone several times to remove the oleic acid Istituto di Structura della Materia-CNR Monterotondo Scalo (RM) 00015, Italy surfactant bound to the particles, producing essentially bare J. Nogués particles. Figure S2, Supporting Information shows the ther­ ICREA mogravimetric curves measured to quantify the content of oleic Pg. Lluís Companys 23 acid before (≈20%, very close to the expected value for a mono­ Barcelona 08010, Spain layer of oleic acid) and after (≈5%) the described washing. J. Nogués Another fraction of each type (doping) of particles was Catalan Institute of Nanoscience and Nanotechnology (ICN2) CSIC and BIST coated with thick silica (SiO2) shells of thickness around 17 nm Campus UAB, Bellaterra, Barcelona 08193, Spain (Figure 1b,d) in order to produce reference magnetically dilute E-mail: josep.nogues@icn2.cat systems with negligible interparticle interactions.[22,40–42] The Small 2022, 18, 2106762 2106762 (2 of 11) © 2022 The Authors. Small published by Wiley-VCH GmbH 16136829, 2022, 28, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202106762 by Readcube (Labtiva Inc.), Wiley Online Library on [10/05/2023]. 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-journal.com the samples exhibit a ZFC maximum (TMAX) that increases, in all three series, with the content of Co (see also Figure 3a and Table 1 for numerical values). The silica-coated particle assem­ blies (Figure 2a) provide the single-particle behavior, as the thick diamagnetic shell makes magnetostatic interactions negli­ gible.[8,22] In these systems, the relaxation time of the nanopar­ ticle macrospin is simply governed by the ratio of the thermal (kBT) to the anisotropy barrier (KefV) energies, where Kef is the effective uniaxial anisotropy constant of the particle, as described by the Néel–Brown model: τ = τ 0 exp(K ef V /kBT ) (1) When this relaxation time is smaller (greater) than the char­ acteristic time of the measurement technique (τm), the magnetic response of the assembly is described as “superparamagnetic” (“blocked”). The crossover temperature between the two regimes (for which τ = τm) is known as the blocking temperature (TB) and is directly proportional to the product of the nanoparticle volume and its effective anisotropy constant (KefV); note that in this work, “effective” refers to the inclusion of surface anisot­ ropy in the uniaxial barrier, but never to any interaction effects. Therefore, given the constant volume across the silica-coated series, the increase in TMAX (often taken as TB in this kind of dilute systems) across the series clearly indicates an anisotropy (Kef ) enhancement due to the introduction of cobalt cations in the spinel structure.[38] Note that the same trends are observed when using the more accurate mean blocking temperature TBm (defined as the peak temperature in the −d(MFC − MZFC)/dT curve,[44–46] see Figure S3, Supporting Information). The effec­ Figure 1. Transmission electron microscopy (TEM) images of the a,b) pure maghemite and c,d) Co-doped 19% maghemite particles. The silica- tive anisotropy constant can be readily calculated from the coated particles are shown on the right side, and the OA-coated particles Néel–Brown equation using the TBm values, the measurement on the left side (scale bar = 20 nm). The (mostly overlapping) size distri- time τm = 100 s (typical for dc SQUID magnetometry) and butions of both samples (pure -blue- and doped -red-) are shown in the the attempt time τ0 = 10−13 s, yielding Kef ≈ 32, 228, 282, and inset. Typical high-resolution scanning electrons microscopy (HRSEM) 317 kJ m−3 for the pure maghemite, 11%, 19%, and 23% Co- images of the surface of discs prepared with e) bare and f) OA-coated doped particles, respectively. Note that this attempt time value nanoparticles. has been previously found to systematically fit the data of sim­ ilar isolated particles better than the customary[22,23,26] τ0 = 10−10s silica coating does not alter significantly the particle anisot­ (in any case, this choice introduces a factor of only 1.25 in Kef ), ropy (through a possible change in the surface anisotropy), as although faster attempt times have also been reported in both concluded from the highly surface-sensitive probe of exchange metallic[47] and spinel cobalt ferrite particles.[48] Comparable Kef bias,[40] which varied less than 10% (measured at T = 5 K) in values have been reported in the literature, for example, 140 and all cases. In short, three series of samples were prepared: sil­ 250 kJ m−3 (using τ0 = 10−10 s) for Co-doped iron oxide particles ica-coated, OA-coated, and bare nanoparticles with different with similar size (5 and 6 nm, respectively) and cobalt content degrees of Co-doping. All powders were subsequently com­ (15% and 19%, respectively).[38,49] pacted under a uniaxial pressure of ≈ 1.0 GPa to make dense In the series of pressed OA-coated nanoparticles (Figure 2b), discs (see Figure 1e,f), resulting in the “magnetic” concentra­ the increase of TMAX with respect to the corresponding iso­ tion values of C = 0.40% (silica-coated), 50% (OA-coated), and lated nanoparticles is stronger for the pure maghemite parti­ 60% (bare nanoparticles), respectively.[43] These pellets repre­ cles (ΔT = 45 K) than for the three Co-doped particle systems sent ideal non-interacting (silica-coated nanoparticles), moder­ (ΔT ≈ 20 K), as better shown in the right panels in Figure 2. ately interacting (OA-coated nanoparticles), and strongly inter­ Interestingly, this offers a first indication that the TMAX shift acting (bare nanoparticles) systems. is not determined solely by interparticle interactions but also depends on the nanoparticle anisotropy barrier. In a first, qualitative, approach, a collective behavior for the OA-coated 2.2. Magnetic Characterization and Discussion maghemite disc is suggested by the flat shape of the field- cooled (FC) magnetization curve below TMAX with a magneti­ Figure 2 depicts the ZFC magnetization curves for the three zation close to MZFC(TMAX) (see the grey line in Figure 2d). series of samples described above: a) silica-coated nanoparti­ Such FC–ZFC irreversibility is a characteristic feature of spin cles, b) OA-coated nanoparticles, and c) bare nanoparticles. All glasses, where the system collectively freezes when the glass Small 2022, 18, 2106762 2106762 (3 of 11) © 2022 The Authors. Small published by Wiley-VCH GmbH 16136829, 2022, 28, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202106762 by Readcube (Labtiva Inc.), Wiley Online Library on [10/05/2023]. 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-journal.com Figure 2. The left column shows the ZFC magnetization curves normalized by MZFC(TMAX) measured in an applied field of μ0H = 0.5 mT in pressed discs of a) nanoparticles coated with a thick silica shell, b) OA-coated nanoparticles, and c) bare nanoparticles. The right column shows the ZFC and FC magnetization curves (measured in the same conditions) of d) pure maghemite, e) 19% and f) 23% Co-doping particles with different coatings: silica (dashed lines), oleic acid (solid light-colored lines), and bare (solid dark-colored lines). transition is reached upon cooling, thus yielding a maximum the low-temperature region where the FC flattens out. In an value of MFC(T) close to MZFC(TMAX), the equilibrium mag­ attempt to make more quantitative this FC–ZFC irrevers­ netization of the paramagnetic system right above the phase ibility argument, Figure S4, Supporting Information plots the transition.[50] This is in contrast with the dynamics of iso­ rise of the FC plateau above the ZFC peak, defined as FCrise = lated nanoparticles with a given size distribution, where the [Mplateau − MZFC(TMAX)]/MZFC(TMAX), for all the particle sys­ rise of MFC well above MZFC(TMAX) reflects the blocking (in tems. There, or directly in Figure 2, it can be seen that in the the timescale of the magnetometer) upon cooling of progres­ three pellets comprising high-anisotropy OA-coated particles sively smaller particles; similarly, the blocking of the larger the FCrise is much higher than in the OA-coated maghemite particles (or, rather, higher KefV) at higher temperatures yields system. This, combined with the mentioned moderate TMAX the FC–ZFC irreversibility onset above TMAX, as modeled by increase with respect to the corresponding isolated nanopar­ different authors.[51,52] Therefore, a flat FC curve in some low- ticles, illustrates how these three compact the strong dipolar temperature region is not indicative on its own of collective interactions at play, similar to those in the disc made with behavior; in fact, such a feature is customarily observed in OA-coated soft (maghemite) particles (in fact considerably systems of isolated particles with narrow size distribution and stronger than those in conventional “dense” frozen ferrofluids high enough TMAX, as is the case of our silica-coated Co-doped or granular solids),[5,25,30,53–55] are not intense enough to pro­ nanoparticles, where all particles have already blocked before duce collective behavior. Small 2022, 18, 2106762 2106762 (4 of 11) © 2022 The Authors. Small published by Wiley-VCH GmbH 16136829, 2022, 28, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202106762 by Readcube (Labtiva Inc.), Wiley Online Library on [10/05/2023]. 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-journal.com Figure 3. a) TMAX (obtained from the peak of the ZFC curve) as a function of the cobalt-doping fraction (fCo) for pressed discs comprising bare, OA- coated and silica-coated identical particles. For the reference (dilute) system (nanoparticles coated with a thick silica shell), TMAX is defined as the blocking temperature TB. The mean blocking temperature (TBm) derived from the FC–ZFC difference in the dilute systems (see text) is also plotted in panel (b). The dashed lines are guides to the eye and the green arrow indicates the decreasing dipolar interaction strength (Tdd) with increasing Co fraction (the range of the variation is estimated for the bare nanoparticle series). c) TMAX (for the interacting systems) plotted as a function of TBm measured in the isolated (silica-coated) nanoparticles. Hollow and solid symbols correspond to systems with individual and collective behavior, respectively. The solid lines are linear fits. Finally, for the assemblies prepared using uncoated (bare) to different particles unless there exists an exceptional crystal­ particles, the strong interactions in the compacts enhance the line coherence between aligned particles.[56,57] In addition, that ZFC peak temperatures well beyond the values measured in the dominating type of interaction in the bare series is dipolar the OA-coated series. All the samples in this series exhibited coupling is hinted by the very similar exchange bias fields (HE) low FCrise values suggesting collective behavior, although clearly measured at 5 K in the discs made of Co-doped nanoparticles modulated by the varying nanoparticle anisotropy, except the with or without coating (see Figure S5, Supporting Information pellet made with the 23% doped nanoparticles (see Figure 2e,f and the corresponding discussion). In short, HE in these sam­ and Figure S4, Supporting Information), which shows a signifi­ ples is ascribed to the presence of surface spin disorder,[58–64] cantly higher FCrise than the other bare particle systems. which would be affected by interparticle exchange interac­ Note that in the OA-coated series, the pressed oleic acid intro­ tions should there be present in the bare nanoparticle systems. duces a uniform separation of about 0.4 nm between nanoparti­ The residual oleic acid bound to the nanoparticles will further cles (estimated from the “magnetic” packing fraction),[43] ruling hamper interparticle exchange. For a more detailed discussion, out the possibility of interparticle exchange coupling. Impor­ see the Supporting Information in Ref. [8]. tantly, even in the bare nanoparticle series direct exchange cou­ To summarize the information gathered from Figure 2, pling is also expected to play only a marginal role.[22] Firstly, it we have marked with a star in Table 1 the dense samples for is rather counter-intuitive that the delicate indirect exchange which the FC–ZFC irreversibility and the increase in TMAX at play in ferrites can propagate between metal ions belonging (with respect to the isolated particles) has been argued to sug­ gest a collective behavior. The question mark assigned to the Table 1. Peak temperatures (TMAX) measured in the ZFC magnetization disc made with 23% Co-doped particles (Table 1) reflects the curves of the 12 samples (pressed discs) studied in this work. The error contrasting observations for this system: it shows a TMAX shift is less than 1 K in all cases. The Co-doping atomic ratio is defined as similar to the other bare systems, yet the shape of the FC–ZFC fCo = Co/(Co + Fe). The estimated particle concentration (or packing fraction, C) for each type of particle coating is also indicated.[40,43] The curves (with high FCrise and irreversibility temperature) is not star (*) marks the samples with expected collective behavior from the characteristic of a collective system. aspect of the FC–ZFC irreversibility and the increase in TMAX with respect The characteristic FC–ZFC irreversibility (with low FCrise to the corresponding isolated particles. The data is inconclusive for the and onset of the irreversibility close to TMAX) in the bare series, 23% bare nanoparticles. combined with the more quantitative features that will be pre­ sented later (i.e., ZFC memory effect and, in the Supporting fCo TMAX (K) Information, critical slowing down of the relaxation), indicate Silica-coated nanoparticles OA-coated nanoparticles Bare nanoparticles a crossover from single-particle to collective (superspin glass- [C ≈ 0.4%] [C ≈ 50%] [C ≈ 60%] like) dynamics with increasing packing fraction of the magnetic 0 17 62* 170* particles. Therefore, in this series, the measured peak tempera­ 0.11 114 129 234* ture (TMAX) reflects the collective freezing of the system upon cooling.[23,26] Yet, despite this collective character (see discus­ 0.19 138 161 255* sion below), TMAX is still not only controlled by the dipolar 0.23 153 171 275? interactions but is also largely affected by the local anisotropy Small 2022, 18, 2106762 2106762 (5 of 11) © 2022 The Authors. Small published by Wiley-VCH GmbH 16136829, 2022, 28, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202106762 by Readcube (Labtiva Inc.), Wiley Online Library on [10/05/2023]. 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-journal.com (nanoparticle energy barrier). This result is at odds with the glasses). It must be emphasized that the Vogel–Fulcher law conceptual phase diagram proposed by Mørup for dipolar- [ from which Equation (3) is derived] describes the divergence interacting particle systems, where the collective freezing tem­ of the relaxation time at a finite temperature Tint, and there­ perature is determined exclusively by the strength of the dipolar fore Equation (3) is a priori only suitable for the analysis of interactions.[18] In fact, Figure 3a (green symbols) shows that strongly interacting systems. For non- or weakly-interacting TMAX increases with nanoparticle anisotropy (i.e., fCo) despite systems, which do not yield such finite-T divergence, a modi­ the concomitant reduction in dipolar interaction strength fied Arrhenius expression should be used instead. In short, the (green arrow in the figure) stemming from the small loss in proposed “TMAX − TBm = bsTdd” relation is one way to introduce saturation magnetization upon Co-doping (see Figure S6, Sup­ the influence of the particle anisotropy in strongly interacting porting Information and the corresponding discussion).[65,66] particle systems, where, assuming that TMAX mimics the glass This small variation of dipolar interactions across the fCo series transition Tg, it suggests Tg = TBm + bsTdd, to be compared with is an undesired effect of our Co-doping strategy, yet it lends Mørup’s expression Tg = b0Tdd. support to the argument. To test our data against Equation (3), Figure 3c plots TMAX Figure 3a, therefore, shows that TMAX in any dipolar inter­ for both the bare and OA-coated series as a function of the TBm acting nanoparticle system is determined by additive contri­ measured in the corresponding dilute systems (in turn plotted butions from the dipolar interactions (characterized by the vs fCo in Figure 3b from the data in Figure S2, Supporting parameter Tdd = µ0MS2V 2 /kB 4π r 3, where r is the mean distance Information). It is important to underline the originality of this between particles) as well as from the nanoparticle anisotropy plot, whose abscissa is not some interaction proxy, as custom­ energy barrier (KefV, here estimated from TBm, measured in arily found in the literature,[18,20,22,24,42] but the local anisotropy the silica-coated nanoparticles). This is as described by modi­ quantified through TBm. The clearly linear dependence and the fied single-particle models, with dynamics still given by the fitted slope (close to 1 in both series) are in good agreement Néel–Brown law (Equation [1]), simply replacing KefV with the with Equation (3), unequivocally evidencing the important role sum (KefV + Δ).[67] However, in such models the relaxation time of the single-particle anisotropy in the freezing temperature of (τ) still diverges at T = 0 K, which does not hold for strongly strongly interacting assemblies. The intercept of the fits gives interacting nanoparticle systems where τ is found to diverge the average interaction temperature in the two series (T∫ ). In at a finite (glass) temperature, signaling a phase transition to the bare series, T∫ = 157 K, which, considering an average Tdd ≈ a superspin glass state. A phenomenological expression satis­ 40 K, yields bs ≈ 3.9 (the range of individual bs values in the fying both requisites (namely, i) TMAX determined by both Tdd bare series is 2.7 – 5.5). This value is indeed smaller than the and TBm, and ii) critical divergence of the relaxation time at a b0 = TMAX/Tdd estimates for several concentrated nanoparticle non-zero temperature) is the well-known Vogel–Fulcher law:[19] systems reviewed by Mørup in Reference [18], in the range 4–8. Moreover, the smaller bs ≈ 2.1 obtained for the OA-coated series K ef V appears consistent with a different qualitative prediction sug­ τ = τ 0 e kB(T −Tint ) (2) gested by Mørup’s diagram, namely the steeper variation of TMAX versus Tdd in systems with strong interactions (providing For τ =τm, T = TMAX, and solving for the latter: superspin glass behavior) compared with those with weaker interactions (presenting modified single-particle dynamics).  τ K V Equation (3), thus, provides a method to estimate the interac­ TMAX =  1/ ln  m   ef + Tint = TBm + bsTdd (3) tion temperature simply from the ZFC curves of isolated and   τ 0   kB dense systems made of the same nanoparticles. In this regard, where TBm is the mean blocking temperature measured by note that in dipolar-interacting systems, as in other systems magnetometry in isolated particles (KefV is taken here as the with similar amounts of ferro- and antiferro-like interac­ mean anisotropy barrier of the nanoparticles), and bs is a pro­ tions,[68,69] Curie–Weiss fits cannot determine the magnitude of portionality constant relating the Vogel–Fulcher divergence the interactions. temperature Tint, customarily ascribed to interparticle interac­ This leads to the question of how high the anisotropy bar­ tions,[19–21] and the dipole–dipole interaction temperature Tdd rier must raise (relative to the interparticle interaction) to sup­ defined above. Although bs in Equation (3) will be systematically press the collective spin glass-like behavior produced by dipolar smaller than b0 in Mørup’s simpler model for strongly inter­ interactions. First, note that the naive notion that dipolar inter­ acting systems, namely TMAX = b0Tdd (where it was estimated actions, of the order of magnitude of the dipole–dipole inter­ to be of the order of 10),[18,67] both parameters have essentially action energy (Edd = kBTdd,), need to overcome the anisotropy the same meaning, except that the influence of local anisot­ energy barrier (KefV) to produce collective behavior must be ropy is overlooked in the latter model. Since Tdd (dipole–dipole dismissed, at least in particle assemblies with a random orien­ interaction) simply sets the interaction energy scale, bs gathers tation of the uniaxial anisotropy axes. Note that the first three everything else affecting the interaction energy as detailed in bare nanoparticle systems studied here, with energy ratios Ref. [18], namely, the summation over many pairs of magnetic KefV/Edd ≈ 35·TBm/Tdd ranging from ≈ 6.6 (pure maghemite) dipoles (long-range character of the dipolar interaction), the to ≈ 118 (fCo = 0.19), show FC–ZFC curves typical of superspin width of the particle size distribution (or “polydispersity”), and a glasses. This is not the case for the bare fCo = 0.23 sample (with factor of the order of unity originally related to spin dimension­ the highest anisotropy), with FC curve still increasing below ality in atomic spin-glass calculations (therefore possibly weakly TMAX and a broader ZFC maximum. This, together with relaxa­ dependent on the nanoparticle anisotropy barrier in superspin tion features presented below, justifies labeling this sample as Small 2022, 18, 2106762 2106762 (6 of 11) © 2022 The Authors. Small published by Wiley-VCH GmbH 16136829, 2022, 28, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202106762 by Readcube (Labtiva Inc.), Wiley Online Library on [10/05/2023]. 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-journal.com “marginal”, marking the crossover from collective to single- particle/collective character of a given nanoparticle system particle dynamics with increasing KefV. Given the unavoidable with the only prior knowledge of the blocking temperature of a distribution in nanoparticle anisotropy barrier, the broader ZFC dilute system of the same particles. For example, pressed bare peak in this sample would reflect the particularly wide distribu­ nanoparticles 8 nm in diameter, with TMAX/TB ≈ 4, have been tion of relaxation times arising from a mixture of Néel (higher previously described as a model superspin glass system.[42] KefV particles) and critical (collective) dynamics. Moreover, the To determine the crossover value we have used the data for single-particle dynamics could operate in few nanoparticle clus­ fCo = 0.23 (namely c ≈ 0.7, bs ≈ 5.2, and (KefV/Edd)c ≈ 134, thus ters (dimers, trimers, etc.) of dipolar-coupled high anisotropy  TB  ≈ 5.1), which yields a crossover ratio  TMAX  ≈ 1.7. This particles, yielding long relaxation times. It is this heterogeneity  T   T  dd c B c in dynamics that defines the mentioned “crossover”. Conse­ value is marked by the pink line in Figure 4, which gathers the quently, our experimental data allows us to estimate a cross­ interacting systems studied here (both the bare and OA-coated over energy ratio of (KefV/Edd)c ≈ 130. Interestingly, this result series), as well as other dense assemblies characterized by us is not far from the ratio implied in Mørup’s phase diagram or other groups.[5,20,23,24,33,40,42,70,71] Although this crossover ratio ((KefV/Edd)c ≈ 150; see Supporting Information), based on the for collective behavior is far from being a universal (in as much experimental data available at the time, separating (modified) as the parameters c and bs in Equation [4] are not), it can be single-particle-like behavior from collective freezing in both seen that the threshold value suggested above agrees very well Mössbauer and magnetometry experiments.[18] with the reviewed studies (all of them dealing with relatively Unfortunately, the ratio KefV/Edd is rather inconvenient to narrow particle size distributions and reporting TMAX, TB and experimentally predict the behavior of dense assemblies of nano­ whether the denser system presents collective or single-particle particles. A more suitable parameter can be found by rewriting dynamics). It is particularly noteworthy that another “marginal” Equation (3), using TBm = cTB (with TB defined as the ZFC peak sample, reported by Hansen et al. in a 5% volume concentrated temperature in the reference system of isolated particles), as FeC ferrofluid) lies also on the proposed crossover ratio.[5] Moreover, the dashed line in Figure 4 is a fit to Equation (4) of TMAX T the bare nanoparticle systems studied here with the addition of = c + bs dd (4) TB TB another disc made of smaller (6.2 nm) maghemite particles.[40] As expected, the resulting value for the fitting parameter bsTdd is which suggests the ratio TMAX/TB, more experimentally acces­ the same (within the error bars) as that obtained for the inter­ sible than KefV/Edd, as a simple parameter to predict the single- cept bsTdd = T∫ in Figure 3c using the equivalent Equation (3). Overall, the data points distribution visually emphasizes the intuitive fact that it is easier to obtain collective behavior in sys­ tems comprising nanoparticles with lower anisotropy energy. From the crossover ratio (KefV/Edd)c ≈ 130 one may also cal­ culate the minimum volume concentration/packing fraction of nanoparticles necessary to reach collective dipolar behavior, µ ϕc, by simply inserting E dd = 0 MS2Vφc ,[67] which yields a par­ 4π 0.1K ticle-size independent φc ≈ . This leads to a realistic φc ≈ µ0MS2 0.58 for our fCo = 0.23 sample. An interesting corollary is that dipolar collective magnetism is not possible (i.e., φc φc ≳ 0.64 in random close-packed assemblies) for nanoparticulate materials K with 2 ≳ 8.3 J kA−2 m−1. This will be the case for hard parti­ MS cles with a modest saturation magnetization, such as ε-Fe2O3 nanoparticles (which yields an impossible φc ≈ 4 when using the K and MS values reported in Ref. [69]) or CoPt, for which φc ≈ 0.60 using bulk values[57] (higher K and lower Ms values Figure 4. Phase diagram of dipolar-interacting nanoparticle systems. are customarily found in nanoparticles, thus pushing the crit­ The solid symbols correspond to systems with reported collective/ ical concentration up to unphysical values). superspin glass behavior, whereas hollow symbols are used for systems where the lack of collective behavior has been proven. Half-solid sym- In the discussion of Figure 3 above we claimed the rele­ bols correspond to systems with reported marginal behavior. The pink vance of the particle anisotropy even in systems showing col­ line, therefore, marks an experimental TMAX/TB threshold for superspin lective dynamics. In this regard, to demonstrate the existence glass behavior. Larger symbols are used for compacts of essentially bare or the lack of such collective behavior, we have performed ZFC nanoparticles.[22,40,42] Grey symbols are used for pressed OA-coated or memory experiments (encompassing the phenomena of aging dendrimer-coated (down-triangle) nanoparticles.[20,22,24,33,71] Dark blue and rejuvenation in spin glass-like systems) probing the system symbols are for frozen ferrofluids.[5] The nanoparticles are always magh- relaxation over several hours. This experiment, together with emite[20,22,24,33,40,42,70] unless otherwise noted.[5,71] Importantly, all samples included in the graph were prepared using nanoparticles with a relatively the previous ZFC/FC magnetization curves, and ac magnetic narrow size distribution. The dashed line is a fit of the green datapoints susceptibility (see Supporting Information), covers three of to Equation (4), equivalent to the fit to Equation (3) in Figure 3. the four “key bulk measurements that determine a magnetic Small 2022, 18, 2106762 2106762 (7 of 11) © 2022 The Authors. Small published by Wiley-VCH GmbH 16136829, 2022, 28, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202106762 by Readcube (Labtiva Inc.), Wiley Online Library on [10/05/2023]. 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-journal.com Figure 5. ZFC memory experiments. The purple dotted lines are the refer- ence curves measured without a halt. The solid lines are the ZFC mag- netization curves measured after 4 h stops at Thalt = 2TMAX/3. The lower inset shows the difference curves, ΔM(T)/Mref(T = Thalt) (“memory dips”), with the depth plotted in the upper inset. The vertical dashed lines of the lower inset marks Thalt for each sample. material to be a canonical spin-glass” (the fourth one being spe­ cific heat), according to a recent review by J. A. Mydosh.[50] The ZFC memory effect is a remarkable phenomenon characteristic of the chaotic non-equilibrium (super) spin-glass phase.[53,54,73,74] Figure 5 shows ZFC magnetization curves recorded after cooling without (reference curves) and with (memory curves) a 4 h halt at Thalt = (2/3)TMAX. A dip in the magnetization of Figure 6. a) ZFC magnetization curves simulated for the end members the latter curve can be appreciated in the vicinity of the halt. (lowest and highest Kef) of the series of dense systems (same filling The stop performed during cooling allows the system to “age”, factor, varying anisotropy). Solid/dash lines are used to denote ZFC curves obtained without/with a halt, respectively. The inset shows a plot slowing down its dynamics towards the particular equilibrium analogous to Figure 3c, with TBm calculated from d(MFC − MZFC)/dT as in state at the halt temperature; a state that is recovered later upon the experiment. b) “Memory curves” obtained as the difference between heating, thus the memory curve magnetization falls below the ZFC curves described above normalized by Mref (T = Thalt). The vertical the reference curve. The corresponding difference curves are lines are the respective halt temperatures. The inset shows the dip depth shown in the lower inset of Figure 5, where ∆M is defined as a function of the anisotropy constant (defined as k = KefV/20kB) of the as the difference between the memory and reference curves nanoparticles across the simulated series. ZFC (M mem (T ) − M ref ZFC (T )) normalized by M ref = M ref ZFC (T = Thalt ). All samples display visible memory dips; however, their magnitude an associated 3D classical macrospin placed at random posi­ is strongly dependent on the doping ratio (see upper inset). tions in a cubic lattice (see a detailed description of the model While the pure maghemite sample exhibits a sharp memory in the Supporting Information).[77–84] The Monte Carlo model effect (6%), the Co-doped samples show weaker memory, barely is designed so that, although it is related to the experiment in noticeable in the 23% doped sample. This trend can be ascribed terms of nanoparticle size, MS, or Keff, it circumvents some of to the net increase of the magnetic anisotropy with Co-doping, the experimental drawbacks (e.g., variations in the size, MS, in turn slowing down the individual nanoparticle relaxation or surface disorder between constituents in the series). In this and, thus, the overall collective effect, as have been previously way, we avoid experimental issues that might complicate the described in both superspin[11,75] and atomic spin glasses.[76] A interpretation of the data while making the results more gen­ similar trend (from sharp collective features in the non-doped eral. The Hamiltonian includes only three terms, namely uni­ sample to marginal/anomalous behavior in the 23% doped axial anisotropy, dipolar interactions, and Zeeman energy. FC sample) is observed in the frequency and temperature depend­ and ZFC (with and without a halt to testing memory) curves ence of the ac susceptibility (see Supporting Information). were simulated for ensembles corresponding to the silica- coated (dilute) and bare nanoparticles (60% packing fraction) compacts, where the uniaxial anisotropy was varied system­ 2.3. Monte Carlo Simulations atically. Figure 6 shows these curves for the end members of the simulated dense series (bare nanoparticles compacts). The In addition to the above experiments, the two questions pre­ qualitative agreement with the experimental data is remarkable, sented in the abstract have also been explored using Monte with the highest Kef dense sample showing a lower memory Carlo simulations of identical spherical magnetic particles with effect. Yet more significantly, the memory dip progressively Small 2022, 18, 2106762 2106762 (8 of 11) © 2022 The Authors. Small published by Wiley-VCH GmbH 16136829, 2022, 28, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202106762 by Readcube (Labtiva Inc.), Wiley Online Library on [10/05/2023]. 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-journal.com fades with increasing anisotropy (see inset in Figure 6b), as acid in the reaction. All the nanoparticles were washed by several cycles observed experimentally. At the quantitative front, the depend­ of coagulation with acetone, centrifugation, disposal of the supernatant ence of TMAX (from simulations of the nanoparticle compacts) solution, and re-dispersion in hexane. Then, a fraction of these nanoparticles was washed repeatedly in acetone to remove the oleic acid with the mean blocking temperature obtained from the corre­ coating, obtaining what we call here bare particles (≈5%w oleic acid), sponding dilute systems (in analogy to Figure 3c) is observed to a second fraction was separated to subsequently grow a silica shell be linear with a slope very close to unity (see inset in Figure 6a), following the method described elsewhere,[41] and a third fraction was in excellent agreement with the experimental data, thus corrob­ left as it obtained (oleic acid-coated). All the different types of resulting orating the model in Equation (3). Finally, the crossover value nanoparticles were dried and the powder was pressed uniaxially under (KefV/Edd)c_MC ≈ 140 was found to transition from collective to approximately 0.8 GPa to form dense discs. TEM images have been acquired in the FEI Tecnai G2 F20 microscope individual behavior (corresponding to the anisotropy reducing operated at 200 kV. The particle size was determined by evaluating the the memory effect by a factor of three, as suggested by the diameter of n > 300 particles using ImageJ. The results were fitted to a experimental results) is remarkably similar to our experimental LongNormal distribution using Origin 8.5. estimate. A Quantum Design EverCool MPMS SQUID magnetometer was used for the magnetic characterization of the pellets with the applied field parallel to the disc plane. ZFC and FC magnetization curves were measured using a magnetic field strength of 0.5 mT (5 Oe) and 3. Conclusion a sweeping rate of 2.5 K min−1. In the ZFC protocol, the sample was cooled in zero-field from room temperature to 5 K, at which the magnetic To summarize, we have systematically explored the role of par­ field was applied, and the magnetization was recorded upon heating. ticle anisotropy on the transition from single particle to col­ Then, in the FC protocol, the sample was cooled in a constant field lective behavior in a series of pellets comprising bare oxide and the magnetization was recorded again upon heating. ZFC memory nanoparticles with the same size, size distribution, and concen­ experiments were carried out using a similar protocol to that described tration, but different degrees of Co-doping as a means to con­ in Reference.[85] In the “memory curve”, the sample was cooled down to 5 K in zero field with a 4 h halt at Thalt = 2TMAX/3. trol the value of the effective anisotropy (Kef ). All the compacts Note that the data presentation was given as (average ± standard made of bare particles display collective glassy behavior (as evi­ deviation) for particle sizes and average (root mean square error in dent, in particular, from the shape of the FC–ZFC irreversibility the last digit) for other parameters. The errors derived from diverse and a significant ZFC memory effect), except the sample with fitting procedures (e.g., Figures 3c and 6a and Table S1, Supporting the highest nanoparticle anisotropy (fCo = 0.23), which exhibits Information) were obtained from linear or non-linear fits using Origin a “marginal” behavior. The experimental results and the Monte 8.5. Carlo simulations consistently evidence that: i) the collective behavior (e.g., freezing temperature, memory effect, ac sus­ ceptibility) unquestionably depends on both the dipolar inter­ Supporting Information actions and the nanoparticle anisotropy energy barrier (KefV), Supporting Information is available from the Wiley Online Library or and ii) the minimum KefV/Edd ratio necessary to suppress the from the author. collective behavior in random assemblies of magnetic nanopar­ ticles is of the order of ∼100, in good agreement with Mørup’s early estimate in his pioneering work on superspin glasses. Our analysis provides (through Equation [3]) a method to esti­ Acknowledgements mate the interaction temperature simply from the ZFC curves The authors acknowledge financial support from grant No. MAT2015- of isolated and dense systems made of the same nanoparticles, 65295-R funded by MCIN/AEI/10.13039/501100011033 and by “ERDF and suggests that the ratio TMAX/TB (easily accessible experi­ A way of making Europe”, grant No. PID2019-106229RB-I00 funded mentally) can be used as a predictor of single-particle/collective by MCIN/AEI/10.13039/501100011033 and the Spanish MEC (through the contract No. BEAGAL18/00095). The authors also acknowledge behavior. The estimated crossover value of (TMAX/TB) ≈ 1.7 sepa­ funding from UCLM’s Plan Propio, the Swedish Research Council (VR), rating the two regimes has been successfully checked against a the Universidad Pública de Navarra (grant No. PJUPNA2020) and the number of previous reports on interacting particle systems with Generalitat de Catalunya (grant No. 2017-SGR-292). ICN2 is funded by a reasonably narrow particle size distribution (broader distri­ the CERCA program/Generalitat de Catalunya and supported by SEV- butions will require higher ratios to reach collective behavior). 2017-0706 grant funded by MCIN/AEI/10.13039/501100011033. K.T., D.P., This value leads to the minimum packing fraction of nanopar­ and M.V. acknowledge support from the European Union’s Horizon 2020 Programme: under gran agreement No. 731976 (MAGENTA) and ticles required to yield collective dipolar magnetism, which in partially the Horizon Europe EIC Pathfinder Programme: under grant fact will never happen in sufficiently hard magnetic materials. agreement No. 101046909 (REMAP). 4. Experimental Section Conflict of Interest Monodisperse spherical nanoparticles were synthesized using an The authors declare no conflict of interest. optimized thermal decomposition route.[8,40] Briefly, in a typical synthesis, iron pentacarbonyl and cobalt pentacarbonyl in different proportions (fCo) are thermally decomposed in the presence of oleic acid (surfactant) and dioctyl ether (solvent) and subsequently oxidized with trimethylamine N-oxide at high temperature. Data Availability Statement The nanoparticle size was controlled by changing the amount of oleic Research data are not shared. Small 2022, 18, 2106762 2106762 (9 of 11) © 2022 The Authors. Small published by Wiley-VCH GmbH 16136829, 2022, 28, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202106762 by Readcube (Labtiva Inc.), Wiley Online Library on [10/05/2023]. 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-journal.com Keywords [28] C. A. M. Vieira, R. C. Gomes, F. G. Silva, A. L. Dias, R. Aquino, A. F. C. Campos, J. Depeyrot, J. Phys.: Condens. Matter 2019, 31, dipolar interactions, magnetic anisotropy, magnetic nanoparticles, 175801. superspin glass [29] D. Farrell, Y. Cheng, R. W. McCallum, M. Sachan, S. A. Majetich, J. Phys. Chem. B 2005, 109, 13409. Received: November 4, 2021 [30] J. A. De Toro, M. A. López de la Torre, J. M. Riveiro, J. Bland, Revised: May 17, 2022 J. P. Goff, M. F. Thomas, Phys. Rev. B 2001, 64, 224421. Published online: June 10, 2022 [31] J. A. De Toro, M. A. López de la Torre, J. M. Riveiro, A. Beesley, J. P. Goff, M. F. Thomas, Phys. Rev. B 2004, 69, 224407. [32] J. M. Vargas, W. C. Nunes, L. M. Socolovsky, M. Knobel, D. Zanchet, Phys. Rev. B 2005, 72, 184428. [1] Y. Deng, A. Ediriwickrema, F. Yang, J. Lewis, M. Girardi, [33] G. C. Papaefthymiou, E. Devlin, A. Simopoulos, D. Yi, S. Riduan, W. M. Saltzman, Nat. Mater. 2015, 14, 1278. S. S. Lee, J. Ying, Phys. Rev. B 2009, 80, 024406. [2] A. Jordan, K. Maier-Hauff, P. Wust, B. Rau, M. Johannsen, Onkologe [34] P. C. Rivas Rojas, P. Tancredi, O. Moscoso Londoño, M. Knobel, 2007, 13, 894. L. M. Socolovsky, J. Magn. Magn. Mater. 2018, 451, 688. [3] O. V. Salata, J. Nanobiotechnol. 2004, 2, 3. [35] N. Pérez, C. Moya, P. Tartaj, A. Labarta, X. Batlle, J. Appl. Phys. 2017, [4] D. Cabrera, A. Coene, J. Leliaert, E. J. Arte, L. Dupre, N. D. Telling, 121, 044304. F. J. Teran, ACS Nano 2018, 12, 2741. [36] B. Aslibeiki, P. Kameli, H. Salamati, J. Appl. Phys. 2016, 119, [5] M. F. Hansen, P. E. Jönsson, P. Nordblad, P. Svedlindh, J. Phys.: 063901. Condens. Matter 2002, 14, 4901. [37] S. Torquato, T. M. Truskett, P. G. Debenedetti, Phys. Rev. Lett. 2000, [6] M. S. Andersson, J. A. De Toro, Su Seong Lee, R. Mathieu, 84, 2064. P. Nordblad, EPL 2014, 108, 17004. [38] E. Fantechi, G. Campo, D. Carta, A. Corrias, C. de Julián Fernández, [7] G. Muscas, G. Concas, S. Laureti, A. M. Testa, R. Mathieu, J. A. De D. Gatteschi, C. Innocenti, F. Pineider, F. Rugi, C. Sangregorio, Toro, C. Cannas, A. Musinu, M. A. Novak, C. Sangregorio, S. S. Lee, J. Phys. Chem. C 2012, 116, 8261. D. Peddis, Phys. Chem. Chem. Phys. 2018, 20, 28634. [39] S. Dutz, N. Buske, J. Landers, C. Gräfe, H. Wende, J. H. Clement, [8] E. H. Sánchez, M. Vasilakaki, S. S. Lee, P. S. Normile, G. Muscas, Nanomaterials 2020, 10, 1019. M. Murgia, M. S. Andersson, G. Singh, R. Mathieu, P. Nordblad, [40] J. A. De Toro, M. Vasilakaki, S. S. Lee, M. S. Andersson, P. C. Ricci, D. Peddis, K. N. Trohidou, J. Nogués, J. A. De Toro, P. S. Normile, N. Yaacoub, P. Murray, E. H. Sánchez, P. Muñiz, Chem. Mater. 2020, 32, 969. D. Peddis, R. Mathieu, K. Liu, J. Geshev, K. N. Trohidou, J. Nogués, [9] F. Vernay, H. Kachkachi, J. Magn. Magn. Mater. 2020, 500, 166286. Chem. Mater. 2017, 29, 8258. [10] R. P. Tan, J. S. Lee, J. U. Cho, S. J. Noh, D. K. Kim, Y. K. Kim, J. Phys. [41] D. K. Yi, S. S. Lee, G. C. Papaefthymiou, J. Y. Ying, Chem. Mater. D: Appl. Phys. 2010, 43, 165002. 2006, 18, 614. [11] M. S. Andersson, J. A. De Toro, S. S. Lee, P. S. Normile, P. Nordblad, [42] M. S. Andersson, R. Mathieu, S. S. Lee, P. S. Normile, G. Singh, R. Mathieu, Phys. Rev. B 2016, 93, 054407. P. Nordblad, J. A. De Toro, Nanotechnology 2015, 26, 475703. [12] H. Gavilán, E. H. Sánchez, M. E. F. Brollo, L. Asín, K. K. Moerner, [43] P. S. Normile, M. S. Andersson, R. Mathieu, S. S. Lee, G. Singh, C. Frandsen, F. J. Lázaro, C. J. Serna, S. Veintemillas-Verdaguer, J. A. De Toro, Appl. Phys. Lett. 2016, 109, 152404. M. P. Morales, L. Gutiérrez, ACS Omega 2017, 2, 7172. [44] I. J. Bruvera, P. Mendoza Zélis, M. P. Calatayud, G. F. Goya, [13] K. Hayashi, M. Nakamura, W. Sakamoto, T. Yogo, H. Miki, S. Ozaki, F. H. Sánchez, J. Appl. Phys. 2015, 118, 184304. M. Abe, T. Matsumoto, K. Ishimura, Theranostics 2013, 3, 366. [45] K. L. Livesey, S. Ruta, N. R. Anderson, D. Baldomir, R. W. Chantrell, [14] B. H. Zhou, J. D. Rinehart, ACS Cent. Sci. 2018, 4, 1222. D. Serantes, Sci. Rep. 2018, 8, 11166. [15] N. Kumar, G. Khurana, A. Gaur, R. K. Kotnala, J. Appl. Phys. 2013, [46] G. Concas, F. Congiu, G. Muscas, D. Peddis, J. Phys. Chem. C 2017, 114, 053902. 121, 16541. [16] B. Balasubramanian, B. Das, R. Skomski, W. Y. Zhang, [47] G. Xiao, S. H. Liou, A. Levy, J. N. Taylor, C. L. Chien, Phys. Rev. B D. J. Sellmyer, Adv. Mater. 2013, 25, 6090. 1986, 34, 7573. [17] X. Liu, N. Kent, A. Ceballos, R. Streubel, Y. Jiang, Y. Chai, P. Y. Kim, [48] A. J. Rondinone, A. C. S. Samia, Z. J. Zhang, Appl. Phys. Lett. 2000, J. Forth, F. Hellman, S. Shi, D. Wang, B. A. Helms, P. D. Ashby, 76, 3624. P. Fischer, T. P. Russell, Science 2019, 365, 264. [49] I. Galarreta, M. Insausti, I. Gil de Muro, I. Ruiz de Larramendi, [18] S. Mørup, EPL 1994, 28, 671. L. Lezama, Nanomaterials 2018, 8, 63. [19] S. Shtrikman, E. P. Wohlfarth, Phys. Lett. A 1981, 85, 467. [50] J. A. Mydosh, Rep. Prog. Phys. 2015, 78, 052501. [20] S. Fleutot, G. L. Nealon, M. Pauly, B. P. Pichon, C. Leuvrey, [51] F. Tournus, A. Tamion, J. Magn. Magn. Mater. 2011, 323, 1118. M. Drillon, J.-L. Gallani, D. Guillon, B. Donnio, S. Begin-Colin, [52] M. Knobel, W. C. Nunes, L. M. Socolovsky, E. De Biasi, J. M. Vargas, Nanoscale 2013, 5, 1507. J. C. Denardin, J. Nanosci. Nanotechnol. 2008, 8, 2836. [21] J. Zhang, C. Boyd, W. Luo, Phys. Rev. Lett. 1996, 77, 390. [53] P. E. Jönsson, Adv. Chem. Phys. 2004, 128, 191. [22] J. A. De Toro, P. S. Normile, S. S. Lee, D. Salazar, J. L. Cheong, [54] M. Östh, D. Hérisson, P. Nordblad, J. A. De Toro, J. M. Riveiro, P. Muñiz, J. M. Riveiro, M. Hillenkamp, F. Tournus, A. Tamion, J. Magn. Magn. Mater. 2007, 313, 373. P. Nordblad, J. Phys. Chem. C 2013, 117, 10213. [55] J. Alonso, M. L. Fdez-Gubieda, J. M. Barandiarán, A. Svalov, [23] J. A. De Toro, S. S. Lee, D. Salazar, J. L. Cheong, P. S. Normile, L. Fernández Barquín, D. Alba Venero, I. Orue, Phys. Rev. B 2010, P. Muñiz, J. M. Riveiro, M. Hillenkamp, F. Tournus, A. Tamion, 82, 054406. P. Nordblad, Appl. Phys. Lett. 2013, 102, 183104. [56] C. Frandsen, K. Lefmann, B. Lebech, C. R. H. Bahl, E. Brok, [24] K. Hiroi, K. Komatsu, T. Sato, Phys. Rev. B 2011, 83, 224423. S. N. Ancoña, L. Theil Kuhn, L. Keller, T. Kasama, L. C. Gontard, [25] D. Parker, V. Dupuis, F. Ladieu, J.-P. Bouchaud, E. Dubois, S. Mørup, Phys. Rev. B 2011, 84, 214435. R. Perzynski, E. Vincent, Phys. Rev. B 2008, 77, 104428. [57] A. López-Ortega, M. Estrader, G. Salazar-Alvarez, A. G. Roca, [26] M. S. Andersson, R. Mathieu, P. S. Normile, S. S. Lee, G. Singh, J. Nogués, Phys. Rep. 2015, 553, 1. P. Nordblad, J. A. De Toro, Mater. Res. Express 2016, 3, 045015. [58] J. Nogués, J. Sort, V. Langlais, V. Skumryev, S. Suriñach, J. S. Muñoz, [27] T. Jonsson, P. Nordblad, P. Svedlindh, Phys. Rev. B 1998, 57, 497. M. D. Baró, Phys. Rep. 2005, 422, 65. Small 2022, 18, 2106762 2106762 (10 of 11) © 2022 The Authors. Small published by Wiley-VCH GmbH 16136829, 2022, 28, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202106762 by Readcube (Labtiva Inc.), Wiley Online Library on [10/05/2023]. 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-journal.com [59] D. Peddis, F. Orrù, A. Ardu, C. Cannas, A. Musinu, G. Piccaluga, [72] M. Gich, A. Roig, C. Frontera, E. Molins, J. Sort, M. Popovici, Chem. Mater. 2012, 24, 1062. G. Chouteau, D. Martín y Marero, J. Nogués, J. Appl. Phys. 2005, 98, [60] M.-H. Phan, J. Alonso, H. Khurshid, P. Lampen-Kelley, S. Chandra, 044307. K. Stojak Repa, Z. Nemati, R. Das, Ó. Iglesias, H. Srikanth, Nano- [73] S. Sahoo, O. Petracic, W. Kleemann, P. Nordblad, S. Cardoso, materials 2016, 6, 221. P. P. Freitas, Phys. Rev. B 2003, 67, 214422. [61] W. Baaziz, B. P. Pichon, S. Fleutot, Y. Liu, C. Lefevre, [74] T. Jonsson, J. Mattsson, C. Djurberg, F. A. Khan, P. Nordblad, J. M. Greneche, M. Toumi, T. Mhiri, S. Begin-Colin, J. Phys. Chem. P. Svedlindh, Phys. Rev. Lett. 1995, 75, 4138. C 2014, 118, 3795. [75] D. Peddis, K. N. Trohidou, M. Vasilakaki, G. Margaris, M. Bellusci, [62] M. Ghoshani, E. H. Sánchez, S. S. Lee, G. Singh, N. Yaacoub, F. Varsano, M. Hudl, N. Yaacoub, D. Fiorani, P. Nordblad, D. Peddis, M. Mozaffari, C. Binns, J. A. De Toro, P. S. Normile, R. Mathieu, Sci. Rep. 2021, 11, 7743. Nanotechnology 2021, 32, 065704. [76] F. Bert, V. Dupuis, E. Vincent, J. Hammann, J. Bouchaud, Phys. Rev. [63] B. Martínez, X. Obradors, L. Balcells, A. Rouanet, C. Monty, Phys. Lett. 2004, 92, 167203. Rev. Lett. 1998, 80, 181. [77] G. Margaris, K. N. Trohidou, V. Iannotti, G. Ausanio, L. Lanotte, [64] K. Nadeem, H. Krenn, T. Traussing, I. Letofsky-Papst, J. Appl. Phys. D. Fiorani, Phys. Rev. B 2012, 86, 214425. 2011, 109, 013912. [78] M. Vasilakaki, I. Chikina, V. B. Shikin, N. Ntallis, D. Peddis, [65] R. H. Kodama, A. E. Berkowitz, E. J. McNiff, S. Foner, Phys. Rev. A. A. Varlamov, K. N. Trohidou, Appl. Mater. Today 2020, 19, 100587. Lett. 1996, 77, 394. [79] P. V. Hendriksen, S. Linderoth, P.-A. Lindgård, Phys. Rev. B 1993, 48, [66] S. Chakrabarti, S. K. Mandal, S. Chaudhuri, Nanotechnology 2005, 7259. 16, 506. [80] A. P. Safronov, I. V. Beketov, S. V. Komogortsev, G. V. Kurlyandskaya, [67] M. F. Hansen, S. Mørup, J. Magn. Magn. Mater. 1998, 184, L262. A. I. Medvedev, D. V. Leiman, A. Larrañaga, S. M. Bhagat, AIP Adv. [68] C. A. M. Mulder, A. J. van Duyneveldt, J. A. Mydosh, Phys. Rev. B 2013, 3, 052135. 1981, 23, 1384. [81] B. K. Chatterjee, C. K. Ghosh, K. K. Chattopadhyay, J. Appl. Phys. [69] P. Svedlindh, K. Gunnarsson, P. Nordblad, L. Lundgren, A. Ito, 2014, 116, 153904. H. Aruga, J. Magn. Magn. Mater. 1987, 71, 22. [82] R. Kretschmer, K. Binder, Z. Phys. B Condens. Matter 1979, 34, 375. [70] Y. El Mendili, J. F. Bardeau, F. Grasset, J. M. Greneche, O. Cador, [83] D. A. Dimitrov, G. M. Wysin, Phys. Rev. B 1996, 54, 9237. T. Guizouarn, N. Randrianantoandro, J. Appl. Phys. 2014, 116, [84] O. Chubykalo, U. Nowak, R. Smirnov-Rueda, M. A. Wongsam, 053905. R. W. Chantrell, J. M. Gonzalez, Phys. Rev. B 2003, 67, 064422. [71] O. Kaman, T. Kořínková, Z. Jirák, M. Maryško, M. Veverka, J. Appl. [85] R. Mathieu, P. Jönsson, D. N. H. Nam, P. Nordblad, Phys. Rev. B Phys. 2015, 117, 17C706. 2001, 63, 092401. Small 2022, 18, 2106762 2106762 (11 of 11) © 2022 The Authors. Small published by Wiley-VCH GmbH