Supraferromagnetic correlations in clusters of magnetic nanoflowers

Magnetic nanoflowers are densely packed aggregates of superferromagnetically coupled iron oxide nanocrystallites, which excel during magnetic hyperthermia experiments. Here, we investigate the nature of the moment coupling within a powder of such nanoflowers using spin-resolved small-angle neutron scattering. Within the powder the nanoparticles are agglomerated to clusters, and we can show that the moments of neighboring nanoflowers tend to align parallel to each other. Thus, the whole system resembles a hierarchical magnetic nanostructure consisting of three distinct levels, i.e. (i) the ferrimagnetic nanocrystallites as building blocks, (ii) the superferromagnetic nanoflowers, and (iii) the \textit{supra}ferromagnetic clusters of nanoflowers. We surmise that such a supraferromagnetic coupling explains the enhanced magnetic hyperthermia performance in case of interacting nanoflowers.


I. INTRODUCTION
The working principle of magnetic hyperthermia (MHT) is to administer a moderate quantity of magnetic nanoparticles within tumors and to heat them up by applying alternating magnetic fields with clinically acceptable parameters (i.e. normally high frequency but low amplitude 1,2 ) to kill selectively the cancer cells containing nanoparticles. In physiological environment nanoparticles usually agglomerate, which can significantly modify their magnetic properties compared to the dilute non-interacting case and which in turn may alter their heating behavior. [3][4][5] Depending on the characteristics of the individual particles and the field parameters, such a clustering can either improve or impair the MHT performance. [6][7][8][9][10] In fact it was observed for so-called nanoflowers, which are densely packed aggregates of iron oxide crystallites, that they excel during MHT experiments compared to the single-crystals. 11 This intriguing result motivated numerous studies regarding synthesis and characterization of such flower-shaped particles. [12][13][14][15][16][17] It can be shown that an exchange coupling between the cores leads to a superferromagnetic magnetization state 18 within the individual nanoflowers, 19 but with a significant internal spin disorder caused by the high defect density, e.g. due to the grain boundaries. 20 It is speculated that such a disordered state enables an increased excitation of the moments also at high-frequency/low-amplitude MHT experiments 21,22 , similar to other defect-rich particles. 23 When introduced into tumors, it is safe to assume that the nanoflowers will agglomerate to clusters, and thus interparticle interactions will be relevant. 24 In Bender et al. 25 we could show for homogeneous superparamagnetic nanoparticles a predominance for antiferromagnetic-like moment correlations within particle clusters via polarized small-angle neutron scattering (SANS). In this work we use the same approach to determine the nature of the moment coupling within a powder of iron oxide nanoflowers.

II. METHODS
The synomag-D nanoflowers were supplied by micromod Partikeltechnologie GmbH, Germany, which consist predominately of γ − Fe 2 O 3 , and are coated with dextran. A detailed study of these particles can be found in Bender et al. 21 which showed that they are around 39 nm in size and consist of crystallites with sizes ranging from 5 − 15 nm. Transmission electron microscopy (TEM) images were taken with a FEI Titan 80-300 TEM, for which the sample was prepared by putting a small droplet of the dilute dispersion of the particles on a carbon-coated copper grid.

2
The polarized SANS experiment of the nanoflower powder 26 was performed with the instrument D33 at the Institut Laue-Langevin (ILL), Grenoble (France) 27 using a mean wavelength of λ = 0.6 nm (∆λ /λ = 10%) and a detector distance of 10.3 m. We employed longitudinal neutronspin analysis (POLARIS) to collect the four spin-resolved intensities I ++ (q), I −− (q), I +− (q) and I −+ (q), where + denotes the polarization state spin-up. This approach enables the separation of nuclear and magnetic scattering contributions, and was applied in several studies to investigate magnetic nanoparticle ensembles. 25,28,29 A homogeneous magnetic field H was applied perpendicular to the neutron beam (H ⊥ k) with a field amplitude of µ 0 H = 2 mT, which was necessary to maintain the neutron beam polarization. Figure 1 shows a typical TEM image of the nanoflowers, in which they are agglomerated to small clusters of 3 and 9 particles, respectively. As can be seen, the nanoparticles are irregular in shape, and around 30-40 nm in size. and of the spin-flip (sf) cross section I +− (q), respectively. For the geometry H ⊥ k the nsf cross sections I ++ (q), I −− (q) can be written as:

III. RESULTS & DISCUSSION
where Θ is the angle between the scattering vector q = (0, q y , q z ) and the magnetic field H and directions, respectively, and the index * denotes the complex conjugate. One remarkable advantage of POLARIS, is that the purely nuclear scattering can be accessed without further assuming a saturated magnetic system (absence of misaligned moments). To be precise, the purely nuclear cross section I nuc (q) ∝ |Ñ| 2 can be determined, in case of isotropic structures, from the sector parallel to H of the nsf intensities.
The sf intensities, on the other hand, are of purely magnetic origin. We assume for our sample that chiral scattering terms can be neglected 30 , and thus we can write I sf (q) = I +− (q) = I −+ (q), with (for H ⊥ k): 31 The nsf intensity in Fig. 2(a) exhibits basically no anisotropy, indicating the dominance of the isotropic nuclear scattering, and thus verifying a randomly oriented microstructure. The purely nuclear 1D cross section I nuc (q) is determined from the sector parallel to magnetic field of I −− (q) and is plotted in Fig. 2(c). As can be seen, I nuc (q) exhibits a peak at around q = 0.17 nm −1 . For particle ensembles the total nuclear cross section is usually written as I nuc (q) ∝ P(q)S(q), where P(q) is the particle form factor and S(q) the structure factor arising from the particle arrangement. 32 For comparison, in Fig. 2(c) we also plot the purely nuclear scattering cross section of the same nanoflowers in dilute colloidal dispersion from Bender et al. 21 . In this case there is no significant structure formation and thus I nuc (q) ∝ P(q). The observed peak for I nuc (q) of the powder can be thus attributed to inter-particle correlations, and which implies an average center-to-center distance between the nanoflowers of 2π/0.17 nm −1 = 36 nm (nearest neighbor correlations) 33,34 .
This estimation is in good agreement with our previous analysis in Bender et al. 21 , where we determined an average particle size of around 39 nm. For q → 0 (i.e. the interparticle length scale) the forward scattering intensity increases, which indicates the presence of larger structures within the samples. 33 Thus we can conclude that no long-range order exists but that the nanoflowers are agglomerated to large clusters with average sizes outside the accessible q-range.
The sf intensity I sf (q) in Fig. 2(b) exhibits a well-pronounced anisotropy, and in Fig. 2(d) we plot I sf (q) integrated over the whole q-range as a function of Θ. The functional form is well described by the trigonometric terms from Eq. 2 without the linear term, which implies equal magnetization along the x-, yand z-direction and a zero net magnetization. This is expected because the sample was in the demagnetized state (i.e., the powder was not exposed to a magnetic field prior to the polarized SANS experiment) and 2 mT is not sufficient to significantly align the moments (as a reminder, the low magnetic field had to be applied to remain the polarization of the neutron beam). In Fig. 2(c) we plot I sf (q) determined perpendicular to the field direction, i.e. Both cross sections are in the high q-range (i.e. the intraparticle q-range) basically identical to each other and to the nuclear particle form factor P(q). This confirms the superferromagnetic magnetization state within the individual nanoflowers. In the interparticle q-range (q < 0.17 nm −1 ), however, both | M x | 2 and | M y | 2 start to deviate from P(q) and increase strongly with decreasing q. Additionally it can be observed in Fig. 2(c) that in the low q-range, | M x | 2 significantly deviates from | M y | 2 . This can be attributed to the anisotropy of the magnetic structure factor and indicates a disordered microstructure without a short range pseudo-crystalline order. 35 The deviation of both magnetic contributions | M x | 2 and | M y | 2 from P(q) is an evidence for interparticle moment correlations between neighboring nanoflowers. To reveal the nature of these interactions we extracted the underlying magnetic correlation functions P(r) from the scattering intensities by indirect Fourier transforms. 36 As can be seen in Fig. 2

IV. CONCLUSIONS
We performed a spin-resolved SANS study on a powder of iron oxide nanoflowers, which enables the separation of nuclear and magnetic scattering contributions. Analysis of the nuclear SANS data shows that the nanoflowers are agglomerated to large clusters. The magnetic scatter-6 ing contributions then indicate that the moments between neighboring particles are preferentially aligned parallel to each other. We interpret this as evidence for a supraferromagnetic magnetization state within the clusters of nanoflowers. Considering that the nanoflowers itself are aggregates of superferromagnetically coupled crystallites, the whole system can be thus regarded as a hierarchical magnetic nanostructure consisting of three distinct levels, i.e. (i) the ferrimagnetic nanocrystallites as building blocks, (ii) the superferromagnetic nanoflowers, and (iii) the supraferromagnetic clusters of nanoflowers. In physiological environments usually a clustering of immersed nanoparticles occurs and hence the tendency for such supraferromagnetic correlations could be beneficial for MHT. Indeed, we surmise that our observation explains the intriguing result in Sakellari et al. 13 where for colloidal dispersions of 50-nm nanoflowers an increased heating with increasing particle concentration was detected, which is in contrast to other nanoparticle ensembles for which usually increasing interactions result in a decrease of the MHT performance. 37,38