Vacancy-Driven Noncubic Local Structure and Magnetic Anisotropy Tailoring in ${\mathrm{Fe}}_x\mathrm{O}\text{−}{\mathrm{Fe}}_{3-\delta }{\mathrm{O}}_4$ Nanocrystals

In contrast to bulk materials, nanoscale crystal growth is critically influenced by size- and shape-dependent properties. However, it is challenging to decipher how stoichiometry, in the realm of mixed-valence elements, can act to control physical properties, especially when complex bonding is implicated by short- and long-range ordering of structural defects. Here, solution-grown iron-oxide nanocrystals (NCs) of the pilot wüstite system are found to convert into iron-deficient rock-salt and ferro-spinel subdomains but attain a surprising tetragonally distorted local structure. Cationic vacancies within chemically uniform NCs are portrayed as the parameter to tweak the underlying properties. These lattice imperfections are shown to produce local exchange-anisotropy fields that reinforce the nanoparticles’ magnetization and overcome the influence of finite-size effects. The concept of atomic-scale defect control in subcritical-size NCs aspires to become a pathway to tailor-made properties with improved performance for hyperthermia heating over defect-free NCs.

Popular Summary

In the battle to fight cancer, heat is emerging as a potential ally. While there are many ways to raise a tumor’s temperature, nanoparticles injected into the cancerous tissue and heated by magnetic fields offer an optimal solution. Large, defect-free particles are attractive because of their high capacity to dissipate heat and their size-optimized functionality in the cellular environment. However, the large particle sizes are alleged to cause patient discomfort, leading to a strong demand for smaller entities, which can compromise the magnetic properties necessary for practical utilization. Here, we combine nanochemistry, detailed characterization, and theoretical considerations to explore the relation of structural defects on the size and shape of iron-oxide nanocrystals and how these couple to magnetic properties relevant to nanobiotechnology.

Our approach shows that, depending on how small the nanoparticle is, the metal-cation oxidation state becomes a critical parameter that implicates complex bonding interactions. Vacant lattice sites created in this way are correlated with local distortions, corroborating our idea that the right kind of lattice imperfections adjust the particle’s anisotropy, which in turn facilitate exploitable thermal energy transfer in small-size magnetic nanocarriers.

The underlying concept presented here is that controlling atomic-scale defects in single-crystal nanoscale particles, typically hampered by finite size effects, can favor the use of anisotropic properties for the engineering of magnetic functionalities, such as heating agents and thermoresponsive cellular processes.

Figure 1

Illustrations of the Fe-site arrangement in archetype face-centered cubic crystal types of bulk iron oxides, namely, wüstite (${\mathrm{Fe}}_x\mathrm{O}$) (a), a defect-mediated rock-salt structure, with octahedrally coordinated (by oxygen–not shown for clarity) ferrous (${\mathrm{Fe}}^{2+}$) sites (Oh; represented by dark green spheres), and interstitial ferric (${\mathrm{Fe}}^{3+}$) tetrahedral sites (Td; depicted by large light green spheres) in the presence of four vacant ($V$) iron positions (light green). Such units compose $V_4-\mathrm{Td}$ defect clusters (b) (oxygen shown by red spheres), whose coalescence (c) [28] offers a likely pathway towards the nucleation of ${\mathrm{Fe}}_{3-\delta }{\mathrm{O}}_4$ (magnetite) (d). The latter represents the ferrospinel family, with Fe atoms in both types of coordination environment, and vacancy-bearing (220) lattice planes (highlighted). Both structural types accommodate trigonal pyramids of Fe atoms as a common building block, forming a pyrochlore-type sublattice in magnetite.

Figure 2

High-resolution TEM images in the [001] zone axes for spherical S8 (a), S15 (c) and cubic C12 (b), C18 (d) morphology nanocrystals. The corresponding diffraction patterns (e, f and h, g) after FFT analysis of each micrograph are shown beneath. Green and yellow circles mark a set of reflections that could be indexed on the basis of either wüstite (green) or/and magnetite (yellow) rock-salt and cubic spinel crystal unit cells (see text for details). Representative real-space images of the (220) atomic lattice planes (inverse FFT synthesis; filtered from specific plane orientations) for the samples S8 (i), C12 (j), S15 (k), and C18 (l), respectively. Lattice planes have been colored with red (possible presence of atomic plane) and green (possible absence of atomic plane) pseudochrome acquired after the inverse FFT process. Lattice phase contrast images obtained by the GPA method (see text) after recentering the diffraction around one of the (220) reflections for samples S8 (m), C12 (n), S15 (o), and C18 (p).

Figure 3

Experimental atomic xPDF data at 80 K for the single-phase S8, C12 and core@shell S15 nanoparticles plotted as a function of the radial distance $r$ up to 50 Å. The corresponding xPDF pattern for the bulk magnetite, measured under the same exact conditions, is provided as a reference material. The line over the data is the best fit based on the cubic spinel atomic configuration model (Fd-3m symmetry, model #1, and $R_w=11.6\%$, the quality of fit factor) and below the corresponding difference between observed and calculated xPDFs for bulk magnetite.

Figure 4

Representative xPDF fits ($T=80\mathrm{K}$) of the “low-$r$” region for (a) the bulk magnetite assuming the cubic spinel atomic configuration [Fd-3m, model #1; $a=8.3913(2)\AA$, $R_w=8.9\%$], (b) the single-phase S8 nanoparticle sample with the same cubic model ($R_w=18.1\%$), (c) the two-phase S15 nanoparticle sample with the cubic rock-salt and spinel ($R_w=13.6\%$) crystallographic models, and (d) the single-phase S8 nanoparticle sample in the tetragonal [${\mathrm{P}4}_3{2}_{1}2$, model #3; $a_{\mathrm{Sp}}=b_{\mathrm{Sp}}=8.4053(1)\AA$, $c_{\mathrm{Sp}}=8.1950(1)\AA$, $R_w=7.5\%$] crystallographic configuration (see text for details). The blue circles and red solid lines correspond to the observed and calculated atomic PDFs, respectively. The green solid lines underneath are the difference curves between observed and calculated PDFs. The quality of fit factor, $R_w$ (%), is given for each case. Vertical dashed lines mark the positions of typical $\mathrm{Fe}─\mathrm{O}$ and $\mathrm{Fe}─\mathrm{Fe}$ bond distances; Td and Oh represent tetrahedral and octahedral cation sites, respectively.

Figure 5

(a) Adequately normalized, observed $G(r)$ patterns ($T=80\mathrm{K}$) of the low-$r$ region for all nanoparticle samples (single-phase, S8 and C12, and two-phase, S15) compared against the bulk magnetite and (b) the simulated xPDF patterns on the basis of the symmetry-lowering (tetragonal) atomic configuration. As a proof of concept, the optimally chosen set of models assumes a substoichiometric Oh Fe-site occupancy ($\eta$; kept constant at 75%, an average occupation derived from refinements of the $G(r)$ data across the samples), while the Td Fe-site occupation level is varied in a stepwise manner ($60<\eta <100\%$). Vertical dashed lines mark the modification of the distribution of the ${\mathrm{Fe}}_{\mathrm{Oh}}-{\mathrm{Fe}}_{\mathrm{Oh}}$ ($r\sim 3.0\AA$) and ${\mathrm{Fe}}_{\mathrm{Oh}}-{\mathrm{Fe}}_{\mathrm{Td}}$ ($r\sim 3.5\AA$) separations from bulk to nanoscale samples.

Figure 6

The temperature evolution of the zero-field cooled (ZFC; solid lines) and field-cooled (FC; dotted lines) susceptibility curves for the single-phase S8 (a), C12 (b), and core@shell S15 (c) nanoparticles under a magnetic field of 50 Oe. The dashed vertical lines indicate the Verwey ($T_V$; orange) and Néel ($T_N$; green) related transition temperatures met in bulk, stoichiometric ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and ${\mathrm{Fe}}_x\mathrm{O}$, respectively. The low-field part of the normalized hysteresis loops ($M/M_S$) at 5 K for the single-phase S8 (d), C12 (e), and the core@shell S15 (f) nanoparticles taken under zero- and field- cooled ($H_{\text{cool}}=50\mathrm{k}\mathrm{O}\mathrm{e}$) protocols. The panels beneath the loops present the differential change ($dM/dH$) of the normalized, isothermal magnetization when it is switched from positive to negative saturation.

Figure 7

The experimentally determined (a) exchange bias ($H_{\mathrm{EB}}$; open symbols) and coercive field ($H_C$; half-filled symbols), as well as (b) low-field demagnetization ($\mathrm{\Delta }M/M_S$; filled symbols, left y axis) and the ratio $M_r/M_S$ ($M_r$, remanence: open symbols, right y axis) obtained at varying cooling-field strengths ($H_{\text{cool}}$). Symbol guide: circular, core-shell spherical nanoparticles (S15), triangular (S8), and diamond (C12) for single-phase spherical and cubic morphology nanoparticles. The lines are a guide to the eye.

Figure 8

Monte Carlo calculations ($H_{\text{cool}}=5J_{\mathrm{FM}}/g{\mu }_B$) of the effect of pinning bonds (vacancy-driven) on the low-field magnetic-moment switching ($\mathrm{\Delta }M/M_S$; filled symbols, left $y$ axis) and the exchange bias ($H_{\mathrm{EB}}$; open symbols, right $y$ axis) of self-passivated ${\mathrm{Fe}}_x\mathrm{O}-{\mathrm{Fe}}_3{\mathrm{O}}_4$ nanocrystals with different morphologies. Symbol guide: circular, core-shell spherical nanoparticles (S15), triangular (S8), and diamond (C12) for single-phase spherical and cubic-shape nanoparticles.

Figure 9

MC simulation of the $M-H$ loops made after field-cooling ($H_{\text{cool}}=5J_{\mathrm{FM}}/g{\mu }_B$) and by assuming an upper maximum fraction of pinning bonds, as this was identified by the xPDF refinements. Snapshots of the spin ensemble during $M-H$ loop calculation for a small ferrimagnetic spherical nanoparticle of $R=5$ lattice constants: (a)—(c) a fully oxidized, defected nanocrystal (S8), and (d)—(f) a defect-free case, assuming a core-surface type of MC model. Spin configurations are shown in the $zy$ plane ($x=-1$) for positive-field ($H=+8J_{\mathrm{FM}}/g{\mu }_B$) magnetization saturation and after field reversal ($H=-0.2J_{\mathrm{FM}}/g{\mu }_B$, $H=-2.0J_{\mathrm{FM}}/g{\mu }_B$) towards negative saturation. The arrow color coding is as follows: core (red), surface (blue), and defects (black) magnetic moments. (g) Specific absorption rate (SAR) of small defected (S8) versus defect-free nanoparticles on the basis of susceptibility losses (ac field amplitude, $H_0$ and $f=500\mathrm{kHz}$), calculated according to the linear response theory of a modified Néel-Brown relaxation Monte Carlo model.