Temperature dependence of magnetic first-order-reversal-curves for hollow Fe₃O₄ submicron particles

Recently, Fe₃O₄ nanoparticles have attracted much attention for biomedical applications, because of their high saturation magnetization and soft magnetic properties. Especially, Fe₃O₄ nanoparticles with a hollow structure have the capability of enclosing drugs inside the shell, enabling for possible application to magnetically targeted drug delivery system. For quantitative understanding of the system, detailed study on magnetic response against applied field is crucially important. So far, hollow nanoparticles with size less than ∼100 nm have been extensively studied and some characteristic behaviors such as spin-glass-like spin freezing and exchange bias effect, originating from large surface effects, have been reported.^1,2 However, reports for hollow Fe₃O₄ submicron particles are rare and their magnetization reversal process is not yet understood in detail.

In this paper, we have synthesized three types of hollow Fe₃O₄ submicron sphere particles with sizes ranging from 400 to 700 nm and have measured magnetic first-order-reversal-curves (FORCs) in the wide temperature range of 10 – 300 K. A FORC measurement is one of analysis methods using minor hysteresis loops and has been originally developed in the field of rock magnetism.^3,4 The resultant FORC diagram gives information about interparticle interaction and coercive field distribution, while the conventional major loop gives information on magnetic properties averaged over whole sample such as saturation magnetization and coercive field. In the present investigation, detailed temperature dependence of FORC diagrams and their correlation with particle size have been studied and discussed.

Three types of Fe₃O₄ submicron particles, which have different outer/inner diameter, were synthesized by solvothermal process.⁵ A typical synthesis method is as follows. 0.1 mol FeCl₃⋅6H₂O was dissolved in 30 mL of ethylene glycol until the solution becomes clear. 0.75-1.5 mol CH₃COONH₄ is mixed into the clear solution and the solution was strongly stirred for 30 min. This mixture was then transferred to a Teflon-lined autoclave cell and then heated at 200 °C or 230 °C for 12 hours in a muffle furnace, followed by cooling at room temperature. The black particles were obtained by washing with distilled water and ethanol for several times, filtered, and dried for 1 day at R.T.

Microstructures of particles were evaluated with transmission electron microscopy (TEM, JEM-2100) and field emission scanning electron microscope (FE-SEM, JSM-7001F). Figure 1 shows a typical example of TEM images for submicron particles with mean outer diameter of 704 nm and their size distribution; there is a bright part for each particle, showing a hollow structure. For all three samples, a hollow structure was confirmed. X-ray diffraction measurements (Rigaku Ultima IV, CuKα, 40kV/40mA) confirmed that all the samples are single phase of Fe₃O₄ and crystallographic domain length determined using Halder-Wagner method is about a few tens nanometer. Morphological parameters obtained are summarized in Table I.

FORC measurements were performed under a maximum magnetic field of 3 kOe in a wide temperature range from 10 to 300 K using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design MPMS-5L). Nanoparticles were well dispersed in epoxy resin, which ensures negligible interparticle interaction. The measurement method of FORCs is as follows; magnetic field H is reduced from saturation magnetic field of H_max = 3 kOe down to a certain reversal magnetic field H_r, and then magnetization was measured while increasing H up to H_max with a field step of ΔH = 100 Oe. This process was repeated by changing H_r from 3 to -3 kOe with a step of ΔH_r = -100 Oe. FORC distribution was calculated with the mixed second derivative:

Calculated FORC distribution was plotted with coercive field (H_c) axis and interaction field (H_u) axis by changing coordinates using equations of H_c=(H-H_r)/2 and H_u=(H+H_r)/2. FORC distribution reflects irreversible switching process and the peak position corresponds to a field at which magnetization process is highly irreversible.

Figures 2(a) and 2(b) show FORCs at T = 10 K and 300 K for the H704 sample, respectively. At T=10 K FORCs form constricted shape, which smears at T = 300 K associated with a narrowing of the loop width. The FORC diagram before coordinate transformation, ρ(H, H_r) for the H704 sample is shown in Fig. 2(c). One can see that FORC distribution exhibits a butterfly-like feature, associated with two strong peaks (denoted by “1” and “2” in Fig. 2(c)) and a weak narrow peak (denoted by “3”). This feature is a manifestation of a spin vortex structure, where spins align circularly around the particle surface so as to minimize magnetostatic energy, and each peak in Fig. 2(c) corresponds to nucleation or annihilation of spin vortex;^6,7 peaks denoted by “1” and “3” correspond to a transition from vortex state to positive saturation state and peak denoted by “2” corresponds to that from negative saturation state to vortex state. Such a vortex state has been observed for sub-100 nm Fe dots^6,7 as well as submicron solid particles,^8,9 however, to our best knowledge, it has not been observed for particles with a hollow structure.

The temperature dependence of FORC diagrams, ρ(H_c, H_u) for the H704 sample is shown in Fig. 3 (the peak numbers in Fig. 3 at T=10 K correspond to those of Fig. 2(c)). One can see that there are three peaks at T = 10 K; peaks “1” and “2” are located at H_u ∼ ± 600 Oe and H_c ∼ 500 Oe, associated with a strong broadening along the H_c direction, and peak “3” is located close to the H_c axis. On the other hand, at higher temperatures above T ∼ 130 K, all the three peaks seem to merge, associated with a shift of their peak position toward lower H_c. Similar behaviors were also observed for samples with different outer/inner diameters.

To investigate the temperature dependence in more detail, interaction field distribution, ρ(H_u), was calculated by integrating FORC distribution along the H_c direction, as below:

Figure 4(a) shows ρ(H_u) as a function of H_u at several temperatures for the H704 sample. One can see a large difference in the temperature dependence below and above T ∼ 130 K, which is Verwey transition temperature, T_v. The pronounced two peaks were observed at H_u ∼ ± 600 Oe below T ∼ 90 K, whose intensity steeply decreases with approaching 90 K. At the same time, a new peak gradually develops around H_u ∼ 0 Oe and there exist three peaks above T ∼ 130K. This peak at around H_u ∼ 0 Oe corresponds to the third peak denoted in Fig. 2(c) and Fig. 3 (T = 10 K). The temperature dependence of the position and area of the three peaks is summarized in Figs. 4(b) and 4(c). It can be seen that the area of ρ(H_u) peak at H_u ∼ ± 600 Oe rapidly decreases with approaching T_v, associated with a shift of the peak position toward lower H_u. Note that peaks “1” and “2” shift towards the origin almost symmetrically and the absolute value of the peak position is almost the same in the wide temperature range, indicating that there exists no exchange bias between Fe₃O₄ submicron particles.

It should be emphasized that the observed decrease of the peak area indicates that a vortex structure becomes unstable as approaching T_v, which is in sharp contrast to previous observations for Fe nanodots where a vortex structure becomes stable at higher temperatures due to increasing in thermal energy.^6,7 The possible origin in the different temperature dependence of a vortex stability for hollow Fe₃O₄ submicron particles may be primarily due to a change of direction and magnitude of magnetic anisotropy at T_v in Fe₃O₄, associated with the structural transition; monoclinic and cubic structures below and above T_v, respectively. Above T_v, the magnetic anisotropy is weak and the easy axis is <111>, whereas below T_v, the easy axis is along the monoclinic c axis and magnetic anisotropy is enhanced at lower temperatures in particular.¹⁰ Therefore, spins are likely to be confined along the easy axis at low temperatures, leading to a stable vortex structure at low temperatures. Also, an increase in thermal energy with increasing temperature can facilitate spin orientation, which affects the stability of a vortex structure.

Furthermore, we also calculated the coercive field distribution, ρ(H_c), by integrating the FORC distribution along the H_u direction. Figure 4(d) shows ρ(H_c) as a function of H_c, for samples with different outer diameter (H417, H538, H704). With increasing outer diameter, the peak position shifts toward higher H_c, indicating that spin reversal under magnetic fields becomes difficult with increasing outer diameter. A change of surface effects, associated with various morphological parameters including outer, inner diameter, mean domain length may affect the FORC properties. Further investigations on morphological effects on FORC distribution with various methods such as TEM and electron-back scatter diffraction (EBSD) are in progress and the results will appear in future papers.

We have measured FORCs for hollow Fe₃O₄ submicron particles with different morphology. At low temperatures below T_v, FORC distribution exhibits a butterfly-like feature with two strong separate peaks, indicating that a vortex structure is formed even at hollow Fe₃O₄ submicron particles. The temperature dependence of the FORC distribution suggests the destabilization of a vortex structure at higher temperatures, associated with a change of magnetic anisotropy. Moreover, the peak in coercive field distribution was found to shift toward higher magnetic fields with increasing outer diameter. This reflects a magnetic hardening accompanying the increase in outer diameter, being indicative of the possible application of the FORC method to evaluation of morphology of hollow particles.