Observing thermomagnetic stability of nonideal magnetite particles: Good paleomagnetic recorders?

The thermomagnetic behavior of remanence‐induced magnetite (Fe3O4) particles in the pseudo‐single‐domain (PSD) size range (~0.1–10 µm), which dominate the magnetic signature of many rock lithologies, is investigated using off‐axis electron holography. Construction of magnetic induction maps allowed for the visualization of the vortex domain state in an individual Fe3O4 grain (~200 nm in diameter) as a function of temperature. Acquisition of a series of electron holograms at 100°C intervals during in situ heating up to 700°C demonstrates the vortex state of the Fe3O4 grain, in this instance, remains thermally stable close to its unblocking temperature and exhibits a similar in‐plane remanent state upon cooling; i.e., the particle is effectively behaving like a uniaxial single‐domain particle to temperatures near TC. Such particles are thought to be robust magnetic recorders. It is suggested that evidence for PSD behavior should therefore not preclude paleomagnetic investigation.


Introduction
Magnetic minerals in rocks record the direction and intensity of the ambient magnetic field during formation, providing, for example, information on the geomagnetic field variation and past tectonic plate motions. The primary form of natural remanent magnetization in igneous rocks is thermoremanent magnetization (TRM) and is acquired by the constituent magnetic minerals on cooling from the Curie temperature (T C (~580°C for magnetite)). Néel's [1949Néel's [ , 1955 TRM theories have been shown to describe the behavior of the smallest magnetically uniform grains (single domain (SD)); however, most rocks contain larger magnetic grains that display nonuniform magnetic structures (multidomain (MD)). The magnetic signature in igneous rocks is usually dominated by small MD grains (~0.1-10 μm), often termed pseudo-single-domain (PSD), as their bulk magnetic characteristics are similar, but not identical, to SD particles. However, there is currently no physical model for PSD TRM acquisition. To construct such model, a numerical algorithm that includes computationally intensive thermal fluctuations is needed. Verification of the numerical predictions through direct observations of the magnetization in submicron grains (<500 nm) at temperature is therefore also required. Both of these aspects are challenging and have not yet been unambiguously resolved, although advances have been made numerically [Thomson et al., 1994;Winklhofer et al., 1997;Muxworthy et al., 2003] and experimentally [Metcalf and Fuller, 1988;de Groot, 2013].
The transmission electron microscopy (TEM) technique of off-axis electron holography permits the nanometer-scale imaging of magnetic induction within and around materials as a function of applied field and temperature [Dunin-Borkowski et al., 1998;Kasama et al., 2010Kasama et al., , 2013. This is the only technique that can produce high-resolution images of magnetic domain states in nanometric grains. It has been applied in mineral magnetism for more than a decade [Harrison et al., 2002;Bryson et al., 2014;Almeida et al., 2014] but has not previously been used to examine thermal behavior above room temperature.
To help advance our understanding, in this paper, the first use of off-axis electron holography to examine local changes in remanent magnetization in a PSD magnetite grain during in situ heating is reported. We observe the evolution of the remanent domain structure of an individual synthetic magnetite grain ALMEIDA ET AL. induced with a room temperature saturation isothermal remanence (SIRM), as it is heated to~700°C and subsequently cooled to room temperature. The observations are complemented by bulk magnetic measurements at room temperature and above.

Experiment
Fe 3 O 4 particles with a diameter ranging from~150 nm to~250 nm (hydrothermally synthesized by Nanostructured and Amorphous Materials, USA) were cleaned with acetone and centrifuged for 6 min at 6000 rpm. The Fe 3 O 4 particles were deposited onto single crystal silicon substrates for crystallographic identification using X-ray diffractometry (PANalytical X'Pert PRO Diffractometer). For the purpose of in situ heating TEM investigations, the particles were dispersed in distilled water using an ultrasonic bath before deposition onto Aduro E-chip TEM sample holder (Protochips, USA). The sample was preheated in situ in the TEM to 700°C for the purpose of evaporating the remaining water and alleviate possible strain induced during particle synthesis. Off-axis electron holograms were acquired at 300 kV in Lorentz mode in a Titan 80-300 TEM with a charge-coupled device camera and an electron biprism operated typically at 160 V (Center for Electron Nanoscopy, Technical University of Denmark). The direction of magnetization in the particle was initially reversed at room temperature in situ in the TEM by tilting the sample by ±30°and turning on the conventional microscope objective lens to apply a magnetic field of 2 T to the sample, parallel to the direction of the electron beam. The objective lens was then turned off and the sample tilted back to 0°for hologram acquisition in field-free conditions (residue field is <0.2 mT) with the particles induced with a room temperature SIRM. The different holograms were recorded with the particle magnetized in opposite directions, and the mean inner potential was separated from the magnetic potential, as described by Dunin-Borkowski et al. [1998]. Electron holograms were then acquired in field-free conditions during in situ heating at 100°C intervals from 100°C up to 700°C at 1°C/s using a Protochips heating holder (as displayed on the Protochips temperature control) and again upon cooling, where the acquisition time was 4 s. The mean inner potential was subtracted from the unwrapped total phase shift, acquired at each temperature interval, to allow the construction of magnetic induction maps representative of the magnetic remanence. In this paper, the temperatures are all nominal as the absolute temperature of the particle itself is not accurately known. To complement the experimental work, a micromagnetic model containing unstructured meshes was used to simulate a magnetic induction map. The meshed grain geometry was based on two-dimensional information acquired from the bright-field TEM image ( Figure 2a). Micromagnetic solutions of the domain structure were calculated for the particle from an initial saturated state parallel to the saturation field of 2 T, as applied during the acquisition of the holography images. Equilibrium magnetic structure solutions were then used to calculate the magnetic vector potential A. Once A was known, the phase shift was computed by integrating the component of A perpendicular to the plane of the TEM image of Figure 2a (A z ) according to equation where c represents a phase amplification factor. The contours of H ij were then colored according to the planar magnetic flux density B. For the purpose of bulk magnetic measurements, the Fe 3 O 4 powder was dispersed in a cement/curing agent mixture and, once dried, examined at the paleomagnetic laboratory at Imperial College London. The focus of this experimental work was observational, and hence, the interparticle spacing was not controlled tightly during sample preparation. Room temperature, first-order reversal curve (FORC), and hightemperature thermomagnetic measurements were performed using a Princeton Measurements Vibrating Sample Magnetometer, fitted with a furnace, with heating performed in flowing He. To replicate the TEM experiments, the thermomagnetic experiment was initially performed to alleviate possible strain induced during synthesis of the particles, and the data were acquired from the second measurement.  Figure 1c displayed PSD/SD-type behavior with a distinct peak [Muxworthy and Dunlop, 2002]. High-temperature thermomagnetic analysis (Figure 1d) indicated that the Fe 3 O 4 NPs were thermally stable. The T C was determined from the heating curve using the second-derivative method [Tauxe, 1998] and calculated as 585 ± 5°C, which is in good agreement with stoichiometric magnetite.

Results
The bright-field TEM image of Figure 2a shows a smooth-surfaced Fe 3 O 4 grain (~200 nm in diameter), as confirmed by SAED (Figure 2a Figures 2i-2p show the effect of cooling from 700°C to room temperature; narrowing of the magnetic contours during cooling demonstrates the recovery of the remanent magnetic field, similar to the initial remanence exhibited prior to heating. The existence of the remanent magnetization at 700°C (Figure 2i) is likely a discrepancy; i.e., the absolute T C is <600°C and is considered in the Discussion section.

10.1002/2014GL061432
By way of supporting information, the micromagnetic model of Figure 3a provides a 3-D representation of the magnetic domain structure in the Fe 3 O 4 grain, presented in Figure 2. Figure 3b shows the model to exhibit central magnetic moments of vortex flowing in a counterclockwise direction. The associated holography simulation of Figure 3c, derived from the model in Figure 3a, presents evenly spaced magnetic contours, spanning from the surface to the center of the grain, flowing in a counterclockwise direction (denoted by arrows), in a similar manner to the experimentally acquired magnetic induction map (Figure 2b). Figures 3d-3f present data acquired from the contribution to the total phase shift after the mean inner potential, acquired at room temperature, is subtracted and used to construct magnetic induction maps ( Figure 2). The room temperature phase image is shown in Figure 3d, and selected line profiles taken along the center of the Fe 3 O 4 grain are plotted in Figure 3e. The reduction in the amplitude of the phase shift with heating from room temperature is indicative of a loss in magnetic remanence, which is then seen to recover upon cooling. Figure 3f shows the variation of amplitude of the phase shift with temperature across the entire temperature range during both heating and cooling. There is a steady decrease in the amplitude of the phase shift from room temperature to 700°C and a subsequent recovery on cooling, which exhibits almost a near linear trend with nominal temperature.

Discussion
The FORC data are consistent with the magnetic behavior of PSD Fe 3 O 4 , complemented by a thermomagnetic curve displaying a T C characteristic of stoichiometric magnetite. The magnetic induction map of the  (Figure 2b) acquired at room temperature clearly shows that the SIRM is carried by a vortex domain state structure. The associated simulated magnetic induction map is near identical to the experimentally acquired induction map, thereby validating the 3-D model of a magnetic vortex, and hence, the Fe 3 O 4 grain exhibits an ideal PSD state for investigating the thermal stability of nonideal recorders. The overall structure is seen to be essentially stable to thermal effects, with widening of the phase contours as a consequence of increasing temperature to 700°C, suggestive of a reduction in total remanent magnetization, which is further emphasized by the decrease in phase amplitude with temperature ( Figure 3f ). It is recognized that 700°C is significantly higher than the T C of Fe 3 O 4 , and hence, no remanent magnetization would be expected. Thermomagnetic analysis (Figure 1d) indicates that this discrepancy lies with the acquired TEM data and is considered to have two contributing factors: First, slight electrostatic charging of both the SiN supporting membrane and the Fe 3 O 4 grain with temperature is likely to result in a net contribution after the room temperature mean inner potential is subtracted from the total phase shift [Beleggia and Pozzi, 2010]. This effect is emphasized by the development of a stray field, seen to be most prominent from 300 to 700°C on heating, in addition to 600°C and 500°C upon cooling. Second, the mean inner potential of the Fe 3 O 4 grain itself may change slightly with increasing temperature due to an associated variation in electrical conductivity [Kamilov et al., 1975], alongside a possible contribution from thermal expansion [Manahan, 1990]. Acquiring the mean inner potential contribution to total phase shift at each temperature interval, in a separate experiment, and then subtracting it from the phase shift, acquired at remanence, could remove this effect in the future. Nevertheless, the relatively linear decrease in the amplitude of the phase shift with increasing nominal temperature up to 700°C is consistent with the thermal behavior of Fe 3 O 4 particles. Subsequent narrowing of the phase contours and associated increase of amplitude upon cooling are representatives of a recovery in magnetic remanence strength.
The direction of the vortex core is unknown, as it lies normal to the plane of this~200 nm Fe 3 O 4 grain; i.e., the core moment aligns either in or out of plane. However, the key finding of this study is that the vortex structure is essentially stable during heating to temperatures close to the T C . As the core moment only aligns in one of the two orientations, this effectively means that the particle is behaving like a uniaxial single-domain particle to temperatures near T C . Such particles found the basis of most TRM models and are thought to be robust magnetic recorders.
It is recognized that there is a spurious addition to the phase shift at elevated temperatures, and hence, the phase shifts do not exclusively represent the magnetic contribution, and work must be done to reduce this effect in the future. Nevertheless, this is the first experiment showing the magnetic remanence of individual nanoscale PSD grains, which dominate the magnetic signal in rocks, as a function of temperature.
While rocks containing such domain structures would not usually be thought of as being ideal paleomagnetic recorders (although their FORC diagram might indicate otherwise), the image sequence ( Figure 2) suggests that they will accurately record both in-plane paleodirection and paleointensity information, and are stable under heating to relatively high temperatures. This finding directly and visually supports recent thermomagnetic work, including Thellier-type paleointensity study, on synthetic magnetite samples produced by electron beam lithography . Muxworthy et al. [2014] found that arrays of near-identical PSD particles with controlled intergrain spacing were reliable recorders of a weak-field thermoremanence, from which accurate paleointensities could be recovered using a Thellier-type protocol [e.g., Tauxe and Yamazaki, 2007]. The effect of multiple repeat heatings as used in typical paleointensity investigations has yet to be investigated using electron holography.

Conclusions
Construction of the magnetic induction maps acquired from a vortex magnetic structure in an~200 nm grain of PSD magnetite as a function of temperature indicates that its magnetic remanence is stable to heating to near its T C . These direct observations visually demonstrate, for the first time, the SD-like stability of small MD, magnetite grains. These findings imply that structures that initially appear to be a nonideal magnetic recorder are in fact likely to reliably record both paleodirectional and paleointensity information.
As a large percentage of rocks appear to be magnetically dominated by PSD grains that contain vortexlike magnetic states (Figure 2), it is suggested that evidence for PSD behavior should not preclude paleomagnetic investigation.