Magnetic Properties of Strontium Hexaferrite Nanostructures Measured with Magnetic Force Microscopy

Magnetic property is one of the important properties of nanomaterials. Direct investigation of the magnetic property on the nanoscale is however challenging. Herein we present a quantitative measurement of the magnetic properties including the magnitude and the orientation of the magnetic moment of strontium hexaferrite (SrFe12O19) nanostructures using magnetic force microscopy (MFM) with nanoscale spatial resolution. The measured magnetic moments of the as-synthesized individual SrFe12O19 nanoplatelets are on the order of ~10−16 emu. The MFM measurements further confirm that the magnetic moment of SrFe12O19 nanoplatelets increases with increasing thickness of the nanoplatelet. In addition, the magnetization directions of nanoplatelets can be identified by the contrast of MFM frequency shift. Moreover, MFM frequency imaging clearly reveals the tiny magnetic structures of a compacted SrFe12O19 pellet. This work demonstrates the mesoscopic investigation of the intrinsic magnetic properties of materials has a potential in development of new magnetic nanomaterials in electrical and medical applications.

Nanoscale magnetic materials are attracting tremendous research interests due to their unusual properties compared to the bulk materials and their applications in many areas of science and technology [1][2][3][4][5][6][7] . M-type strontium hexaferrite (SrFe 12 O 19 ) is an important hard magnetic material with a ferrimagnetic structure. Owing to its unique magnetic properties, it is very suitable for the use in data storage and electronic devices 8 . Bulk SrFe 12 O 19 is traditionally used in the fabrication of permanent magnets and in the design of microwave devices operating at high frequencies because of its large axial magnetic anisotropy, high intrinsic coercivity and high permeability. In recent years, due to the new fundamental and emerging applications in electronics 9 , the research interest in SrFe 12 O 19 has been renewed. SrFe 12 O 19 nanomaterials can be used in the design of electronic components for automobile and wireless communications 8,10 . However, all of these innovative applications based on SrFe 12 O 19 need nanoscale understanding and controlling of the magnetic properties such as the magnitude and orientation of the magnetic moment. It is also well-known that the magnetic properties of SrFe 12 O 19 are strongly dependent on its nanostructure size, shape, orientation, and domain configurations 9,11,12 . Hence, direct investigation and characterization of SrFe 12 O 19 nanostructures with high magnetic sensitivity and nanoscale spatial resolution is highly desirable to understand the origin of the magnetism of SrFe 12 O 19 nanostructures.
Although sensitive techniques such as superconducting quantum interface device (SQUID) and vibrational sample magnetometer (VSM) have been developed for macroscopic measurements of the magnetic properties of magnetic materials, little has been done on the mesoscopic characterization of the magnetic properties of magnetic nanostructures. Thus so far, the direct measurement of magnetic nanostructures is only possible by using microscopy techniques. Magnetic force microscopy (MFM) is such a microscopy tool to detect and localize nanoscale magnetic domains utilizing the magnetic interactions between the magnetized probe and the sample 13 . Recent studies have demonstrated the abilities of the MFM to characterize magnetic nanoparticles with high Scientific RepoRts | 6:25985 | DOI: 10.1038/srep25985 magnetic sensitivity and spatial resolution similar to atomic force microscopy (AFM) [14][15][16][17][18][19][20]

Results
Theory of MFM. MFM is a specialized operation mode of AFM that utilizes the relatively weak but longrange magnetic interactions between the magnetized probe and the sample while minimizing the influence of sample topography 13 . MFM measurements are taken in a dual-pass tapping/lift mode, meaning each line in the MFM image is the compilation of a tapping-mode scan and a lift-mode scan. In the first pass, the topography information was acquired in tapping mode. The tip is then lifted and the topography profile record from the tapping-mode scan is used to maintain a constant height (so-called lift height) between the tip and local surface topography. In this lifted position, the influence of magnetic force F(z) can be measured by directly tracking the shifts in resonant frequency of the tip, is given by where Δ υ is the frequency shift; υ 0 and k are the resonant frequency and the spring constant of the MFM cantilever, respectively. ∂F/∂z is the force gradient.
In general, the magnetic force acting on the tip can be calculated through integrating the tip-sample force density over the tip volume or rather its magnetized part. In order to make the calculations feasible, simplified models for the tip magnetic structure are often used. The simplest way to model a tip is to assume the effective dipole moment of the tip is located in the center of a sphere approximating the tip apex. Thus the interaction between a spherical magnetic particle and a magnetic tip can be considered in a dipole-dipole model, given as 17,21 : where μ 0 is the vacuum permeability; m s and m t are the magnetic moments of the magnetic sample and the MFM tip, respectively; h is the lift height; c is a constant related to distance of the magnetic dipoles within the magnetic particle and MFM tip. By combining Equations (1) and (2), we find Crystalline Structure and Macroscopic Magnetic Property of Strontium Hexaferrite. Figure 1a presents the schematic crystal structure of the M-type SrFe 12 O 19 . The hexagonal structure can be considered to be made up of alternating spinel (S = Fe 6 O 8 2+ ) and hexagonal (R = SrFe 6 O 11 2− ) layers. The O 2− ions are closed packed with the Sr 2+ ion in the hexagonal layer and the Fe 3+ ions are distributed in the octahedral (12 k, 2a and 4f 2 ), trigonal bipyramidal (2b) and tetrahedral (4f 1 ) sites. The magnetic moments of the Fe 3+ ions are coupled to each other by super-exchange interactions through the O 2− ions. The Sr 2+ ion is responsible for the large magnetic uniaxial anisotropy as it causes a perturbation of the crystal lattice 9 . In this study, the SrFe 12 O 19 samples were synthesized by supercritical flow synthesis 22 . Figure 1b shows a typical bright-field transmission electron microscopy (TEM) image of the as-synthesized SrFe 12 O 19 samples. Hexagonal nanoplatelets with a plate diameter of < 100 nm can be clearly observed. It can also be observed that some of the nanoplatelets are superimposed over each other forming stacked nanoplatelets. This is most likely owing to the magnetic interactions between nanoplatelets as the crystallographic c-axis is the magnetic easy axis. The room temperature powder X-ray diffraction (XRD) pattern and Rietveld refinement of the as-synthesized SrFe 12 O 19 samples is shown in Fig. 1c. The results obtained from refinements show the SrFe 12 O 19 to be the main phase present (89 weight%), refined as the magnetoplumbite structure with space group of P6 3 /mmc. The refined lattice parameter values (a = b = 5.8887(2) Å and c = 23.101(4) Å) are in good agreement with the previous reports for SrFe 12 O 19 23,24 . The refined crystallite sizes (of 30.2(4) nm along a-and b-axes and 2.66(3) nm along c axis) extracted from the diffraction data are comparable in magnitude to the nanoplatelet sizes observed in TEM. A secondary phase is also present in the sample. It constitutes 11 weight% and it was identified and refined as the defect-free FeOOH structure reported by Jensen et al. 25 with space group of P-31c. The FeOOH phase is also found forming hexagonal nanoplatelets, of similar refined sizes (18(2) nm along a-and b-axes and 6.4(6) nm along c axis) to those of SrFe 12 O 19 . In order to measure the macroscopic magnetic properties of the as-synthesized SrFe 12 O 19 samples, magnetization-field (M-H) hysteresis loop was performed by VSM at 300 K as shown in Fig. 1d. It is clear that the sample is a hard magnetic material at room temperature with the saturation magnetization (M s ) of about 30 emu/g at H = 20 kOe. The remanence magnetization (M r ) and the intrinsic coercivity (H c ) extracted from the hysteresis loop are of 11 emu/g and 1 kOe, respectively.  O 19 nanoplatelets. In this study, frequency modulation is used to track the shifts in resonant frequency due to its high sensitivity to the magnetic force gradient ( Figure S1). Figure 2 presents the results of MFM measurements of the magnetic properties of a SrFe 12 O 19 nanoplatelet. The AFM height image (Fig. 2a) shows the nanoplatelet with a diameter of about 100 nm and a thickness of about 7.1 nm, as can be seen more clearly from the height profile through the center of the nanoplatelet (Fig. 2b). Magnetic force gradient images (shown as frequency images) of the same nanoplatelet recorded at different lift heights are shown in Fig. 2c (see also Figure S2). As can be seen, the frequency contrast of the nanoplatelet decreases as the lift height increases. This is clearly evident from the frequency shift profiles (Fig. 2d) taken along the dashed lines marked in the frequency images in Fig. 2c. These results are in agreement with previous reports 15,16,18,26 . Figure 2e shows the frequency shifts as a function of the lift height. The dashed red line represents the fitted curve using Equation (3). From the fitting, the calculated magnetic moment of the as-measured nanoplatelet was ~1.2 × 10 −16 emu. In addition, we note that some nanoparticles did not show any MFM frequency contrast even through measured at small lift height ( Figure S2), suggesting that the nanoparticles composition in these cases may be partially or completely nonmagnetic in nature. These nanoparticles are likely to be the FeOOH phase, confirming the similar morphology but non-magnetic nature of these nanoparticles compared to SrFe 12 O 19 . The results further confirm the frequency shift originated from the magnetic interaction alone.
As the magnetic moments of the Fe 3+ ions lie along the c-axis and are coupled by super-exchange interactions through O 2− ions (Fig. 1a), MFM frequency imaging was further performed to characterize the magnetic properties of SrFe 12 O 19 nanoplatelets with different thickness. Figure 3a shows the AFM height images of three SrFe 12 O 19 nanoplatelets with different thickness. The height images clearly reveal the physical dimensions of the nanoplatelets, and the thickness of the nanoplatelets (5.6 nm, 8.4 nm and 11.2 nm for nanoplatelet I, II, and III, respectively) can be easily obtained from the height profiles (Fig. 3b). The MFM frequency images of these nanoplatelets are shown in Fig. 3c. As can be seen, the contrast in MFM frequency images is enhanced as the thickness of nanoplatelet increases. It is even more evident from Fig. 3d, which shows frequency shift profiles taken along the dashed white line marked in the MFM frequency images in Fig. 3c. The negative frequency shift of the SrFe 12 O 19 nanoplatelet with a thickness of 8.4 nm increased ~54% (from − 1.28 Hz to − 1.97 Hz) compared to that of the nanoplatelet with a thickness of 5.6 nm. It further increased by ~89% as the thickness of the nanoplatelet increased to 11.2 nm (from − 1.28 Hz to − 2.42 Hz). These data suggest that the magnetic moment of SrFe 12 O 19 nanoplatelets increase as the thickness of the nanoplatelet increases.
Moreover, the MFM frequency imaging of the SrFe 12 O 19 nanoplatelets shows that although the nanoplatelets had similar lateral size, their MFM frequency contrast can be totally different ( Figure S3). Figure 4a  represents four typical frequency contrasts. As can be seen, the frequency contrast can be dark (Fig. 4a-I´), bright ( Fig. 4a-II´) as well as a combination of dark and bright (Fig. 4a-III´) for individual nanoplatelets and a combination of different dark and bright (Fig. 4a-IV´) for nanoplatelet aggregates.

Discussion
The contrast in MFM frequency image can be explained using Equation (1), it is clear that the frequency shift shows a negative correlation to the magnetic force gradient. Consequently, a dark contrast (Δ υ < 0, dashed red curve in Fig. 4b) in MFM frequency image should be observed when an attractive force is applied to the magnetized probe; on the contrary, a bright contrast (Δ υ > 0, blue dashed curve in Fig. 4b) should be observed when a repulsive force is applied to the magnetized probe. In the present study, dark and bright contrasts of the SrFe 12 O 19 nanoplatelets are observed, indicating that attractive force and repulsive force are detected in the nanoplatelets, respectively. Thus, the appearance of dark and bright contrasts of the nanoplatelet aggregates in the MFM frequency image clearly reveals the magnetization directions of the nanoplatelets in the aggregates. Furthermore, the contrast inversion can be observed by reversing the probe magnetization direction ( Figure S4). The fact that the force directions are reversed through switching the probe magnetization directions suggests that the magnetization direction of the nanoplatelets should be constant. These results further confirm that the contrasts in MFM frequency images are came from the ferrimagnetic nature of the SrFe 12 O 19 nanoplatelets.
After successful characterization of individual SrFe 12 O 19 nanoplatelets, MFM was then employed to characterize a compacted SrFe 12 O 19 pellet (Fig. 5a), produced by Spark Plasma Sintering of the as-synthesized hexaferrite nanoplatelets 22 . Figure 5b presents a typical AFM height image of the compacted pellet. The height image clearly reveals the polished surface structure of the compacted pellet. The corresponding MFM frequency image is shown in Fig. 5c. The presence of domains appeared in different contrasts, indicating that different directions of forces are detected at the surface of the compacted pellet. These provide further evidence on local magnetization of the compacted pellet being responsible for the contrast in the MFM frequency image. The observed domains in the MFM frequency image certainly originate from the magnetic domains, as no such structures are observed in the AFM height image (Fig. 5d). The frequency shift distribution of the domains clearly shows two distinct populations of frequency shifts (Fig. 5e), which correspond to the observed dark and bright contrasts in MFM frequency image in Fig. 5c. A zoom-in AFM height image is shown in Fig. 5f. The bright platelet-like structure in the height image indicates that there are individual SrFe 12 O 19 nanoplatelets on the surface of the compacted pellet. The corresponding MFM frequency image shown in Fig. 5g clearly shows the local magnetization in the compacted pellet. Figure 5h presents a close-up of the MFM frequency image, corresponding to the dashed white square in Fig. 5g, clearly revealing the tiny magnetic structures. These results confirm that MFM can be used to characterize the magnetic properties of complicate magnetic materials.
In conclusion, we demonstrated the applicability of MFM for quantitative imaging of the magnetic nanostructures of SrFe 12

Methods
Synthesis. The SrFe 12 O 19 sample was prepared through supercritical synthesis in a flow reactor. Iron nitrates (Fe(NO 3 ) 3 ·9H 2 O) and strontium nitrates (Sr(NO 3 ) 2 ) were dissolved in deionized water to obtain a precursor solution with Fe/Sr ratio equal to 1. The precursor solution was then pumped into the supercritical reactor, set at a temperature of 390 °C and a pressure of 250 bar. Then the collected sample was centrifuged, and washed with Characterization. TEM imaging was conducted using a Phillips CM20 operated at 200 kV. XRD patterns of the as-synthesized samples were collected on a Rigaku SmartLab diffractometer (Rigaku, Japan) using crossbeam optics and a Ge(220) × 2 monochromator to produce Cu K α1 radiation. In order to extract crystallographic information, Rietveld refinement was performed on the powder diffraction pattern using the Fullprof Suite software. The M-H Hysteresis loop was measured at 300 K with a Quantum Design Physical Property Measurement System equipped with a VSM. MFM measurements were performed with a commercial AFM instrument (Dimension Icon, Bruker) under ambient conditions (temperature, 24 °C; relative humidity, 44%). Commercial rectangular silicon cantilever coated with a Co/Cr layer with a resonant frequency υ 0 of 75 kHz and spring constant k of 2.8 N/m (MESP, Bruker) was used for MFM imaging. The magnetic moment m t of the magnetic tip is ~10 −13 emu. The tip radius of the magnetic tip is 35 nm. The tip lift height is 10 nm if there is no specific clarification.