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Register a new userUncertainty Analysis of Stray Field Measurements by Quantitative Magnetic Force Microscopy
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Magnetic force microscopy (MFM) measurements generally provide phase images which represent the signature of domain structures on the surface of nanomaterials. To quantitatively determine magnetic stray fields based on an MFM image requires calibrated properties of the magnetic tip. In this work, an approach is presented for calibrating a magnetic tip using a Co/Pt multilayered film as a reference sample which shows stable well-known magnetic properties and well-defined perpendicular band domains. The approach is based on a regularized deconvolution process in Fourier domain with a Wiener filter and the L-curve method for determining a suitable regularization parameter to get a physically reasonable result. The calibrated tip is applied for a traceable quantitative determination of the stray fields of a test sample which has a patial frequency spectrum covered by that of the reference sample. According to the Guide to the expression of uncertainty in measurement, uncertainties of the processing algorithm are estimated considering the fact that the regularization influences significantly the quantitative analysis. We discuss relevant uncertainty components and their propagations between real domain and Fourier domain for both, the tip calibration procedure and the stray field calculation, and propose an uncertainty evaluation procedure for quantitative magnetic force microscopy.
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A nanometric needle sensor mounted in an Atomic Force Microscopy allows systematic picometer-range distance measurements. This force sensing device is used in Piezoresponse Force Microscopy (PFM) as a distance sensor, by employing the cantilever spring constant as the conversion factor opening a pathway to explore the piezoelectric effect at the nanoscale. The force-distance equivalence is achieved if the force sensor does not disturb the system to study, solely. In this manuscript we report a systematic study in which different Lead Zirconate Titanate (PZT) materials, having different d33 values, are measured following the standard theory available for PFM. Both in resonance and out of resonance measurements demonstrate that PFM cannot be considered quantitative. After performing the measurements, we propose a correction of the standard theory employed in PFM by considering the force exerted by the material as a variable. The g33 parameter, inherent to piezoelectricity, governs the amount of force available from the system. A comparison of piezoelectric stiffness for the case of a nanoscale site contact region, similar to the one it is found while performing PFM, is provided. Such stiffness is well below the cantilever stiffness, limiting and diminishing the material movement, as the piezoelectric material does not have enough stroke to induce the intended displacement. A correction factor, named Open Piezopotential Gauge, accounts for these effects, which is used to correct the measurements carried out in PZT materials towards a real quantitative PFM.
Cu$_2$OSeO$_3$ is an insulating skyrmion-host material with a magnetoelectric coupling giving rise to an electric polarization with a characteristic dependence on the magnetic field $vec H$. We report magnetic force microscopy imaging of the helical real-space spin structure on the surface of a bulk single crystal of Cu$_2$OSeO$_3$. In the presence of a magnetic field, the helimagnetic order in general reorients and acquires a homogeneous component of the magnetization, resulting in a conical arrangement at larger fields. We investigate this reorientation process at a temperature of 10~K for fields close to the crystallographic $langle 110rangle$ direction that involves a phase transition at $H_{c1}$. Experimental evidence is presented for the formation of magnetic domains in real space as well as for the microscopic origin of relaxation events that accompany the reorientation process. In addition, the electric polarization is measured by means of Kelvin-probe force microscopy. We show that the characteristic field dependency of the electric polarization originates in this helimagnetic reorientation process. Our experimental results are well described by an effective Landau theory previously invoked for MnSi, that captures the competition between magnetocrystalline anisotropies and Zeeman energy.
Thin-film ferromagnetic disks present a vortex spin structure whose dynamics, added to the small size (~10 nm) of their core, earned them intensive study. Here we use a scanning nitrogen-vacancy (NV) center microscope to quantitatively map the stray magnetic field above a 1 micron-diameter disk of permalloy, unambiguously revealing the vortex core. Analysis of both probe-to-sample distance and tip motion effects through stroboscopic measurements, allows us to compare directly our quantitative images to micromagnetic simulations of an ideal structure. Slight perturbations with respect to the perfect vortex structure are clearly detected either due to an applied in-plane magnetic field or imperfections of the magnetic structures. This work demonstrates the potential of scanning NV microscopy to map tiny stray field variations from nanostructures, providing a nanoscale, non-perturbative detection of their magnetic texture.
This paper develops a resolution enhancement method for post-processing the images from Atomic Force Microscopy (AFM). This method is based on deep learning neural networks in the AFM topography measurements. In this study, a very deep convolution neural network is developed to derive the high-resolution topography image from the low-resolution topography image. The AFM measured images from various materials are tested in this study. The derived high-resolution AFM images are comparable with the experimental measured high-resolution images measured at the same locations. The results suggest that this method can be developed as a general post-processing method for AFM image analysis.
Scattering-type scanning near-field optical microscopy (s-SNOM) is instrumental in exploring polaritonic behaviors of two-dimensional (2D) materials at the nanoscale. A sharp s-SNOM tip couples momenta into 2D materials through phase matching to excite phonon polaritons, which manifest as nanoscale interference fringes in raster images. However, s-SNOM lacks the ability to detect the progression of near-field property along the perpendicular axis to the surface. Here, we perform near-field analysis of a micro-disk and a reflective edge made of isotopically pure hexagonal boron nitride (h-11BN), by using three-dimensional near-field response cubes obtained by peak force scattering-type near-field optical microscopy (PF-SNOM). Momentum quantization of polaritons from the confinement of the circular structure is revealed in situ. Moreover, tip-sample distance is found to be capable of fine-tuning the momentum of polaritons and modifying the superposition of quantized polaritonic modes. The PF-SNOM-based three-dimensional near-field analysis provides detailed characterization capability with a high spatial resolution to fully map three-dimensional near-fields of nano-photonics and polaritonic structures.
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