Force-Detected Magnetic Resonance Imaging of Influenza Viruses in the Overcoupled Sensor Regime

Long and thin scanning force cantilevers are sensitive to small forces, but also vulnerable to detrimental noncontact interactions. Here we present an experiment with a cantilever whose spring constant and static deflection are dominated by the interaction between the tip and the surface, a regime that we refer to as “overcoupled.” The interactions are an obstacle for ultrasensitive measurements such as nanoscale magnetic resonance imaging (nano-MRI). We discuss several strategies to overcome the challenges presented by overcoupling, and demonstrate proton nano-MRI measurements of individual influenza virus particles.

Figure 1

Static cantilever deflection. (a) Illustration of the spatial arrangement of the cantilever apex positioned 10–100 nm above a nanomagnet that is fabricated on top of a microstrip antenna. The image is composed of two individual scanning electron micrographs taken of the cantilever and the antenna chip. Inset: image of a nanorod apex (a different device was used in this study). Individual virus particles are marked by the arrows. The scale bar has a length of 200 nm. (b) Cantilever tip position during an approach curve next to the nanomagnet. Inset: schematics of the bent cantilever (not to scale). We define the cantilever deflection as the difference between the tip position and the scanner position, which is set to $a_{\mathrm{cant}}=0\mathrm{nm}$ at the starting point in this case. (c) Cantilever deflection and (d) cantilever frequency during an MRFM scan across the microstrip antenna at a cantilever-nanomagnet distance of 10 nm. Points indicate the measurement positions. In this measurement, a virus particle was centered above the nanomagnet at $x=910\mathrm{nm}$, interacting strongly with it between $x\approx 650\mathrm{nm}$ and 1165 nm.

Figure 2

Schematic illustration of the nanomagnet, two resonant slices, and the position of blind spots for positive (blue) and negative (red) scan directions in $x$. The color coding inside the resonance slices indicates the absolute value of the magnetic field gradient $G$ generated by the nanomagnet (light gray); see Appendix pp3 for details. The dashed yellow line indicates the height of a typical $x$–$y$ scan with various blind spots. The tip-surface interactions decrease with increasing separation $\mathrm{\Delta }z$ and the blind spots vanish for $\mathrm{\Delta }z\gtrsim 100\mathrm{nm}$.

Figure 3

MRFM measurements in the overcoupled sensor regime. (a) A two-dimensional MRFM scan recorded as a function of the $x$ and $y$ position of the scanning stage on a regular grid with a step size of approximately 30 nm. We used $f_{\mathrm{rf}}=255.5\mathrm{MHz}$ and $\mathrm{\Delta }{f}_{\mathrm{rf}}=800\mathrm{kHz}$ at a cantilever-nanomagnet separation of 30 nm to detect ${}^1\mathrm{H}$ spins (see main text for explanation). The total measurement time per data point was 100 s (40 s of calibration routine + 60 s of signal integration time). The position of the nanomagnet was approximately in the center of the field of view. (b) Same data as in (a), but plotted as a function of the actual cantilever tip position. Arrows indicate the opening of the blind spots. To obtain the tip position, the scanner position is corrected by the static cantilever deflection. Note that the $y$ position of the tip is not corrected, as the cantilever is much stiffer in this direction and static deflections are assumed to be negligible.

Figure 4

Iterative reconstruction process. (a) Measured MRFM data $I_m$ recorded at a cantilever-nanomagnet distance of $\mathrm{\Delta }z=110\mathrm{nm}$. For the reconstruction, the cantilever tip positions are coerced to nearest-neighbor positions on a $10\times 10\times 10$ nm³ grid. (b) Example of the calculated MRFM signal $I_r$ at $\mathrm{\Delta }z=110\mathrm{nm}$ after a successful reconstruction with three $x$–$y$ planes (110 nm, 130 nm, 150 nm). During each iteration, the reconstruction algorithm reduces the error $\mathrm{\Delta }I=I_m-I_r$ between both data sets until it drops below a threshold.

Figure 5

Reconstructed nano-MRI image $O_r$ of influenza viruses. (a) Isosurface image of the three-dimensional hydrogen nuclear spin density calculated from the MRFM data. The image shows two regions of high spin density whose sizes agree with an interpretation of a single virus (left) and an aggregation of two or three viruses (right). The three monochromatic images show hydrogen nuclear spin density in planes at (b) $z=80\mathrm{nm}$, (c) $x=1\mu \mathrm{m}$, and (d) $y=0.9\mu \mathrm{m}$. The blue lines in (b) indicate the positions of the planes shown in (c) and (d). All scale bars are 500 nm long. Bright (dark) color scale corresponds to high (low) measured spin density.

Figure 6

Dependency of (a) effective spring constant and (b) effective damping coefficient on the $x$ and $y$ position at $\mathrm{\Delta }z=30\mathrm{nm}$. The data were obtained simultaneously with the MRFM signal shown in Fig. 3.

Figure 7

(a),(b) Raw data of the two additional scans used for the reconstruction shown in Fig. 5. (c) Demonstration of the cantilever tip position hysteresis between scans in opposite directions, shown in blue and red. This scan was performed at $\mathrm{\Delta }z=40\mathrm{nm}$ on a smaller scan range than in (a) and (b). (d) Spin signal image combined out of the two scans performed in opposite directions in (c). (e),(f) Scans performed at the same height $\mathrm{\Delta }z=40\mathrm{nm}$ with different pulse central frequencies $f_{\mathrm{rf}}$, resulting in different information captured. Because of the smaller diameter of the resonant slice used for recording the data shown in (f), the signal is more localized around the blind spots than in (e); cf. Fig. 8 for a quantitative field simulation. The square frame in (f) shows the measurement range of the zoom scan in (d). The MRFM signal regions coincide without additional alignment, indicating the excellent mechanical stability of our setup.

Figure 8

(a) Numerical simulation of the magnetic field $B_0+B_{\mathrm{tip}}(\overrightarrow{r})$ and (b) the field gradient $G$ around the nanomagnet. The $B_0$ field of 5.88 T points along the $z$ direction. The contour lines indicate regions of constant Larmor frequency (isochromats). The gray shaded area represents the shape of the resonant slice in which the spins are inverted by the inversion pulses. The scale bars have a length of 100 nm. (c),(d) Illustration of the shape of resonant slices in three dimensions. The colored contours indicate where the product between the magnetic field gradient and the PSF drops below a threshold value of $0.5\mathrm{MT}/\mathrm{m}$. Simulations were performed for the measured magnet shape, an external field of $B_0=5.88\mathrm{T}$, a saturation magnetization of 1.88 T inside the magnet, and $f_{\mathrm{rf}}=255\mathrm{MHz}$ and $f_{\mathrm{rf}}=265\mathrm{MHz}$ in (c) and (d), respectively.

Figure 9

Topography scan of the $870\times 630$ nm² rectangular nanorod apex with the attached virus samples. The scan was performed at room-temperature after performing the three-dimensional MRFM scan.