Figure 1

Schematic of the MRFM setup. The sample, consisting here of MgF${}_2$ (red; encircled by small oval within larger oval) and KPF${}_6$ (green) crystals, is glued onto the cantilever. Depending on the spin orientation, the sample experiences an attractive or repulsive force due to the ferromagnetic gradient source placed over the sample. The spins are inverted periodically using radio-frequency irradiation at the mechanical resonance frequency of the cantilever. The resulting cantilever oscillation is detected by a laser-beam deflection sensor. To achieve a homogeneous magnetic field for spectroscopic encoding in the imaging experiments, a piezo bender is included in the setup, which can flip the gradient source away from the sample position.Reuse & Permissions

Figure 2

Pulse sequences for mechanically detected chemical-shift imaging. For spectral encoding and Fourier spatial encoding the gradient is in the “off” position; otherwise, it is “on.” The $F^{\mathrm{spe}}S$ experiment (a), consists of a $t_1$ evolution time combined with a magic echo[24] for homonuclear dipolar decoupling. (b) The encoding schematically depicts the $F^{\mathrm{spa}}{H}_N^{\mathrm{spe}}{H}_{Mq}^{\mathrm{spa}}$ experiment and turns into the $H_N^{\mathrm{spe}}{H}_{Mq}^{\mathrm{spa}}$ experiment if the “rotating-frame $x$ encoding” is omitted. Hyperbolic secant pulses are used to accomplish the Hadamard encoding, which is applied only to a selected region of interest. A polarization cycle is applied in the $H_N^{\mathrm{spe}}$ dimension to remove experimental artifacts.Reuse & Permissions

Figure 3

(a) Idealized frequency-dependent $M_z$ magnetization obtained with single-sided excitation over one cantilever period $T_c$. The magnetization oriented parallel to the external magnetic field is shown in red; antiparallel magnetization, in blue. (b) Time-dependent force profile of the magnetization for spins with Larmor frequencies ${\omega }_1$ and ${\omega }_2$. In the MRFM detection process the resulting step function is projected onto the functions $\cos \left({\omega }_{\mathrm{can}}t\right)$ and $\sin \left({\omega }_{\mathrm{can}}t\right)$, which yields a phase shift of ${180}^{\circ }$ between the two ends of the excitation bandwidth.Reuse & Permissions

Figure 4

(a) Thirty-seven localized fluorine chemical-shift spectra ($F^{\mathrm{spe}}S$) of the phantom sample. The MgF${}_2$ and KPF${}_6$ peaks are virtually separated in both the spatial and the spectral dimensions. The KPF${}_6$ peak has a narrower linewidth due to the smaller dipolar coupling. The red and green areas at the right represent integrals over the chemical-shift range of MgF${}_2$ and KPF${}_6$, respectively. (b) Hadamard-CSI spectrum $H_8^{\mathrm{spe}}{H}_{4q}^{\mathrm{spa}}$ of the same sample. Trigonometric interpolations of the eight spectral points were applied. (c) Chemical-shift resolved spatial 1D ${}^{19}$F image $H_2^{\mathrm{spe}}{H}_{4q}^{\mathrm{spa}}$ of the phantom sample containing KPF${}_6$ and MgF${}_2$ crystals. The blue line represents the ${}^{19}$F spin density from a 1D $H_{4q}^{\mathrm{spa}}$ reference experiment. The red and green lines represent the spin density corresponding to the MgF${}_2$ and KPF${}_6$ signals. (d) Comparison of the chemical-shift selective images obtained in a $H_2^{\mathrm{spe}}S$ and $F^{\mathrm{spe}}S$ experiment. The acquisition scheme differs only in the chemical-shift dimension. The KPF${}_6$ is represented in green and blue and the MgF${}_2$ signal in red and magenta for the $H_2^{\mathrm{spe}}S$ and $F^{\mathrm{spe}}S$ experiments, respectively.Reuse & Permissions

Figure 5

(a) 3D image $F^{\mathrm{spa}}{H}_8^{\mathrm{spe}}{H}_{8q}^{\mathrm{spa}}$ of a sample containing KPF${}_6$ and MgF${}_2$, with a 1D spectral dimension combined with a spatial 2D ${}^{19}$F image. The planes represent the eight spectral slices and show the spatial distribution within a slice. The intensities of the planes are projected along each spatial dimension. Projections were trigonometrically interpolated to 16 points. Intensities of the spectral planes as well as of the projections are plotted with a logarithmic color scaling. (b) Chemical-shift resolved spatial 2D ${}^{19}$F image $F^{\mathrm{spa}}{H}_2^{\mathrm{spe}}{H}_{8q}^{\mathrm{spa}}$ of the same sample. The red and green contour lines represent the spin density in the spectral range located up to 50 kHz to each side of the carrier frequency, allowing discrimination of MgF${}_2$ (red) and KPF${}_6$ (green) signals. The $z$ position is referenced to the distance from the gradient source.Reuse & Permissions