Figure 1

(Color online) Rotating-frame MRFM setup. To create an image of the sample, here a ${\left({\text{NH}}_4\right)}_2{\text{SO}}_4$ crystal glued to the cantilever (indicated by bar and vibrational direction by a double arrow), we encode the magnetization in two dimensions over the sample. In the $z$ direction we encode the spatial position of the magnetization by the Larmor frequency of the spins in the inhomogeneous field produced by an iron cylinder gradient source. In the $x$ direction we use an rf pulse, which nutates the spins closer to the coil entrance faster than the spins further away due to the gradient in the $B_1$ field, creating a Fourier encoding over the object. As the field gradient produced by the iron cylinder would influence the nutation frequencies by off-resonance contributions, we flip away the gradient source with a piezo bender for the duration of the $x$-encoding pulse.Reuse & Permissions

Figure 2

Pulse sequence for 2D MRFM rotating-frame imaging. The gradient source is flipped away with a piezo bender actuator during the first off-resonance pulse, which does not act on the spins but preheats the cantilever and reduces artifacts. The following rf pulse performs the rotating-frame $x$ encoding. The Rabi nutation frequency is about $\frac{{\omega }_1}{2\pi }\approx 350\text{kHz}$ at the sample center. The rf field is set to relatively high values to minimize offset effects in the residual $B_0$ inhomogeneity and to minimize the encoding time required. After the gradient is flipped back the magnetization is encoded in the $z$ direction by a Hadamard-16 sequence and finally detected.Reuse & Permissions

Figure 3

(Color online) (a) 2D MRFM image of the test sample. The signal intensity at the position of the dotted lines is plotted on top and to the right of the image. (b) SEM micrograph of the same sample. The view is approximately the same as for (a). (c) Top view of the sample. The logo is clearly thinner at the bottom and at the beginning of the E: a feature reproduced by the signal intensity of image (a).Reuse & Permissions

Figure 4

(Color online) (a) Simulation of the rf field from the coil used in our experiments (Ref. 34). The diameter of the wire, $30\mu \text{m}$, can be used as a size scale. (b) Simulation of the static magnetic field of the iron gradient source (cylinder diameter $200\mu \text{m}$) magnetized in an external 6.0 T field (Ref. 35). The colors display the field in the $z$ direction and the contours show the lines of constant field amplitude with a step distance of 100 mT and the dashed white line is the central sensitive slice in the sample at 6.176 T.Reuse & Permissions