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Diagram of the apparatus used to collect data. The sample is Au on Ti coated GaAs with its surface in the XZ plane. B0 is parallel to the Z-axis and is normal to the page. The RF coil is a spiral with its axis and its generated B1 parallel to the X-axis. The cantilever oscillates in the XY-plane (double headed arrow) and its position is measured with a fiber based interferometer. Diagram not to scale.
(a) Magnetic particle near sample surface with iso-Bz lines defining the bulk region and the sensitive slices. The dotted line marks the angle at which the force gradient changes sign from Bulk to Slice regions. (b) A typical MRFM scan using the CERMIT protocol. Changes in the cantilever’s frequency Δf c are proportional to the magnetization along the Zeeman axis. Here Δf c is shown as a function of the background magnetic field B0 while keeping f ARP constant. In order to measure T1 during inversion recovery, an 800 kHz wide ARP sweep is done for 20 ms through the entire region of bulk and sensitive slices to invert the spins.
(a) Typical inversion recovery data for temperatures: 4.8, 9.3, 16.6, 24.9 K. At t = 0 s the ARP is applied using the RF coil, which generates the B1, inverting the spins in the sample and causing a net negative change in the driven cantilever’s natural frequency, Δf c. During spin recovery, the cantilever tracks back to the initial condition before inversion. (b) Example of fit for 4.8 K. Each data set is fit with the inversion recovery curve of the form .
Nuclear magnetization and relaxation rate as a function of temperature. (a) Magnetization (squares) is directly proportional to the driven cantilever’s frequency, , is plotted with a dotted line predicted by Boltzmann theory (see Ref. 22). (b) The relaxation rate (diamond) 1/T1 is plotted with two solid lines, each through two points. The relaxation rate shows two regimes—a low-temperature regime in which relaxation is caused by fluctuating magnetic fields created by paramagnetic donors and a high-temperature regime in which relaxation is caused by phonon-induced electric field gradient fluctuations.
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