Spin-mediated dissipation and frequency shifts of a cantilever at milliKelvin temperatures

Abstract

We measure the dissipation and frequency shift of a magnetically coupled cantilever in the vicinity of a silicon chip, down to 25 mK. The dissipation and frequency shift originates from the interaction with the unpaired electrons, associated with the dangling bonds in the native oxide layer of the silicon, which form a two-dimensional system of electron spins. We approach the sample with a 3.43 μm-diameter magnetic particle attached to an ultrasoft cantilever and measure the frequency shift and quality factor as a function of temperature and the distance. Using a recent theoretical analysis [J. M. de Voogd et al., arXiv:1508.07972] of the dynamics of a system consisting of a spin and a magnetic resonator, we are able to fit the data and extract the relaxation time T 1 = 0.39 ± 0.08 ms and spin density σ = 0.14 ± 0.01 spins per nm 2 . Our analysis shows that at temperatures 500 mK magnetic dissipation is an important source of noncontact friction.

Density and T1 of Surface and Bulk Spins in Diamond in High Magnetic Field Gradients

“…The measurements were performed using an MRFM setup comparable to the one used in earlier experiments [6]. To establish the magnetic interaction, we use a spher-arXiv:1801.07535v1 [cond-mat.mes-hall] 23 Jan 2018 In blue we see the NbTiN RF-wire, not used in the current experiment.…”

“…Our group has previously demonstrated surface spin density measurements of dangling bonds on a silicon oxide surface [6]. Here we present spin density measurements of paramagnetic impurities on a diamond surface and also expand our method to probe impurity spins in the bulk of the sample.…”

Dissipation and resonance frequency shift of a resonator magnetically coupled to a semiclassical spin

“…From κ we can calculate the frequency and Q-factor shifts as seen in experiments by den Haan et al . 16 . For the susceptibility has a maximum around the natural frequency .…”

Mechanical Generation of Radio-Frequency Fields in Nuclear-Magnetic-Resonance Force Microscopy

“…A detailed description of the setup can be found in Refs. [8,11]. Here, we will only give a short summary.…”

“…The sensitivity of this technique for the purpose of imaging a magnetic moment μ min is limited by the force noise on the sensor, and the force generated by the field gradients: μ min ¼ ð1=∇BÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4k B TΓf BW p . Here, Γ is the friction of the cantilever, currently limited by noncontact friction caused by dielectric [7] and magnetic dissipation [8]. The field gradient ∇B is generated by a micrometer-sized magnetic particle, which is typically 10 5 -10 6 T=m and can be further increased using an even smaller magnetic particle [9].…”