Atomic-Scale Magnetometry of Dynamic Magnetization

The spatial resolution of imaging magnetometers has benefited from scanning probe techniques. The requirement that the sample perturbs the scanning probe through a magnetic field external to its volume limits magnetometry to samples with pre-existing magnetization. We propose a magnetometer in which the perturbation is reversed: the probe’s magnetic field generates a response of the sample, which acts back on the probe and changes its energy. For an ${\mathrm{NV}}^{-}$ spin center in diamond this perturbation changes the fine-structure splitting of the spin ground state. Sensitive measurement techniques using coherent detection schemes then permit detection of the magnetic response of paramagnetic and diamagnetic materials. This technique can measure the thickness of magnetically dead layers with better than 0.1 Å accuracy.

Figure 1

(a) The ${\mathrm{NV}}^{-}$ center’s ground state spin $J=1$ is split by the crystal field and magnetic field. Conventional ${\mathrm{NV}}^{-}$ magnetometry utilizes the splitting of the $|J_z=\pm 1⟩$ states. We propose a way to measure magnetic response of materials using the splitting between the $|J_z=0⟩$ and $|J_z=\pm 1⟩$ states. (b) Implementation of magnetic-energy magnetometry. The spin of an ${\mathrm{NV}}^{-}$ center is located at the apex of a scanning probe tip, optically initialized (green) and detected (red). The spin’s magnetic induction (blue) is perturbed by the presence of the sample (gray), leading to modifications of the magnetic induction (diamagnetic, yellow; paramagnetic, purple).

Figure 2

(a) A spin is placed in region I with relative magnetic permeability ${\mu }_r^{\mathrm{I}}$, adjacent to a semi-infinite region II with ${\mu }_r^{\mathrm{II}}$, filling the half-space $z>d$. The spin makes an angle $\eta$ with respect to the normal of the interface between the two regions. The color indicates the magnitude of the (image) current distribution for $\mathcal{P}(r)={[j_0(\pi r/R)]}^2$, a spherical Bessel function of zeroth order, and ${\mu }_r^{\mathrm{II}}=2$. (b) The calculated magnetic induction for the situation as described in (a). The magnetic induction near the interface is parallel to the interface for diamagnetic substances (${\mu }_r^{\mathrm{II}}=0$, left), though perpendicular to the interface for paramagnetic materials (${\mu }_r^{\mathrm{II}}\gg 1$, right). The magnitude of the magnetic induction is indicated by color, and its direction by the arrows of the streamlines.

Figure 3

The magnetic energy contribution $D_{\mathrm{mag}}$ to the fine-structure constant as function of the distance $d$ between the ${\mathrm{NV}}^{-}$ center and the sample, for samples having different magnetic permeabilities. The grey lines indicate the measurable change in $D$ for a measurement time of 100 s, reported for a bulk ${\mathrm{NV}}^{-}$ center (dot-dash) and estimated for surface ${\mathrm{NV}}^{-}$ centers (dash); see text for details. We took the low-frequency values for ${\mu }_r$ and assumed the superconductor to be a perfect diamagnet (i.e., vanishing penetration depth). The ${\mu }_r$ of pyrolytic carbon, bismuth, and water are, respectively, 0.999 590, 0.999 834, and 0.999 992.

Figure 4

The accuracy at which the thickness $t$ of a magnetically dead layer (${\mu }_r$ is about 1) can be determined, as a function of the distance $d$ between the ${\mathrm{NV}}^{-}$ center and the magnetically active region (${\mu }_r\gg 1$), for different minimal detectable changes $D_{\min }$. Based on Ref. [14], $D_{\min }=0.2\mathrm{kHz}$ for a bulk ${\mathrm{NV}}^{-}$ center and a measurement time of 100 s. See Fig. 3 and its discussion in the text to determine an estimated $D_{\min }$ close to the surface.