Suppression of Spin Diffusion near a Micron-Size Ferromagnet

We have used the large gradients generated near the ferromagnetic tip of a magnetic resonance force microscope to locally suppress spin diffusion in a silica sample containing paramagnetic electron spins. By controlling the slice location with respect to the tip, the magnetic field gradient was varied from 0.01 to $36\mathrm{m}\mathrm{T}/\mu \mathrm{m}$, resulting in a fourfold decrease in $T_1^{-1}$ and a similar decrease in $T_{1\rho }^{-1}$. The observed dependence of the relaxation rates on field gradient is consistent with the quenching of flip-flop interactions that mediate the transport of magnetization between slow and fast relaxing spins.

Figure 1

Schematic of MRFM apparatus. Two slice locations are indicated for different values of the external field. Effective slice thickness ($\zeta$) is calculated for $\Omega /2\pi =20\mathrm{M}\mathrm{H}\mathrm{z}$. (a) $B_{\mathrm{e}\mathrm{x}\mathrm{t}}=80\mathrm{m}\mathrm{T}$, $d_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{c}\mathrm{e}}=4.3\mu \mathrm{m}$, $\zeta =240\mathrm{n}\mathrm{m}$. (b) $B_{\mathrm{e}\mathrm{x}\mathrm{t}}=50\mathrm{m}\mathrm{T}$, $d_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{c}\mathrm{e}}=2.5\mu \mathrm{m}$, $\zeta =90\mathrm{n}\mathrm{m}$.

Figure 2

ESR spectrum of silica sample containing $E^{\prime }$ centers. The plot was obtained by integrating the derivative line shape measured using a cw ESR spectrometer.

Figure 3

Polarization as a function of recovery time for three different field gradients: ●, $G_{zz}\simeq 0.9\mathrm{m}\mathrm{T}/\mu \mathrm{m}$, $T_1=5.6\pm 0.1\mathrm{s}$; ▪, $G_{zz}\simeq 9\mathrm{m}\mathrm{T}/\mu \mathrm{m}$, $T_1=11\pm 0.5\mathrm{s}$; ▴, $G_{zz}\simeq 27\mathrm{m}\mathrm{T}/\mu \mathrm{m}$, $T_1=17.8\pm 1.2\mathrm{s}$. The lines show exponential recovery curves fit to the data.

Figure 4

Spin-lattice relaxation rate $T_1^{-1}$ versus gradient. The measured data (●) is plotted as a function of external field (top axis). Values for the tip gradient (bottom axis) for a given external field are calculated numerically using a model for the tip. The overlap function $\Phi (G_{zz})$ (solid curve) is calculated assuming an average axial separation $\overline{z}=5\mathrm{n}\mathrm{m}$ between spins.

Figure 5

Decay of magnetization in the rotating frame as a function of the spin-lock time ${\tau }_{\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k}}$. The solid curves are double exponential fits to the data that serve as visual guides. (a) $G_{zz}\simeq 2\mathrm{m}\mathrm{T}/\mu \mathrm{m}$, $T_{1\rho }\simeq 0.33\mathrm{s}$. (b) $G_{zz}\simeq 6\mathrm{m}\mathrm{T}/\mu \mathrm{m}$, $T_{1\rho }\simeq 0.53\mathrm{s}$. (c) $G_{zz}\simeq 12\mathrm{m}\mathrm{T}/\mu \mathrm{m}$, $T_{1\rho }\simeq 0.80\mathrm{s}$.