The study of magnetic fluctuations – time-dependent deviations of a magnetic system from equilibrium – is of high intrinsic interest and provides a powerful tool to gain insight into magnetic coupling mechanisms. For example, magnetic fluctuations provide important information on the physics of highly correlated electron systems. Experimentally, however, access to fluctuations is frequently challenging, for two reasons: Firstly, fluctuations can extend over an excessively large range of frequencies. Secondly, many relevant magnetic systems are small entities with dimensions in the nanometer range, such as single molecules, clusters, or magnetic domains. Hence, the study of magnetic fluctuations requires a measurement technique featuring simultaneously nanoscale resolution and a wide frequency bandwidth.
Here we show that the nitrogen-vacancy (NV) center in diamond employed as a magnetic field sensor  simultaneously provides access to both nanoscale objects and a frequency bandwidth spanning 10 orders of magnitude. By employing different interrogation techniques we monitor thermal magnetization reversals of single biological nanomagnets from cryogenic to room temperature.
We study ferritin protein complexes adsorbed onto a diamond surface (Fig. 1(a)). Besides its physiological importance for the iron storage in mammals, ferritin attracted much attention as a model system for nanoparticle magnetism. Each of these proteins encloses a cluster of up to 4500 Fe atoms whose net magnetic moment of approximately 300μB exhibits strong thermally activated fluctuations. We detect the magnetic stray field of these clusters with NV defect centers embedded 5–10 nm below the diamond surface. This center enables the precise determination of the local magnetic field via the Zeeman shift of its spin sublevels, which can be measured by optically detected magnetic resonance (ODMR) techniques . Because of its atomic size, an individual NV center can be placed as a sensor spin in nanometer proximity to the sample, allowing for coupling to only a single ferritin complex. Moreover, it can sense magnetic field fluctuations on various frequency scales from the sub-Hz to the GHz range, depending on the spectroscopy protocol employed. As a notable extension of previous studies, here we demonstrate nanosensing in a variable temperature setup between 5 K and 300 K in ultrahigh vacuum .
The Fe core of the ferritin is generally considered as single magnetic domain with uniaxial anisotropy; therefore, the magnetic moment fluctuates thermally activated between the two directions along the easy axis of magnetization with a temperature-dependent rate. The dynamics of these stochastic magnetization reversals is characterized by the spin lifetime
(1) τ(T, Ea) = τ0 × exp(Ea/kBT),
with the inverse attempt frequency τ0 ≈ 2·10−11 s and the anisotropy barrier Ea. The magnetization reversals of an individual molecule with the temperature-dependent relaxation rate τ(T) (Fig. 1(b)) generates magnetic field fluctuations resembling random telegraph noise. Our method to detect these fluctuations is based on changes in the longitudinal (T1) or transverse (T2, T2*) spin relaxation time of the NV center in response to the ferritin spin noise. To access different frequency ranges, we probe the relaxation of the NV center by the inversion recovery protocol, two-pulse spin echo spectroscopy, and one-pulse ODMR spectroscopy. In Fig. 2 the corresponding response functions and spectral sensitivity ranges are summarized.
With decreasing temperature, the ferritin noise spectrum is subsequently shifted through these distinct sensitivity windows, which we verify by measurements on an ensemble of ferritin molecules (Fig. 3). Without adsorbed ferritin we measure T1 = 0.67 ± 0.15 ms at T = 300 K, which increases to >2.5 ms at low temperature, i. e., above the longest decay time detectable in our setup. Upon the adsorption of ferritin molecules, the T1 time at room temperature is reduced by approximately a factor of 5. The ferritin-induced reduction in T1 vanishes at low temperatures, since the cutoff frequency of the ferritin noise spectrum shifts below the NV transition frequency. The data show thus a strong increase in T1 below the blocking temperature of TB ≈ 50 K, which we can well describe within our model using Ea = 15 ± 5 meV and effective coupling strength <B> = 0.79 ± 0.15 mT.
To probe the temperature dependence of the ferritin magnetization dynamics in the range 0.1–1 MHz, we employ spin echo spectroscopy. The coherence time T2 time is rather unaffected by the ferritin spin noise at 300 K, due to the low noise amplitude in the probed frequency range (Fig. 3(b)). This changes at low temperatures; as the cutoff frequency of the ferritin noise spectrum decreases, the noise amplitude in the probed frequency range initially increases. The ferritin contribution to the relaxation rate becomes dominant for T ≲ 80 K, leading to a reduction of T2. At T ≲ 35 K, the cutoff frequency of the ferritin noise spectrum shifts below the detection window of the spin echo sequence, resulting in a recovery of the T2 time. The minimum in T2 at roughly 35 K corresponds to the blocking temperature for the probed frequency range. We reach an overall good agreement when fitting the data with the above-described model, yielding Ea = 25 ± 5 meV and <B> = 0.39 ± 0.15 mT.
We obtain further insight into the ferritin spin dynamics especially at low frequencies by ODMR spectroscopy (Fig. 3(c)). We detect at 5 K an increase of the resonance linewidth by ≈5 MHz compared to data measured at 77 K, which can be interpreted in the framework of the ODMR filter function: At T ≥ 77 K, the fluctuations of the magnetic moments are fast compared to the inverse microwave pulse length (500 ns), such that only the average magnetization of the molecular ensemble is detected (motional narrowing regime). At 5 K, the spin dynamics of most molecules is blocked, i.e., their magnetization is static over the measurement time (≈103 s), and thus the local magnetic field differs for each NV center depending on the size and the orientation of the nearby molecules (inhomogeneous broadening). The low-temperature linewidth of ≈15 MHz corresponds to an effective internal field in the NV center ensemble of ≈0.53 mT, which is comparable to the coupling strength estimated from the T1 and T2 measurements. This value is consistent with the expected stray field of ferritin molecules on the diamond surface.
An important advantage of the NV sensor is the very high sensitivity with the potential for the investigation of single molecules. To utilize this capability we used a diamond substrate with low NV concentration enabling us to optically address and readout individual centers. Ferritin was deposited with reduced coverage such that isolated molecules are obtained, which was confirmed by atomic force microscopy. The low-temperature resonance linewidth in the ODMR spectra of single NV centers depends on the anisotropy barrier of the nearby molecules. We observe a broadening at 5 K for roughly 20% of the investigated NV centers (Fig. 3(d), top panel), which we attribute to the magnetic fluctuations of molecules with rather low anisotropy energy such that TB < 5 K. In contrast, most NV centers show similar line shapes at 5 and 77 K (Fig. 3(d)), bottom panel), suggesting that nearby molecules are blocked at 5 K.
In conclusion, we demonstrated the detection of the temperature-dependent relaxation dynamics of ferritin molecules by employing NV magnetometry. The main advantages of this approach are the wide frequency range that can be covered and the high sensitivity enabling single molecule experiments. While in the single NV center experiments demonstrated here the number of detected ferritin molecules could only be estimated, future experiments using NV spin sensors in a scanning probe architecture  will facilitate single molecule investigations with enhanced control and precision. For example, this method could be used to address the validity of Eq. (1) and to determine the preexponential factor, which is still under debate in the literature. Because of its high sensitivity and its intrinsic spatial resolution, the technique can also be applied to investigate systems with smaller magnetic moment, such as molecular magnets, radicals, or, ultimately, nuclear spins.