Probing near-field EM fluctuations in superparamagnetic CoFeB with NV quantum dephasometry

TL;DR

This paper addresses the challenge of noninvasively characterizing superparamagnetism in nanoscale magnetic layers integrated into devices. It introduces NV center-based quantum dephasometry to probe low-frequency near-field EM fluctuations, complemented by relaxometry and SQUID magnetometry, enabling spectral decomposition of noise sources. The authors demonstrate MHz-range EM fluctuations arising from thermally driven domain flipping in a 1.1 nm CoFeB layer, reveal a nonmonotonic temperature dependence of NV dephasing, and show distance-dependent scaling of T1 and T2 consistent with a quasi-two-dimensional magnetic layer. The findings advance on-chip quantum sensing of nanoscale magnetism and pave the way for hybrid quantum spintronic devices with integrated quantum probes for materials characterization.

Abstract

Superparamagnetism in nanoscale magnetic layers is a critical property for a wide range of spintronic-based sensor and computing applications. While conventional magnetization measurements can detect superparamagnetic signatures, they often require the application of high perturbative fields and are difficult to implement for magnetic layers integrated within functional devices. In this study, we non-invasively investigate the superparamagnetic spin dynamics of a nanoscale CoFeB layer of thickness 1.1 nm, deposited on a diamond substrate, by probing its low-frequency near-field electromagnetic (EM) fluctuations using nitrogen-vacancy (NV) centers-based quantum dephasometry. Our measurements reveal an unconventional, non-monotonic temperature dependence of the dephasing time of NV centers, which we attribute to EM fluctuations produced by thermally driven superparamagnetic domain flipping in CoFeB. Our findings are further supported by the theoretical interpretation of the dephasing dynamics of NV centers and the complementary SQUID-based magnetization characterizations of the CoFeB layer. Additionally, exploiting the technique of NV dephasometry, we extract the spectral density of the EM fluctuations in CoFeB, which is used to isolate different components of the EM fluctuations acting on NV centers. We also measure the CoFeB-to-NV distance-dependent coherence times of NV centers to investigate the effect of the dimensionality of the CoFeB layer on the generated near-field EM fluctuations. These results provide critical insight into the magnetization dynamics and near-field EM environment of nanoscale magnetic layers. It also has significant implications for the development of hybrid quantum spintronic devices and applications involving nanoscale opto-magnetic materials.

Figures (5)

• Figure 1: Magnetization responses of nanoscale CoFeB layers. (a) A 1.1 nm thick CoFeB deposited diamond sample with an embedded NV layer. For a CoFeB layer with such thickness, superparamagnetism arises due to the formation of nanoscale magnetic elements with a smaller anisotropy barrier energy ($E_b$). (b) Frequency dependence of the magnetic susceptibility in superparamagnetic CoFeB. Non-monotonicity appears in MHz frequency response due to the transition from the superparamagnetic state to the blocked state. The temperature corresponding to the susceptibility peak value is termed as the blocking temperature. The transition point for GHz susceptibility is beyond the plotted temperature range. (c) SQUID-based magnetization curves of superparamagnetic CoFeB. $\mu_{IP}$ and $\mu_{OOP}$ are the average moments of the nanoscale magnetic elements along the in-plane and out-of-plane directions, respectively. (d) A diamond sample with a 10 nm thick CoFeB layer. Ferromagnetism is retained in this continuous magnetic layer due to a higher anisotropy barrier energy. (e) MHz and GHz frequency responses of magnetic susceptibility for ferromagnetic CoFeB. For both cases, there is no phase transition in the magnetization state. (f) SQUID-based magnetization curve for the ferromagnetic CoFeB layer.
• Figure 2: NV-based quantum spectroscopy of near-field EM fluctuations: Relaxometry vs. Dephasometry. (a) Schematic illustration of the spectroscopy of near-field EM fluctuations with NV center spin qubits in diamond. A CoFeB layer is deposited on the diamond sample, with variable distances (d1, d2, d3) from the NV layer. A 532 nm green laser is used for optical initialization and readout of the NV spin states. An MW antenna delivers control signals for spin manipulation during dephasometry measurement. The ground state spin energy levels of NV center are shown at the top. (b) Pulse sequence and spin state evolution in the quantum relaxometry protocol. The spin is initialized into a pure state along the quantization axis, which undergoes relaxation due to interactions with EM fluctuations components resonant with the NV transition frequency ($\approx 2.87\ GHz$). The relaxation time $T_1$ is extracted from the exponential decay of spin polarization. The presence of proximal CoFeB enhances the relaxation rate, as shown in the accompanying data. (c) Schematic of the quantum dephasometry protocol. Here, the NV spin is initialized into a superposition state oriented perpendicular to the quantization axis. The phase coherence of the superposition state is sensitive to low-frequency, non-resonant EM fluctuations. The dephasing time $T_2$ is extracted from the decay rate of the phase coherence.
• Figure 3: Probing CoFeB superparamagnetism via temperature-dependent coherence measurements of NV centers. (a) Schematic illustration of the diamond sample with an ultrathin CoFeB layer showing superparamagnetic behavior. (b) Dephasing measurements of NV centers near the CoFeB layer. The temperature-dependent scaling behavior of this low-frequency noise-sensitive measurement highlights the differences with that of relaxation measurements shown in the inset. (c) Diamond sample with a thicker CoFeB layer showing ferromagnetic behavior. (d) Dephasing measurement near the ferromagnetic CoFeB layer. The relaxation measurement in shown in the inset.
• Figure 4: Low-frequency spectroscopic characterization of the EM fluctuations from CoFeB film. (a) Spectra near CoFeB film at different temperatures. The intrinsic EM fluctuations spectrum (without CoFeB) at 295 K is primarily dominated by the nuclear spin bath and divacancy centers formed during implantation. In contrast, the presence of the CoFeB film induces added fluctuations. The theoretical fittings are plotted on the experimental data using a continuous bold line. (b) Effect of magnetic field on the CoFeB-induced fluctuations at 295 K. The applied magnetic field modifies the sub-10 MHz fluctuation component, likely due to changes in the diamond nuclear spin bath. However, the fluctuations above 10 MHz remain largely unaffected, consistent with the weak magnetic-field dependence of the EM fluctuations in superparamagnetic CoFeB. (c) Comparison of the spectra of superparamagnetic and ferromagnetic CoFeB layers at different temperatures.
• Figure 5: Dependence of the coherence times of NV centers on NV-to-CoFeB distance. (a) Relaxation time of NV centers as a function of their distance from the CoFeB layer. The relaxation time follows a distance-dependent scaling of $d^4$. (b) Dephasing time as a function of distance from the CoFeB layer. The dephasing time exhibits a $d^2$ dependence on the distance. (c) EM fluctuations spectrum measured at various distances from the CoFeB layer. The spectrum reveals how the amplitude at different frequency components varies with distance from the magnetic source.