Spurious Ferromagnetic Remanence Detected by Hybrid Magnetometer

TL;DR

This paper demonstrates how a hybrid atomic magnetometer can detect and analyze spurious ferromagnetic remanence in polymeric sample containers using nuclear magnetic resonance in ultra-low fields.

Contribution

It introduces a novel method combining NMR and atomic magnetometry to identify and interpret remanent magnetization components in materials.

Findings

Detection of static and dynamic magnetic fields from the container

Frequency shifts and decay rate variations linked to remanence

Modeling of signal interactions based on geometry

Abstract

Nuclear magnetic resonance detection in ultra low field regime enables the measurement of different components of a spurious remanence in the polymeric material constituting the sample container. A differential atomic magnetometer detects simultaneously the static field generated by the container and the time-dependent signal from the precessing nuclei. The nuclear precession responds with frequency shifts and decay rate variations to the container magnetization. Two components of the latter act independently on the atomic sensor and on the nuclear sample. A model of the measured signal allows a detailed interpretation, on the basis of the interaction geometry.

Full text

††preprint: AIP/123-QED

Optical atomic magnetometers (OAMs) find a variety of applications ranging from fundamental science Afach et al. (2018); Pendlebury et al. (2015) to security Deans et al. (2016), nondestructive tests Bevington et al. (2018), and nuclear magnetic resonance (NMR) detection in the regimes of zero and ultra-low-field Tayler et al. (2017); Bevilacqua et al. (2013) (ULF), including imaging Savukov and Karaulanov (2014); Oida, Tsuchida, and Kobayashi (2012).

OAM instrumentations are implemented in diverse designs, which lead to different complexity, sensitivity and robustness levels. Record sensitivities exceeding the fT/Hz1/2 have been achieved with the spin-exchange-relaxation-free magnetometers, at expenses of a limited bandwidth and need of operating at vanishing field, so to require accurate shields and compensation systems. Less performing but more versatile implementations achieve 100 fT/Hz1/2 in unshielded environment, and miniaturized devices with analogous performance are nowadays developed Schultze et al. (2012); Gerginov, Krzyzewski, and Knappe (2017).

Excellent sensitivities are also obtained by radio-frequency magnetometers, which are designed to detect high-frequency variations of the magnetic field. Recently a radio-frequency magnetometer was demonstrated to discriminate the polarization of the detected field Gerginov (2019). Other implementations reported in the literature, make use of cold atomic samples to improve the spatial resolution Cohen et al. (2019).

In this paper we consider an OAM operating in unshielded environment with a bandwidth extending up to 200 Hz, which found recently application in ULF-NMR Bevilacqua et al. (2009, 2016a, 2017) and imaging Bevilacqua et al. (2019a) experiments.

We present a peculiar arrangement, where the ULF-NMR setup enables the characterization of weakly magnetized material on the basis of simultaneous analyses of the atomic and the nuclear precession signals. This arrangement leads to a hybrid measurement method, in which different components of the magnetization affect the nuclear and atomic spins, respectively.

The experimental setup (see Fig.1) is built around a dual OAM operating in a Bell & Bloom configurationBevilacqua et al. (2016b) briefly described below.

The OAM uses Cs vapor that is optically pumped into a stretched state by means of laser radiation at the milli-Watt level. This pump radiation is circularly polarized and tuned to the Cs $D_{1}$ line. It is periodically tuned in resonance with the $F_{g}=3\rightarrow F_{e}=4$ transition of the $D_{1}$ line set, to produce both light-narrowing Scholtes et al. (2011); Bevilacqua, Biancalana, and Dancheva (2016) due to strong hyperfine pumping to the $F_{g}=4$ ground state and Zeeman pumping due to the weak (far detuned) resonances starting from the $F_{g}=4$ level excited with circular polarization. A co-propagating weak (micro-Watt level) and linearly polarized beam probes the time evolution of the atomic state being tuned to the proximity of the $F_{g}=4$ manyfold in the $D_{2}$ line.

The periodicity of the pumping matches the precession frequency around a magnetic field oriented transversely to the optical axis. Let $\omega_{M}$ and $\Omega_{L}$ be the angular frequency of the laser modulation signal and of the atomic precession, respectively. A scan of $\omega_{M}$ around $\Omega_{L}$ makes it possible to characterize the resonance profile, and linewidths as narrow as 25 Hz –set by spin exchange relaxation– are recorded in operative conditions. The presence of buffer gas (23 Torr N2) avoids line broadening due to Cs-wall collision and prevents radiation trapping phenomena.

Following interaction with the vapour, the pump radiation is stopped by an interference filter, and the polarization of the probe beams is analyzed by balanced polarimeters. During the measurements, $\omega_{M}$ is made resonant and kept constant. The magnetic field and its variation in time are extracted from the phase of the polarimetric signals.

The homogeneous B0 field in which the sensors operate is obtained by partially compensating the environmental field and is oriented along the $z$ axis. $B_{0}$ has typical strengths of $1-10\,\mu$T.

The system operates in an unshielded environment and the external magnetic disturbances are first actively compensated Belfi et al. (2010); Bevilacqua et al. (2019b) and then cancelled by recording two signals differentially Bevilacqua et al. (2016b). To this end two identical Cs cells are used.

The sources of the measured signals can be modeled in terms of both static and precessing dipoles. It is important to consider the response of the magnetometer to field variations caused by such kind of sources, in dependence of their orientation.

The scalar nature of the magnetometer makes it responding maximally to field-modulus variations, i.e. to variations of the field component parallel to $\vec{B}_{0}$. Accordingly to the geometry –sketched in Fig.2– such variations are induced by dipolar sources located in the sample position and oriented along $y$ (red arrows in the figure), while dipolar sources oriented along $z$ produce (green arrows) smaller (second order response) field-modulus variations. Moreover, the latter gives a common mode signal that is compensated and cancelled. A similar condition would occur for an $x$ oriented dipole. In contrast, dipolar sources oriented along $y$ produce difference-mode field modulus variations ($\Delta B_{\mbox{D}M}$) to which the response of the differential setup is maximal.

The container of the NMR sample is a sealed polymeric cartridge. In this experiment, it is filled with distilled water, other liquid substances can be analyzed as well, as previously reported Bevilacqua et al. (2017, 2016a). The sample is remotely polarized (at about 1 T) in a Halbach magnetic array and pneumatically shuttled to the detection region Biancalana, Dancheva, and Stiaccini (2014).

During the shuttling from the premagnetization Halbach array to the measurement region, the sample runs across a cylindrical pipe oriented along $x$. Unpredictable sample rotations by an angle $\theta$ may occur around the $x$ direction.

The nuclear magnetization follows adiabatically the external field so that it is oriented along $z$, when the sample reaches the measurement region.

The ULF-NMR signal is obtained by the application of an appropriate tipping pulse. In consequence of a $\pi/2$ pulse, the nuclear spins start precessing in the $xy$ plane and produce a time-dependent dipolar field that is optimally detected as a difference-mode signal.

Beside the signal oscillating at the nuclear precession frequency, a difference-mode static signal proportional to the $y$ component of the polymer magnetization is detected. Such static term appears with an amplitude dictated by the aleatory angle $\theta$, and is namely proportional to $\sin\theta$. In Fig.2, the two cases of $\theta=0$ and $\theta=\pi/2$ are presented and they correspond to an additional static field represented by green and red arrows, respectively.

Beside the above mentioned static signal, the small but non-negligible magnetization $\vec{M}$ of the cartridge may cause a variation of the modulus of the field in which the protons precess. This variation comes with some degree of inhomogeneity over the water volume, so that the nuclear spins experience slightly different local fields, with the emergence of an additional relaxation mechanism for the NMR signal.

Also in this respect, only the spurious field component along the static field $\vec{B}_{0}$ has first order effects, so that both the nuclear frequency shift and the decay rate are extreme when $\vec{M}$ is parallel (or antiparallel) to $\vec{B}$ while they are negligible when the two vectors are orthogonal (i.e. when $\theta=\pm\pi/2$ and maximal $\Delta B_{\mbox{D}M}$ is detected).

A homogeneous magnetization $\vec{M}$ of an axially indefinite hollow cylinder, would not produce any field in the inner volume. In contrast, in our case, an internal field is present. This field is not homogeneous, has an average direction parallel to $\vec{M}$, and is caused by the finite length of the cylindrical distribution, by the presence of end caps Varga and Beyer (1998), and possibly by inhomogeneities of the magnetization itself.

The Figs. 3 and 4 show the nuclear precession frequency and decay rate over large set of ULF-NMR measurements. Both the quantities are estimated, trace by trace, making use of a Bertocco-Yoshida approach Bertocco, Offelli, and Petri (1994); Duda (2012). It is worth noting that in our case the NMR signal is not expected to decay with a simple exponential law, because specific field inhomogeneities generated by the cartridge geometry drive the dephasing process. However, the development of a model that reproduces quantitatively the dynamics of the dephasing process is beyond the scope of this work. The mentioned procedure, provides a qualitatively significant estimation of the decay rate, and clearly shows that shots where $\theta\approx 0$ (or $\pi$) result in larger $\gamma_{2}$ values, while smaller decay rates are obtained when the cartridge magnetization is perpendicular to the bias field ($\theta\approx\pm\pi/2$), so to maximize the static field term detected by the differential OAM.

In conclusion, we have discussed the use of an ULF-NMR setup to measure simultaneously the field variation caused by the cartridge magnetization both inside and outside the sample, based on the precession of protons and atoms, respectively. Such hybrid (atomic-nuclear) magnetometry provides -despite the scalar nature of the sensors- two independent and complementary kinds of measurements from which it is possible to infer both the modulus and the orientation of the magnetization.

The method can be of interest to characterize the spurious remanence of NMR samples. Sample ferromagnetic contamination constitutes a problem in ULF-NMR applications, whenever it increases relevantly the $\gamma_{2}$ parameter with respect to its intrinsic value. Moreover it reduces the accuracy in the determination of the nuclear precession frequency. And, finally, when cycled measurements is necessary to improve the signal to noise ratio by trace averaging, the parasitic magnetization hinders the reproducibility of the nuclear precession frequency, so to cause a $\gamma_{2}$ overestimation in the averaged signal.