Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is an RNA based virus that causes coronavirus disease 2019 (COVID-19) [1] . SARS-CoV-2 with a dimeter ranging from about 60 to 140 nm has spike, envelope, membrane and nucleocapsid proteins [2, 3] .
Spike protein is the one for allowing the virus to bind to the receptor ACE2 of a host cell and to enter the host cell [4] [5] [6] [7] [8] . A patient infected with SARS-CoV-2 may suffer from severe pneumonia and acute respiratory distress syndrome [3, 9, 10] . Since the first infection case of SARS-CoV-2 reported in December, 2019 [10, 11] , SARS-CoV-2 has spread across the whole world, which causes severe problems in medical systems, economics and other social issues.
Till early October 2020, World Health Organization (WHO) has reported more than 35 million cases of infection and 1 million deaths in the world [12] . In addition to other control measures, e.g. social distance and hand washing, WHO has strongly recommended a large amount of testing not only of symptomatic persons and their contacts but also of asymptomatic contacts.
Therefore, large amounts of tests are one of the most important measures to control the outbreak of SARS-CoV-2.
To date, polymerase chain reaction (PCR) based tests with high sensitivity and specificity are the gold standard for the diagnostics of SARS-CoV-2 infection [13, 14] . PCR tests include several complex experimental procedures, which costs at least a few hours to get the test results.
In a PCR test, most experimental procedures require sophisticated and very expensive instrumentation and should be handled by experienced experts. Otherwise, there is a high chance for a false positive/negative result. It leads to huge efforts for medical staffs in the clinics, especially during the exponential increase in infection cases. In developing and underdeveloped countries, the situation for the diagnostics of SARS-CoV-2 with PCR is even worse due to the lack of equipped labs, instrumentation and experienced experts. Therefore, it is of extreme importance and necessity to develop new methods and/or instrumentation for rapid diagnostics of SARS-CoV-2 with reasonable costs. WHO highly encourages researches on the performance of rapid diagnostics approaches and potential diagnostic utilities. However, Page 3 of 21 the development of new approaches for rapid diagnostics, in addition to PCR-based tests, is still a challenging research topic.
Homogeneous biosensing based on magnetic nanoparticles (MNPs) is one of the most promising approaches for rapid and sensitive detection of specific biomolecules, e.g. protein, DNA/RNA and virus. It employs the change in the magnetization dynamics and consequent magnetic response of the MNPs exposed to time-varying magnetic fields [15] . The binding behavior of the biomolecules to functionalized MNPs, dominated by Brownian relaxation, increases their hydrodynamic size or forms cross-linking structures, which significantly changes the Brownian relaxation time of the MNPs and their dynamic magnetization in timevarying magnetic fields [16] [17] [18] . For instance, for MNPs bound with biomolecules, the harmonics in magnetic particle spectroscopy (MPS) dominated by Brownian relaxation decrease when exposed to a sufficiently strong ac magnetic field. Especially, higher harmonics decrease faster than the fundamental harmonic, thus showing a decrease in the harmonic ratio that is independent of the MNP concentration [16, 19] . Thus, the measurement of the MNP magnetization and its susceptibility/spectra in ac magnetic fields can be used to detect the quantity of specific biomolecules. An MPS system has been demonstrated to be a low-cost, versatile and sensitive tool to measure MNP magnetization and dynamics for biomolecule detection [16, 20] . For instance, a mixing-frequency MPS system was designed to measure the mixing components of protein G-functionalized MNP magnetization for antibody detection [21] . Zhang et al. reported on the measurement of the harmonic ratio of anti-thrombin DNA aptamers-functionalized MNPs for the detection of thrombin [22] . Zhong et al. investigated the effect of binding behavior on MNP relaxation time and harmonic ratio for the detection and imaging of biotinylated IgG using streptavidin functionalized MNPs [16, 19] . Yang et al. demonstrated the feasibility of wash-free, sensitive and specific assays for the detection of different viruses, e.g. orchid and influenza viruses, with antibody-functionalized MNPs by measuring the reduction in the ac susceptibility in mixed-frequency ac magnetic fields [23] [24] [25] .
Tian et al. reported on homogeneous detection of SARS-CoV-2 utilizing an opto-magnetic measurement system for the detection of the RND-dependent RNA polymerase coding Page 4 of 21 sequence of SARS-CoV-2 [26] . All these approaches have demonstrated that MNP-based homogeneous biosensing is a wash-free and mix-and-measure approach for rapid and sensitive detection of specific biomolecules. Therefore, it is of great interest and importance to investigate MNP-based biosensing for rapid and sensitive detection of SARS-CoV-2.
In this paper, we propose the detection of SARS-CoV-2 via the measurement of the MPS 
In this paper Exposed to a sufficiently strong ac magnetic field with excitation frequency f0, the MPS signal consists of not only the fundamental harmonic at frequency f0 but also higher harmonics at frequency i×f0. 
The custom-built SMPS was used to measure the 1 st and 3 rd harmonics (M1 and M3) of the output voltage from the gradiometric detection coils on experimental samples in ac magnetic fields with different excitation frequencies f0, where the harmonic at frequency i×f0 is defined as i th harmonic Mi. Figure 4 shows 
The limit of detection (LOD) is one of the most important measures for sensitive detection.
To evaluate the LOD, the measurement sensitivity  and noise level on the harmonic ratio are calculated. The measurement sensitivity, defined as the relative change in R3rd/1st to cmv Page 13 of 21 dR3rd/1st/dcmv, is calculated by a linear fitting of the R3rd/1st vs. cmv curves shown in Fig. 5 . Figure 6a shows the measurement sensitivity vs. frequency curve for different excitation frequencies. It indicates that with increasing frequency from 140 to 1418 Hz the measurement sensitivity  decreases from 0.017 nM -1 to 0.004 nM -1 , which quantitatively fits well with published results [16] . The noise level is calculated with the standard deviation  of 10-repeated measurements on the harmonic ratio of an MNP sample with cmv = 0 nM. In principle, with increasing the excitation frequency, the signal-to-noise ratio (SNR) of the measured harmonic gets improved, which would improve the standard deviation in measured harmonic ratio due to Faraday's law. However, the data in frequencies of 299 Hz and 459 Hz show higher noise levels than that in 180 Hz, which may be caused by instabilities of the measurement system. Figure 6b shows the LOD , estimated from the measurement sensitivity  and standard deviation  by  = [30, 31] . It indicates that the LOD is in the range from about 0.10 to 0.37 nM. Note that the estimated LOD is obtained for a single measurement. With n-time repeated measurements, the LOD can be further improved by a factor of √n. the current approach employs the measurement of magnetic signal of the functionalized MNPs, which does not have depth limitation. When combining with multi-color magnetic particle imaging [33] [34] [35] , the present approach can be extended to visualize the spatial distribution of SARS-CoV-2 in vivo, which is of great significance and interest not only to control the outbreak of SARS-CoV-2 but also to fundamental researches, e.g. understanding the underlying mechanisms of the infection process and virus proliferation.
This paper investigated rapid and sensitive detection of SARS-CoV-2 with functionalized
MNPs. For a proof-of-concept, functionalized MNPs were used as sensors to detect a mimic virus consisting of 100 nm-polystyrene beads conjugated with SARS-CoV-2 spike proteins.
Experiments on ACS spectra and MPS signal of samples with different mimic virus concentrations were performed. Experimental results showed that the binding behavior between mimic SARS-CoV-2 and functionalized MNPs increases the effective Brownian relaxation time and changing the MPS signal. The change in the ratio of the 3 rd to 1 st harmonics with the mimic virus concentration was used to analyze the measurement sensitivity and limit of detection. We believe that the proposed approach is of great promise to highly sensitive and rapid detection with a low cost, easy handling of the sample to be detected (mix-and-measure).
We envisage that the present work is of great interest and significance to develop new methods and design point-of-care devices for rapid diagnostics of SARS-CoV-2 to control its outbreak, as well as fundamental researches on the virus infection.