We study the third harmonic signal of magnetic nanoparticles (MNPs) for use in narrow-band magnetic nanoparticle imaging. We measured the properties of the third harmonic signal, such as frequency and magnetic field dependencies, when the behavior of MNPs was dominated by Neel relaxation. It was shown that the third harmonic signal had both real and imaginary parts, although only the real part is expected from the conventional Langevin function. The real and imaginary parts exhibited different dependences on the frequency and magnetic field. The dynamic behavior of MNPs was analyzed by taking into account the Neel relaxation of MNPs. It was shown that the imaginary part was generated due to Neel relaxation. We obtain an analytical expression for the third harmonic signal, in which distributions of magnetic moment and anisotropic energy of MNPs in the sample were also considered. We show that the analytical results quantitatively explain the experimental results. Our results indicate that the properties of the third harmonic signal of immobilized MNPs are significantly affected by Neel relaxation.
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