Quantitative explanation of the difference in AC magnetization curves between suspended and immobilized magnetic nanoparticles for biomedical application

We study the difference in AC magnetization (M−H) curves between suspended and immobilized magnetic nanoparticles (MNPs). We use three commercial MNP samples that are often used for biomedical application. First, we measure the hysteresis area of the AC M−H curve, A, when the amplitude of the excitation field, H_ac, is changed. The A vs H_ac curve is compared with previously obtained analytical results by taking account of the MNP size distribution in the sample. We show that they quantitatively agree for both suspended and immobilized samples. From the comparison, we clarify the mechanism that determines the AC M−H curve of a suspended sample. For high H_ac, the Néel relaxation becomes dominant in the suspended sample, and alignment of easy axes caused by the AC field increases the hysteresis loss compared to the immobilized case. The effect of Brownian relaxation in the suspended sample increases with decreasing H_ac and gives additional loss at low field. The portion of Néel-relaxation- and Brownian-relaxation-dominant MNPs in the sample is quantitatively evaluated. We also clarify the difference in harmonic signals between suspended and immobilized samples. Finally, we discuss the condition for the MNP parameters and excitation field that determines the dominant relaxation mechanism in a suspended sample.