Quantifying the complex permittivity and permeability of magnetic nanoparticles

Abstract

The complex permittivity and permeability of superparamagnetic iron-oxide nanoparticles has been quantified using a circular waveguide assembly with a static magnetic field to align the nanoparticle's magnetization. The high sensitivity of the measurement provides the precise resonant feature of nanoparticles. The complex permeability in the vicinity of ferromagnetic resonance (FMR) is in agreement with the nanoparticle's measured magnetization via conventional magnetometry. A rigorous and self-consistent measure of complex permittivities and permeabilities of nanoparticles is crucial to ascertain accurately the dielectric behaviour as well as the frequency response of nanoparticle magnetization, necessary ingredients when designing and optimizing magnetic nanoparticles for biomedical applications.Magnetic nanoparticles, with their diameters varying from nanometers to hundreds of nanometers, are under extensive investigation currently for biomedical applications, from MRI contrast agents, microwave imaging enhancement to hyperthermia and drug delivery [1][2][3][4]. The principle attraction of magnetic nanoparticles for these applications is that their sizes are significantly smaller than, e.g. target cells, so that magnetic nanoparticles can be in close contact, and their manipulation through their frequency resonant response from external magnetic fields makes it possible to affect or probe cells and tissue. An outstanding challenge to enable such applications has been a thorough understanding of the nanoparticle's magnetization response (i.e. spin dynamics) when superparamagnetic at high frequencies in complex media such as tissue -knowledge revealed by way of the complex permittivity and permeability that has been problematic to measure.In principle, a calculation based on the Debye equation and the Kramers-Krönig relations should predict the static and dynamic magnetic behavior of nanoparticles. [5][6][7] However, values of the required parameters are often an open question as they could be significantly affected by the material, size and measuring device fabrication process.[7] To effectively utilize magnetic nanoparticles for biomedical applications over the frequencies of interest (often in the microwave regime) it is important to accurately characterize not only the magnetic response quantified by the permeability of the nanoparticles, but also the electric response ascertained by the permittivity. [8] Transmission methods could be used for determining the permittivity (ǫ) and permeability (µ) of material over the requisite wide range of frequencies.[8-10] Usually, ǫ and µ are obtained by measuring reflection and transmission coefficients in free space or via waveguide. Calibration is required to adjust the reference plane to sample surfaces using complicated, multi-step processes includ-ing through-reflection-line calibration, which demand expert technique and complex instrumentation.[10] Irrespective of calibration, an accurate measurement of ǫ and µ is very challenging for nanoparticles due to the nano...

Top-down design of magnonic crystals from bottom-up magnetic nanoparticles through protein arrays

“…Here, the long-range magnetic stray fields and demagnetization effect depend critically on the surfaces and alter the internal magnetic field. The internal magnetic field rules the microwave response and spin-wave (magnon) modes [13] which are of relevance in very different fields ranging from biomedicine [14] to microwave devices [15] and magnonics [16]. Non-flat or irregular surfaces do not allow one to precisely determine the demagnetization factors necessary for a detailed data analysis.…”

“…[14][15][16] Often, randomly oriented magnetic NPs have been addressed. [14,15,18] In the research field of magnonics, however, strictly periodic magnetic nanostructures that form artificial crystals are of crucial interest. [16] To fully exploit the rich advantages offered by magnonics technology, it was very recently argued that mastering spin waves with sub-100 nm wavelengths is key [19].…”

“…[14][15][16] Often, randomly oriented magnetic NPs have been addressed. [14,15,18] In the research field of magnonics, however, strictly periodic magnetic nanostructures that form artificial crystals are of crucial interest.…”

On-chip artificial magnon-polariton device for voltage control of electromagnetically induced transparency

“…For example, CMP effect has recently been observed by setting miligrams of magnetic nano-particles inside a special circular waveguide cavity 11 , where the CMP coupling can be analyzed in the simple 1D configuration by using either the straightforward transfer matrix method 11 , or equivalently, the 1D scattering theory 12 . It is found that the CMP coupling enables quantifying the complex permeability of magnetic nanoparticles with high sensitivity, which was an outstanding challenge for the biomedical applications of magnetic nanoparticles 11 . In 3D microwave cavities, it is shown that the CMP coupling leads to the electromagnetically induced transparency (EIT), which is tuneable by applying an external magnetic field 5 .…”

Indirect coupling between two cavity modes via ferromagnetic resonance

“…Recently, strong coupling between a microwave cavity mode and ferromagnetic resonance (FMR) has been realized at room temperature [6][7][8][9][10][11][12][13][14][15][16][17] . Exchange interactions lock the high density of spins in YIG into a macro-spin state, leading to strong coupling with a cavity mode which can be adjusted using an external magnetic field.…”