Transverse susceptibilities of ferromagnetic spin wave interacting with phonon reservoir, II: Temperature dependence of line shapes

A form of the transverse magnetic susceptibility of a ferromagnetic spin system with a uniaxial anisotropy energy and an anisotropic exchange interaction, interacting with a phonon reservoir, is derived in the spin-wave approximation using the TCLE method, where the phonon reservoir interacts with not only the x and y components of each spin but also its z component. The transverse magnetic susceptibility is numerically and analytically studied for the system of one-dimensional infinite spins in the lowest spin-wave approximation, by assuming a damped oscillator model of the phonon reservoir. The temperature dependence and wave number dependence of the susceptibility are numerically investigated for the half-widths and peak-heights of the line shapes in the resonance region. It is shown that as the temperature increases, the half-widths of the line shapes increase and the peak heights decrease in the resonance region, and that as the wave number increases, the half-widths of the line shapes decrease and the peak heights increase in the resonance region. It is also shown that as the uniaxial anisotropy energy of the z direction increases or as the exchange interaction between the z components of spins increases, the half-widths of the line shapes decrease and the peak heights increase in the resonance region. It is besides shown that as the characteristic frequency of the phonon increases, the line shapes show ‘motional broadening’ at the low temperature and show ‘motional narrowing’ at the high temperature. Furthermore, the resonance frequency is shown to increase as the wave number increases or as the temperature increases. The numerical results are examined analytically.     

Intra-well relaxation process in magnetic fluids subjected to strong polarising fields

We report on the frequency and field dependent complex magnetic susceptibility measurements of a kerosene-based magnetic fluid with iron oxide nanoparticles, stabilized with oleic acid, in the frequency range 0.1-6 GHz and over the polarising field range of 0-168.4 kA/m.By increasing polarising field, H, a subsidiary loss-peak clearly occurs in the vicinity of the ferromagnetic resonance peak, from which it remains distinct even in strong polarising fields of 168.4 kA/m. This is in contrast to other reported cases in which the intra-well relaxation process is manifested only as a shoulder of the resonance peak, which vanishes in polarising fields larger than that of 100 kA/m.The results of the XRD analysis connected to the anisotropy field results confirm that the investigated sample contains particles of magnetite and of the tetragonal phase of maghemite.Taking into account the characteristics of our sample, the theoretical analysis revealed that the intra-well relaxation process of the small particles of the tetragonal phase of maghemite may be responsible for the subsidiary loss peak of the investigated magnetic fluid.     

A simple and accurate relative alternative magnetic susceptibility measurement technique

Investigation of relative AC magnetic susceptibility interests for many magnetic transition studies such as superconductor transition. A technique based on mutual or self inductive measure provides a fast and relatively easy (no contact) way to determinate the temperature of any transition affecting the magnetic susceptibility. The half Wheatstone inductive/resistive bridge is used instead of the usual RLC quarter bridge in order to balance the bore inductance of the coil. A comparison between quarter and half bridge measurements illustrates the accuracy of our device.     

Magnetic properties of Fe/ZnSe/Fe trilayers

The magnetic properties of Fe/Zn/Fe trilayers have been studied by ferromagnetic resonance and magnetization measurements. These measurements have been used to investigate the magnetic anisotropy of the iron layers and the magnetic coupling across the semiconductor spacer. The angular dependence of the resonance spectra has been measured in-plane and out-of-plane in order to deduce magnetic anisotropy constants of the samples. Experimental data were fitted by using an energy-density expression that includes bulk cubic anisotropy, growth-induced uniaxial in-plane anisotropy and perpendicular-surface anisotropy terms. A small ferromagnetic coupling is observed in the trilayers with spacer thickness up to .     

Magnetic material arrangement in oriented termites: a magnetic resonance study

Temperature dependence of the magnetic resonance is used to study the magnetic material in oriented Neocapritermes opacus (N.o.) termite, the only prey of the migratory ant Pachycondyla marginata (P.m.). A broad line in the g=2 region, associated to isolated nanoparticles shows that at least 97% of the magnetic material is in the termite’s body (abdomen + thorax). From the temperature dependence of the resonant field and from the spectral linewidths, we estimate the existence of magnetic nanoparticles 18.5 ± 0.3 nm in diameter and an effective magnetic anisotropy constant, K_eff between 2.1 and 3.2 × 10⁴ erg/cm³. A sudden change in the double integrated spectra at about 100 K for N.o. with the long body axis oriented perpendicular to the magnetic field can be attributed to the Verwey transition, and suggests an organized film-like particle system.     

1H/31P双核并行磁共振成像线圈的研究与设计

本文通过对鸟笼线圈原理和阵列线圈去耦原理的分析，提出了一种适用于自主研发的多核并行磁共振成像（MRI）系统的双核并行成像线圈设计方案，并在电感去耦的基础上提出LC并联trap去耦法，提高了去耦方法的可适性．依据设计方案制作了¹H/³¹P双核并行成像线圈，并将其应用于4.7 T磁体系统，利用自主研发的多核并行MRI系统进行了并行成像实验测试，成功获得了¹H和³¹P的并行磁共振图像，验证了设计方案的可行性．     

Anisotropy-induced quantum critical behavior of magnetite nanoparticles at low temperatures

The classical, thermally driven transition from ferrimagnets to superparamagnets in Fe₃O₄ nanoparticles can be converted into another quantum phase by a transverse microwave magnetic field or by a strong internal anisotropic field. These fields, perpendicular to the Ising axis, can destroy the magnetic long-range order to quantum paramagnets as the fields exceed some critical values. We have exploited the spin resonance spectrometer to determine the dynamic spin susceptibility and the critical exponent γ, which is a power-law dependent spanning of the quantum critical point. Quantum phase transition observed at low temperatures for small magnetite nanoparticles induced by strong surface anisotropic field illustrates the fascinating interplay between thermal and quantum fluctuations in the vicinity of a quantum critical point.     

Magnetic susceptibility curves of a nanoparticle assembly, I: Theoretical model and analytical expressions for a single magnetic anisotropy energy

We study a model system made of non-interacting monodomain ferromagnetic nanoparticles, considered as macrospins, with a randomly oriented uniaxial magnetic anisotropy. We derive a simple differential equation governing the magnetic moment evolution in an experimental magnetic susceptibility measurement, at low field and as a function of temperature, following the well-known Zero-Field Cooled/Field Cooled (ZFC/FC) protocol. Exact and approximate analytical solutions are obtained, together for the ZFC curve and the FC curve. The notion of blocking temperature is discussed and the influence of various parameters on the curves is investigated. A crossover temperature is defined and a comparison is made between our progressive crossover model (PCM) and the crude “two states” or abrupt transition model (ATM), where the particles are assumed to be either fully blocked or purely superparamagnetic. We consider here the case of a single magnetic anisotropy energy (MAE), which is a prerequisite before considering the more realistic and experimentally relevant case of an assembly of particles with a MAE distribution (cf. part II that follows).     

Electron magnetic resonance and magnetooptical studies of nanoparticle-containing borate glasses

We report electron magnetic resonance (EMR) and magnetooptical studies of borate glasses of molar composition 22.5K₂O-22.5Al₂O₃-55B₂O₃ co-doped with low concentrations of Fe₂O₃ and MnO. In as-prepared samples the paramagnetic ions, as a rule, are in diluted state. However, in the case where the ratio of the iron and manganese oxides in the charge is 3/2, magnetic nanoparticles with characteristics close to those of manganese ferrite are formed already at the first stage of the glass preparation, as evidenced by both magnetic circular dichroism (MCD) and EMR. After thermal treatment all glasses show characteristic MCD and EMR spectra, attesting to the presence of magnetic nanoparticles, predominantly including iron ions. Preliminary EXAFS measurements at the Fe K-absorption edge show an emergence of nanoparticles with a structure close to MnFe₂O₄ after annealing the glasses at 560 °C.By computer simulating the EMR spectra at variable temperatures, a superparamagnetic nature of relatively broad size and shape distribution with the average diameter of ca. 3-4 nm. The characteristic temperature-dependent shift of the apparent resonance field is explained by a strong temperature dependence of the magnetic anisotropy in the nanoparticles.The formation of magnetic nanoparticles confers to the potassium-alumina-borate glasses magnetic and magneto-optical properties typical of magnetically ordered substances. At the same time, they remain transparent in a part of the visible and near infrared spectral range and display a high Faraday rotation value.     

Magnetic, resonance and transport properties of nanopowder of La0.7Sr0.3MnO3 manganites

X-ray powder diffraction, magnetization, transport and magnetic resonance measurements of nanosize La_0.7Sr_0.3MnO₃ (LCMO) manganites have been performed. The nanosize manganites were synthesized with a co-precipitation method at different (600, 700, 800 and 1000 °C) temperatures. The crystal structure of the nanopowders obtained was determined to be perovskite-like with a rhombohedral distortion (the space group R3¯c). The average size of synthesized nanoparticles (from 17 to 88 nm) was estimated using the X-ray diffraction and low temperature adsorption of argon methods. All the nanosize manganites show ferromagnetic-like ordering. Both the Curie temperature and magnetization decrease with reducing the particle size. The decrease of magnetization is due to the disordered surface shell of particles. The disordered surface layer is a source of the surface anisotropy and is responsible for the increase of coercivity. Temperature dependences of the magnetic resonance spectra parameters have allowed obtaining information on dynamics of magnetic properties in the nanoparticle systems. The resistivity was established to become higher by reducing the particles’ size and increases to a great extent in nanoparticles with the smallest average size at low temperatures. The magnetic entropy was shown to be smaller for the small particles. Using the temperature dependence of magnetic entropy the relative cooling power of the nanosize samples studied was evaluated.     

Ferromagnetic resonance in systems with competing uniaxial and cubic anisotropies

We develop a model for ferromagnetic resonance in systems with competing uniaxial and cubic anisotropies. This model applies to (i) magnetic materials with both uniaxial and cubic anisotropies, and (ii) magnetic nanoparticles with effective core and surface anisotropies; We numerically compute the resonance frequency as a function of the field and the resonance field as a function of the direction of the applied field for an arbitrary ratio of cubic-to-uniaxial anisotropy. We also provide some approximate analytical expressions in the case of weak cubic anisotropy. We propose a method that uses these expressions for estimating the uniaxial and cubic anisotropy constants, and for determining the relative orientation of the cubic anisotropy axes with respect to the crystal principle axes. This method is applicable to the analysis of experimental data of resonance type measurements for which we give a worked example of an iron thin film with mixed anisotropy.     

Spatial confinement of ferromagnetic resonances in honeycomb antidot lattices

We report on a theoretical investigation of the magnetic static and dynamic properties of a thin ferromagnetic film with honeycomb lattice of circular antidots using micromagnetic simulations and analytical calculations. The theoretical model is based on the Landau–Lifshitz equations and directly accounts for the effects of the magnetic state nonuniformity. A direct calculation of local dynamic susceptibility tensor yields that the resonance spectra consist of four different quasi-uniform modes of the magnetization precession related to the confinement of magnetic domains by the hole mesh. Three of four resonant modes follow a two-fold variation with respect to the in-plane orientation of the applied magnetic field. The easy axes of these modes are mutually rotated by 60° and combine to yield the apparent six-fold configurational anisotropy. Additionally, a mode with intrinsic six-fold symmetry behavior exists, as well. Micromagnetic calculations of the local dynamic susceptibility tensor allow identifying the magnetic unit cell areas/domains responsible for each resonance mode.     

Ferromagnetic resonance in arrays of highly anisotropic nanoparticles

We present in this study computational simulations of the ferromagnetic resonance response of magnetic nanoparticles with a uniaxial anisotropy considerably larger than the microwave excitation frequency (in field units). The particles are assumed to be randomly oriented in a two dimensional lattice, and are coupled by dipolar interactions through an effective demagnetization field, which is proportional to the packing fraction. We have included in the model fluctuations in the anisotropy field (H_K) and allowed variations in the demagnetizing field. We then analyzed the line shape and line intensity as a function of both fields. We have found that when H_K is increased the line shape changes drastically, with a structure of two lines appearing at high fields. The line intensity has a maximum when H_K equals the frequency gap and decreases considerably for larger values of the anisotropy. The effects of fluctuations in H_K and variations in the packing fraction have been also studied. Comparison with experimental data shows that the overall observed behavior is dominated by the particles with lower anisotropy.     

Multi-objective optimization of gradient coil for benchtop magnetic resonance imaging system with high-resolution

Significant high magnetic gradient field strength is essential to obtaining high-resolution images in a benchtop mag- netic resonance imaging （BT-MRI） system with permanent magnet. Extending minimum wire spacing and maximum wire width of gradient coils is one of the key solutions to minimize the maximum current density so as to reduce the local heating and generate higher magnetic field gradient strength. However, maximum current density is hard to optimize together with field linearity, stored magnetic energy, and power dissipation by the traditional target field method. In this paper, a new multi-objective method is proposed to optimize the maximum current density, field linearity, stored magnetic energy, and power dissipation in MRI gradient coils. The simulation and experimental results show that the minimum wire spacings are improved by 159% and 62% for the transverse and longitudinal gradient coil respectively. The maximum wire width increases from 0.5 mm to 1.5 mm. Maximum gradient field strengths of 157 mT/m and 405 mT/m for transverse and lon- gitudinal coil are achieved, respectively. The experimental results in BT-MRI instrument demonstrate that the MRI images with in-plane resolution of 50 ~tm can be obtained by using the designed coils.     

Singularity in high-frequency susceptibility of thin magnetic films with uniaxial anisotropy

A sharp peak of magnetic susceptibility has been observed in the ferromagnetic resonance spectra of uniaxial magnetic films placed in a planar field directed orthogonal to the easy magnetization axis, along which a pumping high-frequency magnetic field has been oriented. The peak width is considerably narrower than the line width of the uniform ferromagnetic resonance, and its position in a field equal to the film anisotropy field does not depend on the pumping frequency. The nature of the peak is associated with a drastic increase in the static transverse susceptibility of the film in the vicinity of the anisotropy field. It is shown phenomenologically that the peak can be observed only for quality samples with small angular and amplitude dispersion of the uniaxial anisotropy.     

Ferromagnetic resonance of cobalt nanoparticles in the polymer shell

The magnetic properties of cobalt spherical nanoparticles (～ 5–9 nm in size) in a polymer shell are investigated using ferromagnetic resonance (FMR) spectroscopy. The metal-polymer complex is prepared through the frontal polymerization of the cobalt acrylamide (CoAAm) complex, followed by the thermolysis at a temperature of 643 K. Analysis of the ferromagnetic resonance spectra demonstrates that the material has a high blocking temperature of ～700 K. The anisotropy constant equal to 0.5 erg/cm³ is somewhat larger than the anisotropy constants characteristic of cobalt macrostructures. This difference is associated with the predominance of the surface anisotropy of nanoparticles. The surface anisotropy constant is calculated to be 0.17 erg/cm², and the anisotropy field is determined to be ～350 Oe. It is revealed that the polymer shell affects the magnetic properties of nanoparticles.     

Giant magnetic susceptibility enhancement in field-structured nanocomposites

We demonstrate through experiment and simulation that when mono-domain Fe nanoparticles are formed into chains by the application of a magnetic field, the susceptibility of the resulting structure is greatly enhanced (11.4-fold) parallel to the particle chains and is much larger than transverse to the chains. Simulations show that this significant enhancement is expected when the susceptibility of the individual particles approaches 5 in MKS units, and is due to the spontaneous magnetization of individual particle chains, which occurs because of the strong dipolar interactions. This large enhancement is only possible with nanoparticles, because demagnetization fields limit the susceptibility of a spherical multi-domain particle to 3 (MKS). Experimental confirmation of the large susceptibility enhancement is presented, and both the enhancement and the susceptibility anisotropy are found to agree with simulation. The specific susceptibility of the nanocomposite is 54 (MKS), which exceeds the highest value we have obtained for field-structured composites of multi-domain particles by a factor of four.     

Uniform spin wave modes in antiferromagnetic nanoparticles with uncompensated moments

In magnetic nanoparticles the uniform precession (q = 0 spin wave) mode gives the predominant contribution to the magnetic excitations. We have calculated the energy of the uniform mode in antiferromagnetic nanoparticles with uncompensated magnetic moments, using the coherent potential approximation. In the presence of uncompensated moments, an antiferromagnetic nanoparticle must be considered as a kind of a ferrimagnet. Two magnetic anisotropy terms are considered, a planar term confining the spins to the basal plane, and an axial term determining an easy axis in this plane. Excitation energies are calculated for various combinations of these two anisotropy terms, ranging from the simple uniaxial case to the planar case with a strong out-of-plane anisotropy. In the simple uniaxial case, the uncompensated moment has a large influence on the excitation energy, but in the planar case it is much less important. The calculations explain recent neutron scattering measurements on nanoparticles of antiferromagnetic α-Fe₂O₃ and NiO.     

双层磁性薄膜系统中铁磁共振性质

利用能量极小原理研究了双层磁性薄膜系统中的铁磁共振特性,给出共振频率与线宽随外加磁场的变化关系.以及考虑应力各向异性、交换各向异性和单轴各向异性后,系统共振频率与线宽的变化情况.数值计算结果表明:外应力场和交换各向异性场对铁磁共振频率、频谱宽度以及磁化行为均有影响.