Reversible Transverse Susceptibility Research Articles

Parametric amplification of reversible transverse susceptibility in single domain magnetic nanoparticles

We propose, model, and experimentally demonstrate the enhancement of reversible transverse susceptibility in single domain magnetic nanoparticles through the principle of parametric amplification. It has previously been demonstrated that properly oriented anisotropic single domain magnetic nanoparticles have an appreciable peak in transverse susceptibility at the particle anisotropy field. Here we show theoretically and experimentally that an additional parametric AC magnetic field applied at a proper phase and at twice the frequency (2f) of the transverse field further enhances transverse susceptibility peaks through the process of parametric amplification. We model this effect numerically and describe it through the energy formalism of the single magnetic domain Stoner-Wohlfarth model. The proper phase relationships of the transverse and parametric fields to obtain either parametric amplification or attenuation of the transverse susceptibility signals are also described. We experimentally demonstrate such parametric tuning of transverse susceptibility in single domain magnetic nanoparticles of a commercial audio tape in a prototypical inductive transverse susceptibility set-up.

Effect of magnetic nanoparticle shape on flux amplification in inductive coil magnetic resonance detection

We model and analyze the effect of particle shape on the signal amplification in inductive coil magnetic resonance detection using the reversible transverse magnetic susceptibility of oriented magnetic nanostructures. Utilizing the single magnetic domain Stoner-Wohlfarth model of uniform magnetization rotation, we reveal that different ellipsoidal particle shapes can have a pronounced effect on the magnetic flux enhancement in detection configurations typical of magnetic resonance settings. We compare and contrast the prolate ellipsoids, oblate ellipsoids, and exchange-biased spheres and show that the oblate ellipsoids and exchange-biased spheres have a significantly higher flux amplification effect than the prolate ellipsoids considered previously. In addition, oblate ellipsoids have a much broader polarizing magnetic field range over which their transverse flux amplification is significant. We show the dependence of transverse flux amplification on magnetic resonance bias field and discuss the resulting signal-to-noise ratio of inductive magnetic resonance detection due to the magnetic nanoparticle-filled core of the magnetic resonance detection coil.

Transverse susceptibility study of the effect of varying dipolar interactions on anisotropy peaks in a three-dimensional assembly of soft ferrite nanoparticles

Collective magnetization dynamics in nanoparticle assemblies is of current interest as it forms the basis of high density storage media. It is important to understand how interparticle interactions in a three-dimensional (3D) arrangement of superparamagnetic nanoparticles would affect the overall effective magnetic anisotropy of the system. We have studied the influence of varying strengths of dipolar interaction on the static and dynamic magnetic properties of surfactant-coated monodispersed manganese zinc ferrite nanoparticles using reversible transverse susceptibility. We track the evolution of the anisotropy peaks with varying magnetic field, temperature, and interaction strength. The blocking temperature shows an increase from 28 to 32 K and the coercive field (at 10 K) shows an increase from 144 to 192 Oe as the system changes from the case of weakly interacting to strongly interacting 3D assembly of the particles.

Monte Carlo study of the transverse susceptibility in ordered arrays of magnetic nanoparticles

We present Monte Carlo simulations of the reversible transverse susceptibility (RTS) for a hexagonal array of dipolar interacting magnetic nanoparticles with random anisotropy. RTS curves with the bias field in-plane and out-of-plane are compared. With increasing temperature the RTS curves evolve from a three-peak $({H}_{C},\ifmmode\pm\else\textpm\fi{}{H}_{K})$ structure to a double-peak and eventually a single-peak at the blocking temperature of the system. This trend is preserved for weak interactions. Dipolar interactions at low temperature are responsible for the suppression of the ${H}_{C}$ peak in the out-of-plane geometry and its progressive merge to the ${H}_{K}$ peak with decreasing interparticle separation in the in-plane geometry. The ${H}_{K}$ peaks are located at higher field values in the out-of-plane geometry relative to the in-plane one. When the bias field lies in-plane (out-of-plane) the ${H}_{K}$ peaks are shown to shift to lower (higher) field values with decreasing interparticle separation. The ${H}_{C}$ peak shifts to lower field values in both geometries. Our results are compared with recent experimental findings in self-assembled arrays of Fe nanoparticles.

Angular Dependence of Reversible Transverse Susceptibility in Magnetic Nanoparticles

We present angular dependence measurements of reversible transverse susceptibility for two different single magnetic domain nanoparticle systems. A modified alternating gradient magnetometer was used for the measurements. This study supplements previous reversible transverse susceptibility measurements, usually performed at a limited number of angles by inductive techniques. The angular dependence measurements reveal several features in reversible transverse susceptibility of oriented magnetic nanoparticles that have previously gone undetected. The theoretically predicted peaks at the coercive magnetic field, HC, appear only at certain narrow, primarily nonorthogonal angular orientations. In addition, we find that the magnitude of the reversible transverse susceptibility has a maximum at angles different from both the easy and hard nanoparticle axes, which might have important consequences for use of such nanoparticles in enhancement of magnetic resonance signals

Ferromagnetic ordering in nanostructured Mn-doped InP

We report the observation of ferromagnetic ordering at 25K in a diluted magnetic semiconductor (DMS) nanoparticle system: In0.9Mn0.1P, sized 3nm. These particles were synthesized using a novel nanochemical technique without using any external surfactant. Structural and elemental characterizations established the occurrence of the zinc-blende phase of the DMS without any separate or induced impurity phase. A robust onset of ferromagnetic order is observed in magnetization measurements at around 25K with blocked state behavior below 15K characteristic of magnetic nanoparticles. The system shows strong frequency dependence of the susceptibility, similar to the behavior observed for spin glasses. Reversible transverse susceptibility experiments done using a resonant radio-frequency (rf) method reveal a strong temperature-dependent effective anisotropy.

Magnetic nanostructures as amplifiers of transverse fields in magnetic resonance

We introduce the concept of amplifying the transverse magnetic fields produced and/or detected with inductive coils in magnetic resonance settings by using the reversible transverse susceptibility properties of magnetic nanostructures. First, we describe the theoretical formalism of magnetic flux amplification through the coil in the presence of a large perpendicular DC magnetic field (typical of magnetic resonance systems) achieved through the singularity in the reversible transverse susceptibility in anisotropic single domain magnetic nanoparticles. We experimentally demonstrate the concept of transverse magnetic flux amplification in an inductive coil system using oriented nanoparticles with uni-axial magnetic anisotropy. We also propose a composite ferromagnetic/anti-ferromagnetic core/shell nanostructure system with uni-directional magnetic anisotropy that, in principle, provides maximal transverse magnetic flux amplification.

Generalized reversible susceptibility tensor

A theory of reversible susceptibility tensor based on magnetization vector dynamics, as described by the Landau–Lifshitz equation of motion, is given. It is shown that the reversible transverse susceptibility (RTS) is in fact the zero frequency limit of the ferromagnetic resonance (FMR). Thus, the methods which have been developed previously for the theoretical description of FMR may be applied to predict the RTS behavior. The importance of these results resides in the generality of the approach which allows one to find the reversible susceptibility tensor for virtually any magnetic system if an expression for the magnetic free energy density is known.

Observation of charge ordering and the ferromagnetic phase transition in single crystal LSMO using rf transverse susceptibility

We performed temperature and field-dependent reversible transverse susceptibility (TS) measurements on a La0.85Sr0.15MnO3 single crystal at radio frequency (10MHz) using a resonant tunnel-diode oscillator technique. These dynamic experiments probe the coupled electronic, magnetic and structural transition in LSMO giving rise to the ferromagnetic transition and the charge-ordered phase. The effective magnetic anisotropy fields are directly probed across the entire range from the Curie temperature to lower temperatures well into the charge-ordered state. Overall, the TS experiments are demonstrated to be useful for studying magnetic anisotropy in the presence of structural and electronic transitions in these strongly coupled systems.

Sensitive measurement of reversible parallel and transverse susceptibility by alternating gradient magnetometry

Reversible susceptibility tensor measurements reveal important information about the switching fields and anisotropies of magnetic materials. We show that a simple reconfiguration of an alternating gradient magnetometer can be used to measure both reversible parallel and transverse susceptibilities with high sensitivity. It is demonstrated that positioning the sample off axis with respect to the magnetometer gradient field coils results in a signal at twice the frequency of the gradient field that is directly proportional to the reversible susceptibility. Offsetting the sample along the x axis results in a sensor signal proportional to the reversible parallel susceptibility, while rotating the sample holder by 90° and offsetting it along the y axis results in a sensor signal proportional to the reversible transverse susceptibility. Examples of reversible parallel and transverse susceptibility measurements of aligned nanoparticle systems are demonstrated.

Magnetic anisotropy obtained from demagnetization curves: Influence of particle orientation and interactions

The influence of easy axis orientation and interparticle interactions on the apparent magnetic anisotropy distribution, obtained from the demagnetization curve analysis, has been studied. For any particle orientation, the method is useful in detecting multimodal distributions as well as effective anisotropy field values. In the case of interacting particulate systems, the range of interaction strength that can be studied is wider than that of the reversible transverse susceptibility method. Analytical expressions for the distribution curves are given, allowing numerical predictions for different distributions of particle orientations and interaction strengths.

Deconvolution of anisotropy field distributions from transverse susceptibility measurements

The reversible transverse susceptibility is a measurement often used to determine the anisotropy field of magnetic materials. A maximum entropy approach issued to determine the dispersion of H k values for a system of randomly oriented CrO 2 particles.

Thermomagnetics of interacting magnetic particles

Thermomagnetics of a system of interacting particles with log normal distribution of particle size and anisotropy constant was studied self-consistently using a Monte Carlo calculation within the mean-field approximation. Characteristic hysteretic behavior and reversible transverse susceptibility (RTS) were investigated. The salient features are as follows: The hysteresis loops become sheared with increasing anisotropy distribution, /spl sigma//sub K/, while their slopes steepen with the mean field strength /spl alpha/. For a homogeneous systems RTS peaks increase sharply with /spl alpha/, both at the anisotropy field H/sub K/ and coercive field H/sub c/. For random systems, both peaks become shallower and blunted with increasing /spl sigma//sub K/. Mean field strength /spl alpha/ causes the peak positions of RTS at H/sub K/ to shift to lower values, while the shift at H/sub c/ depends subtly upon the interplay among /spl alpha/, /spl sigma//sub K/ and texture of the system. For random systems the shift is toward higher H/sub c/ values with increasing /spl alpha/. For systems with constant /spl alpha/, however, it shifts toward lower values with increasing /spl sigma//sub K/.

Characterization of the magnetic switching properties of single-domain particles

We investigated the characteristics of the magnetic switching of the single-domain particles (SDP) and studied its variation as a function of the field orientation, sweep rate, textural distribution and thermal relaxation effects. Our analysis is based on the non-interacting bi-state model using the probabilistic approach. The hysteresis loops measured at high sweep rates are much wider and the corresponding coercivities H c much larger than those taken at slower sweep rates. An increase in the field-angle orientation from the easy axis reduces the H c field, while decreasing the sweep rate flattens the trend of the variation of the curve until a very large angle is reached. The thermal factor KV/k BT, on the other hand, plays essentially the same role as the sweep rate does to the H c values: the larger the value of KV/k BT, the larger the value of H c . The transition energy barrier is roughly equal to ≈ 25 k B T if the field sweep period is 1 h, in agreement with the usual concept of the blocking temperature. However, this concept is subject to dispute if the sweep period is comparatively faster or slower. The variation of the reversible transverse susceptibility (RTS) with respect to the field orientation and thermal relaxation has also been systematically investigated. The cusps or trenches of the RTS due to thermal relaxation were shown to be substantially shaved or filled, while the corresponding H c values were shifted and reduced. The RTS of the SDPs may exhibit one, two or three prominent cusps at high values of KV/k BT depending upon the configuration and texture or randomness of the system given. The height of the cusp also varies with the field-orientation angles, and the corresponding switching-field distribution becomes broadened and decreases with the values of KV/k BT.

Thermal relaxation, textural and sweep rate effects on reversible transverse susceptibility of magnetic particles

We investigated the effect of thermal relaxation on reversible transverse susceptibility (RTS), χ, of single domain Stoner–Wohlfarth particles. We studied such an effect as a function of the orientation β of the easy axis with respect to the drive field (the z axis) within a non-interacting bi-state model. At β=00 one prominent cusp occurs for both χt1 and χt2 along the direction perpendicular to the drive field at H≂HC<HN (nucleation field) at high values KV/kBT (the ratio of the anisotropy energy versus thermal energy). The height of the cusp varies with β and reduces with decreasing values of KV/kBT. Correspondingly, the switching field distribution (SFD) becomes broadened with decreasing values of KV/kBT. The RTS may exhibit one, two, or three prominent cusps at high values of KV/kBT depending upon the textural distribution of the easy axes. For cos2 θ distribution of the easy axis about the x axis, y axis, and z axis there exists two, three, and one cusps, respectively. For random distribution of the easy axis in 2-D in the XZ and YZ plane there are one and three cusps, respectively, while there are three for random distribution in 3-D. Finally, we studied coercivity, RTS and SFD as a function of sweep rate. All these quantities are found to increase with sweeping frequency of the drive field. The peak field value of RTS is consistently the smallest of the three, while that of SFD is equal to or a shade larger than HC depending upon whether the hysteresis loop is rectangular or severely sheared.

Transverse susceptibility of particulate recording media in different remanence states

Transverse susceptibility measurements were performed on isotropic and aligned γ-Fe2O3 and ZnTi-doped barium-ferrite powder samples in different remanence states. Measurement results obtained on a sintered NdFeB sample are given for comparison. Deviations of the experimental result from the Stoner–Wohlfarth theory are ascribed to inhomogeneous magnetization states and particle–particle interactions. The remanent reversible transverse susceptibility appears to be much more sensitive to these influences than standard remanence-curve analysis and thus provides a new experimental approach to the interaction problem.

Textural and sweep rate effects on transverse susceptibility of magnetic particles

Depending on the textural distribution of easy axes of the particles there could exhibit one, two or three prominent cusps in the curves for the reversible transverse susceptibility at high KV/kBT. Experimentally, the number of cusps detected at low KV/kBT may be one less since the cusp at Hc is fairly sensitive to thermal relaxation.

Transverse susceptibility and magnetic anisotropy of CoTi-doped barium hexaferrite single crystals

Measurements of the reversible transverse susceptibility (RTS) were performed on BaFe12−x−yCoxTiyO19 single crystals with doping concentrations x≊y≤0.77 under different angles ϑ0 between the easy axis and applied field. For intermediate doping concentrations the occurrence of a peak in the RTS curve for ϑ0=90° indicates that the domain walls are not free to move. This assumption is confirmed further by the large component of the RTS being out of phase with respect to the excitation field HE. The phase angle of the initial susceptibility measured parallel to the easy axis becomes maximum at a characteristic excitation field value HE,C and a relaxation of the susceptibility is observed if HE steps from zero to a value larger than HE,C. Using the RTS curve for ϑ0=0 and assuming that the peak of the RTS is located at the same field strength as if the particle were single domain, the first-order anisotropy field HA=2K1/(μ0Ms) and the second-order anisotropy constant K2 can be determined. The values found this way are compared to results from magnetization-curve analysis and from other authors.

Detection of anisotropy in the reversible transverse susceptibility

A model of reversible transverse susceptibility is proposed. It is based on the Stoner–Wohlfarth coherent rotation model, but with a macroscopic mean field interaction included to represent mutual interaction between particles. Unlike previous predictions, our calculated results show that the determination of the magnetic anisotropy field strength by means of the location of the peak in the transverse susceptibility curve works only in a weakly interacting particle system. For a strongly correlated system, nucleation does not start at the anisotropy field; therefore, it can be concluded that the peak detection method of anisotropy in transverse susceptibility should fail in this system.

Reversible transverse susceptibility of particulate recording media

The response of a system to an infinitesimal perturbation becomes singular if the system changes its degree of metastability, i.e., if it has an inflection point. This theory is used to calculate the reversible transverse susceptibility χt of a single domain particle executing a major hysteresis loop under the influence of a field H(t) applied at an angle β to the easy axis. Thermal relaxation is taken into account and the response of the nonequilibrium system to the infinitesimal field h(t)=h sin ωt, h⊥H, is found. The resultant χt is studied as a function of β, temperature, and of the frequency Ω of the biasing field H.