Magnetization and magnetic susceptibility of InAs nano-rings

In this work, we investigate theoretically the magnetic susceptibility of the three-dimensional cut-torus-shaped quantum rings. The calculations are carried out for the realistic three-dimensional model of InAs/GaAs nano-rings with the hard-wall confinement potential, three-dimensional effective one-electronic-band Hamiltonian with position and energy-dependent effective mass, and Ben Daniel–Duke boundary conditions. This allows us to describe the penetration of the magnetic field into the torus region. At zero temperature, the ring's differential susceptibility demonstrates delta-like paramagnetic peaks, which are generated by aperiodic oscillations of magnetization. With increasing temperature, the peaks gradually transform into Lorenz-shaped peaks and then disappear. As opposed to meso-scopic quantum rings we found a dependence of the peak's amplitude on the dimensions of the rings.     

Low-frequency complex magnetic susceptibility of magnetic composite microspheres in colloidal dispersion

A procedure is presented to determine the permanent magnetic dipole moment of composite microspheres containing magnetic nanoparticles with a blocked magnetic dipole moment. The composite particles are dispersed in a solvent, and the complex magnetic susceptibility is measured from 0.1 to 1000 Hz using a highly sensitive new setup. Composite particles with a permanent magnetic dipole moment are revealed by a characteristic frequency that corresponds to the Brownian rotation of the microspheres. From measured susceptibility spectra, we calculate the permanent magnetic dipole moment of recently developed cobalt ferrite-doped silica and latex microspheres.     

Scaling laws and approximate expressions for the dynamic magnetic susceptibility of Brownian nanoparticles

We present simplified expressions for the out-of-phase component of the dynamic susceptibility χ″ of lognormal-sized magnetic nanoparticles under Brownian rotation. These expressions are based on transforming the general integral functions used for χ″ in the convolution of gaussian functions. χ″ can thus be expressed as a sum of gaussians with parameters directly related to those of the size distribution and to the saturation magnetization. The gaussian fit of χ″(ω) (where ω is the ac field frequency) is a simpler way to determine these structural and magnetic parameters as it avoids fitting χ″(ω) to an integral function. The expressions derived for χ″ suggest that χ″T data collapses in a ωη(T)/T scale (where T is the temperature and η the fluids viscosity), which is confirmed by numerical calculations. We also discuss the limits of validity of these approximations in real systems where both Néel and Brownian relaxation mechanisms coexist and we present further approximations for the relation of ω_χ with the average volume (being ω_χ the frequency at which χ″ is maximum). The ωη(T)/T scale can be used to qualitatively evaluate the dominance of the Brownian relaxation mechanism.     

Nanocrystalline magnetic PrFeCrB alloys

Ribbons of Pr₅Fe_77−xCr_xB₁₈ (x=0$x=0$, 1, 2, 2.5, 3, 4, 5) were produced by melt spinning and then annealed to develop an enhanced-remanence nanocrystalline magnetic material. These nanocomposites with Cr present a coercive field at least 50% higher than the Cr-free ones, which makes them promising materials for bonded magnets. Four different types of annealing were used in order to develop the nanocrystalline state and to optimize the magnetic properties of these alloys. The first was a conventional annealing, where the ribbons were wrapped in a tantalum foil and annealed in an argon atmosphere, but not encapsulated. The second was a flash annealing, where the ribbons were annealed by passing a current through them. The third was a conventional annealing in an external magnetic field. Finally, the fourth was a conventional annealing, where the ribbons were wrapped in a tantalum foil and encapsulated in quartz tubes with argon gas and then annealed. The annealed samples were studied by magnetic measurements, X-ray diffraction, scanning and transmission electron microscopy and atomic force microscopy. The best magnetic properties are found for Pr₅Fe₇₄Cr₃B₁₈, annealed by the fourth method, which resulted in the lowest oxygen content in the annealed nanocrystalline material as confirmed by scanning electron microscopy. The value for the coercive field for this composition is at least 50% higher than for the material without Cr (≈560 vs. ≈320 kA/m) and 40% higher than for the Nd₂Fe₁₄B/Fe₃B nanocomposite with Cr. Curie temperature measurements and X-ray diffraction data showed that the main phases present in all the samples are Pr₂Fe₁₄B, Fe₃B and α-Fe, Pr₂Fe₁₄B being the majoritary phase. From Curie temperature measurements it was also found that Cr atoms preferentially dissolve in the Fe₃B phase.     

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.     

Special features of the functional dependences of magnetic susceptibility of magnetic colloids in porous media

The frequency and temperature dependences of the magnetic susceptibility of magnetic colloids with large particle sizes placed in porous media have been found to be different from the similar dependences for bulk samples. The observed peculiarities can be explained by the influence of surface phenomena on the processes of relaxation of the magnetic moment of colloidal particles.     

Anderson impurity model: Double occupancy contribution to the magnetic susceptibility

After solving the single Anderson impurity model (SIAM) within the non-crossing approximation with a finite Coulomb repulsion, U, and vertex corrections (NCAf²v), we focus on the magnetic susceptibility. Using the same diagrammatic expansion the susceptibility can be dressed with two factors, namely, the double state occupancy and the vertex corrections. In this work we analyse the effect of double occupancy on the dynamic and static susceptibility as a function of U and on the degeneracy of the total impurity angular moment, S.     

Structure-dependent magnetic susceptibility of sharp poly(ethylene oxide) fractions

Nine sharp fractions of poly(ethylene oxide) (PEO) glycol with number-average molar masses (M _n) in the range from 0.6 × 10³ to 20 × 10³ (PEO-0.6 to PEO-20) were characterized by magnetic susceptibility χ measured in the temperature interval 293 K to 378 K. In contrast to the liquidlike PEO-0.6 with temperature-invariant χ, the values of χ for each of the remaining solid samples, after the initial increase, exhibited two plateaus separated by a relatively narrow temperature interval of their second increase. The jumps of χ at lower and higher temperatures were attributed to a solid-state transition of unspecific nature and to the melting of the crystal fraction, respectively.

The temperature-invariant values of χ_n in the melt state above T _m pass through a minimum for the sample PEO-2.0 and then increase again with (M_n) to a limiting value χ_∞ = ?0.622 × 10^?6. It is concluded that a considerable contribution of the molar-mass-dependent “paramagnetism” χ_P = χ ^? χ_d (where χ_d is the diamagnetic contribution estimated by Kirkwood's equation) to the total magnetic susceptibility of PEO fractions reflects distortions of the spherical symmetry of the electron shells around chain atoms resulting from the discontinuous change of both inter- and intrachain interactions as the (M_n) increases through and above the critical crossover molar mass (M_cr ) = 2 × 10³.     

Microhydrodynamical modeling of transverse susceptibility of magnetic inks (Theory of ‘DIMAG’)

The time and field dependence of the transverse susceptibility, χ_t, of a suspension of single domain ferromagnetic Brownian particles in a viscous fluid is calculated. Magnetic interactions are taken into account through the mean field model. The model is used to interpret (so far qualitatively) the so-called DIMAG experiment, in which a DC field is applied to the ink sample for a short period of time and a small perpendicular AC field probes χ_t before, during and after the DC field impact. The relative increase in χ_t, after the DC field is switched on was used earlier to characterize the dispersion quality of inks. We show that in the systems with negative interactions (acicular particles) this increase has a maximum when plotted as a function of the DC field. The maximum shifts to higher fields as the interaction increases, which corresponds to what happens in the DIMAG testing of less dispersed inks.     

Annealing temperature effect on microstructure,magnetic and microwave properties of Fe-based amorphous alloy powders

Fe₇₄Ni₃Si₁₃Cr₆W₄ amorphous alloy powders were annealed at different temperature (T) for 1.5 h to fabricate the corresponding amorphous and nanocrystalline powders. The influences of T on the crystalline structure, morphology, magnetic and microwave electromagnetic properties of the resultant samples were investigated via X-ray diffraction, scanning electron microscopy, vibrating sample magnetometer and vector network analyzer. The results show that the powder samples obtained at T of 650 °C or more are composed of lots of ultra-fine α-Fe(Si) grains embedded in an amorphous matrix. When T increases from 350 to 750 °C, the saturated magnetization and coercivity of the as-annealed powder samples both increase monotonously whereas the relative real permittivity shows a minimal value and the relative real permeability shows a maximal value at T of 650 °C. Thus the powder samples annealed at 650 °C show optimal reflection loss under −10 dB in the whole C-band. These results here suggest that the annealing heat treatment of Fe-based amorphous alloy is an effective approach to fabricate high performance microwave absorber with reasonable permittivity and large permeability simultaneously via adjusting T.     

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).     

Dynamics of uniform quantum gases, II: Magnetic susceptibility

A general expression for temperature-dependent magnetic susceptibility of quantum gases composed of particles possessing both charge and spin degrees of freedom has been obtained within the framework of the generalized random phase approximation. The conditions for the existence of dia-, para-, and ferro-magnetism have been analyzed in terms of a parameter involving single-particle charge and spin. The limit T→0 retrieves the expressions for the Landau and the Pauli susceptibilities for an electron gas. It is found for a Bose gas that on decreasing the temperature, it passes either through a diamagnetic incomplete Meissner-effect regime or through a paramagnetic-ferromagnetic large magnetization fluctuation regime before going to the Meissner phase at .     

Magnetic susceptibility curves of a nanoparticle assembly II. Simulation and analysis of ZFC/FC curves in the case of a magnetic anisotropy energy distribution

Starting from the theoretical results established in Tournus and Bonet (2010 [1]) to describe ZFC/FC (zero-field cooled/field cooled) susceptibility curves, we examine the limitations of the widely used two states model (or abrupt transition model) where the magnetic particles are supposed to be either fully blocked or fully superparamagnetic. This crude model appears to be an excellent approximation in most practical cases, i.e. for particle assembly with broad enough size distributions. We improve the usual model by taking into account the temperature sweep existing in experimental measurements. We also discuss a common error made in the use of the two states model. We then investigate the relation between the ZFC peak temperature and the particle anisotropy constant, and underline the strong impact of the size dispersion. Other useful properties of ZFC/FC curves are discussed, such as invariance properties, the reversibility of the FC curve and the link between the susceptibility curves and the magnetic anisotropy distribution. All these considerations lay solid bases for an accurate analysis of experimental magnetic measurements.     

Imaging magnetic responses of nanomagnets by XPEEM

The Spin-resolved Photoelectron Emission Microscope (SPEEM) is a permanently installed set-up at Helmholtz-Zentrum Berlin (HZB). Due to its specific contrast it is mainly used for magnetic imaging and micro-spectroscopy with quantitative analysis. A crucial point in magnetic imaging is the application of magnetic fields. Many experiments require observation of magnetic responses or the preparation of a certain magnetic state during the measurement. We present a dedicated magnetic sample holder combining magnetic field during imaging with additional temperature control. This set-up enables SPEEM to measure magnetization curves of individual Fe nanocubes (18 nm)³ in size. If additionally alternating magnetic fields are applied we can image the local magnetic AC susceptibility (χ_AC) as a function of temperature. The latter is ideally suited to visualize local variations of the Curie temperature (T_C) in nano- and microstructures.     

AC susceptibility of magnetic markers in suspension for liquid phase immunoassay

AC susceptibility of magnetic markers in solution was studied for biosensor applications. First, frequency dependence of the susceptibility was measured, and size distribution of the markers was estimated by analyzing the experimental result with the so-called singular value decomposition (SVD) method. The size distribution estimated with the magnetic measurement agreed with that obtained from conventional optical measurement. Next, susceptibility measurement was applied to the liquid-phase immunoassay without bound/free (B/F) separation. We performed the detection of biotin-coated polymer beads in suspension using avidin-coated magnetic markers. Changes of the susceptibility and the size distribution caused by the binding reaction were shown.     

Multichannel enhanced Faraday rotations in magnetic heterostructures

Transmittance and Faraday rotation (FR) spectra of one-dimensional magnetic heterostructures are investigated using 4 by 4 transfer matrix method. It is revealed that in a simple magnetic heterostructure the enhanced FR at a desired wavelength can be realized considering a special design of substructures and adjusting the thicknesses of constituent magnetic layers. In addition, a complex magnetic heterostructure with capability of providing the multichannel enhanced FRs at desired wavelengths is introduced. It is shown that such a heterostructure could support high transmittance enhanced FRs at telecommunication wavelengths of 1300 and 1550 nm, simultaneously. The results may have potential applications in designing the multi-function single magneto-optical devices such as multichannel Faraday rotators and wavelength division multiplexing systems.     

Microstructures evolution and physical properties of laser induced NbC modified nanocrystalline composites

The nanoscale quasicrystals (NQs), amorphous and ultrafine nanocrystals (UNs) modified hard composites are produced by laser cladding (LC) of the Ni60A-TiC-NbC-Sb mixed powders on the additive manufacturing (AM) TA1 titanium alloy. The LC technique is favorable to formations of icosahedral quasicrystals (I-phase) with five-fold symmetry due to its rapid cooling and solidification characteristics. The formation mechanism of this I-phase is explained here. Under the actions of NQs, amorphous and UNs, such LC composites exhibited an extremely high micro-hardness. UNs may also intertwin with amorphous, forming yarn-shape materials. This research provides essential theoretical basis to improve the quality of laser-treated composites.     

Spectroscopic analysis and magnetic susceptibility of CuO-TeO2-V2O5 glasses

This article reports on the structure of the glassy system xCuO-65TeO₂-(35−x)V₂O₅, 5≤x≤10 mol% which was studied using infrared (IR) and Raman spectroscopy methods as well as magnetic susceptibility measurements. IR and Raman spectroscopy analysis reveals the presence of four main absorption bands attributed to [TeO₃], [TeO₄], [VO₄], and [VO₅] structure units. It suggests that Cu²⁺ ions occupy the available open spaces of the Te-O network without straining the bonds too much. Increasing the concentration of Cu²⁺ ions beyond 5 mol% results in the modification of the glass by straining and locally distorting the surrounding of the Te-O network. The magnetic susceptibility of these materials was investigated in the temperature range of 5-200 K revealing the paramagnetic behavior described by the Curie-Weiss law and indicating the presence of weak antiferromagnetic exchange interactions between Cu ions. The magnetic entropy change of the glasses was determined based on the temperature and magnetic field dependence of magnetization.     

Magnetic susceptibility of mixed valence compounds

Magnetic susceptibility of mixed-valence compounds has been calculated as a function of pressure using Falicov-Kimball model wherein thef-s hybridisation has been taken into account. This model can very well explain the continuous as well as discontinuous transitions from ground states of integral to intermediate valence. Our results for magnetic susceptibility are in qualitative agreement with recent experimental results on some mixed-valence compounds.