The resonance decay function method in the determination of the pre-factor of the Néel relaxation time of single-domain nanoparticles

In its simple form, the relaxation time of the Néel relaxation process of the magnetic moment of single-domain particles is given by τ_N=τ_0Nexp(σ), σ being the ratio of anisotropy energy to thermal energy. The pre-factor, τ_0N, is normally given a value of 10⁻⁹ s, but values ranging from 10⁻⁸ to 10⁻¹² s have been reported in literature. Here, by means of the field and frequency dependence of the complex magnetic susceptibility, χ(ω,H)=χ′(ω,H)−iχ″(ω,H), of a magnetic fluid sample, in the MHz-GHz range, in conjunction with the determination of the sample decay function, b(t), the pre-factor τ_0N is determined. b(t) is readily obtained through the inverse Fourier transformation relationship, which exists between b(t) and χ″(ω).     

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.     

On the high-frequency measurement of the dynamic properties of nano-particle colloids

Measurement of the magnetic complex susceptibility, χ(ω)=χ′(ω)−iχ″(ω) by means of the transmission line technique, is a well established method for the determination of the dynamic properties of nano-particle colloids, such as magnetic fluids. From polarising studies one can obtain accurate data on the anisotropy constant, K, anisotropy field, H_A, gyromagnetic constant γ, and the damping parameter, α. From data on χ(ω), one can determine the loss tangent, tan δ, of the samples and also a value of the precessional decay time, τ₀. From polarized studies, one can investigate the presence of any hysteresis. The technique is also suitable for the investigation of the magnetic properties of composite samples. In this paper a review of the above mentioned topics are presented with examples of results obtained for a number of magnetic fluids.     

χ polarization induced in molecular glass of conjugated compound by all-optical poling

The paper presents the first report on χ⁽²⁾ polarization induced in molecular glass of conjugated compound by all-optical poling. Transparent thin film of molecular glass of 1,4-bis[2-[4-[N,N-di(p-tolyl)amino]phenyl]vinyl]benzene (BTAPVB) was prepared using a spin-cast technique. Dipolar as well as octupolar components in BTAPVB contributed to the formation of photoinduced χ⁽²⁾ polarization. Growth rate of χ⁽²⁾ polarization has good linear relation with E_ω⁴E_2ω, which suggested that the simultaneous processes of two-photon (ω + 2ω) and three-photon (ω + ω + ω) excitation on the same electronic level contributed to the formation of photoinduced χ⁽²⁾ polarization.     

An improved technique for the measurement of the complex susceptibility of magnetic colloids in the microwave region

Measurements by means of the short-circuit (S/C) and open circuit (O/C) transmission line techniques are well established methods for investigating the magnetic and dielectric properties of magnetic colloids, respectively. In particular, the S/C technique has been used in the investigation of the resonant properties of ferrofluids; resonance being indicated by the transition of the real component of the magnetic complex susceptibility, χ(ω)=χ′(ω)−iχ″(ω), from a positive to a negative value at a frequency, f_res. However, under certain circumstances, the accuracy of the S/C technique is affected by the dielectric properties of the sample, hence incurring errors in the measurement of χ(ω) and indeed of f_res. Here we present a model which, by combining short-circuit and open circuit measurements, is developed in a manner in which the permeability, μ, and the permittivity, ε, contribute simultaneously to the calculation of χ(ω), thereby providing superior experimental results in comparison to those obtained by the S/C technique alone. For the two ferrofluid samples measured it is demonstrated that the dielectric properties affect the high frequency content of the susceptibility spectrum.     

Investigation of the non-linear loss properties of magnetic fluids subject to large alternating fields

The non-linear relaxational properties of a water-based magnetic fluid are investigated by means of measuring the frequency dependent complex susceptibility, χ(ω) in the presence of an external potential. The results obtained are discussed in terms of the magnetic analogue of the Coffey and Paranjape model as modified by Déjardin. The loss processes in the magnetic fluid in the non-linear region are investigated in the context of the loss tangent, tan(δ), and the power dissipation per unit volume. These measurements are of importance because of the continuing interest in the clinical applications of magnetic fluids, where large alternating magnetic fields can be applied to magnetic fluids to induce loss processes and heating effects, often driving the magnetic fluid into the non-linear region of magnetisation. We evaluate the increment of the susceptibility, Δχ, due to the non-linear response, through measurement of χ(ω), and extend this formulism to the non-linear increment of the loss tangent, Δ tan(δ) and the increment of the heating rate, ΔU_heat.     

Magnetic layer thickness dependence of magnetization reversal in electrodeposited CoNi/Cu multilayer nanowires

The magnetization reversal of electrodeposited CoNi/Cu multilayer nanowires patterned in an array using a hole template has been investigated. The reversal mode is found to depend on the CoNi layer thickness t(CoNi); with increasing t(CoNi) a transition occurs from coherent rotation to a combination of coherent and incoherent rotation at around t(CoNi)=51 nm. The reversal mode has been identified using the magnetic hysteresis loops measured at room temperature for CoNi/Cu nanowires placed at various angles between the directions of the nanowire axis and external fields using a vibrating sample magnetometer. The nanowire samples have a diameter of ∼250 nm and constant Cu layer thickness of 4.2 nm with various t(CoNi) ranging from 6.8 nm to 7.5 μm. With increasing t(CoNi), the magnetic easy axis moves from the direction perpendicular to nanowires to that parallel to the nanowires at around t(CoNi)=51 nm, indicating a change in the magnetization reversal mode. The reversal mode for the nanowires with thin disk-shaped CoNi layers (t(CoNi)=6.8, 12 and 17 nm) is of a coherent rotation type, while that for long rod-shaped CoNi layers (t(CoNi)=150 nm, 1.0, 2.5 and 7.5 μm) can be consistently explained by a combination of coherent rotation and a curling mode. The effects of dipole–dipole interactions between nanowires and between adjacent magnetic layers in each nanowire on the reversal process have been discussed.     

Effect of nanoparticle size on magnetic damping parameter in Co92Zr8 soft magnetic films

Co₉₂Zr₈(50 nm)/Ag(x) soft magnetic films have been prepared on Si (111) substrates by oblique sputtering at 45°. Nanoparticle size of Co₉₂Zr₈ soft magnetic films can be tuned by thickening Ag buffer layer from 9 nm to 96 nm. The static and dynamic magnetic properties show great dependence on Ag buffer layer thickness. The coercivity and effective damping parameter of Co₉₂Zr₈ films increase with thickening Ag buffer layer. The intrinsic and extrinsic parts of damping were extracted from the effective damping parameter. For x=96 nm film, the extrinsic damping parameter is 0.028, which is significantly larger than 0.004 for x=9 nm film. The origin of the enhancement of extrinsic damping can be explained by increased inhomogeneity of anisotropy. Therefore, it is an effective method to tailor magnetic damping parameter of thin magnetic films, which is desirable for high frequency application.     

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.     

Crystal field investigation on the magnetic properties of Yb in Yb(CF3SO3)3·9H2O

Ytterbium tri-fluoromethanesulfonate (YbTFMS) single crystals are prepared from the slow evaporation of the aqueous solution of YbTFMS and the principal magnetic susceptibility perpendicular to the c-axis of the hexagonal crystal (χ_⊥) is measured from 300 K down to 13 K. Principal magnetic anisotropy Δχ(=χ_∥−χ_⊥) is measured from 300 K down to 80 K which provides principal magnetic susceptibility parallel to the c-axis (χ_∥) down to 80 K. Very good theoretical simulation of the observed magnetic properties of YbTFMS has been obtained using one electron crystal field (CF) analysis having C_3h site symmetry. No signature of ordering effect in the observed magnetic data is noticed down to the lowest temperature (13 K) attained, indicating the inter-ionic interaction to be of predominantly dipolar type. The calculated g-values are found to be g_∥=2.67 and g_⊥=2.51, respectively. CF analysis provides the electronic specific heat which gives two Schottky anomalies in its thermal variation down to ∼13 K. The temperature dependences of quadrupole splitting and hyperfine heat capacity are studied from the necessary information obtained from the CF analysis.     

Second-order optical nonlinearities from χ gratings induced by holographic all-optical poling

The paper presents the second-order optical nonlinearities from χ⁽²⁾ gratings induced by holographic all-optical poling for azobenzene polymer. Second harmonic (SH) signal along the directions with two different vectors was measured. One is strong SH signal diffracted in the same direction as 2ω writing beam with wave vector k_2ω and the other is weak SH signal diffracted in the direction of wave vector of 4k_ω - k_2ω + Δk where k_ω is wave vector of ω beam and Δk is the wave vector mismatch whose vector is parallel to k_ω. The latter signal was used as a tool to monitor the formation of holographic χ⁽²⁾ gratings in real-time because it has off-axis wave vector different from both k_ω and k_2ω. The increase of 2ω intensity on poling process led to the large increase of second-order optical nonlinearity. The real-time monitoring showed that it also gave the large relaxation of second-order optical nonlinearity on poling process. The increase of 2ω (532 nm) energy enhanced the increase of local heating, which led to easier alignment of azobenzene chromophore and also larger relaxation of aligned chromophore.     

Synthesis of magnetite nanoparticles for AC magnetic heating

Magnetite particles with different average diameter (D_m) suitable for magnetic fluid hyperthermia (MFH) were synthesized by controlled coprecipitation technique. In this method, the reaction pH was stabilized using the pH buffer and the average particle diameter decreased with increasing reaction pH. The size-dependent magnetic behavior of the magnetite nanoparticles was studied and the optimum size range required for magnetic fluid hyperthermia (MFH) has been arrived at. Among the samples studied, the maximum specific absorption rate of 15.7 W/g was recorded for the magnetite sample with D_m of 13 nm, when exposed to an AC magnetic field strength of 3.2 kA/m and a frequency of 600 kHz. The AC magnetic properties suggested that the size distribution of the sample was bimodal with average particle size less than ∼13 nm.     

Magnetic properties of RPd5Al2 (R=Y, Ce, Pr, Nd, Sm, Gd)

Polycrystalline samples of a new rare-earth series RPd₅Al₂ crystallizing in the tetragonal ZrNi₂Al₅-type structure have been prepared. Their physical properties by electrical resistivity ρ, magnetic susceptibility χ, magnetization M and specific heat C_p measurements are reported. The ingots are composed of elongated grains preferentially aligned in the c direction; therefore, measurements were conducted parallel and perpendicular to the grains. Antiferromagnetic ordering appears in R=Ce, Nd, Gd, and Sm at low temperatures. CePd₅Al₂ has two AFM transitions at 4.1 and 2.9 K and ρ(T) indicates a Kondo metal behavior with large anisotropy. In PrPd₅Al₂ no magnetic transition was observed down to 0.4 K. The C_p(T) shows a broad peak around 13 K due to the CEF effect, suggesting a non-magnetic singlet ground state. In NdPd₅Al₂, χ(T) shows anisotropy and the C_p(T) shows a sharp peak at 1.2 K. The magnetic entropy at 3 K is very close to Rln2, indicating a Kramers doublet ground state. In SmPd₅Al₂, C_p(T) shows a magnetic transition at 1.7 K. C_p(T) for GdPd₅Al₂ shows a peak at 6 K, followed by a broad anomaly around 3 K. Within this series, T_N's for CePd₅Al₂ and NdPd₅Al₂ clearly deviate from the relation predicted by de Gennes scaling, which is ascribed to the CEF effect.     

Structural, microstructural and magnetic properties of NiFe2O4, CoFe2O4 and MnFe2O4 nanoferrite thin films

The structural, microstructural and magnetic properties of nanoferrite NiFe₂O₄ (NF), CoFe₂O₄ (CF) and MnFe₂O₄ (MF) thin films have been studied. The coating solution of these ferrite films was prepared by a chemical synthesis route called sol-gel combined metallo-organic decomposition method. The solution was coated on Si substrate by spin coating and annealed at 700 °C for 3 h. X-ray diffraction pattern has been used to analyze the phase structure and lattice parameters. The scanning electron microscopy (SEM) and atomic force microscopy (AFM) have been used to show the nanostructural behavior of these ferrites. The values of average grain's size from SEM are 44, 60 and 74 nm, and from AFM are 46, 61 and 75 nm, respectively, measured for NF, CF and MF ferrites. At room temperature, the values of saturation magnetization, M_s∼50.60, 33.52 and 5.40 emu/cc, and remanent magnetization, M_r∼14.33, 15.50 and 1.10 emu/cc, respectively, are observed for NF, CF and MF. At low temperature measurements of 10 K, the anisotropy of ferromagnetism is observed in these ferrite films. The superparamagnetic/paramagnetic behavior is also confirmed by χ′(T) curves of AC susceptibility by applying DC magnetizing field of 3 Oe. The temperature dependent magnetization measurements show the magnetic phase transition temperature.     

Ac magnetic susceptibility measurements in nanoparticulate powders of iron-doped ZnO

Low temperature (T) ac magnetic susceptibility (χ_ac) measurements were performed in powder samples of the Zn_1−xFe_xO (x=0-0.078) prepared by a combustion reaction method. The amplitude of the ac magnetic field was kept constant (1 mT) while its frequency (f) varied in the range 10-10⁴ Hz for 5≤T≤300 K. The diluted samples presented cusps with maxima distributed around T_f=17.5±0.5 K while no such feature was observed for the pure sample (x=0). The cusp was found to become more pronounced with the increasing Fe content. Also it decreased and shifted to higher values of T by increasing f. The shift in T_f was found to follow a Vogel-Fulcher law with E_a/k_B=317.6 K, T₀=4.65 K and τ₀=10⁻¹⁴ s, for the activation energy, critical temperature and characteristic time-constant, respectively. The energy gap of the sample was measured and they were found to vary in the range 3.75-3.80 eV. The overall χ_ac-data resembles those obtained for cluster spin-glass state.     

Fabrication and magnetic response probed by RF transverse susceptibility in La0.67Ca0.33MnO3 nanowires

The temperature and magnetic field dependence of the radio-frequency (RF) transverse susceptibility (χ_T) of La_0.67Ca_0.33MnO₃ crystalline nanowires has been studied using a very sensitive self-resonant tunnel-diode oscillator (TDO) technique. The nanowires were synthesized using porous templates of anodized alumina by chemical solution deposition technique, and the crystalline nature of the nanowires with the average diameter of 70 nm was confirmed by TEM, SAED, and HREM. RF transverse susceptibility experiments reveal the presence of a double-peak structure at T≤245 K (the Curie temperature) but a single peak at T>245 K. This distinguishes the low temperature ferromagnetic state from the high temperature paramagnetic state. The effective magnetic anisotropy field (H_K), which corresponds to the peak location of χ_T, has been found to increase with decrease in temperature from the Curie temperature.     

Magnetic properties for the Mn2GeTe4 compound

Measurements of magnetic susceptibility χ, in the temperature range from 2 to 300 K, and of magnetization M vs. applied magnetic field B, up to 5 T, at various temperatures were made on polycrystalline samples of the Mn₂GeTe₄ compound. It was found that Mn₂GeTe₄ has a Néel temperature T_N of about 135 K, shows mainly antiferromagnetic behavior with a very weak superimposed ferromagnetic component that is attributed to spin canting. Also, the magnetic results suggest that a possible spin-glass transition takes place at T_f≈45 K. The spin-glass order parameter q(T), determined from the susceptibility data, was found to be in agreement with the prediction of conventional spin-glass theory. The M vs. B results indicated that bound magnetic polarons (BMPs) occur in the compound, and that the effects from BMPs disappear at approximately 80 K. The M vs. B curves were well fitted by a Langevin type of equation, and the variation of the fitting parameters determined as a function of temperature. Using a simple spherical model, the radius of the BMP in the material was found to be about 27 Å; this value is similar to the effective Bohr radius for an acceptor in the II-IV-V₂ and I-III-VI₂ ternary semiconductor compounds.     

Organic thin films based on a dicyanovinyl-quaterthiophene: Influence of electrode configuration on third-order nonlinear optical properties measured by electroabsorption spectroscopy

Electroabsorption (EA) studies at room temperature on organic thin films based on a dicyanovinyl-quaterthiophene 4T-V(CN)₂ are reported. An electric field modulation is applied to the samples for two different electrode geometries, i.e. sandwich and coplanar versus the organic layer. Changes in optical absorption coefficient of 4T-V(CN)₂ based thin films are measured and analyzed to determine the character of the optical transition in the visible range (400-800 nm). Depending on the experimental electrode configuration, magnitude of electroabsorption responses are different, possibly due to different distribution of the externally applied electric field. The results indicate a higher resolution of EA response for the sandwich electrode configuration and confirm the charge transfer exciton character of 4T-V(CN)₂ in contrast to the unsubstituted quaterthiophene 4T. Finally, a third-order nonlinear susceptibility χ⁽³⁾ (−ω; ω, 0, 0) of 16 × 10⁻¹² e.s.u. is obtained.     

Electrical and optical properties of thermally-evaporated thin films from A2[TiO(C2O4)2] (A = K, PPh4) and 1,8-dihydroxyanthraquinone

In this work, the synthesis of molecular materials formed from A₂[TiO(C₂O₄)₂] (A = K, PPh4) and 1,8 dihydroxyanthraquinone is reported. The synthesized materials were characterized by atomic force microscopy (AFM), infrared (IR) and ultraviolet-visible (UV-vis) spectroscopy. IR spectroscopy showed that the molecular-material thin-films, deposited by vacuum thermal evaporation, exhibit the same intra-molecular vibration modes as the starting powders, which suggests that the thermal evaporation process does not alter the initial chemical structures. Electrical transport properties were studied by dc conductivity measurements. The electrical activation energies of the complexes, which were in the range of 0.003-1.16 eV, were calculated from Arrhenius plots. Optical absorption studies in the wavelength range of 190-1090 nm at room temperature showed that the optical band gaps of the thin films were around 1.9-2.3 eV for direct transitions Eg_d. The cubic NLO effects were substantially enhanced for materials synthesized from K₂[TiO(C₂O₄)₂], where χ⁽³⁾ (−3ω; ω, ω, ω) values in the promising range of 10⁻¹² esu have been evaluated.