Rotational effects on the magnetic properties of an ensemble of free metal clusters

The magnetization of an ensemble of free magnetic metal clusters in an inhomogeneous external magnet field is calculated. In particular we have investigated the effects of the combined lattice anisotropy and cluster rotation on the magnetic properties. If weak anisotropy is present, almost superparamagnetic behavior is obtained. For stronger anisotropies deviations from this are calculated as a consequence of spin resonance due to the anisotropy field and the cluster rotation. This was proposed recently by de Heer et al. to explain his experimental data as generally expected, since a rotating cluster in a static magnetic field should behave similarly than a nonrotating one in an oscillating magnetic field. The magnetization depends also sensitively on the relaxation times.     

Effective magnetization of rotating free ferromagnetic metal clusters

The deflection of free magnetic metal clusters in a Stern-Gerlach magnetic field is studied. In particular we investigate magnetic resonance effects resulting from lattice anisotropy and cluster rotation. In analogy to small suspended particles in an oscillating magnetic field the anisotropy field fixed to the rotating atomic lattice of the cluster acts on the cluster magnetization like an rf field in NMR experiments. In our calculation we have used the Bloch equations and assumed different anisotropy field symmetries (uniaxial, cubic). A minimum in the magnetization as a function of the Stern-Gerlach field and also of the cluster size, as observed recently, is obtained under certain conditions. However, such a resonance behavior occurs only if the distribution of the rotation frequency _rot is relatively narrow, while a broad distribution of _rot yields an almost superparamagnetic behavior. In addition, the strength of the anisotropy field and the relaxation time are important variables which determine the magnetic behavior of the clusters.     

Brownian dynamics investigation of magnetization and birefringence relaxations in ferrofluids

Brownian dynamics simulations are used to investigate the dynamics of orientational properties of real charge-stabilized ferrofluids, i.e. stable colloidal dispersions of magnetic nanoparticles. The relaxation times of the magnetization and of the birefringence, data accessible by experimental techniques, have been computed at several volume fractions. Besides, the effect of hydrodynamic interactions has been investigated. Equilibrium simulations without field are found to be inadequate to determine the aforementioned relaxation times for the systems under study, the dipolar interaction being too weak. Thus a nonequilibrium simulation procedure that mimics the experimental operating mode has been developed. After equilibrium simulations under a magnetic field, both birefringence and magnetization decays are recorded once the field is suppressed. Birefringence and magnetization decays are markedly impeded as the volume fraction increases, whereas they are barely enhanced when the intensity of the initial magnetic field is increased at a fixed volume fraction. Eventually, hydrodynamic interactions exhibit a slight but systematic lengthening of the relaxation times.     

Magnetic properties of small nickel oxide clusters enclosed inY-zeolite

The magnetization of small nickel oxide clusters containing less than four nickel atoms (sample A) and about ten atoms (sample B), respectively, formed inside the supercages ofY-zeolite, was studied in the magnetic field below 50 kOe and in the temperature range of 2 to 600 K. The magnetic susceptibility of sample A obeyed a Curie-Weiss' (C-W) law above about 20 K with a C-W temperature of 12 K. A saturation behavior was observed in the magnetization versus field (M-H) curve below about 20 K. A hysteresis in the M-H curve and a remanent magnetization were found below about 7 K. A similar behavior was observed for sample B. The observed positive C-W temperature indicates a ferromagnetic interaction between nickel ions in each cluster, which is semiquantitatively consistent with nearest neighbor ferromagnetic interactions previously reported for antiferromagnetic NiO single crystals. The hysteresis suggests an enhanced magnetic anisotropy energy in the present clusters.     

Linear Orientational Magnetodynamics of a Ferrogel

The dynamics of magnetization is theoretically studied for a system of ferromagnetic nanoparticles suspended in a gel (a ferrogel). The Brownian motion impedes orientation of the particles determined by the elastic matrix. Therefore, the main parameter of the medium determining the static magnetic susceptibility value is the ratio of the modulus of elasticity of matrix to the temperature. The dispersion factors of dynamic susceptibility components include combinations of the velocities of several processes: elastic restoration of the orientation of particles, their rotational Brownian diffusion, and viscous relaxation of the inertial motion. The absorption of the energy of the alternating field in a ferrogel is found to be lower than in an isotropic magnetic suspension. The effect of the interaction of elastic and Brownian forces on the effective times of ferrogel magnetization relaxation is monitored.     

Evidence of superparamagnetic co clusters in pulsed laser deposition-grown Zn0.9Co0.1O thin films using atom probe tomography

Nanosized Co clusters (of about 3 nm size) were unambiguously identified in Co-doped ZnO thin films by atom probe tomography. These clusters are directly correlated to the superparamagnetic relaxation observed by ZFC/FC magnetization measurements. These analyses provide strong evidence that the room-temperature ferromagnetism observed in the magnetization curves cannot be attributed to the observed Co clusters. Because there is no experimental evidence of the presence of other secondary phases, our results reinforce the assumption of a defect-induced ferromagnetism in Co-doped ZnO diluted magnetic semiconductors.     

Magnetic properties in three electrons under Rashba spin-orbit interaction and magnetic field

In this work, we study three-electron magnetic susceptibility in quantum dots under Rashba spin-orbit interaction (SOI) and magnetic field by an analytical methodology. The Hamiltonian of the system is separated to center of mass and relative terms using the Jacobi transformations and the hyperspherical coordinates. By solving Schrodinger equation, energy levels and thereby the susceptibility are calculated using canonical ensemble. At zero temperature, the magnetization reduces with increasing magnetic field with and without Rashba SOI in three-electron-quantum dot without electron-electron (e-e) interaction. Also, SOI slightly changes the magnetization for three-electron-quantum dot without e-e interaction. At nonzero temperature, the magnetization shows a paramagnetic peak when the magnetic field increases. This peak position changes under the SOI. In the presence of e-e interaction, the susceptibility enhances with raising magnetic field and it shows a maximum. The susceptibility at low magnetic field is negative and then it becomes positive. The susceptibility with e-e interaction and without SOI is always diamagnetic and its magnitude reduces with enhancing magnetic field. The susceptibility shows a transition between diamagnetic and paramagnetic with e-e interaction and SOI.     

On the theory of the effective nuclear magnetic relaxation time T2e and its application to polymer melts

A general expression for the magnetization decay of a multipulse group is derived. This formula is applied to a three-component model of molecular motions in polymer melts. The influence of the several components on the magnetization decay is discussed. The relation of the effective nuclear magnetic relaxation time T_2e to the Anderson-Weiss formula is also shown, and an analytical expression for the transverse relaxation in melts is derived. Finally T_2e is compared with the relaxation time in the rotating frame T_1ρ in the melt. The theoretical results for T_2e are tested with measurements of frequency dependence in polyethylene melts.     

Static magnetic-field-induced phase lag in the magnetization response of tris(dipicolinato)lanthanides

Alternating-current (ac) magnetic susceptibility measurements for tris(dipicolinato) complexes with a trivalent heavy lanthanide ion, [N(C2H5)4]3[Ln(dipic)(3)] x nH2O (dipic = pyridine-2,6-dicarboxylate; Ln = Tb, Dy, Ho, Er, Tm, or Yb) are reported. While none of the six complexes showed a magnetization lag from the ac magnetic field of 10-10(3) Hz above 1.8 K, the Dy, Er, and Yb complexes with odd numbers of 4f electrons exhibited the magnetization lag in a static magnetic field. This phenomenon is explained to be caused by the elimination of a fast relaxation path, which is only effective for the Kramers doublet ground states in near zero field. At higher static fields, the remaining paths such as Orbach and/or direct processes govern the dynamics of the two-level systems comprised of spin-up and spin-down states. The non-Kramers complexes were found to have a nondegenerate ground state with large energy gaps from higher states, which is consistent with their fast magnetization relaxation.     

Magnetic properties of iron clusters in a molecular beam: resolution of a controversy

Magnetic properties of small iron clusters in a supersonic molecular beam are investigated. The magnetization is probed as function of magnetic field, temperature and cluster size. Temperatures are controlled by changing the source temperature (100 K to 500 K) and the expansion conditions. The clusters also may be heated in flight with light from a pulsed laser. Hot clusters are found to be superparamagnetic however cold clusters are not but show strongly reduced magnetization which furthermore is non-linear with the applied field. Experimentally it is found that the anomalies are related to the cluster rotations. We also address a controversy between our earlier findings [1] and those by Bucher et al. [2], and demonstrate that their temperature determinations and consequent conclusions are incorrect.     

Remarkable Energy Barrier for Magnetization Reversal in 3D and 2D Dysprosium-Chloranilate-Based Coordination Polymers

Herein, two coordination polymers (CPs) [{Dy(Cl₂An)_1.5(CH₃OH)} ⋅ 4.5 H₂O]_n ( 1 ) and [Dy(Cl₂An)_1.5(DMF)₂]_n ( 2 ), in which Cl₂An is chloranilate (2,5-dihydroxy-1,4-benzoquinone dianion), exhibiting field-induced single-molecule magnet behavior with moderate barrier of magnetization reversal are reported. Detailed structural and topological analysis disclosed that 1 has a 3D network, whereas 2 has a 2D layered-type structure. In both CPs, magnetic measurements showed weak antiferromagnetic exchange interaction between the dysprosium centers and field-induced slow magnetic relaxation with barriers of 175(9)K and 145(7)K for 1 and 2 , respectively. Notably, the energy barriers of magnetization reversal of 1 and 2 are remarkable for metal–chloranilate-based 3D ( 1 ) and 2D ( 2 ) CPs. The temperature and field dependence of relaxation time indicate the presence of multiple relaxation pathways, such as direct, quantum tunneling of magnetization, Raman, and Orbach processes, in both CPs. Ab initio theoretical calculations reinforced the experimentally observed higher energy barrier in 1 as compared with 2 due to the presence of large transverse anisotropy in the ground state in the latter. The average transition magnetic moment between the computed low-lying spin–orbit states also rationalized the relaxation as Orbach and Raman processes through the first excited state. BS-DFT calculations were carried out for both CPs to provide more insight into the exchange interaction.     

An NMR-relaxation study of the effect of albumin on aggregation of magnetic iron oxide nanoparticles

The dependence of the aggregation of magnetic iron oxide nanoparticles in aqueous suspensions under the action of human serum albumin is analyzed based on the data of proton magnetic relaxation. It is shown that albumin adsorption on magnetic nanoparticles gives rise to the formation of a protein corona and clusters of magnetic nanoparticles, decreasing the aggregation stability of the suspension in a 7.1-T magnetic field. Clustering of magnetic iron oxide nanoparticles enhances the relaxation efficiency of magnetic suspensions during NMR measurements.     

Strong Exchange Couplings Drastically Slow Down Magnetization Relaxation in an Air‐Stable Cobalt(II)‐Radical Single‐Molecule Magnet (SMM)

The energy barrier leading to magnetic bistability in molecular clusters is determined by the magnetic anisotropy of the cluster constituents. By incorporating a highly anisotropic four‐coordinate cobalt(II) building block into a strongly coupled fully air‐ and moisture‐stable three‐spin system, it proved possible to suppress under‐barrier Raman processes leading to 350‐fold increase of magnetization relaxation time and pronounced hysteresis. Relaxation times of up to 9 hours at low temperatures were found.     

Rapid and reagent-saving immunoassay using innovative stirring actions of magnetic beads in microreactors in the sequential injection mode

We developed new ELISA techniques in sequential injection analysis (SIA) mode using microreactors with content of a few microliters. We immobilized antibodies on magnetic beads 1.0 μm in diameter, injected the beads into microreactors and applied rotating magnetic fields of several hundred gauss. Magnetic beads, suspended in liquid in density of approximately 10⁹-10¹⁰ particles per millilitre, form a large number of thin rod clusters, whose length-wise axes are oriented in parallel with the magnetic field. We rotate the Nd magnets below the center of the microreactor by a tiny motor at about 2000-5000 rpm. These rotating clusters remarkably accelerate the binding rate of the antibodies with antigens in the liquid. The beads are trapped around the center of the rotating magnetic field even in the flowing liquid. This newly found phenomenon enables easy bead handling in microreactors. Modification of reactor walls with selected blocking reagents was essential, because protein-coated beads often stick to the wall surface and cannot move freely. Washing steps were also shortened.     

Magnetization of ferromagnetic clusters

The magnetization and deflection profiles of magnetic clusters in a Stern-Gerlach magnet are calculated for conditions under which the magnetic moment is fixed in the intrinsic frame of the cluster, and the clusters enter the magnetic field adiabatically. The predicted magnetization is monotonic as a function of the ratio of magnetic energy ₀ B to the rotational thermal energyk _BT. In low field the average magnetization is 2/3 of the Langevin function. The high-field moment approaches saturation asymptotically asB ^–1/2 instead of theB ^–1 dependence in the Langevin function     

Numerical and experimental studies of long-range magnetic dipolar interactions

We describe several numerical methods developed to analyze the behavior of spin polarized liquids in the presence of long-range magnetic dipolar interactions and external field gradients. Two of the methods use a discrete lattice of spins. In the first we calculate the magnetic field from the lattice of spins directly, either in the rotating frame, or in the lab frame. In the second method we include the dipolar fields from linear magnetization gradients analytically and calculate the dipolar fields from higher order gradients in Fourier space, where they are a local function of the magnetization. In the third method the magnetization is expanded in a Taylor series and the dipolar fields are calculated analytically for each term. The results of these calculations are compared to experimental data, in which we use two superconducting quantum interference device magnetometers adjacent to a spherical sample of hyperpolarized liquid 129Xe to detect the evolution of magnetization gradients. In particular, we observe an increase by a factor of 100 of the spin dephasing time in a longitudinal magnetic field gradient due to dipolar interactions of the spins. While each of the numerical techniques has certain limitations, they are generally in agreement with each other and with experimental data.     

Single-molecule magnets: structure and properties of [Mn18O14(O2CMe)18(hep)4(hepH)2(H2O)2](ClO4)2 with spin S = 13

The reaction of 2-(hydroxyethyl)pyridine (hepH) with a 2:1 molar mixture of [Mn3O(O2CMe)6(py)3]ClO4 and [Mn3O(O2CMe)6(py)3] in MeCN afforded the new mixed-valent (16Mn(III), 2Mn(II)), octadecanuclear complex [Mn18O14(O2CMe)18(hep)4(hepH)2(H2O)2](ClO4)2 (1) in 20% yield. Complex 1 crystallizes in the triclinic space group P. Direct current magnetic susceptibility studies in a 1.0 T field in the 5.0-300 K range, and variable-temperature variable-field dc magnetization studies in the 2.0-4.0 K and 2.0-5.0 T ranges were obtained on polycrystalline samples. Fitting of magnetization data established that complex 1 possesses a ground-state spin of S = 13 and D = -0.18 K. This was confirmed by the value of the in-phase ac magnetic susceptibility signal. Below 3 K, the complex exhibits a frequency-dependent drop in the in-phase signal, and a concomitant increase in the out-of-phase signal, consistent with slow magnetization relaxation on the ac time scale. This suggests the complex is a single-molecule magnet (SMM), and this was confirmed by hysteresis loops below 1 K in magnetization versus dc field sweeps on a single crystal. Alternating current and direct current magnetization data were combined to yield an Arrhenius plot from which was obtained the effective barrier (U(eff)) for magnetization reversal of 21.3 K. Below 0.2 K, the relaxation becomes temperature-independent, consistent with relaxation only by quantum tunneling of the magnetization (QTM) through the anisotropy barrier via the lowest-energy MS = +/-13 levels of the S = 13 spin manifold. Complex 1 is thus the SMM with the largest ground-state spin to display QTM.     

The Metallofullerene Field‐Induced Single‐Ion Magnet HoSc2N@C80

The low‐temperature magnetic properties of the endohedral metallofullerene HoSc₂N@C₈₀ have been studied by superconducting quantum interference device (SQUID) magnetometry. Alternating current (ac) susceptibility measurements reveal that this molecule exhibits slow relaxation of magnetization in a small applied field with timescales in the order of milliseconds. The equilibrium magnetic properties of HoSc₂N@C₈₀ indicate strong magnetic anisotropy. The large differences in magnetization relaxation times between the present compound and the previously investigated DySc₂N@C₈₀ are discussed.     

Magnetic properties of free alkali and transition metal clusters

The Stern-Gerlach deflections of small alkali clusters (N<6) and iron clusters (10<N<500) show that the paramagnetic alkali clusters always have a non-deflecting component, while the iron clusters always deflect in the high field direction. Both of these effects appear to be related to spin relaxation however in the case of alkali clusters it is shown that they are in fact caused by avoided level crossing in the Zeeman diagram. For alkali clusters the relatively weak couplings cause reduced magnetic moments where levels cross. For iron clusters however the total spin is strongly coupled to the molecular framework. Consequently this coupling is responsible for avoided level crossings which ultimately cause the total energy of the cluster to decrease with increasing magnetic field so that the iron clusters will deflect in one direction when introduced in an inhomogeneous magnetic field. Experiment and theory are discussed for both cases.     

Slow magnetic relaxation in a novel carboxylate/oxalate/hydroxyl bridged dysprosium layer

A new 2D dysprosium layer compound has been successfully synthesized from reaction with 2-(3-pyridyl) pyrimidine-4-carboxylic acid (H3-py-4-pmc), in which the Dy³⁺ ions reside in square antiprismatic coordination environments and are connected by carboxylate/oxalate/hydroxyl bridges. Magnetic studies reveal ferromagnetic interactions between Dy³⁺ ions, slow magnetic relaxation with an effective energy barrier U _eff of 186 K under zero dc field and pronounced hysteresis loops at low temperatures. Further dilution magnetic study suggests that the slow magnetic relaxation originates from the single-ion magnetic behavior of Dy³⁺ ion and that magnetic coupling suppresses the quantum tunneling of magnetization at low temperature. In addition, theoretical calculation indicates strong Ising anisotropy of the Dy³⁺ ion that is due to the strong interaction between Dy³⁺ ions and hydroxyl groups.