Non-Langevin behaviour of the uncompensated magnetization in nanoparticles of artificial ferritin

The magnetic behaviour of nanoparticles of antiferromagnetic artificial ferritin has been investigated by ⁵⁷Fe M?ssbauer absorption spectroscopy and magnetization measurements, in the temperature range 2.5-250 K and with magnetic fields up to 7 T. Samples containing nanoparticles with an average number of ⁵⁷Fe atoms ranging from 400 to 2 500 were studied. By analysing the magnetic susceptibility and zero field M?ssbauer data, the anisotropy energy per unit volume is found, in agreement with some of the earlier studies, to have a value typical for ferric oxides, i.e. a few 10⁵ ergs/cm³. By comparing the results of the two experimental methods at higher fields, we show that, contrary to what is currently assumed, the uncompensated magnetization of the ferritin cores in the superparamagnetic regime does not follow a Langevin law. For magnetic fields below the spin-flop field, we propose an approximate law for the field and temperature variation of the uncompensated magnetization, which was early evoked by Néel but has so far never been applied to real antiferromagnetic systems. More generally, this approach should apply to randomly oriented antiferromagnetic nanoparticles systems with weak uncompensated moments. Received 20 January 2000     

Anisotropy and dynamic properties of Co2MnGe Heusler thin films

Co₂MnGe films of 30 and 50 nm in thickness were grown by RF-sputtering. Their magnetic anisotropies, dynamic properties and the different excited spin wave modes have been studied using conventional ferromagnetic resonance (FMR) and Microstrip line FMR (MS-FMR). From the in-plane and the out-of-plane resonance field values, the effective magnetization (4πM_eff) and the g-factor are deduced. These values are then used to fit the in-plane angular-dependence of the uniform precession mode and the field-dependence of the resonance frequency of the uniform mode and the first perpendicular standing spin wave to determine the in-plane uniaxial, the four-fold anisotropy fields, the exchange stiffness constant and the magnetization at saturation. The samples exhibit a clear predominant four-fold magnetic anisotropy besides a smaller uniaxial anisotropy. This uniaxial anisotropy is most probably induced by the growth conditions.     

Magnetization curves of randomly oriented ferromagnetic single-domain nanoparticles with combined symmetry of magnetic anisotropy

The magnetization curves of randomly oriented nanoparticles with combined symmetry of magnetic anisotropy were studied. The composite mode of the Stoner–Wolfarth model has been used. In terms of this model each nanoparticle is characterized by random cubic crystalline magnetic anisotropy and by random uniaxial magnetic anisotropy. The series of simulated magnetization curves have been obtained. Each curve corresponds to different contributions of cubic and uniaxial magnetic anisotropy energy to the full energy of an individual nanoparticle k_u. Within this series we discuss the values of remnant magnetization, coercive force, both initial and maximal susceptibilities as the function of k_u. It is found that the magnetic properties are not monotonous functions of k_u. We discuss the possibility of comparing the calculated magnetization curves with the experimental curves in order to obtain new information on the magnetic constant.     

Magnetic structure and anisotropy of YFe 6 Ga 6 and HoFe 6 Ga 6

The magnetic structure of RFe₆Ga₆ intermetallic compounds with R = Y, Ho have been determined by neutron powder diffraction, ⁵⁷Fe M?ssbauer spectroscopy, AC susceptibility, TGA (Thermo-Gravimetric Analysis) and magnetization measurements. Both compounds crystallize in the tetragonal ThMn₁₂ structure (space group I4/mmm) with the magnetic structure of YFe₆Ga₆ consisting of a simple ferromagnetic alignment of Fe moments in the basal plane with a Curie temperature of 475(5) K. Gallium atoms are found to fully occupy the 8i site, with Fe and Ga atoms equally distributed over the 8j site, whilst Fe atoms fully occupy the 8f site. The average Fe moments are 1.68(10) and 1.46(10) at 15 and 293 K, respectively. The average room temperature Fe magnetic moments determined by neutron diffraction are in overall agreement with the average Fe moment deduced from M?ssbauer spectroscopy and bulk magnetization measurements on this compound. The magnetic anisotropy of the compound HoFe₆Ga₆ is also planar in the temperature range 6-290 K, with Ho magnetic moments of 9.28(20) and 2.50(20) at 6 K and 290 K, respectively, coupled anti-ferromagnetically to the Fe sublattice and a Curie temperature of 460(10) K. The magneto-crystalline anisotropies of both compounds are comparable at low temperatures. Received 8 March 2001 and Received in final form 18 June 2001     

Double-Q magnetic structures and strong planar anisotropy in tetragonal ErRu2Ge2and ErRu2Si2

Single crystal magnetization measurements and powder neutron diffraction on tetragonal ErRu₂Ge₂ as well as anisotropy of the paramagnetic susceptibility and specific heat measurements on ErRu₂Si₂ are presented. Besides the huge crystal field contribution to the uniaxial anisotropy, which favors the basal plane, a strong in-plane anisotropy is evidenced. From these features and neutron diffraction experiments it is shown that magnetic structures of these materials are double-Q and accordingly non-colinear below their Néel temperature (5.2 and 6.0 K for Ge and Si based compounds, respectively). The magnetic structures induced during the metamagnetic processes are discussed. Received 24 December 1999     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

Phase diagram of uniaxial antiferromagnetic particles: Field perpendicular to the easy axis

We consider a spherical uniaxial antiferromagnetic particle in the presence of an external magnetic field perpendicular to its easy axis. The model is described by a classical Heisenberg Hamiltonian including a single-ion uniaxial anisotropy, where the magnetic moments of the particle are represented by continuous spin vectors. We employ mean-field calculations and Monte Carlo simulations to determine the phase diagram of the system. The phase diagram in the plane field versus temperature is obtained for particles with radii ranging from three up to twelve spacing lattice units. We have seen that a particle with more than nine shells behaves as a true thermodynamic system. We find the explicit dependence of the zero temperature critical field and the Néel temperature on the diameter of the particle. At low temperatures, we have also shown that, for particles with three or more shells, the critical field follows a T² law, which is in agreement with the predictions of the spin-wave theory, when the field is perpendicular to the easy axis.     

In-plane magnetic anisotropies in Ni/FeMn and Ni90Fe10/FeMn exchange biased bilayers

The in-plane magnetic anisotropy in Ni/FeMn and Ni₉₀Fe₁₀/FeMn exchange-biased bilayers prepared by co-evaporation under molecular beam epitaxy conditions is investigated employing longitudinal magneto-optical Kerr effect (MOKE) and ferromagnetic resonance (FMR). The exchange anisotropy was induced by a magnetic field cooling immediately after the deposition of the bilayers. Besides the induced term, the presence of an additional uniaxial anisotropy in the FM layers was detected both by MOKE and FMR, and the characteristic directions of these two anisotropy terms are not coincident. The interplay between the anisotropy contributions is discussed considering micromagnetic simulations and the in-plane resonance condition for different magnetic field orientation. X-ray diffraction, X-ray photoelectron spectroscopy, and Mössbauer spectroscopy were used to complement the characterization of the samples.     

Surface anisotropy energy of thin amorphous magnetic films of (Gd1−xCox)1−yMoy alloys; experimental results

Surface excitations in thin amorphous (Gd_1?xCo_x)_1?yMo_y films obtained by the rf sputtering technique were studied. A microwave spectrometer at X-band was used for magnetic resonance investigation with external magnetic field rotating from perpendicular to parallel resonance orientations. The critical angle and angular dependence of the position of the surface mode and the uniform mode were determined. The Surface Inhomogeneity (SI) model was applied with symmetrical boundary conditions. The surface anisotropy energy term was assumed as a superposition of the uniaxial anisotropy term and a biaxial anisotropy term. The origin of the latter term is not known yet. We also performed the resonance experiment for different temperatures ranging from 180 to 300 K. From the experiment, the uniaxial surface anisotropy constant K′_s1 and the biaxial surface anisotropy constant K′_s2 were found as functions of the temperature; the uniaxial anisotropy energy against temperature changes the sign for y=0.02 from easy axis to easy plane while the biaxial surface anisotropy does not change its character.     

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.     

Mechanism of the formation of an uncompensated magnetic moment in bacterial ferrihydrite nanoparticles

The magnetic properties of antiferromagnetic nanoparticles of FeOOH · nH₂O with sizes of 3–7 nm, which are products of vital functions of Klebsiella oxytoca bacteria, have been studied. Particles exhibit a superparamagnetic behavior. The characteristic blocking temperature is 23 K. Analysis of the magnetization curves shows that the mechanism of the formation of the uncompensated magnetic moment of particles is the random decompensation of magnetic moments of Fe³⁺ ions both on the surface and in the bulk of the antiferromagnetic particle. In this mechanism, the exchange coupling between the uncompensated magnetic moment of the particle and its antiferromagnetic “core” is implemented. It has been found that the temperature dependence of the uncompensated magnetic moment has the form 1 — constT ².     

Size and anisotropy effects on magnetic properties of antiferromagnetic nanoparticles

Based on the Heisenberg model taking into account single-ion anisotropy and using a Green's function technique we have studied the influence of size and anisotropy effects on magnetization M, Neel temperature T_N, coercive field H_c and spin excitation energy of antiferromagnetic nanoparticles. The properties are compared with those of ferromagnetic nanoparticles. We have shown that the enhanced magnetization M and coercive field H_c of antiferromagnetic nanoparticles is a surface effect, which is due to uncompensated surface spins. Moreover, the shape of the coercive field curve can be significantly influenced by surface magnetic anisotropy.     

Crystal and magnetic structure of Ho2NiGe6

The crystal and magnetic structure of Ho₂NiGe₆ was studied by powder neutron diffraction. The paramagnetic neutron diffraction data confirmed the Ce₂CuGe₆-type crystal structure reported earlier for this compound. Below the Néel temperature equal to 11 K the Ho magnetic moments form a uniaxial antiferromagnetic ordering. The Ho magnetic moments equal to 8.16(7)μ_B at 1.5 K are parallel to the b-axis. The data are compared with those published for HoNi_0.46(6)Ge₂.     

Magnetic anisotropy in Ni–Si nanoparticle films produced by ultrashort pulsed laser deposition

Pulsed laser deposition (uPLD) in vacuum by means of subpicosecond laser pulses is a powerful, versatile technique for the production of films constituted by nanoparticles. On impact with the deposition substrate, the nanodrops ejected from the target assume an oblate ellipsoidal shape, solidifying with the major cross-section parallel to the substrate plane. These features and the difficult coalescence among the deposited nanoparticles are peculiar characteristics specific to the films obtained by uPLD. In the case of magnetic nanoparticle films obtained by means of this technique, a magnetization isotropy in the film plane and a hard magnetization axis orthogonal to the film plane are expected. This simple assumption, generated by the specific shape and orientation of the deposited nanoparticles, was not experimentally verified up to now. The present investigation represents the first experimental validation of magnetic anisotropy, determined by the peculiar morphology and topology of the constituent particles, in the uPLD Ni_xSi_100−x nanoparticle films. The in-plane isotropic magnetization behaviour, as well as the presence of a hard magnetization axis perpendicular to the sample surface were demonstrated for all investigated films. The difficult coalescence among the magnetic nanoparticles, even at high Ni volume fractions, is confirmed by the behaviour of the initial magnetization curve, typical for single-domain nanoparticles systems.     

Determination of anisotropy constants of protein encapsulated iron oxide nanoparticles by electron magnetic resonance

Angle-dependent electron magnetic resonance was performed on 4.9, 8.0, and 19 nm iron oxide nanoparticles encapsulated within protein capsids and suspended in water. Measurements were taken at liquid nitrogen temperature after cooling in a 1 T field to partially align the particles. The angle dependence of the shifts in the resonance field for the iron oxide nanoparticles (synthesized within Listeria-Dps, horse spleen ferritin, and cowpea chlorotic mottle virus) all show evidence of a uniaxial anisotropy. Using a Boltzmann distribution for the particles’ easy-axis direction, we are able to use the resonance field shifts to extract a value for the anisotropy energy, showing that the anisotropy energy density increases with decreasing particle size. This suggests that surface anisotropy plays a significant role in magnetic nanoparticles of this size.     

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.     

Structure and magnetism on iron oxide clusters Fe nO m ( n = 1-5): Calculation from first principles

We have studied structural and magnetic properties in small iron oxide clusters, Fe_nO_m (n = 1-5), by means of the first-principles calculation based on the density functional theory. We have used not only the usual spin polarized scheme, but also the scheme for noncollinear magnetism to carry out efficient optimization in magnetic structure. The result of FeO_m (m = 1-4) is in good agreement with the previous work. We found the stable adduct clusters in FeO₅ and FeO₆. The bridge site of oxygen atom is more favorable in energy than any other site for the clusters of Fe_nO (n = 2-5). As increasing the number of oxygen atoms, the alignment of Fe magnetic moments changes from ferromagnetic configuration to antiferromagnetic one at Fe_nO_n (n = 2-4). Received 10 September 2002 Published online 3 July 2003     

Phase separation effects in charge-ordered Pr<Subscript>0.5</Subscript>Ca<Subscript>0.5</Subscript>MnO<Subscript>3</Subscript> thin film

Compressed Pr_0.5Ca_0.5MnO₃ films (250 nm) deposited on LaAlO₃ have been studied by Electron Spin Resonance technique under high frequency and high magnetic field. We show evidences for the presence of a ferromagnetic phase (FM) embedded in the charge-order phase (CO), in form of thin layers which size depends on the strength and orientation of the magnetic field (parallel or perpendicular to the substrate plane). This FM phase presents an easy plane magnetic anisotropy with an anisotropy constant 100 times bigger than typical bulk values. When the magnetic field is applied perpendicular to the substrate plane, the FM phase is strongly coupled to the CO phase whereas for the parallel orientation it keeps an independent ferromagnetic resonance even when the CO phase becomes antiferromagnetic.     

Analysis of magnetic interactions and structure in R6Mn23

The magnetic properties of R₆Mn₂₃ compounds are examined, with emphasis on representatives of the light rare earths. An exceptional antiferromagnetic coupling of light rare earth and transition metal moments is found to exist. A non-collinear model for the rare earth sublattice suggested elsewhere is generally satisfactory, but calculations of the exchange parameters suggest partial moment reorientation from the proposed configurations. Properties associated with important coercive materials such as large rare-earth transition metal exchange and uniaxial anisotropy are absent in the R₆Mn₂₃.     

Tunable magnetic anisotropy of antiferromagnetic superlattice and resultant exchange bias of ferromagnetic layer on it

Exchange biasing of ferromagnetic layer deposited on the antiferromagnetic superlattice was investigated in (Co₇₀Fe₃₀/Ru)_29.5/Ru/Co₉₀Fe₁₀ multilayers. Uniaxial magnetic anisotropy (K_AF) was induced and tuned in the antiferromagentic superlattice by uniaxial substrate bending method through the inverse effect of magnetostriction. The exchange bias increased and tended to be saturated with increasing the K_AF, while it was not observed at K_AF=0.