Hysteresis in small arrays of interacting magnetic nanoparticles

The out-of-plane hysteresis loops of small arrays of magnetic nanoparticles, under the influence of an external field applied perpendicular to the array and the dipolar interaction are investigated. The particles are assumed to have a perpendicular anisotropy energy that tends to align the magnetic moments to be perpendicular to the array. The magnetization is found to exhibit a plateaux-and-jumps structure as the external field is swept up and down. These jumps are associated with jumps in the energy of the system, and correspond to transition from one configuration of the moment orientation to another. The energy of different configurations of the magnetic moments for a 3×3 array in the limit of weak dipolar interaction is analyzed, as a means to understand the hysteresis loop. These jumps are more pronounced in arrays of smaller sizes and when the dipolar interaction is weak. The configuration of magnetic moments at zero external field as the field is swept up and down is found to be highly sensitive to the dipolar interaction.     

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.     

Monte Carlo calculation of the magnetization behavior and the magnetocaloric effect of interacting particles

The magnetization behavior and the magnetic entropy change of a system made up of ferromagnetically interacting particles are calculated by using Monte Carlo simulation. The effect of the magnetic anisotropy of particles and the dipolar–dipolar interaction between particles on the magnetization and the magnetic entropy change of the system are discussed. It is found that there is no spontaneous magnetization, both the magnetic anisotropy of particles and the dipolar–dipolar interaction between particles restrains the system's magnetizing in the external magnetic field. The magnetic entropy change decreases with the increase in temperature in the system without the dipolar–dipolar interaction; however, the dipolar–dipolar interaction between particles makes the magnetic entropy change of the system have maximum value at low temperatures.     

Magnetostatic interactions in dense nanowire arrays

We demonstrate the importance of magnetostatic interactions in dense arrays of ferromagnetic nanowires. Beginning from a simple micromagnetic model, we have calculated the interaction field for saturated magnetization in the plane of the array (perpendicular to the axes of the wires) and normal to the plane, using a hybrid (numerical and analytical) strategy. The slope of interaction field versus wire length changes dramatically at the transition between a dipolar regime (at very small lengths) and a monopolar regime (for longer nanowires). We present the interaction fields and the applied fields at saturation for large nanowire arrays. These results are compared with experiment for electrodeposited arrays, and very good agreement is obtained. This shows that the high field behavior of such arrays is dominated by magnetostatic effects and that a nanowire array behaves like a double-sided distribution of magnetic monopoles.     

Negative differential thermal resistance in coupled rotor lattices

Contributions of homogeneous and Goldstone modes of the spin precession were distinguished in FMR spectra of Cr_1/3NbS₂ chiral helimagnet. The resonance field of homogeneous mode is determined by uniaxial magnetic anisotropy. The resonance field of Goldstone mode is determined by six-fold anisotropy in basal plane. For the first time, it has been shown experimentally that effective excitation of Goldstone mode is realized only when microwave magnetic field vector h is perpendicular to wave vector of magnetic structure Q.     

Effects of magnetic structure distortion near a μ + meson in μSR spectroscopy

Possible effects of strong local anisotropy in the vicinity of a μ meson occupying a rare-earth metal interstitial site are considered. The distortion of the magnetic structure and the corresponding contribution to the dipolar field at the muon are calculated. A threshold-type change of the dipolar field depending on the local anisotropy or external magnetic field is predicted for the case where the direction toward the muon is perpendicular to the magnetic moment of one in the ions. The possibility of existence of two strengths of the dipolar field for the ferromagnetic phases of Dy and Tb, and of its abrupt change depending on the direction of the magnetic moment of the plane is predicted for helical antiferromagnetic structures. Fiz. Tverd. Tela (St. Petersburg) 40, 1298–1304 (July 1998)     

Transverse anisotropy field and lattice plane anisotropy of stress annealed Fe–Cu–Nb–Si–B ribbons

The transverse magnetic anisotropy and lattice plane anisotropy of stress-annealed Fe–Cu–Nb–Si–B amorphous ribbons have been studied. The GMI effect or impedance ratio decreased gradually with increasing applied tensile stress. The transverse anisotropy field (H_k) corresponded to the full width at half maximum (FWHM) of the GMI curves. A linear response was found between the applied tensile stress (σ) and the transverse anisotropy field (H_k), and it was seen from the linear expression that annealing without stress resulted in a very small H_k of ～200 A/m. We also calculated the strains from the elongations obtained during the stress annealing process, the results showed that the strain and applied stress were linearly related and for a zero-tensile stress, the elastic strain was negative (?0.0219) showing that contraction dominates during annealing without tensile stresses. The lattice plane anisotropy (Δd) calculated from XRD peaks was also linearly related to the applied tensile stress. The lattice spacing in the direction parallel to the tensile stress was elongated while the lattice spacing in the direction perpendicular to the tensile stress was compressed.     

Phase diagram of a two-dimensional square lattice of magnetic particles with perpendicular anisotropy

The ground state of an array of small single-domain magnetic particles having perpendicular anisotropy and forming a square two-dimensional lattice is studied in the presence of a magnetic field. The stability of some basic states with respect to nonuniform perturbations is analyzed in a linear approximation, and analytical model calculations and numerical simulation are used for an analysis. The entire set of states at various anisotropy constants and magnetic fields is considered when a field is normal to the array plane. Two main classes of states are possible for an infinite system, namely, collinear and noncollinear states. For collinear states, the magnetic moments of all particles are normal to the array plane. At a sufficiently high anisotropy, a wide class of collinear states exists. At low fields, a staggered antiferromagnetic order of magnetic moments takes place. An increase in the magnetic field causes an unsaturated state, and this state transforms into a saturated (ferromagnetic) state with a parallel orientation of the magnetic moments of all particles at a sufficiently high field. At a lower anisotropy, the ground state of the system is represented by noncollinear states, which include a complex four-sublattice structure for the components of the magnetic moments in the array plane and a nonzero projection of the magnetic moments of the particles onto the field direction. A phase diagram is plotted for the states of an array of anisotropic magnetic particles in the anisotropy constant-magnetic field coordinates. For a finite array of particles, sample boundaries are shown to play a significant role, which is particularly important for noncollinear states. As a result of the effect of the boundaries at a moderate field or anisotropy, substantially heterogeneous noncollinear states with a heterogeneity size comparable with the sample size can appear in the system.     

Cluster analysis of an Ising-Preisach interacting particle system

The paper deals with the analysis of clusters' size in diverse magnetization states of a system of ferromagnetic particles organized in a perfect 2D array with all the anisotropy axes perpendicular to the plane (perpendicular medium) following the evolution of the clusters in correlation with various parameters like applied field or interaction strength. We present numerical simulations for a two-level Ising-type model each magnetic entity being characterized by a Stoner-Wohlfarth nonlinear energy barrier and a rectangular hysteresis loop (Ising-Preisach hysteron). In the simulations we took into account, the long-range inter-particle magnetostatic interactions in an attempt to mimic as accurately as possible with a still simple model, materials like Bit-Patterned media that are now considered as good candidates for the magnetic memories of the future.     

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.     

垂直场下磁性薄膜中的铁磁共振现象

将铁磁共振频率看成外磁场的函数, 讨论了垂直场下磁性膜中的铁磁共振现象. 结果显示: 当外磁场平行于膜面, 并考虑磁膜具有垂直磁晶各向异性情形时, 其磁共振频率随外磁场的变化分为高频支和低频支两种情况, 具体的依赖关系取决于磁膜内磁晶的各向异性; 当外磁场垂直于膜面, 其磁共振频率随外磁场的关系仅存在一支, 一般地, 磁共振频率随外磁场的增加单调地非线性减小, 但当立方磁晶各向异性场H_k1 与单轴磁晶各向异性场H_a之比值介于2/3 < H_k1/H_a <1时, 其磁共振频率随外磁场的增加单调增加, 这与相关的实验结果一致. 研究结果表明: 磁薄膜中有无垂直于膜面的磁各向异性可以通过其磁共振谱的测量进行辨析.     

Magnetic properties of field-annealed FeCo thin films

Fe₅₀Co₅₀ thin films with thickness of 30 and 4 nm have been produced by rf sputtering on glass substrates, and their surface has been observed with atomic force microscopy (AFM) and magnetic force microscopy (MFM); MFM images reveal a non-null component of the magnetization perpendicular to the film plane. Selected samples have been annealed in vacuum at temperatures of 300 and 350 °C for times between 20 and 120 min, under a static magnetic field of 100 Oe. DC hysteresis loops have been measured with an alternating gradient force magnetometer (AGFM) along the direction of the field applied during annealing and orthogonally to it. Samples with a thickness of 4 nm display lower coercive fields with respect to the 30 nm thick ones. Longer annealing times affect the development of a harder magnetic phase more oriented off the film plane. The field applied during annealing induces a moderate magnetic anisotropy only on 30 nm thick films.     

Preparation and FMR analysis of Co nanowires in alumina templates

Magnetic and structural properties of a high aspect ratio Co nanowire (NW) array electrodeposited in free-standing porous alumina template with a pore diameter of ∼200 nm are studied. Considered collectively, X-ray diffraction analysis, magnetometer and ferromagnetic resonance (FMR) measurements indicate that both the c-axis of crystal structure and the easy axis of magnetization are aligned preferentially perpendicular to the NW axis. The FMR spectra are characterized with very broad (a few kG) breadths and exhibit asymmetric shape in low field region due to under-saturation effects. Surprisingly, FMR spectra also revealed the presence of a spin-wave mode (SWM) as the applied field direction approached parallel to the film plane, i.e. perpendicular to the NWs. A brief discussion on this observation is provided. Further, characteristic magnetic parameters of the studied NW array were obtained by fitting the field angle-dependent FMR spectra and resonance field by using an analytical model that considers various factors affecting the total anisotropy.     

Magnetic domain structures and magnetotransport properties in Co-Ag granular thin films

The magnetic microstructures and magnetotransport properties in granular Co_xAg_1-x films with 17%≤x≤62% were studied. Magnetic force microscopy (MFM) observations showed the presence of magnetic stripe domains in as-deposited samples with x≥45% and the evolution of the magnetic domain patterns to in-plane domains with annealing. A perpendicular magnetic anisotropy as high as about 8×10⁵ ergs/cc for as-deposited Co₆₂Ag₃₈ and about 6×10⁵ ergs/cc for as-deposited Co₄₅Ag₅₅ was observed by magnetization and torque measurements. With increasing annealing temperature, the perpendicular magnetic anisotropy became negative. The origin of the perpendicular magnetic anisotropy may be attributed to a rhombohedral distortion of the cubic cell due to residual substrate-film stresses. The magnetic stripe domains are the consequence of the interplay of the indirect or direct exchange, perpendicular magnetic anisotropy and dipolar interactions. Finally, magnetoresistance (MR) curves displayed training behaviours and different shapes when measured with different configurations (parallel, transverse and perpendicular). It is proposed that the existence and the evolution of the magnetic domain structures strongly affect the magnetotransport properties due to the extra contribution of the electron scattering at the domain walls. Furthermore, an anisotropic MR also contributes to the overall MR curves. Received: 2 March 2000 / Accepted: 28 March 2000 / Published online: 23 May 2001     

Dynamics of two interacting dipoles

We study the deterministic spin dynamic of two interacting magnetic moments with anisotropy and dipolar interaction under the presence of an applied magnetic field, by using the Landau–Lifshitz equation with and without a damping term. Due to different kinds of interactions, different time scales appear: a long time scale associated with the dipolar interaction and a short time scale associated with the Zeeman interaction. We found that the total magnetization is not conserved; furthermore, for the non-dissipative case it is a fluctuating function of time, with a strong dependence on the strength of the dipolar term. In the dissipative case there is a transient time before the total magnetization reaches its constant value. We examine this critical time as a function of the distance between the magnetic moments and the phenomenological damping coefficient, and found that it strongly depends on these control parameters.     

In plane to out of plane magnetic reorientation transition in partially ordered FePd thin films

It is demonstrated that perpendicular magnetic anisotropy may be obtained with a room temperature growth process in ordered (FePd) alloys. Indeed, using atomic layer by atomic layer epitaxy, a partial chemical ordering into the L1₀ structure is obtained, with a corresponding intermediate perpendicular anisotropy (). These samples provide an appropriate template for the study of the magnetic reorientation from in plane to out of plane magnetization upon layer's thickness increase. VSM, transverse Kerr measurements and magnetic force microscopy have been used in order to determine the relevant magnetic parameters and the occurrence of the reorientation transition. Received 13 October 1998 and Received in final form 5 February 1999     

Configurational spin reorientation phase transition in magnetic nanowire arrays

Classical microscopic spin reorientation phase transitions (RPT) are the result of competing magnetocrystalline anisotropies. RPTs can also be observed in discrete macroscopic systems induced by competing shape anisotropies and magnetostatic coupling. Such a configurational RPT was recently observed in series of self-organized hexagonal arrays of 2.5 μm long, 25-60 nm diameter circular permalloy nanowires grown in anodic alumina matrix. This RPT is a crossover transition from a one-dimensional easy axis “wire” behavior of weakly interacting uniaxial nanowires to a two-dimensional behavior of strongly coupled “wire film” having an easy plane anisotropy. It is shown that RPT takes place due to the competition between the intrinsic dipolar forces in individual wires and the external dipolar field of interacting nanowires in the array. The crossover occurs at a volume ratio of 0.38 for 65 nm periodicity. The experimental results are in agreement with the semi-analytical calculations of the dipolar interaction fields for these arrays of circular ferromagnetic nanowires, and are interpreted in terms of the Landau phase transition theory. The conditions for the crossover and the order of the phase transition are established. Based on the contribution to the magnetic energy from the flower state at the ends of the wires, it is concluded that the observed transition is of the first order.     

Low-energy excitations of Yb As in a magnetic field

We discuss the effects of an applied magnetic field on the low-energy excitations in the low temperature phase of Yb₄As₃. We show also why the magnetic interaction of the Yb³⁺ ions is nearly of an isotropic Heisenberg spin-1/2 type. A small anisotropy due to an intrachain dipolar interaction leads to the opening of a gap when a magnetic field is applied. The model agrees with available experimental data. Simple experiments are suggested in order to further test the present theory. Received 3 February 1999     

Fabrication and magnetic properties of amorphous Co0.71Pt0.29 nanowire arrays

Highly ordered Co_0.71Pt_0.29 alloy nanowire arrays have been fabricated successfully by direct current electro-deposition into the pores of a porous anodic aluminum oxide (AAO) template. SEM and TEM images reveal that the nanowires of array are uniform, well isolated, and parallel to one another. The aspect ratio of nanowires is over 200. XRD and EDS pattern indicates that amorphous Co_0.71Pt_0.29 structure was formed during electro-deposition. In amorphous sample, magnetocrystal anisotropy is very small, therefore, shape anisotropy plays a dominant role which leads to strong perpendicular anisotropy. High coercivity (Hc=1.7 kOe) and squareness (Mr/Ms) around 0.7 were obtained in the samples when the field was applied parallel to the axis of the nanowires. However, when it changed to polycrystalline structure after annealing, due to the competition of magnetocrystal anisotropy and shape anisotropy, the sample did not display perpendicular anisotropy.     

Bias voltage and temperature dependence of magneto-electric properties in double-barrier magnetic tunnel junction with amorphous Co-Fe-B electrodes

Bias voltage and temperature dependence of magneto-electric properties in double-barrier magnetic tunnel junctions(DBMTJs) with a structure of [IrMn/CoFe/Ru/CoFeB]/Al-O/CoFeB/Al-O/[CoFeB/Ru/CoFe/IrMn], have been investigated. The DBMTJs show a large tunnel magnetoresistance (TMR) ratio of up to 57.6%, a high V_1/2 value of 1.26 V and small switching field H_c of 9.5 Oe at room temperature (RT). The TMR reaches the maximum at 30 K, about 89.0%, and decreases slightly from 30 to 4.2 K. A novel zero-bias anomaly (ZBA) in the P state is found and is temperature dependent, more sharply at low temperature, whereas a normal ZBA exists in the AP state. These effects are ascribed to magnon-, phonon- and impurity-assisted tunneling, and variation of density of states. The DBMTJ with a large TMR ratio, a high V_1/2, and small switching field H_c is promising for developing the future spin electronic devices.