Phase transformations of the magnetic structure in film nanobridges

The magnetic structure of a plane nanobridge consisting of two ferromagnetic film electrodes connected by a nanosized crossbar of the same material is studied. Due to their magnetoresistive properties, such bridges are of considerable interest for microelectronics. Using a numerical micromagnetics method, it is shown that a domain wall is displaced from the center of the bridge crossbar as the anisotropy constant of the system decreases and reaches a critical value. A phase diagram is constructed, which makes it possible to determine the possible magnetic states of real nanobridges. The mechanism of the phase transformation is described in terms of an analytical model. This model explains the shape of the phase diagram of the nanobridge. Formally, the transformations of the magnetic structure of the nanocontact can be described in terms of the Landau theory of phase transitions in a certain range of parameters of the system.     

Entanglement spectrum and magnetization plateaus in an S = 1 bond-alternative Heisenberg chain with single-ion anisotropy and magnetic field

Entanglement spectrum and quantum phase transitions (QPTs) in S = 1 bond-alternative antiferromagnetic Heisenberg chain with single-ion anisotropy and magnetic field are investigated by the infinite time-evolving block decimation (iTEBD) method. The combined effects of the single-ion anisotropy and magnetic field have been discussed, and a rich ground-state phase diagram is obtained. We find that the single-ion anisotropy is advantageous to the stability of the 1/2 magnetization plateau. Both entanglement entropy and entanglement spectrum, as two model-independent measures, are capable of describing all the QPTs. Especially, doubly degenerate entanglement spectrum on even bond is observed in the 1/2 plateau phase. Besides constant spontaneous magnetization, three magnetization plateaus (M ^z = 0, 1/2, and 1) are found to have constant entanglement entropy, entanglement spectrum, and nearest-neighbor correlation. In addition, all the QPTs in such a model have been determined to belong to the second-order category.     

Features of magnetization reversal in trilayer nanostructures

The process of magnetization reversal in an ultrathin magnetic trilayer is analyzed. It is shown that the shape of magnetization hysteresis loops and the giant magnetoresistance essentially depend on the relative magnitudes of magnetic parameters of the top and bottom layers. Hysteresis loops are found for characteristic relative magnitudes of the parameters. Analysis is performed of the dependence of the shape of hysteresis loops on the magnitude of interlayer exchange. A phase diagram is constructed, which determines the regions of existence of characteristic hysteresis loops for different relative magnitudes of the uniaxial anisotropy constant and exchange constant J ₁.     

Monte Carlo simulation of magnetic phase transitions in amorphous alloys of the Re-Tb system

The magnetic properties of amorphous alloys of the Re-Tb system and pure amorphous terbium have been investigated by the Monte Carlo method within the Heisenberg model. The temperature dependences of the spontaneous magnetization and magnetic susceptibility have been constructed for different ratios of the anisotropy constant to the exchange constant, D/J. The minimum value of D/J at which the spin-glass transition occurs is determined. The magnetic phase diagram of amorphous Re-Tb alloys, obtained by the simulation, is in qualitative agreement with the experimental data.     

The influence of magnetoelastic interaction on structural phase transitions in cubic ferromagnetics

In the framework of the Landau theory of phase transitions, the influence of the magnetoelastic interaction on structural transitions in cubic ferromagnetics with a positive first magnetic anisotropy constant is analyzed. It is shown that structural transitions are not accompanied by a reorientation of magnetization in this case. The phase diagrams of such ferromagnetics either contain a termination point of the structural transition or a critical point in which the first-order transition is replaced by a second-order one. Magnetoelastic interaction also leads to the appearance of an interval of the ferromagnetic parameters in which a coupled first-order structural-magnetic transition exists. The phase T?x diagram for Heusler Ni_2+x Mn_1?x Ga alloys is calculated, which is in good agreement with the experimental phase diagram of these alloys.     

Transition De Phase Metamagnetique Du Bromure Ferreux

In a magnetic field parallel to the magnetization axis of an antiferromagnetic Fe Br₂ single crystal, a caracteristic metamagnetic behaviour is observed. The transition from an antiferromagnetic phase to a paramagnetic phase is studied by help of magnetization measurements in a steady field (H < 60 kOe). The measurement precision has allowed a detailed study of the magnetization isotherms, caracteristic of a first order magnetization phase transition (T < T_c = 4, 7 K) and of a second order phase transition (T_c < T < T_N = 14, 2 K).We have observed an original phase diagram. In a certain temperature and field range, the ordered phase is stable on the high temperature side of the transition point. Some theoretical studies in an Ising model, or in the hypothesis of a strong magnetoelastic coupling forecast the existence of such a magnetic phase diagram.At present, we proceed to a theoretical study, in a molecular field approximation, of the magnetic phase diagram of compounds similar to Fe Br₂ where we take into account the relative values of parameters J₁, J₂ and D associated with ferromagnetic and antiferromagnetic interactions and crystalline anisotropy.     

Magnetodielectric coupling by exchange striction in Y<Subscript>2</Subscript>Cu<Subscript>2</Subscript>O<Subscript>5</Subscript>

We have studied the magnetodielectric response of Y₂Cu₂O₅, the so-called blue phase in the Y₂O₃-CuO-BaO phase diagram. Based on symmetry principles, we predict and demonstrate magneto-dielectric coupling on a single crystal sample. We report an anomaly in the dielectric constant at the ordering temperature of the Cu spins. We probe the magnetic field-induced phase transitions between four different magnetic phases using magneto-capacitance measurements, demonstrating relatively strong magnetodielectric coupling. We observe an increase in dielectric constant in the spin-flip phase where there exists spontaneous magnetization. We construct a detailed magnetic phase diagram. The magnetodielectric coupling is analyzed in terms of striction induced by symmetric superexchange and optical phonon frequency shifts.     

Features of magnetic and magnetoelectric properties of rare-earth multiferroic PrFe3(BO3)4 with the singlet ground state

The features of magnetization of rare-earth multiferroic PrFe₃(BO₃)₄ with the singlet ground state have been investigated theoretically. The magnetic anisotropy of the crystal has been studied. The temperature dependences of anisotropy constants have been calculated. The phase H-T diagram has been constructed. The dependences of the behavior of magnetization vectors of magnetic sublattices on the external magnetic field have been obtained. The magnetoelectric effect has been investigated, and the dependences of polarization on the temperature and field have been found for its various orientations. The theoretical data have been compared with the experimental data and their good agreement has been established.     

Effect of hydrogenation on spin-reorientation phase transitions and magnetic anisotropy constants of RFe11Ti single crystals (R=Lu, Ho, and Er)

The magnetic anisotropy and spin-reorientation phase transitions in single crystals of the RFe₁₁Ti (R=Lu, Ho, and Er) compounds and their hydrides are investigated. Measurements are carried out on capacitance and torque magnetometers. The magnetic anisotropy constants K ₁ and K ₂ are determined by the mathematical processing of experimental magnetization curves in terms of the phenomenological theory of the anisotropic ferromagnet magnetization. It is demonstrated that the hydrogenation strongly affects the magnitude and the sign of magnetic anisotropy constants, as well as the spin-reorientation phase transitions. The hydrogenation of the HoFe₁₁Ti compound leads to the change in sign of the magnetic anisotropy constant K ₁. The inference is made that a change in the atomic volume and the axial ratio c/a cannot result in the observed effects. A change in the magnetic anisotropy constants upon hydrogenation is primarily due to the change in the interaction of the quadrupole moment of a 4f electron subshell of rare-earth ions with surrounding ions of the crystal lattice and also with valence and conduction electrons.     

Theory of stripe domains in magnetic shape memory alloys

The evolution of multivariant patterns in thin plates of magnetic shape memory materials with an applied magnetic field was studied theoretically. A geometrical domain-model is considered composed of straight stripe-like martensite variants with constant internal magnetization (high anisotropy limit) and magnetic domain wall orientation fixed by the twin boundaries. Through integral transforms of the demagnetization energy, the micromagnetic energy is cast into a form convenient for direct numerical evaluation and analytical calculations. The equilibrium geometrical parameters of multivariant patterns with straight and oblique twin boundaries have been derived as functions of the applied field and the material parameters of a plate. It is shown that the oblique multivariant states exist only in plates with thicknesses L larger than a certain critical value L₀. In samples with L<L₀ a magnetic-field-driven transformation occurs directly between single variant states.     

Theory of first order magnetization processes: Uniaxial anisotropy

The first order magnetization process (FOMP) is associated with the irreversible rotation of the magnetization vector M_s between inequivalent states. The critical field H_cr and the amplitude ΔM of the jump observed in the direction parallel to the applied magnetic field are functions of the anisotropy constants of the crystal. A complete phenomenological analysis is given for the case of uniaxial anisotropy in terms of the first three anisotropy constants K₁, K₂ and K₃, as well as in terms of the anisotropy coefficients χ_2,0, χ_4,0, χ_6,0. Computer plots of the critical parameters and the magnetic phase diagram are given together with an analytical treatment of the problem. The results give a unified view of the FOMP in uniaxial crystals and provide a method for the accurate determination of the anisotropy constants at the temperatures where the phenomenon is present.     

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.     

Hard magnetic properties of ErCo7−xCux [0.3⩽x⩽1] system

We report the observation of excellent hard magnetic properties on purely single phase ErCo_7−xCu_x compounds with x=0.3, 0.5, 0.8 and 1. Cu substitution leads to a decrease in the saturation magnetization, but enhances the uniaxial anisotropy in this system. The large anisotropy field (∼100 kOe) is attributed to the Er and the Co sublattices. Domain wall pinning effect seems to play a crucial role in determining the temperature and field dependences of magnetization in these compounds. The hard magnetic properties obtained at room temperature (RT) are comparable to the best results obtained in other RCo₇ based materials.     

Magnetic properties of Y-type trigonal ferrites first-order magnetization processes in trigonal systems

Magnetic properties of the single crystal ferrite Ba₂(Zn_1-xCo_x)₂Fe₁₂O₂₂ with O ? x ? 1, which has a trigonal symmetry around the c-axis, were investigated. The presence of Co ion strongly affects the properties of the Y-type ferrite: easy cone of magnetization, spin reorientation phase transition and first-order magnetization processes (FOMP) have been observed in this system. The observed effects as well as the origin of the magnetocrystalline anisotropy are discussed on the basis of a phenomenological analysis. The anisotropy constants K₁, K₂ and K_t trigonal of the ferrite are given versus temperature and composition. The magnetic phase diagram of a trigonal system is also presented. The condition for the existence of FOMP are obtained in term of the anisotropy constants ratios.     

Phase Transitions of Fel2 in high magnetic field parallel to the spin direction,static field up to 150 kOe,pulsed field up to 250 kOe

Study of parallel and perpendicular susceptibilities shows that ferrous iodide presents at low temperature an antiferromagnetic order, with spins oriented along the anisotropy axis (c axis).Phase transitions of Fel₂ in a magnetic field parallel to c axis are studied by help of magnetization measurements. At low temperature (2.2 K) saturation is reached only for a magnetic field of 140 kOe. Results obtained in high static fields (Bitter and supraconductive coils allowing respectively 140 and 150 kOe) and in pulsed field are presented.At low temperature, two successive first order phase transitions are observed at 46 and 120 kOe. In the intermediate phase, the magnetization presents two minor discontinuities. An original phase diagram is given.The complexity of the Fel₂ behavior, in parallel magnetic field shows that the magnetic structure is not the same as the two sublattices one characteristic of FeCl₂ and FeBr₂. An estimate of the principal exchange coupling parameters and a study by neutron diffraction measurements (to be published) confirm an original magnetic structure.     

The use of Lorentz microscopy for the determination of magnetic reversal mechanism of exchange-biased Co30Fe70/NiMn bilayer

Lorentz transmission electron microscopy (LTEM) combined with in-situ magnetizing experiments is a powerful tool for the investigation of the magnetization of the reversal process at the micron scale. We have implemented this tool on a conventional transmission electron microscope (TEM) to study the exchange anisotropy of a polycrystalline Co₃₅Fe₆₅/NiMn bilayer. Semi-quantitative maps of the magnetic induction were obtained at different field values by the differential phase contrast (DPC) technique adapted for a TEM (SIDPC). The hysteresis loop of the bilayer has been calculated from the relative intensity of magnetic maps. The curve shows the appearance of an exchange-bias field reveals with two distinct reversal modes of the magnetization: the first path corresponds to a reversal by wall propagation when the applied field is parallel to the anisotropy direction whereas the second is a reversal by coherent rotation of magnetic moments when the field is applied antiparallel to unidirectional anisotropy direction.     

Domain structure and magnetization processes in permalloy propagation elements

A review of domain structures and magnetization processes in permalloy overlays is given, together with some new results. The simplest domain structure for a given element consists of a loop of magnetic flux, but in elements with irregular geometry the circulating flux is not constant. More complex structures arise when an element contains internal closure domains. In-plane anisotropy in permalloy affects the distribution of closure domains but with decreasing bar width the influence of anisotropy is reduced. Reversible wall motion in weak fields gives way to hysteresis effects when the applied field exceeds a certain level, H_s. In particular magnetization buckling may occur. Some details of buckling in asymmetric chevrons and half-discs are given and compared with the behaviour in an I-bar. The proximity of a bubble medium containing stripe domains is shown to reduce considerably the applied fields needed for buckling in overlay components. Following saturation, changes in the demagnetized state are usually apparent. On a simple level, the spin structure and polarity of Bloch walls is altered. More noticeably the wall pattern itself can change when closure domains are created or annihilated in pairs. The significance of these fluctuations for bubble propagation is assessed by considering the intrinsic stray field profile of a Bloch wall segment. A simple wall model is employed. It is demonstrated that a curved domain wall provides a reasonable basis for modelling the field of a magnetized bar up to saturation. Calculated values of H_s agree qualitatively with experiment. The external field of the bar is rather insensitive to the exact distribution of free-pole density. Together with the observed complexities of domain behabiour this reaffirms the validity of the continuum approach to modelling.     

Crystallographic anisotropy and distortions in helicoidal magnetic structure

The appearance and development of aperiodic distortions in a helicoidal, layered magnetic structure with increasing crystallographic magnetic anisotropy in the magnetization rotation plane have been theoretically studied. A simple phase diagram for this system is proposed. It is established that, at a weak anisotropy, the spiral splits into regions of various lengths with an approximately uniform rotation of the magnetization in each region and a deviation from uniformity at the boundaries; the stronger the anisotropy, the shorter the regions and the greater the deviations. In the limit of high anisotropy, the minimum energy of the system corresponds (depending on the ratio of interlayer exchange integrals J ₁ and J ₂) to either a spiral with constant angular pitch (a multiple of the angle between easy axes) or a double antiferromagnetic structure with a four-layer period. In the case of sixth-order anisotropy with |J ₁| = −J ₂, the energies of phases with different periods (four and six layers for J ₁ > 0; four and three layers for J ₁ < 0) coincide and the excess boundary energy vanishes. In the case of a fourth- and second-order anisotropy, the analogous anomalies appear at |J ₁| = −2J ₂. As a result, the magnetic structure at these points becomes unstable and the phase diagram exhibits the corresponding singularities.     

Microscopic origin of asymmetric magnetization reversal of Co/Pt multilayers with perpendicular magnetic anisotropy

We have comprehensively investigated asymmetric magnetization reversal behaviors of (x-Å Co/7.7 Å Pt)₅ multilayers (x = 3.1 and 4.7) with perpendicular magnetic anisotropy. Our direct observation of magnetic domain structures by means of magneto-optical microscopy reveals that the asymmetry arises both from nucleation and wall-motion processes. An asymmetric nucleation behavior is observed, which could be originated from the preexisting non-reversed domains which might have a reproducible or random spatial distribution, controllable by tuning the field profile. An asymmetric wall-motion behavior stemming from asymmetric stripe domain evolution is also observed.     

Magnetic interface-anisotropy of amorphous iron in contact with nonmagnetic metals

The magnetic properties of very thin ferromagnetic Fe films (1–10 atomic layers) in contact with nonmagnetic amorphous metals are investigated. Apart from the demagnetization energy, which supports a magnetization in the film plane, an energy of magnetic anisotropy occurs in the interlayer, which has the tendency to turn the magnetization perpendicular to the surface. The anomalous Hall effect of the ferromagnetic films is used to investigate their magnetic properties. From the measurements we get the applied magnetic fieldB _s , which is necessary to turn the magnetization perpendicular to the film surface.B _s is, besides a constant term, proportional to 1/d, which is typical of surface effects and yields the energy of the interface anisotropy. The value of this energy is strongly dependent on the nonmagnetic metal and is smaller for the system Pb/Fe than for Sn/Fe. Furthermore, the experimental results show no drastic reduction of the atomic magnetic moment in the surface layer.