Magnetoelastic contribution in domain wall dynamics of amorphous microwires

We studied the domain wall (DW) propagation of magnetically-bistable Fe–Co-rich microwires paying attention to the effect of applied and internal stresses. Magnetic field, H, dependences of DW velocity, v, were measured in Co_41.7Fe_36.4Si_10.1B_11.8 microwires with metallic nucleus diameters (from 13 μm to 18 μm) and with different ρ-ratio between the metallic nucleus diameter, d, and total microwire diameter, D. DW velocity decreased under the application of stresses. From measured dependences we evaluated DW mobility, S, dependence on the applied stresses. The results obtained for Co_41.7Fe_36.4Si_10.1B_11.8 sample show that S decreases with the increasing of applied stresses, σ_a. The observed dependences manifest that increasing of magnetoelastic anisotropy results in the decreasing of DW mobility and DW velocity     

On the limiting velocity and forced motion of ferromagnetic domain walls in an external field perpendicular to the easy-magnetization axis

A theory is constructed for the dynamics and braking of domain walls in ferromagnets when a magnetic field is applied perpendicular to the axis of easy magnetization (i.e., a transverse field H _⊥). The theory is valid for velocities v up to the limiting domain wall velocity v c. The Landau-Lifshitz equations in the dissipationless approximation are used to investigate the motion of domain walls and the change in the character of the wall motion as its velocity v approaches v _c. The force acting on a domain wall due to viscous friction is calculated within the framework of generalized relaxation theory, and the dependence of the domain wall velocity v on the forcing field H _z is investigated. Calculations of the braking force show that the contributions of various dissipation mechanisms to the friction force have different dependences on the domain wall velocity, which affects the form of the function v=v(H _z). The shapes of the curves v(H _z) differ very markedly from one another for different values of the field H _⊥. The theory developed here can be used to describe the experimental results, in particular the almost linear behavior of v=v(H _z) for small H _⊥ and its strongly nonlinear behavior when H _⊥∼H _a, whereas these data cannot be reconciled within the standard theory based on relaxation terms of Hilbert type. Zh. éksp. Teor. Fiz. 112, 953–974 (September 1997)     

DC magnetization processes in bistable glass-coated ferromagnetic microwires

Interaction of a single magnetic domain wall with an inhomogeneous magnetic field and distribution of local nucleation fields along glass-coated Fe_77.5−xNi_xB₁₅Si_7.5 (x=0, 27.9, 34.9) microwires were experimentally studied. It was shown that the wall separating two axial domains and moving along the wire can be stopped by an inhomogeneous magnetic field. The wall remains stable and trapped in a local potential minimum after external fields are switched off. Wall coercivity increases with Ni content. For all samples the minimum of critical field for axial magnetization reversal was observed near the end of the wire. For samples with non-zero Ni content a distribution of nucleation fields lower than 950 A/m was observed in regions far enough from the wire ends. In Ni-free samples the nucleation fields were higher than 950 A/m.     

Stress dependence of the domain wall dynamics in the adiabatic regime

In this work, we determine the domain wall velocity in the low field region and study the domain dynamics in as-cast and annealed bi-stable amorphous glass-covered Fe_77.5Si_7.5B₁₅ microwires. In particular, from the relation between the domain wall velocity and magnetic field in the adiabatic regime, the power-law critical exponent β, the critical field H₀ and the domain wall damping η were obtained. It has been verified that the main source of domain wall damping is the eddy current and spin relaxation, both with a strong relation with the magnetoelastic energy. This energy term is changed by the axial applied stress, which, by its time, modifies the damping mechanisms. It was also verified that the domain wall damping terms present different behavior at low (mainly eddy currents) and high applied stress (spin relaxation).     

AC-current-induced magnetization switching in amorphous microwires

We studied the influence of AC current flowing through microwires, on magnetization dynamics. We used a previously developed Sixtus-Tonks modified setup to evaluate the domain wall (DW) velocity within the microwire. However, instead of a magnetizing solenoid, we used a current flowing through the microwire. We observed that the AC current flowing through the annealed Co-rich microwire leads to remagnetization by fast domain wall propagation. The estimated DW velocity was approximately 4.5 km/s, which is similar to and even higher than that reported for the magnetic-field-driven domain wall propagation in Fe- and Co-rich microwires. We measured the DW velocity under tensile stress, and found that the DW velocity decreases under applied stress. An observed DW propagation induced by the current flowing through the microwire is explained considering the influence of an Oersted magnetic field on the outer domain shell. This field has a circular easy magnetization direction and magnetostatic interaction between the outer circumferentially magnetized shell and the inner axially magnetized core.     

Field-driven creep motion of a composite domain wall in a Pt/Co/Pt/Co/Pt multilayer wire

We have studied the field-driven motion of a pair of coupled Bloch domain walls in a perpendicular magnetic anisotropy Pt/Co/Pt/Co/Pt multilayer Hall bar. The nucleation of an isolated but coincident pair of walls in the two Co layers, observed by Kerr microscopy, took place at an artificial nucleation site created by Ga⁺ ion irradiation. The average velocity v of the wall motion was calculated from time-resolved magnetotransport measurements at fixed driving field H, where the influence of the extraordinary Hall effect leads to the observation of voltages at the longitudinal resistance probes. We observed a good fit to the scaling relation lnv∝H^−1/4, consistent the motion of a single 1-dimensional wall moving in a 2-dimensional disordered medium in the creep regime: the two walls are coupled together into a 1-dimensional composite object.     

Numerical simulation of wall dynamics in (111)-oriented garnet films in the presence of an in-plane magnetic field

The domain wall motion in the presence of an in-plane magnetic field H_y perpendicular to the wall is simulated using a fall implicit numerical scheme. Calculations are performed for the drive fields 0 Oe<H_z<15 Oe and in-plane fields -210 Oe?H_y?210 Oe. The relation between the average wall velocity $\text{v}$ and the drive field H_z is discussed considering the wall structure. It was found that an in-plane field increases the peak velocity of the wall and extends the range of the drive fields, where the linear mobility relation is valid. A dynamical Bloch line stacking was found for sufficiently large drives. The influence of an in-plane field on the angular span of horizontal Bloch lines is discussed also. In particular the occurrence of 2π-horizontal Bloch lines is described. Numerical results obtained with a full implicit method are compared with the experimental observations of bubble motion and good agreement is found for |H_y|≤100 Oe.     

Magnetic field dependence of asymmetry in the magnetization reversal of ultrathin Co films and Co/Pt multilayers with perpendicular anisotropy

We studied the magnetization reversal in ultrathin [Co/Pt]_n films (n=1, 2, and 4) using magneto-optical Kerr microscopy. These materials demonstrate unusual asymmetries in the activity of nucleation centers and domain wall motion. It was found that application of very high holding magnetic field prior to magnetization reversal, exceeding some critical value much larger than the apparent saturation field, suppresses the subsequent ‘asymmetric’ nucleation centers, activity. We revealed that the ‘asymmetric’ nucleation centers become active again after subsequent reversal cycles coming from a smaller holding field and studied how the asymmetry returns with the decrease of applied holding field. It was found that in low-coercivity ultrathin Co films, the asymmetry in domain wall velocity decreased sharply with the applied field increase and disappeared when the reversal field is greater than μ₀H=1.5 mT.     

Current induced domain wall motion in nanostripes with perpendicular magnetic anisotropy

We report micromagnetic modeling results of current induced domain wall (DW) motion in magnetic devices with perpendicular magnetic anisotropy by solving the Landau-Lifschitz-Gilbert equation including adiabatic and non-adiabatic terms. A nanostripe model system with dimensions of 500 nm (L)×25 nm (W)×5 nm (H) was selected for calculating the DW motion and its width, as a function of various parameters such as non-adiabatic contribution, anisotropy constant (K_u), saturation magnetization (M_s), and temperature (T). The DW velocity was found to increase when the values of K_u and T were increased and the M_s value decreased. In addition, a reduction of the domain wall width could be achieved by increasing K_u and lowering M_s values regardless of the non-adiabatic constant value.     

Temperature dependence of coercivity and metamagnetism in Tb0.5Y0.5Ni

The temperature dependences of magnetic properties of the FeB structure compound Tb_0.5Y_0.5Ni are examined with the aim to elucidate the origin of intrinsic magnetic hardness in this compound. The easy a axis coercivity of an aligned powder sample is found to be strongly temperature dependent. A domain wall activation model is employed to obtain the parameters H₀(0)=30kOe, V_V(0)=0.24K^?1, and β=0.016K^?1, where H₀(0) is the coercive force at absolute zero, V_T(0) the domain wall activation parameter, and β the coefficient for the linear temperature dependence of the reduced anisotropy. From polycrystalline data, we find a strong temperature dependence of the c axis metamagnetic transition only for the ferromagnetic (F) to antiferromagnetic (AF) direction. From the relative constancy of the AF to F c axis metamagnetic transition compound to the a axis coercivity we conclude that the coercive force is not directly related to the local molecular fields as had been previously suggested.     

Effect of an external magnetic field and a trapped magnetic flux on the current-voltage characteristics of a granular high-temperature superconductor YBa2Cu3O7−δ

A comparative study of the current-voltage characteristics of the high-temperature ceramic superconductor YBa₂Cu₃O_～6.95 at T = 77.3 K is performed over wide ranges of external magnetic fields H _ext and “treatment” fields H _treat. It is found that the field dependences of the parameters a and j _c involved in the exponential equation E = a(j ? j _c)^v describing the current-voltage characteristics depend substantially on the method used for applying the magnetic field, whereas the exponent v ～ 2 depends on neither the method of application nor on the magnetic field strength. The field dependence of the trapped magnetic field H _trap is determined.     

Trapping and injecting single domain walls in magnetic wire by local fields

A single domain wall (DW) moves at linearly increasing velocity under an increasing homogeneous drive magnetic field. Present experiments show that the DW is braked and finally trapped at a given position when an additional antiparallel local magnetic field is applied. That position and its velocity are further controlled by suitable tuning of the local field. In turn, the parallel local field of small amplitude does not significantly affect the effective wall speed at long distance, although it generates tail-to-tail and head-to-head pairs of walls moving along opposite directions when that field is strong enough.     

Experimental detection of domain wall propagation above the Walker field

The domain wall (DW) velocity above the Walker field drops abruptly with increasing magnetic field, because of the so-called Walker breakdown, where the DW moves with a precessional mode. On applying the higher field, the DW velocity again starts to increase gradually. We report the DW propagation around this local minimum regime in detail, investigated through the time-resolved electrical detection technique, with a magnetic tunnel junction. Just above the Walker field, we succeeded in detecting the precessional motion of the DW in a real-time regime, while a different mode appeared around the local minimum of the DW velocity.     

Anomalous magnetization processes and non-symmetrical domain wall displacements in L10 FePt particulate films

Anomalous magnetization processes and non-symmetrical domain wall displacements in the minor loop of L1₀ FePt particulate films were investigated by magnetization measurements and in situ magnetic force microscopy. Magnetization (M) decreases dramatically on increasing the magnetic field to ∼3 kOe after which M becomes small and constant in the range of 5–20 kOe as observed in the successive measurement of minor loops. The domain wall displacement is non-symmetrical with respect to the field direction. The anomalous magnetization behavior was attributed to the non-symmetrical domain wall displacement and large magnetic field required for domain wall nucleation. Energy calculations from modeling suggest that non-symmetrical domain wall displacement is caused by the existence of metastable domains in which the domain edges are stuck to the particle boundaries.     

Characteristic fields of a Bi2Sr2CaCu2Oy crystal

The field dependences of the transverse resistance of a Bi₂Sr₂CaCu₂O_y (BSCCO) layered superconducting single crystal with T _c0≥92 K are studied in a perpendicular (H⊥(ab)) pulsed magnetic field up to 50 T in a wide temperature range, 4.2–300 K. The temperature dependences of the characteristic fields identified with the “irreversibility curve” and the field corresponding to the nucleation of the superconducting phase are determined. The results obtained for the latter field are compared with the theoretical dependences.     

Local approximation oscillatory differential method for the analysis of physical processes at the interface between vortex and Meissner regions in superconductors

A “differential” method for local diagnostics of superconductors has been developed. Regular steps with identical heights through certain intervals of an external field have been revealed on the magnetic-field dependences of the trapped magnetic flux density B _tr(H ₀) and the effective demagnetizing factor n _eff (H ₀) of bulk and film YBCO samples. It has been shown that the sample in high magnetic fields “decays” stepwise into subcrystallites and nanocrystallites whose size is much smaller than the depth of penetration of the magnetic field λ.     

Controlling depinning and propagation of single domain-walls in magnetic microwires

The magnetization reversal in magnetostrictive amorphous microwires takes place by depinning and propagation of a single domain wall. This is a consequence of the particular domain structure determined by the strong uniaxial anisotropy from the reinforcement of magnetoelastic and shape contributions. In the present study, after an overview on the current state-of-the art on the topic, we introduce the general behaviour of single walls in 30 to 40 cm long Fe-base microwires propagating under homogeneous field. Depending on the way the walls are generated, we distinguish among three different walls namely, standard wall, DW _st , depinned and propagating from the wire’s end under homogeneous field which motion is the first one to switch on; reverse wall, DW _rev , propagating from the opposite end under non-homogeneous field, and defect wall, DW _def , nucleated around local defect. Both, DW _rev and DW _def are observed only under large enough applied field. In the subsequent section, we study the propagation of a wall under applied field smaller than the switching field. There, we conclude that a minimum field, H _dep,0, is needed to depin the DW _st , as well as that a minimum field, H _prop,0, is required for the wall to propagate long distances. In the last section, we analyse the shape of induced signals in the pickup coils upon the crossing of the walls and its correlation to the domain walls shape. We conclude that length and shape of the wall are significantly distorted by the fact that the wall is typically as long as the measuring coils.     

Domain wall propagation in Fe-rich amorphous microwires

The domain wall (DW) propagation in magnetically bistable Fe₇₄Si₁₁B₁₃C₂ amorphous microwires with metallic nucleus diameters of 12–16 μm has been investigated in order to explain high DW velocities observed in Sixtus–Tonks like experiments. In micrometric wires, the boundary between two head-to-head domains is very elongated. The DW mobility normal to the wall surface is reduced by the domain aspect ratio and is in the range of a few m/s/Oe in the linear regime. The experimental results in the viscous regime could be quantitatively explained in terms of the domain length and normal mobility limited by the eddy currents and spin relaxation losses.     

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 the magnetic anisotropy energy distribution of MnSb clusters on spontaneous magnetization reversal of GaMnSb thin films

Temperature m(T) and time m(t) dependences of the magnetic moment of GaMnSb thin films with MnSb clusters have been measured. The m(t) dependences are straightened in semilogarithmic coordinates m(lnt). The temperature dependences of magnetic viscosity S(T) corresponding to the slope of straight lines m(lnt) have been studied. It have been demonstrated that the behavior of dependences S(T) is governed by the lognormal distribution of the magnetic anisotropy energy of MnSb clusters. It have been found that the behavior of dependences m(T) measured after the films were cooled in zero magnetic field and in magnetic field H = 10 kOe is also governed by the lognormal distribution of the magnetic anisotropy energy of MnSb clusters.