Field Sweep Rate Research Articles

Crackling noise, power spectra, and disorder-induced critical scaling

Crackling noise is observed in many disordered non-equilibrium systems in response to slowly changing external conditions. Examples range from Barkhausen noise in magnets to acoustic emission in martensites to earthquakes. Using the non-equilibrium random field Ising model, we derive universal scaling predictions for the dependence of the associated power spectra on the disorder and field sweep rate, near an underlying disorder-induced non-equilibrium critical point. Our theory applies to certain systems in which the crackling noise results from avalanche-like response to a (slowly) increasing external driving force, and is characterized by a broad power law scaling regime of the power spectra. We compute the critical exponents and discuss the relevance of the results to experiments.

Magnetic anisotropy field dispersion characterization of advanced perpendicular and longitudinal media

Previous models regarding the field sweep rate dependence of coercivity for granular type recording media are extended to an arbitrary distribution of easy axis orientation and field variation law. The values of H/sub K/ and KV/(k/sub B/T) obtained using the proposed model are in agreement with those obtained from the time dependence of coercivity and DC demagnetization coercivity. For high-density recording media, the shift of the anisotropy field distribution measured by switching methods to lower values with respect to that measured by stiff methods is shown to be the effect of thermal relaxation. Particle interactions are acting only on the width of the anisotropy field distribution measured using different methods, without affecting the position of its maximum.

Switching field distribution of 40 Gbit/in.2 longitudinal media obtained by subtracting thermal agitation of magnetization

Switching field distributions (SFDs), are presented for longitudinal media of ∼40 Gbit/in.2 and the influence of thermal agitation of magnetization is discussed. Two remanence curves were measured at different sweep rates of applied field of ∼10 and ∼108 Oe/s, respectively, and SFD curves were obtained by differentiating the remanence curves. The SFD becomes significantly narrower at the higher field sweep rate. A SFD curve without the effect of thermal agitation was calculated using Sharrock’s equation. The full width at half maximum of the SFD curve at 10 Oe/s, ΔHr/Hr, is 0.45 for an isotropic medium, while that estimated without the thermal agitation effect ΔH0/H0 is 0.24, indicating that the SFD at the recording frequency is nearly half that measured at vibrating sample magnetometer (VSM) time scales. The ΔH0/H0 of the ∼40 Gbit/in.2 medium is much smaller than that of a 15 Gbit/in.2 medium used for comparison, although the ΔHr/Hr is ∼1.4 times larger than that of the 15 Gbit/in.2 medium due to thermal agitation. The value of ΔH0/H0 is not influenced by the uniaxial anisotropy induced by substrate texture KuTX. This result indicates that the KuTX is not effective for reducing SFD at recording frequencies, although the KuTX strongly affects the SFD at VSM times scales. The improvement of recording performance with increasing KuTX may be related to suppression of thermal relaxation of the remanent magnetization at bit transitions, immediately after the writing process.

Thermally activated sweep-rate dependence of magnetic switching field in nanostructured current-perpendicular spin-valves

We report on the thermal-activation nature of magnetic switching in magnetic nanostructures, using the junction magnetoresistance of a current-perpendicular magnetic spin-valve device as a probe. A spin-valve junction structure was fabricated using electron-beam lithography. A sweep-rate-dependent magnetic switching field was obtained in the quasi-static limit. Results confirm the predictions of a single-domain thermal activation model. The scaling relation between the magnetic field sweep rate, the magnetic switching field, and the sample size is verified for sample dimensions of 0.1×0.2 μm 2 .

Giant non-linear response of superconducting single crystal niobium in a sweeping magnetic field

Giant enhancement of the non-linear response of a single crystal of Nb placed in a sweeping magnetic field has been experimentally observed. The rectified signal from Nb ( T c=9.15 K) has been measured by means of an inductive method as a function of temperature, dc field, dc field sweep rate, and the amplitude of ac field. The Nb sample was excited by an amplitude modulated ac field. Under a stationary regime, the rectified signal appears only for magnetic fields ( H 0) in the range H c2< H 0< H c3. However, when the dc field was swept slowly, the rectified signal appears at H 0> H c1. This experiment shows that the amplitude of the rectified signal is two orders of magnitude larger than the amplitude of the signal seen under stationary field conditions. Moreover, the amplitude of the rectified signal is a power function of the sweep rate, with the power exponent close to 1.

Chirped-pulse multiphoton transitions between Rydberg states

Rydberg atoms in a static electric field provide an experimental system with which many aspects of strong atom-field interactions can be tested. We report measurements of multiphoton transitions in Rydberg states of potassium driven by chirped pulses of rf radiation. Pulses of rf are produced with frequencies swept from 675 to 825 MHz at rates from 0.25 MHz/ns to 7.5 MHz/ns. We present measurements of population transfer in a two-level system as a function of rf field strength and sweep rate. The data is analyzed with a dynamical Floquet model using Landau-Zener transition probabilities; this model accurately describes these transitions.

Model for reversal dynamics of ultrathin ferromagnetic films

We propose a phenomenological model for the dynamic magnetization reversal of epitaxial ultrathin ferromagnetic films with uniaxial in-plane anisotropy. The model assumes that the reversal proceeds via the nucleation of small reversed domains and subsequent domain wall propagation, and that the domain wall velocity depends linearly on the applied magnetic field strength. Two regimes in the dynamic coercive field (H * c ) versus applied field sweep rate [In(ΔH/Δt)] data are found in good agreement with experiments. For ultrathin films, the mobility of the domain wall (μ) is found to vary with the thickness of the film (t) according to a power law.

Dynamical Properties of Magnetization Reversal of (Ga, Mn) As Layers Studied by MOKE Measurements

In this work, we report on a study of the magnetization reversal of (Ga, Mn) As/GaAs systems. Four 0.5 μm thick Ga1-χ Mn χ As layers (χ = 0.017, 0.025, 0.051 and 0.057) grown by low temperature molecular beam epitaxy on GaAs substrate are investigated using magneto-optical Kerr effect (MOKE). Firstly we analyze static magnetic properties and we identify a four-fold in-plane anisotropy. Using a modified Stoner-Wohlfart model, the magnetocrystalline anisotropy constants are estimated. In last part of this paper we study the dynamic effects on the magnetization reversal when increasing the applied field sweep rate.

Tunneling of magnetization versus spin–phonon and spin–spin transitions in LiY 0.998Ho 0.002F 4

Strong hyperfine coupling in a 0.2% holmium-doped LiYF 4 single crystal induces staircase-like hysteresis loops of the magnetization at very low temperatures. The field sweep rate dependence of hysteresis loops allows the study of two different regimes in the magnetic relaxation of these weakly coupled magnetic moments. At slow field sweep rates, quantum tunneling of the magnetization occurs at avoided level crossings in the low-energy scheme of a single ion Ho 3+. At faster sweep rates, nonequilibrated spin–phonon and spin–spin transitions, mediated by weak dipolar interactions, lead to magnetization oscillations and additional steps.

Sensitive loop tracer for measuring the dynamical response of thin films in a wide audio-frequency range

We have implemented and tested a sensitive AC loop tracer, based on the principle of electro-magnetic induction, which can operate in the frequency range from 10 Hz to 10 kHz. We have studied the dynamic coercivity and loop area of thin exchange-coupled Fe/Co multilayers as a function of the magnetic field sweep-rate.

An alternate model formagnetization plateaus in the molecular magnet V15

Starting from an antiferromagnetic Heisenberg Hamiltonian forthe 15 spin-1/2 ions in V15, we construct aneffective spin Hamiltonian involving eight low-lying states(spin-1/2 and spin-3/2) coupled to a phonon bath. Wenumerically solve the time-dependent Schrödinger equation ofthis system, and obtain the magnetization as a function oftemperature in a time-dependent magnetic field. Themagnetization exhibits unusual patterns of hysteresis andplateaus as the field sweep rate and temperature are varied. The observed plateaus are not due to quantum tunnelling but are aresult of thermal averaging. Our results are in good agreementwith recent experimental observations.

Low-frequency dynamic hysteresis in exchange-coupledNi81Fe19/Ir22Mn78bilayers

The dynamics of hysteresis, including the training effect, the field sweep rate dependence, and the field strength dependence of the exchange bias and coercivity, is experimentally investigated in exchange-coupled ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}{/\mathrm{I}\mathrm{r}}_{22}{\mathrm{Mn}}_{78}$ bilayers in the low-frequency range. The dependence of the exchange field and the coercivity with the number of measurement cycles is well described by a power-law function in which the index varies with the ${\mathrm{Ir}}_{22}{\mathrm{Mn}}_{78}$ thickness. We have also found that the exchange bias depends upon the sweep rate according to a power law. This ``training effect'' and the dynamic response of the exchange biasing can be explained by a thermal fluctuation model in which the antiferromagnet is assumed to be composed of grains which undergo thermal fluctuations.

Dynamical properties of magnetization reversal in exchange-coupled NiO/Co bilayers

Real time dynamic magnetization reversal measurements at room temperature have been performed on polycrystalline exchange-coupled NiO/Co bilayers over 10 decades of applied field sweep rates. Domain wall displacement and domain nucleation regimes govern the magnetization reversal at low and high sweep rates, respectively. The crossover between the two regimes depends on the relative thickness of the two layers. Thicker Co favors propagation, whereas thicker NiO favors nucleation. The coupling energy at the interface was found to be inversely proportional to the square root of the area corresponding to the activation (Barkhausen) volume. These results are consistent with a model of exchange anisotropy in which a randomness of the coupling along the ferromagnetic (F)/antiferromagnetic (AF) interface is combined with a thermally activated switching process of the AF magnetization.

Flux dynamic behaviour of a melt-textured YBa2Cu3O7-δsample

The flux dynamics behaviour of a melt texturedYBa2Cu3O7-δ sample was studied by measuring the sweeping ratedependence of magnetization at different temperatures. First, J(T,B) curveswere obtained from the extended Bean model in order to discuss themagnetization dependence on the sweeping rate. Then the curves of ln E-ln J and the thermal excited potential U0(T,B) were derived fromthe magnetic measurements. Thereby the magnetic response of this sample,especially the influence of the field sweeping rate to the second peak wasanalysed. Thus, the peak effect of this sample and the factorsaffecting the magnitude and position of the second peak were discussed.

Dynamics of large-spin molecules in a time-dependent magnetic field

A numerically exact solution of the time-dependent Schr\odinger equation for noninteracting large-spin $(S=10)$ molecules in the presence of crystal-field anisotropy and time-dependent longitudinal magnetic field is performed. Crystal-field parameters and a field sweeping rate to fit experiment on ${\mathrm{Fe}}_{8}$ and ${\mathrm{Mn}}_{12}$ molecules are used. Magnetization steps are found for values of the sweeping field at which anticrossing of two energy levels occurs. The size of the step depends crucially on the field sweeping rate and on the presence of a transverse field. An efficient approximation is proposed in order to reduce the solution of the original $(2S+1)$-level problem to a sequence of two-level problems. This approach allows us to solve the time-dependent Schr\odinger equation with the experimental field sweeping rate, which is prevented in the original $(2S+1)$-level problem because of the huge computing time.

Nuclear spin driven quantum relaxation in LiY0.998Ho0.002F4.

Staircaselike hysteresis loops of the magnetization of a LiY0.998Ho0.002F4 single crystal are observed at subkelvin temperatures and low field sweep rates. This behavior results from quantum dynamics at avoided level crossings of the energy spectrum of single Ho3+ ions in the presence of hyperfine interactions. Enhanced quantum relaxation in constant transverse fields allows the study of the relative magnitude of tunnel splittings. At faster sweep rates, nonequilibrated spin-phonon and spin-spin transitions, mediated by weak dipolar interactions, lead to magnetization oscillations and additional steps.

Magnetization ofMn12acetate in a slowly varying magnetic field: A quantum mechanical study

Beginning with a Heisenberg spin Hamiltonian for the manganese ions in the Mn_12 Ac molecule, we find a number of low-energy states of the system. We use these states to solve the time-dependent Schrodinger equation and find the magnetization of the molecule in the presence of a slowly varying magnetic field. We study the effects of the field sweep rate, fourth order anisotropic spin interactions and a transverse field on the weights of the different states as well as the magnetization steps which are known to occur in the hysteresis plots in this system. We find that the fourth order term and a slow field sweep rate are crucial for obtaining prominent steps in magnetization in the hysteresis plots.

Magnetization reversal in the pinned layer of PtMnCr/NiFe exchange biased bilayers

A study has been made on the effect of annealing time on magnetization reversal of the pinned layer in NiFe(100 Å)/PtMnCr(500 Å) bilayers. In the as-deposited state, the PtMnCr layer is in a metastable, nonmagnetic, disordered fcc phase. Heating progressively transforms the alloy to the stable fct phase which is antiferromagnetic, providing the pinning layer for the soft ferromagnetic NiFe layer. The samples were annealed in a magnetic field at 250 °C for 1, 1.5, 2, and 8 h. The effect of annealing is to both increase the shift of the loops along the field axis and the coercivity of the pinned ferromagnetic layer. Although the widening of the loop is correlated with the degree of antiferromagnet transformation, the exact mechanism for the increased coercivity is unclear. Measurements of loops made at different field sweep rates and after different waiting times at saturation, on the sample annealed for 1.5 h, indicate two possible mechanisms for the increased coercivity: (i) thermally activated reversal of some of the antiferromagnetic layer (AFM) during the measurement of the hysteresis loop and/or (ii) spin-flop coupling between the AFM and ferromagnet moments at a partially compensated interface.

Magnetization reversal dynamics in exchange-coupled NiO–Co bilayers

We performed a detailed study of the magnetization reversal in polycrystalline exchange-coupled NiO/Co bilayers over 10 decades of field sweep rate dH/dt for different NiO and Co thicknesses. For all sweep rates and thicknesses, the symmetry of the hysteresis loops shows that an identical pinning strength has to be overcome in both directions of the reversal. At low dH/dt the reversal is governed by domain wall displacement while domain nucleation is dominant at higher ones. The dH/dt at which the transition between the two regimes takes place depends on the relative thickness of the NiO and Co layers. It increases (decreases) when the Co (NiO) thickness is increased. Experimentally, it was found that the energy barrier varies linearly with the square root of the area corresponding to the activation (Barkhausen) volume which is consistent with a random walk model of the coupling between antiferromagnetic and ferromagnetic layers. The results can be explained in terms of a thermally activated switching of the NiO magnetization dragged by the Co reversal.

Thickness-dependent dynamic hysteresis scaling behavior in epitaxial Fe/GaAs(001) and Fe/InAs(001) ultrathin films

The dynamic hysteresis scaling behavior in epitaxial Fe/GaAs(001) and Fe/InAs(001) thin films (thickness range 7.3–150 Å) has been investigated as a function of Fe film thickness in the field sweep rate range 0.005–1000 kOe/s using the magneto-optic Kerr effect. The hysteresis loop area A follows the scaling relation A∝(dH/dt)α. We find two distinct dynamic regimes: the low dynamic regime in the sweep rate range 0.005–250 kOe/s, and the high dynamic regime beyond 250 kOe/s. There is a marked increase in α between the low and high dynamic regimes which we attribute to the dominant reversal mechanism changing from domain wall motion to nucleation. In the low dynamic regime α is a decreasing function of Fe film thickness, and this behavior is attributed to the effect of interface-induced pinning.