Investigation of scaling laws in frequency-dependent minor hysteresis loops for ferromagnetic steels

Scaling laws in dynamical magnetic minor hysteresis loops have been investigated in the magnetizing frequency range of 0.05-300 Hz for various steels including Cr-Mo-V steel subjected to creep, cold rolled steels, and plastically deformed Ni. Although scaling laws in the medium magnetization range found previously fail in the high magnetization frequency regime owing to a significant contribution of eddy currents, a scaling power law of the relation between remanence and remanence work of minor loops, associated with a constant exponent of approximately 1.9, holds true in a very low magnetization regime, irrespective of magnetization frequency and investigated materials. The coefficient of the law is proportionally related to Vickers hardness over the wide frequency range. These observations demonstrate that the scaling analysis of dynamical minor loops enables us to evaluate materials degradation in a short measurement time with low measurement field and high sensitivity to defect density.     

Thermo-magnetic history effects in the giant magnetostriction across the first-order transition and minor hysteresis loops modeling in Fe0.955Ni0.045Rh alloy

Results of temperature- and magnetic field-dependent strain measurements across the first-order antiferromagnetic to ferromagnetic phase transition in Fe(0.955)Ni(0.045)Rh are presented. Distinct thermal and magnetic field hystereses are observed in the measured strain across the phase transition. The minor hysteresis loops inside the hysteretic regime across the temperature-driven transition are modeled using the Preisach model of hysteresis. The applicability of the Preisach model to explain the general features of minor hysteresis loops is discussed for a disorder influenced first-order transition. The minor hysteresis loops show the property of retaining the memory of the starting or end point of the temperature cycle followed within the hysteretic region. A larger temperature excursion within the hysteretic region wipes out the memory of a smaller temperature cycle which contains one of the extrema of the larger cycle. The end-point memory and the wiping-out property of the minor hysteresis loops can be described quite well within the Preisach model, irrespective of the temperature history followed to reach a particular starting point. Thermo-magnetic history effects across the magnetic field-induced transition are explained, which will enable the choice of the starting point of an experimental cycle in the field-temperature phase space so as to achieve the desired functionality. Our results highlight the necessity to understand the influence of disorder on a first-order phase transition so as to achieve a repeatable performance of materials whose functionalities are based on such a transition.     

Minor hysteresis loops model based on exponential parameters scaling of the modified Jiles–Atherton model

In this present work, the minor hysteresis loops model based on parameters scaling of the modified Jiles–Atherton model is evaluated by using judicious expressions. These expressions give the minor hysteresis loops parameters as a function of the major hysteresis loop ones. They have exponential form and are obtained by parameters identification using the stochastic optimization method “simulated annealing”. The main parameters influencing the data fitting are three parameters, the pinning parameter k, the mean filed parameter α and the parameter which characterizes the shape of anhysteretic magnetization curve a. To validate this model, calculated minor hysteresis loops are compared with measured ones and good agreements are obtained.     

Universal hysteresis scaling for incommensurate magnetic order in dysprosium

We study the scaling properties of magnetic minor hysteresis loops in a polycrystalline dysprosium metal, varying temperature and magnetic-field amplitudes. We observe irreversibility-related hysteresis loss in the helical antiferromagnetic phase, which is related with remanent flux density as a power law with the same scaling exponent of 1.25±0.05 as that in ferromagnetic materials. In contrast to hysteresis scalings in ferromagnets associated with 180° Bloch walls, the observed law is governed by spiral walls which separate helical domains with oppositely rotating spins.     

铌锰锆钛酸铅铁电陶瓷电滞回线的温度和频率响应

研究了Pb［(Zr052Ti048)095(Mn1/3Nb2/3)005］O3 (PMnN_PZT) 铁电陶瓷电滞回线的温度和频率响应,结果显示在高频和室温条件下测试铁电特性时,电滞回线呈现“束腰”形状,而不是通常所看到的方形回线 . 在低频和高温条件下测试时才能观察到正常的方形回线,同时,诸如矫顽场、极化强度、 内偏场这些重要的铁电参数也会随频率和温度发生显著的变化. 剩余极化强度随频率和温度 的大幅增长表明“束腰” 电滞回线有可能是由于缺陷偶极子引起的. 电滞回线形状与温度 和频率存在较强的相关性说明缺陷偶极子存在一特征弛豫时间,缺陷偶极子反转响应速度由 此弛豫时间决定. 关键词： 电滞回线 氧空位 频率响应 温度响应     

Quantitative evaluation of dislocation density using minor-loop scaling relations

Relationships between minor hysteresis loops and dislocation density have been investigated at various temperatures from 10 to 600 K in polycrystalline nickel with tensile deformation. It was revealed that coefficients obtained from scaling relations between parameters of minor-loops are in linear proportion to stress at all measuring temperatures below its Curie temperature. Considering that dislocation density is generally in proportion to the square root of true stress, it is concluded that the coefficients are related with the square root of dislocation density. This method using minor hysteresis loops is useful for quantitative evaluation of dislocation density because of its very low measurement field.     

Thermally-assisted tunnelling of magnetization in （Mn0.96Cr0.04）12-ac

The thermally assisted resonant tunnelling in a single crystal (Mn_{0.96}Cr_{0.04})12-ac is studied in this paper. The obtained hysteresis loops at seven different temperatures between 1.8 and 3K show obvious dependence on temperature. The magnetization steps occur at specific field values of nH_R with H_R≈0.46T, which are approximately independent of the temperature. As the temperature decreases, the area enclosed in the hysteresis loops and the actual number n of the resonances increase, which provides clear evidence of thermally assisted resonant tunnelling in (Mn_{0.96}Cr_{0.04})12-ac.     

Coercive field vs. temperature in Fe/Ag nanogranular films

We investigate the temperature dependence of the coercive field of a nanogranular co-sputtered Fe/Ag film. The sample is superparamagnetic at room temperature and displays a 3% giant magnetoresistance. As temperature decreases from 40 to 9 K, hysteresis appears in magnetization loops. The coercive field dependence on temperature turns out to be different from the power law expected for single-domain monodispersed ferromagnetic particle ensembles. The results are analyzed in terms of a model taking into account the effect of magnetic grain size distribution on coercive field. The agreement between experiment and the model is excellent. The possibility to gain information concerning width and symmetry of the particles volume distribution from the study of coercivity's scaling with temperature is discussed.     

Rayleigh relation and scaling power laws in minor hysteresis loops

Seven scaling power-law relations were discovered in the minor hysteresis loops of ferromagnetic materials several years ago. These relations include universal constants that are independent of the type of material and temperature, along with coefficients that provide information about the material and lattice defects. Four universal constants and four coefficients are explained in connection with the Rayleigh relation, which is caused by two scaling laws for l(H) and p(H), where l(H) is the pinning and unpinning length in the domain wall displacement, H is the magnetic field, and p(H) is the number of domain walls involved. The dependence of the coefficients on the dislocation density, ρ, is explained to increase in proportion to the square root of ρ. This result agrees with experimental results. The force profile of the domain walls has similar structures at every point.     

Exchange bias with Fe substitution in LaMnO<Subscript>3</Subscript>

We observe the negative shift of the magnetic hysteresis loop at 5 K, while the sample is cooled in external magnetic field in case of 30% of Fe substitution in LaMnO₃. The negative shift and training effect of the hysteresis loops indicate the phenomenon of exchange bias. The cooling field dependence of the negative shift increases with the cooling field below 7.0 kOe and then, decreases with further increase of cooling field. The temperature dependence of the negative shift of the hysteresis loops exhibits that the negative shift decreases sharply with increasing temperature and vanishes above 20 K. Temperature dependence of dc magnetization and ac susceptibility measurements show a sharp peak (T_p) at 51 K and a shoulder (T_f) around 20 K. The relaxation of magnetization shows the ferromagnetic and glassy magnetic components in the relaxation process, which is in consistent with the cluster-glass compound.     

Hysteresis losses of magnetic nanoparticle powders in the single domain size range

Magnetic iron oxide nanoparticle powders were investigated in order to optimise the specific hysteresis losses for biomedical heating applications. Different samples with a mean particle size in the transition range from superparamagnetic to ferromagnetic behaviour (i.e. 10–100 nm) were prepared by two different chemical precipitation routes. Additionally, the influence of milling and annealing on hysteresis losses of the nanoparticles was investigated. Structural investigations of the samples were carried out by X-ray diffraction, measurement of specific surface area, and scanning and transmission electron microscopy. The dependence of hysteresis losses of minor loops on the field amplitude was determined using vibrating sample magnetometry and caloric measurements. For small field amplitudes, a power law was found which changes into saturation at amplitudes well above the coercive field. Maximum hysteresis losses of 6.6 J/kg per cycle were observed for milled powder. For field amplitudes below about 10 kA/m, which are especially interesting for medical and technical applications, hysteresis losses of all investigated powders were at least by one order of magnitude lower than reported for magnetosomes of comparable size.     

Hysteresis of the Magnetic Particle in a Dipolar Ising Model

Zero-temperature Monte Carlo simulations are used to investigate the hysteresis of a magnetic particle in a dipolar Ising model.The magnetic particle is described in a systemm of permanent dipoles,and the dipoles are located in a cubic lattice site.The effects of the shape and the size of the particle on the hysteresis loop at zero temperature are obtained.For strong exchange interactions,the shapes of magnetic hysteresis loops approach rectangle.For weak exchange interactions,the effects of the size and the shape of the particle on the loops are more remarkable than those of strong exchange interactions case.The slope of the hysteresis loop decreases with the increase of the ratio of the semi major axis to the semi minor axis of the ellipsoidal magnetic particle,and there is an increase of the slope of the hysteresis with the decrease of the size of the magnetic particle.The effects of the shape and size of the particle on the coercive force at zero temperature are also investigated.     

Double-hysteresis-like loops in Mn-doped (Pb,La)(Zr,Ti)O3 ceramics

PLZT12/40/60 ceramics doped with different Mn content were prepared by a conventional mixed oxide method. The shrinkage of some local crystal cells was confirmed by XRD diffraction. The effect of Mn doping on the hysteresis loop was investigated. A peculiar double-hysteresis-like loop was found and various possible mechanisms were discussed. Random local strains caused by shrunk crystal cells can satisfactorily explain the double hysteresis characteristics. The dependence of the double-hysteresis-like loops on temperature was also investigated. Due to the heat activation of polar moments in shrunk crystal cells, the double-hysteresis-like loops can transform into a normal one when the temperature is rising.     

Specific features of magnetic properties of ferrihydrite nanoparticles of bacterial origin: A shift of the hysteresis loop

The results of the experimental investigation into the magnetic hysteresis of systems of superparamagnetic ferrihydrite nanoparticles of bacterial origin have been presented. The hysteresis properties of these objects are determined by the presence of an uncompensated magnetic moment in antiferromagnetic nanoparticles. It has been revealed that, under the conditions of cooling in an external magnetic field, there is a shift of the hysteresis loop with respect to the origin of the coordinates. These features are associated with the exchange coupling of the uncompensated magnetic moment and the antiferromagnetic “core” of the particles, as well as with processes similar to those responsible for the behavior of minor hysteresis loops due to strong local anisotropy fields of the ferrihydrite nanoparticles.     

Asymmetrical phase separation in Nd0.25La0.25Ca0.5MnO3

The highly metastable region across the metal-insulator transition in Nd_0.25La_0.25Ca_0.5MnO₃ is probed by transport and magnetic measurements. The metal-insulator transition observed around 130 K is associated with large thermal hysteresis between temperatures 50-150 K. Observation of minor hysteresis loops across the region indicates coexistence of both metallic and insulating phases. The field-cooled heating and the zero-field-cooled heating susceptibilities deviate from each other from 205 K, signifying thermo-magnetic irreversibility arising from magnetic pinning and/or glassy magnetic behaviour. The magnetoresistance measured on the heating and cooling loops are found to be different in magnitude and nature. The cooling-cycle magnetoresistance was found to be highly irreversible with an open-ended hysteresis loop. We also observe change in the nature of the magnetic relaxation data on the heating and cooling protocols. This indicate strong thermal history dependence of magneto-transport behaviour in the present compound.     

The remagnetization process in spin-valve structures

The process of magnetization reversal in 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 the bottom layers. New types of hysteresis loops are found for characteristic relative magnitudes of the parameters. Analysis of the dependence of the shape of hysteresis loops on the magnitude of interlayer exchange is performed. The phase diagram which determines the regions of existence of characteristic hysteresis loops for different relative magnitudes of the uniaxial anisotropy constant and exchange constant J₁ is constructed.     

Magnetostrictive properties of Ni-ferrite

Initial curve, major and minor magnetostriction hysteresis loops of the NiFe₂O₄ ferrite as the functions of static magnetic field were investgated. Magnetostriction hysteresis loops as the functions of static induction are also presented. The experimental phenomenon of “liftoff” value of the magnetostriction loop is detected.     

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.     

Constricted hysteresis loops in Fe and Ni single crystals

Magnetic hysteresis loops reflect the variety of magnetic domain structures and have been considered to have normal rectangular or leaf-like shapes in standard ferromagnets such as Fe and Ni metals. We report on observations of constricted hysteresis loops in Fe and Ni single crystals with very low defect densities. The constricted loops were observed below T=150 K and in a medium temperature range from 150 to 430 K in Fe and Ni single crystals, respectively. These constricted loops disappear by weak plastic deformation for both single crystals. The origin of constricted hysteresis loops was explained by eddy current effects under less domain wall pinning due to dislocations.     

Hysteresis loop construction for the metal-semiconductor phase transition in vanadium dioxide films

Thermal hysteresis of the reflectivity of vanadium dioxide films observed upon the metal-semiconductor phase transition is studied. The major hysteresis loop is assumed to form when the phase equilibrium temperature in film grains and the grain size vary and correlate with each other. Within the suggested concept of hysteresis loop formation, it is demonstrated that the major loop may be asymmetric, i.e., broadened (shifted) toward lower temperatures. Unlike hysteresis branches for VO₂ bulk single crystal, those for VO₂ films are extended along the temperature axis and may exhibit a step if the grain size distribution has several maxima. The validity of the concept is verified experimentally. It is also shown that atomic force microscopy (AFM) data for the grain size distribution can serve to determine the distribution parameters from the phase equilibrium temperatures without constructing a complete set of minor hysteresis loops, as was required before.