Amorphous Ferromagnets Research Articles

Anisotropy of magnetoelectric effects in an amorphous ferromagnet-piezoelectric heterostructure

In-plane anisotropy of linear and nonlinear magnetoelectric (ME) effects in a heterostructure composed of mechanically coupled layers of amorphous iron-based ferromagnet and piezoelectric lead zirconate-titanate ceramics has been investigated. The measurements were performed on a disk-shaped sample subjected to a low-frequency excitation magnetic field h oriented either parallel or perpendicular to a bias magnetic field H0. The first harmonic of the voltage response was recorded in the case of the linear ME effect, which was excited at frequencies of acoustic resonances of the sample, and the second harmonic in the case of the nonlinear ME effect excited in the non-resonance regime. Strong uniaxial or biaxial anisotropy for different directions of the bias field within the sample plane was observed. The uniaxial anisotropy of the ME effect occurs due to the uniaxial magnetic and magnetostrictive anisotropy of the amorphous ferromagnetic layer that is a result of its fabrication by the ultrafast cooling method. The biaxial anisotropy at resonant frequencies is the manifestation of the spatial structure of the excited acoustic modes. The anisotropy of ME effects should be taken into account when developing magnetoelectric devices based on composite heterostructures.

Effects of Cr substitution on the low temperature magnetization behavior in amorphous Fe68+xCr12-xSi8B12 ribbons

Amorphous Fe68+xCr12-xSi8B12 alloys (x=0, 2, 4, 6, 8 and 10) were prepared using single wheel melt spinning technique. Magnetic measurements were carried out in the temperature range from 5–300 K and at an external applied field of 30 kOe. The Curie temperature was found to increase by substituting Cr by Fe. The magnetic behavior at low temperature was analyzed using spin wave theory. The low temperature magnetization curve was found to obey Bloch's T3/2 law. Some parameters are extracted like the spin wave stiffness constant (D) and mean square range of exchange interaction for the different compositions. The values of spin waves constant (D) determined were found to increase with substitution the Cr by Fe. The values of the mean square range of exchange interaction were found to be characteristic of amorphous ferromagnets. The local random anisotropy constant KL was derived from the approach of saturation in the magnetization. KL increases as Cr concentration decreases.

Study of the low-field irreversibility line in the transverse component spin-glass phase of the amorphous Fe90Zr10 alloy

Amorphous FexZr100−x alloys display a complex magnetic phase diagram, particularly in the range 89% ≲ x ≲ 93% in which the phase transition from the paramagnetic to a soft ferromagnetic (FM) state at a critical temperature Tc precedes a second transition at Txy < Tc to a transverse spin-glass (SG) phase, with frozen spin components transverse to the magnetization. The softness of the FM phase and the coexistence of FM and SG orderings complicate exploring the low-temperature and low-field critical properties of the glassy transition. Here we study the irreversibility Almeida-Thouless (AT) line that marks the onset of the transverse SG phase in the Fe90Zr10 alloy in the low-field regime up to H = 60 Oe. While ZFC measurements give rise to an AT exponent ϕ = 4.6, similar to that of another amorphous FM compound with random local anisotropy, the induction of magnetic shiftings upon cooling the sample in a large field, − 85 kOe, displaces down the AT line and separates it into two distinct regimes: one also with ϕ = 4.6 for H above 20 Oe, nearly corresponding to the typical field to flip the remanent magnetization, and a new second regime at lower H, with field-induced remanent clusters and exponent ϕ = 3.6 that approaches the mean-field value ϕ = 3. Our findings are discussed on the light of the results from a random nonuniform anisotropy model with FM exchange interactions, which also reported the existence of a two-regimes scenario in the AT line with similar exponents.

Parametric Generation of Subharmonics in a Composite Multiferroic Resonator

Parametric generation of subharmonics in a composite multiferroic resonator is observed and investigated. The resonator has the form of a disk and contains two mechanically coupled layers, one of which is amorphous ferromagnet $\mathrm{Fe}\text{\ensuremath{-}}\mathrm{B}\text{\ensuremath{-}}\mathrm{Si}\text{\ensuremath{-}}\mathrm{C}$ and the other piezoelectric lead zirconate titanate. The resonator is placed inside two planar electromagnetic coils with orthogonal axes. A static magnetic field of 0--100 Oe is applied parallel to the plane of the resonator. The resonator is excited in the frequency range f = 9--10 kHz by either a harmonic magnetic field with an amplitude of up to 5 Oe generated by one of the coils, or a harmonic electric field with an amplitude of up to 500 V/cm applied to the piezoelectric layer. When the pump field is above a certain threshold, generation of a subharmonic of half-frequency (f/2) is observed for three different excitation methods. The first two employed either the direct magnetoelectric effect or the converse magnetoelectric effect, while in the third a transformer system is utilized. The subharmonic is generated in a limited range of pump frequencies and its amplitude is a nonlinear function of both the pump-field amplitude and the strength of static magnetic field. A theory of parametric generation of the subharmonic in a multiferroic resonator is developed, taking into account the magnetoacoustic nonlinearity of the ferromagnetic layer of the structure and excitation of acoustic resonances near the pump and subharmonic frequencies. The theory qualitatively describes the main characteristics of the subharmonic generation.

Effective Excitation of Magnetoelectric Voltage Harmonics in a Ferromagnet–Piezoelectric Structure by Current Passing through the Magnetic Layer

The magnetoelectric (ME) effect in a planar amorphous ferromagnet–piezoelectric lead zirconate titanate (PZT) composite structure can be effectively excited by passing alternating current through the magnetic layer. The absence of demagnetizing (stray) field and the orientation of the exciting magnetic field perpendicular to the constant field allow this structure to generate the even harmonics of electric field with efficiency several times that for the ME effect produced by volume coils. It is established that the second harmonic amplitude is proportional to the piezomagnetic coefficient of the magnetic layer and the square amplitude of current and inversely proportional to the bias magnetic field.

Geometry-induced nonequilibrium phase transition in sandpiles.

We study the sandpile model on three-dimensional spanning Ising clusters with the temperature T treated as the control parameter. By analyzing the three-dimensional avalanches and their two-dimensional projections (which show scale-invariant behavior for all temperatures), we uncover two universality classes with different exponents (an ordinary BTW class, and SOC_{T=∞}), along with a tricritical point (at T_{c}, the critical temperature of the host) between them. The transition between these two criticalities is induced by the transition in the support. The SOC_{T=∞} universality class is characterized by the exponent of the avalanche size distribution τ^{T=∞}=1.27±0.03, consistent with the exponent of the size distribution of the Barkhausen avalanches in amorphous ferromagnets Durin and Zapperi [Phys. Rev. Lett. 84, 4705 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.4705]. The tricritical point is characterized by its own critical exponents. In addition to the avalanche exponents, some other quantities like the average height, the spanning avalanche probability (SAP), and the average coordination number of the Ising clusters change significantly the behavior at this point, and also exhibit power-law behavior in terms of ε≡T-T_{c}/T_{c}, defining further critical exponents. Importantly, the finite-size analysis for the activity (number of topplings) per site shows the scaling behavior with exponents β=0.19±0.02 and ν=0.75±0.05. A similar behavior is also seen for the SAP and the average avalanche height. The fractal dimension of the external perimeter of the two-dimensional projections of avalanches is shown to be robust against T with the numerical value D_{f}=1.25±0.01.

Nonlinear magnetoelectric effect in a layered ferromagnetic-piezoelectric heterostructure excited by transverse magnetic field

The nonlinear magnetoelectric effect in a heterostructure containing layers of amorphous ferromagnet FeBSiC and piezoelectric lead zirconate titanate ceramics has been investigated. The heterostructure was subjected to permanent, H0, and alternating, h, magnetic fields applied in the structure plane. In contrast to previous studies, the excitation field was directed perpendicular to the permanent field (h⊥H0). The generation of even voltage harmonics across the piezoelectric layer was observed for excitation fields in the range of 0–3 Oe. The dependence of the second harmonic amplitude on the permanent field strength was found to differ significantly from a similar dependence upon longitudinal excitation, h//H0. A theory was developed, which describes the field dependence of voltage harmonic amplitudes for the magnetoelectric effect excited by a transverse magnetic field.

Эффективное возбуждение магнитоэлектрического эффекта в структуре ферромагнетик-пьезоэлектрик током через магнитный слой

The effective excitation of the magnetoelectric effect in a planar structure amorphous ferromagnet – piezoelectric lead zirconate titanate by alternating current flowing through the magnetic layer was demonstrated. Due to orientation of the exciting magnetic field perpendicular to the constant field and absence of demagnetization, the structure generates even voltage harmonics with efficiency, several times higher than the efficiency of excitation of the effect by volume coils. It was shown that the amplitude of the second harmonic is proportional to the piezomagnetic coefficient of the magnetic layer,increases quadratically with the amplitude of the current and decreases inversely with the biasing magnetic field

Local Magnetic Anisotropy of the Co-Based Amorphous Alloy

The magnetization, initial magnetic susceptibility, and magnetostriction of a multicomponent Co-based amorphous alloy have been studied. The exchange constant a and the Curie temperature TC of the alloy are determined. On the basis of a method based on the theory of stochastic magnetic structure for amorphous ferromagnets and using the magnetization curves, the correlation field Hℓ, the field Ha, the effective constant of local magnetic anisotropy Keff, and the stochastic characteristics of local anisotropy – the mean square field fluctuations and the correlation radius – have been calculated. The temperature behavior of the examined magnetic characteristics is analyzed. The results of magnetostriction research allow a conclusion to be drawn that the local magnetic anisotropy of the alloy has a single-ion origin.

Amorphous magnetic semiconductors with Curie temperatures above room temperature

Recently, amorphous magnetic semiconductors as a new family of magnetic semiconductors have been developed by oxidizing ferromagnetic amorphous metals/alloys. Intriguingly, tuning the relative atomic ratios of Co and Fe in a Co-Fe-Ta-B-O system leads to the formation of an intrinsic magnetic semiconductor. Starting from high Curie-temperature amorphous ferromagnets, these amorphous magnetic semiconductors show Curie temperatures well above room temperature. Among them, one typical example is a p-type Co28.6Fe12.4Ta4.3B8.7O46 magnetic semiconductor, which has an optical bandgap of ~2.4 eV, room-temperature saturation magnetization of ~433 emu/cm3, and the Curie temperature above 600 K. The amorphous Co28.6Fe12.4Ta4.3B8.7O46 magnetic semiconductor can be integrated with n-type Si to form p–n heterojunctions with a threshold voltage of ~1.6 V, validating its p-type semiconducting character. Furthermore, the demonstration of electric field control of its room-temperature ferromagnetism reflects the interplay between the electricity and ferromagnetism in this material. It is suggested that the carrier density, ferromagnetism and conduction type of an intrinsic magnetic semiconductor are controllable by means of an electric field effect. These findings may pave a new way to realize magnetic semiconductor-based spintronic devices that work at room temperature.

Scattering of Microwaves by a Passive Array Antenna Based on Amorphous Ferromagnetic Microwires for Wireless Sensors with Biomedical Applications.

Co-based amorphous microwires presenting the giant magnetoimpedance effect are proposed as sensing elements for high sensitivity biosensors. In this work we report an experimental method for contactless detection of stress, temperature, and liquid concentration with application in medical sensors using the giant magnetoimpedance effect on microwires in the GHz range. The method is based on the scattering of electromagnetic microwaves by FeCoSiB amorphous metallic microwires. A modulation of the scattering parameter is achieved by applying a magnetic bias field that tunes the magnetic permeability of the ferromagnetic microwires. We demonstrate that the OFF/ON switching of the bias activates or cancels the amorphous ferromagnetic microwires (AFMW) antenna behavior. We show the advantages of measuring the performing time dependent frequency sweeps. In this case, the AC-bias modulation of the scattering coefficient versus frequency may be clearly appreciated. Furthermore, this modulation is enhanced by using arrays of microwires with an increasing number of individual microwires according to the antenna radiation theory. Transmission spectra show significant changes in the range of 3 dB for a relatively weak magnetic field of 15 Oe. A demonstration of the possibilities of the method for biomedical applications is shown by means of wireless temperature detector from 0 to 100 °C.

Magnetoelectric direct and converse resonance effects in a flexible ferromagnetic-piezoelectric polymer structure

Abstract The direct and converse magnetoelectric (ME) effects in a flexible structure containing a mechanically coupled layers of amorphous ferromagnet FeBSiC and a piezo-copolymer poly(viniledene fluoride trifluoroethylen) (P(VDF-TrFE)) are investigated. The mutual transformation of magnetic and electric fields in the structure arises due to a combination of magnetostriction and piezoelectric effects in the ferromagnetic and piezoelectric layer, respectively. The ME effects were induced by exciting the structure with alternating magnetic fields of 0–100 kHz frequency and 1–5 Oe amplitude, or alternating electric fields of amplitudes up to 500 V/cm in the presence of a constant H field. For the direct ME effect the conversion coefficient reached 7.2 V/(cm·Oe) at a bending resonance frequency of 412 Hz and 44 V/(cm·Oe) at a planar resonance frequency of 25.15 kHz. Increasing the excitation magnetic field at the bending resonance frequency, the nonlinear second harmonic generation with an efficiency of 0.24 V/(cm·Oe2) was observed. For the converse ME effect, the conversion coefficient at the planar resonance frequency was 0.09 G·cm/V. The dependences of the efficiencies for the direct and converse ME transformations on the constant field and the amplitudes of the excitation fields are well explained by theory. These results could be used to develop magnetic and electric field sensors, as well as autonomous energy harvesting sources.

Magnetoelectric doubling and mixing of electric and magnetic field frequencies in a layered multiferroic heterostructure

Abstract Nonlinear magnetoelectric effects in a disk-like heterostructure composed of a layer of amorphous ferromagnet (FeBSiC) mechanically coupled to a layer of piezoelectric ceramics (lead zirconate titanate) were studied both experimentally and theoretically. The structure was excited by alternating electrical and magnetic fields far from its acoustic resonance frequency. This induced changes in the magnetic induction within the heterostructure which were recorded using an electromagnetic coil. The experiments were performed for excitations with electric and magnetic fields up to 250 V/cm and 6 Oe, respectively, and bias permanent magnetic fields up to 60 Oe. For large excitation fields, a generation of the second harmonic and harmonics corresponding to the sum and difference frequencies were observed. The coefficient of the frequency doubling for the converse magnetoelectric effect and the coefficient of mixing of electrical and magnetic field frequencies were found to be 4.6∙10−6 G cm2/V2 and ∼1∙10−2 G cm/(Oe∙V), respectively. A simple theoretical model qualitatively describing the experimental findings was proposed. It was shown that the nonlinearity in the converse magnetoelectric effect arises due to the nonlinear dependence of magnetic induction in the ferromagnetic layer on mechanical stress.

Magnetoelectric Monolithic Resonator Based on the Ferromagnetic-Piezoelectric Structure Excited With a Linear Current

A monolithic magnetoelectric (ME) resonator for applications in magnetic field sensors was manufactured and investigated. The resonator contains a piezoelectric lead zirconate titanate plate of dimensions 20 mm × 4 mm × 0.2 mm with Ag electrodes, located between two layers of a magnetostrictive amorphous ferromagnet FeBSiC, each of which is 25 μ m thick. Planar acoustic oscillations with a frequency of 74 kHz in the resonator were excited by a magnetic field of linear alternating current I = 0–100 mA flowing through conductive copper strips that are 20 μ m thick, deposited on both external surfaces of the resonator. The voltage u generated by the ME resonator depends linearly on the tangential dc magnetic field in the range H = 0–130 Oe. The excitation efficiency of the resonator with a linear current reached u / I = 1.5 V/A. The use of strips with a current, instead of electromagnetic coils, to excite ME resonators will allow reduction of the size and increase the frequency of the resonators, expand the range of operating magnetic fields, and, by order of magnitude, reduce the power required to excite the resonators.

Nonlinear converse magnetoelectric effects in a ferromagnetic-piezoelectric bilayer

The strain mediated nonlinear converse magnetoelectric effect (CME) is investigated in a bilayer of an amorphous ferromagnet FeBSiC and piezoelectric lead zirconate titanate (PZT). The magnetic response of the sample to an AC electric field (e) applied to PZT at an acoustic resonance frequency of 76 kHz was measured with a coil wound around the bilayer. With an increase in the amplitude of e over the range 0–250 V/cm, the variation in amplitude of the first and the second harmonics of the induced voltage due to the variation in the magnetic induction B was measured for DC bias magnetic field H = 0–80 Oe. The coefficients of the linear and nonlinear converse ME effects were 5.5 G cm/V and 1.9 × 10−2 G cm2/V2, respectively. The nonlinearity of the CME arises due to the nonlinear dependence of the magnetic induction on the stress. A theoretical model for the nonlinear CME is discussed.

Magnetoelectric effects in a layered ferromagnet-electrostrictor heterostructure

Magnetoelectric (ME) effects in a heterostructure consisting of mechanically coupled layers of amorphous ferromagnet FeBSiC and electrostrictive lead magnesium niobate-lead titanate (PMN-PT) ceramics are observed and investigated. Magnetoelectric characteristics of the structure strongly differ from those of the ferromagnetic-piezoelectric one. The FeBSiC-PMN-PT structure did not show the direct ME effect under excitation with an alternating magnetic field. For the converse ME effect, when the structure was excited with alternating electric fields, the frequency doubling and mixing of electric fields frequencies were observed. Nonlinear ME effects arise due to the nonlinear electrostrictive strain vs electric field dependence. Efficiency of nonlinear ME conversion is proportional to the piezomagnetic coefficient of the ferromagnetic layer, nonlinear electrostriction coefficient of the electrostrictive layer, and amplitudes of the excitation fields. A theory for nonlinear ME effects in the ferromagnet-electrostrictor heterostructures was developed.

Scaling of the Hall effects beyond the quantum resistance threshold in oxidized CoFeB

The ordinary and the extraordinary Hall effects were studied in gradually oxidized amorphous CoFeB ferromagnets over six orders of resistivity from the metallic to the strongly insulating regime. Polarity of the extraordinary Hall effect reverses, and the amplitude of both the ordinary and the extraordinary Hall effects increases quadratically with resistivity when resistance exceeds the quantum resistance threshold. The absolute value of the extraordinary Hall effect scales linearly with the ordinary one in the entire range over eight orders of magnitude between the metallic and the insulating states. The behavior differs qualitatively and quantitatively from theoretically predicted and experimentally known in other materials.

Nonlinear magnetoelectric effects in flexible composite ferromagnetic – Piezopolymer structures

Nonlinear magnetoelectric (ME) effects in a flexible composite planar structure, containing mechanically coupled layers of amorphous FeBSiC ferromagnet and PVDF piezoelectric polymer have been experimentally investigated. Under the action of a weak harmonic magnetic field h with frequency f=50–1000Hz and tangential bias magnetic field H=1–80Oe, the structure generated a voltage of the same frequency. The efficiency of linear ME conversion reached 3.4V/(cm·Oe) for the optimum bias field Hm≈15Oe. On increasing the excitation field up to h ∼7Oe, the structure generated second and third harmonics with efficiencies of ∼25mV/(cm·Oe2) and ∼2.5mV/(cm·Oe3), respectively. The amplitudes of the harmonics were not monotonous functions on the bias field H and grew with the increase in the alternating field h. Under the action of two alternating fields with different frequencies f1 and f2, the structure generated ac voltages with frequencies equal to the sum and difference frequencies f1±f2. The efficiency of magnetic fields mixing reached a maximum of ∼30mV/(cm·Oe2) in the absence of the bias field. The effects of harmonics generation and magnetic fields mixing arise due to the nonlinear dependence of the ferromagnet’s magnetostriction λ on the bias field H. The efficiency of the nonlinear processes is proportional to the derivatives of the magnetostriction over magnetic field. The nonlinear ME effects in the ferromagnet-piezopolymer flexible structures can be used to design high-sensitivity dual ac/dc magnetic field sensors and energy harvesting devices.

Law of approach to magnetic saturation in nanocrystalline and amorphous ferromagnets with improved transition behavior between power-law regimes

New law of the approach to magnetic saturation is proposed based on scaling in ferromagnets with random magnetic anisotropy. This law is consistent with the known laws derived within perturbation theory in extreme cases, but it describes the transition mode between the power-low asymptotic regimes better. The improved law is proper for reliable fitting the approach magnetization to saturation in nanocrystalline and amorphous ferromagnets.

Perpendicular Magnetic Anisotropy and Interfacial Dzyaloshinskii-Moriya Interaction in Pt/CoFeSiB Structures

Magnetic materials exhibiting perpendicular magnetic anisotropy (PMA) have an important role in the development of high-density magnetic random-access memory and domain-wall devices. Exotic physical phenomena result from spin-orbit coupling, such as PMA and the interfacial Dzyaloshinskii-Moriya interaction (iDMI), at interfaces between nonmagnetic (NM) and ferromagnetic (FM) materials. We report on the NM Pt thickness dependence of PMA and iDMI in Ta/Pt/CoFeSiB/Ta films and the MgO thickness dependence of PMA in Ta/Pt/CoFeSiB/MgO/Ta films. We selected amorphous FM CoFeSiB because of its lower saturation magnetization (560 emu/cm3) than that of Co or CoFeB, which may be beneficial for lowering the current density for switching. All samples were deposited by dc magnetron sputtering and annealed at 300 °C for 1 h. The Ta(3)/Pt(5)/CoFeSiB(1.5)/Ta(5) (nm) film exhibited PMA in the as-deposited state as well as after heat treatment. This structure possessed an iDMI energy density of 0.386 mJ/m2.