Remanent State Research Articles

Magnetic configurations in a Co/Cu/NiFe multilayered rhombic ring

We have studied the magnetization reversal of Co/Cu/NiFe giant-magnetoresistance (GMR) rhombic-ring structures by using electrical measurements and analytical calculations. GMR rhombic rings include magnetic domain walls (DWs) at the remanent state owing to their shape anisotropy. Therefore, the magnetization reversal evolves via DW motion caused by an external magnetic field. The rhombic ring has multiple intermediate states, such as vortex, hard-axis onion, and horseshoe states, making it difficult to recognize its specific magnetic configuration in the GMR measurements. Simple GMR calculations were employed to understand the magnetization reversal based on several prospective magnetic states, and the results were consistent with the experimental data.

Switchable field-tuned control of magnetic domain wall pinning along Co microwires by 3D e-beam lithographed structures

Three-dimensional magnetic circuits composed of Co microwires crossed by elevated Co bridges have been patterned on Si substrate by e-beam lithography and lift-off process. The lithographic procedure includes a double resist procedure that optimizes the shape of the bridge, so that 200nm air gaps can be routinely achieved in between the wire and bridge elements. Microwire magnetization reversal processes have been analyzed by magneto-optical Kerr effect microscopy with different remanent bridge configurations. When the Co bridge is magnetized along the in-plane direction parallel to the wire axis, its stray field induces a marked pinning effect on domain wall propagation along the wire below it, even without being in contact. Changing the sign of the remanent state of the bridge, domain wall pinning can be selected to occur in either the ascending or descending branches of the wire hysteresis loop. Thus, these wire-bridge 3D circuits provide a simple system for tunable domain wall pinning controllable through the pre-recorded bridge remanent state.

Electric field-controlled magnetization in bilayered magnetic films for magnetoelectric memory

Bilayered magnetic films (Co50Fe50 (CoFe)/Metglas) were RF sputtered on both (001)-oriented and (011)-oriented PMN-PT (lead magnesium niobate-lead titanate) substrates. Electric field-controlled magnetization changes were observed in all these samples: 65 nm CoFe/24 nm Metglas/(001) PMN-PT, 65 nm CoFe/24 nm Metglas/(011) PMN-PT, and 30 nm CoFe/12 nm Metglas/(011) PMN-PT. The maximum magnetic remanence ratio change (ΔMr/Ms) was 46% for CoFe/Metglas/(001) PMN-PT. In this heterostructure, the electric-field created two new non-volatile switchable remanence states and the as-grown remanence state was altered permanently. High-resolution transmission electron microscopy images show a sharp and smooth interface between Metglas and substrate and conversely a rougher interface was observed between Metglas and CoFe films. In the 30 nm CoFe/12 nm Metglas/(011) PMN-PT sample, a large ΔMr/Ms of 80% along the [100] direction was measured, while the ΔMr/Ms along the [01-1] direction was 60% at the applied electric field of 5 kV/cm, corresponding to a giant magnetoelectric coupling constant α = μoΔMr/E = 2.9 × 10−6 s/m.

Experimental observation of the interaction of propagating spin waves with Néel domain walls in a Landau domain structure

The interaction of propagating dipolar spin waves with magnetic domain walls is investigated in square-shaped microstructures patterned from the Heusler compound Co2Mn0.6Fe0.4Si. Using magnetic force microscopy, the reversible preparation of a Landau state with four magnetic domains separated by Néel domain walls is confirmed. A local spin-wave excitation using a microstructured antenna is realized in one of the domains. It is shown by Brillouin light scattering microscopy that the domain structure in the remanence state has a strong influence on the spin-wave excitation and propagation. The domain walls strongly reflect the spin waves and can be used as spin-wave reflectors. A comparison with micromagnetic simulations shows that the strong reflection is due to the long-range dipolar interaction which has important implications for the use of these spin waves for exerting an all-magnonic spin-transfer torque.

Cyclic electric field response of morphotropic Bi1/2Na1/2TiO3-BaTiO3 piezoceramics

In this study, the evolution of field induced mechanisms in lead-free piezoelectric ceramics (1−x)Bi1/2Na1/2TiO3-xBaTiO3 with x = 0.06 and 0.07 was investigated by transmission electron microscopy, neutron, and X-ray diffraction. Preliminary investigations revealed a strong degradation of macroscopic electromechanical properties within the first 100 bipolar electric cycles. Therefore, this structural investigation focuses on a comparative diffraction study of freshly prepared, poled, and fatigued specimens. Transmission electron microscopy and neutron diffraction of the initial specimens reveal the coexistence of a rhombohedral and a tetragonal phase with space group R3c and P4bm, respectively. In situ electric field X-ray diffraction reveals a pronounced field induced phase transition from a pseudocubic state to a phase composition of significantly distorted phases upon poling with an external electric field of 4 kV/mm. Although the structures of the two compositions are pseudocubic and almost indistinguishable in the unpoled virgin state, the electric field response shows significant differences depending on composition. For both compositions, the application of an electric field results in a field induced phase transition in the direction of the minority phase. Electric cycling has an opposite effect on the phase composition and results in a decreased phase fraction of the minority phase in the fatigued remanent state at 0 kV/mm.

Tailoring ergodicity through selective A-site doping in the Bi1/2Na1/2TiO3–Bi1/2K1/2TiO3 system

The morphotropic phase boundary composition Bi1/2Na1/2TiO3-20 mol. % Bi1/2K1/2TiO3 was chosen as initial material to do selective A-site aliovalent doping replacing Na and K by 1 at. % La, respectively. The materials were studied macroscopically by measuring dielectric and electromechanical properties. The Na-replaced material has a lower freezing temperature Tfr, lower remanent polarization and remanent strain, and thus a higher degree of ergodicity than the K-replaced material. These results are contrasted with local poling experiments and hysteresis loops obtained from piezoresponse force microscopy. The faster relaxation of the tip-induced local polarization and the lower remanent state in bias-on and -off loops confirm the higher degree of ergodicity of the Na-replaced material. The difference in functional properties is attributed to small variations in chemical pressure achieved through selective doping. Raman results support this working hypothesis.

Exchange coupling in ferromagnetic/antiferromagnetic/ferromagnetic [Pd/Co]n/NiO/Co trilayers with different [Pd/Co] anisotropy

Exchange coupling in NiO/Co bilayers and [Pd/Co(tCo)]n/NiO/Co trilayers prepared by magnetron sputtering has been investigated. With decreasing thickness (tCo) of the Co layers in [Pd/Co] multilayers (MLs) and increasing number of [Pd/Co] repeats (n), the ferromagnetic easy axis of the [Pd/Co] MLs switches from in-plane to out-of-plane direction. Ferromagnetic and non-collinear interlayer couplings between the [Pd/Co] MLs and the Co layer across the antiferromagnetic NiO spacer are found in trilayers. After cooling at in-plane and out-of-plane remanent state, respectively, for tCo=1nm and n=2, a larger in-plane exchange bias field of 724Oe is observed which vanishes at temperatures above 90K which is the same as the in-plane blocking temperature observed in the NiO/Co bilayer. For tCo=0.3nm and n=7, the in-plane blocking temperature in the trilayer enhances up to 210K, which strongly depends on orientation and strength of the ferromagnetic [Pd/Co] ML anisotropy axis.

Magnetoresistive system with concentric ferromagnetic asymmetric nanorings

A structure consisting of two concentric asymmetric nanorings, each displaying vortex remanent states, is studied with micromagnetic calculations. By orienting in suitable directions, both the asymmetry of the rings and a uniform magnetic field, the vortices chiralities can be switched from parallel to antiparallel, obtaining in this way the analogue of the ferromagnetic and antiferromagnetic configurations found in bar magnets pairs. Conditions on the thickness of single rings to obtain vortex states, as well as formulas for their remanent magnetization are given. The concentric ring structure enables the creation of magnetoresistive systems comprising the qualities of magnetic nanorings, such as low stray fields and high stability. A possible application is as contacts in spin injection in semiconductors, and estimations obtained here of magnetoresistance change for a cylindrical spin injection based device show significant variations comparable to linear geometries.

In-plane hysteresis of permalloy nanorings: a study of micromagnetic simulation

Magnetic hysteresis of isotropic permalloy nanorings with outer diameter 200 nm and thickness 20 nm has been studied. The inner diameter is varied from 0 to 190 nm to accommodate wide range of samples from nanodisk to thin nanorings. Micromagnetic simulation of in-plane hysteresis curve of these nanorings reveals that the magnetic properties change gradually with the change of inner diameter. The hysteresis loss indicated by the area of the hysteresis loop, increases gradually with the increase in inner radius up to d in = 174 nm. For inner diameter of 176 nm, the loop area decreases drastically and remains so for up to d in = 180 nm. After that, a small increment of d in results in a large increment of loop area. The remanent states are found to be vortex states for d in = 0–180 nm and onion states for d in > 180 nm. The changes are attributed to two parameters mainly: exchange energy and demagnetization energy. These two parameters depend on inner curvature of the ring, which is treated as a variable in this simulation work. The changes in loop area have been discussed in light of variation of these parameters.

Dynamic control of metastable remanent states in mesoscale magnetic elements

The formation of the vortex-antivortex-vortex (v-av-v) metastable remanent states in elongated magnetic elements have been systematically investigated using micromagnetic modeling. It is demonstrated that the v-av-v magnetization pattern can be effectively stabilized by exciting the single vortex state with an external RF field. Furthermore, we show that a set of different polarity combinations of the vortex cores can be achieved by adjusting the frequency and amplitude of the excitation field. The corresponding dynamic response in time- and frequency-domain has also been presented. Owing to the diversity of the collective modes with different vortex-antivortex combinations, this system may open promising perspectives in the area of spin transfer torque oscillators.

Effect of domain structure on the impedance of ferromagnetic wire with circumferential anisotropy

Circumferential domain structure contribution to the impedance of amorphous Co68.2Fe4.3Si12.5B15 ferromagnetic wire in a zero external field was measured in two cases. With as-cast wire, changes in the impedance caused by removal of the domain structure in remanent state were measured. Uniform helical anisotropy was induced in the wire by thermal treatment. An inhomogeneous magnetic field applied in a low axial field region caused the formation of a domain structure consisting of two circular domains separated by a single domain wall in this wire. Changes in the impedance caused by removal of this domain structure were measured. In both cases characteristic frequency dependence with a single maximum in the range 1–2MHz was observed. It is probable that this typical shape originates predominantly from frequency dependence of domain wall oscillations. In the high frequency region, changes in volume magnetization distribution and thus also in transverse permeability can play a significant role. Interpretation based on a stray field generated by axial magnetization inhomogeneities is proposed.

Micromagnetic Studies of Ultrahigh Resolution Magnetic Force Microscope Tip Coated by Soft Magnetic Materials

Magnetic force microscope (MFM) tips coated by soft magnetic materials can achieve a spatial resolution above 10 nm. It is interesting to analyze why tips coated with soft magnetic materials can achieve such a high resolution. In experiment, an MFM tip coated by amorphous FeB can achieve a resolution of 8 nm; therefore, we chose an FeB tip as an example and establish a micromagnetic model to understand the measurement mechanism of the soft magnetic MFM tip. In the FeB film simulation, the random crystalline anisotropy results in a soft magnetic loop with an in-plane coercivity of 0.2 Oe, and the film surface roughness will raise the coercivity to the order of 1 Oe. In the tip simulation, it is found that the FeB-coated tip can be switched in a uniform field of the order of 100 Oe, but can remain near a remanent state in a stray field resulting from media. A simple model is set up to analyze the MFM images of bits in hard disk drivers using the simulated magnetic properties of the tip and resolution ~10 nm is confirmed.

Different remanence states and their resistance to external effects. Discussing the “method of magnetic memory”

The remanence of a ferromagnet is formed under the influence of many factors, the main of which are a magnetic field (DC and AC), temperature, mechanical stress, and chemical transformations. Remanences obtained by different ways are differently resistant to external influences. Remanence observed in structural elements may result from one factor or from all of the above. It is shown that the use of remanence as a parameter for assessing the stress-strain state, i. e. the “method of magnetic memory”, without taking into account the conditions of the formation of the remanence state in a product area under testing will have low assessment reliability.

Observing thermomagnetic stability of nonideal magnetite particles: Good paleomagnetic recorders?

AbstractThe thermomagnetic behavior of remanence‐induced magnetite (Fe3O4) particles in the pseudo‐single‐domain (PSD) size range (~0.1–10 µm), which dominate the magnetic signature of many rock lithologies, is investigated using off‐axis electron holography. Construction of magnetic induction maps allowed for the visualization of the vortex domain state in an individual Fe3O4 grain (~200 nm in diameter) as a function of temperature. Acquisition of a series of electron holograms at 100°C intervals during in situ heating up to 700°C demonstrates the vortex state of the Fe3O4 grain, in this instance, remains thermally stable close to its unblocking temperature and exhibits a similar in‐plane remanent state upon cooling; i.e., the particle is effectively behaving like a uniaxial single‐domain particle to temperatures near TC. Such particles are thought to be robust magnetic recorders. It is suggested that evidence for PSD behavior should therefore not preclude paleomagnetic investigation.

Single-vortex magnetization distribution and its reversal behaviour in Co–Pt nanotubes

Using template-assisted electrodeposition in partially Au-covered polycarbonate templates, we have successfully deposited equiatomic Co–Pt nanotubes with an external radius R of 100nm, lengths L of 800–2000nm and tube-wall thicknesses of 70nm. By applying different characterization methods – vibrating-sample magnetometry and combined atomic and magnetic force microscopy – we have shown that in as-deposited face-centred cubic Co–Pt nanotubes the magnetization in the remanent state can be described with a vortex-type of closure. Such curling of the magnetization distribution has its origin in the minimization of the demagnetizing field that arises from the surface or volume charges. The demagnetization of single-vortex-type nanotubes proceeds gradually and exhibits only a modest hysteresis. Such nanotubes with a single vortex-type of magnetization distribution possess the unique property of emitting no stray fields in the remanent state, despite their elongated shape, and therefore represent perfect candidates for magnetoresistive random-access-memory devices and for biomedical applications such as targeted drug delivery.

Uniaxial Stress Dependence of the Permittivity and the Hardening Effect in the Na0.5Bi0.5TiO3–K0.5Bi0.5TiO3 System

The dependence of the permittivity on the uniaxial compressive stress was investigated for the case of Na0.5Bi0.5TiO3–K0.5Bi0.5TiO3 ceramics. For the morphotropic sample the results showed a strong increase in the stress dependence compared to pure Na0.5Bi0.5TiO3. Nevertheless, a threshold stress was observed, below which the domain switching was hindered. The threshold stress value and, thus, the “hardness” of the materials increased with increasing K0.5Bi0.5TiO3 content. In the “hard” tetragonal samples the permittivity increased with the stress loading; however, if the mechanical load exceeded a threshold level, the “hardening” effect vanished. The results are discussed in terms of the defect dipole model for the stabilization of the domain configuration. The stabilization was the highest in pure K0.5Bi0.5TiO3, for which a poled remanent state was preserved at stresses higher than 200 MPa.

Measure-valued solutions for models of ferroelectric materials

In this work we study the solvability of the initial boundary-value problems that model the quasi-static nonlinear behaviour of ferroelectric materials. Similar to the metal plasticity, the energy functional of a ferroelectric material can be additively decomposed into reversible and remanent parts. The remanent part associated with the remanent state of the material is assumed to be a convex non-quadratic function f of internal variables. In this work we introduce the notion of the measure-valued solutions for the ferroelectric models, and show their existence in the rate-dependent case, assuming the coercivity of the function f. Regularizing the energy functional by a quadratic positive-definite term, which can be viewed as hardening, we show the existence of measure-valued solutions for the rate-independent and rate-dependent problems, avoiding the coercivity assumption on f.

High-resolution imaging of remanent state and magnetization reversal of superdomain structures in high-density cobalt antidot arrays

Remanent state and magnetization reversal processes of a series of cobalt antidot arrays with a fixed hole diameter (d ≈ 55 nm) and an array periodicity (p) ranging between 95 and 524 nm were studied by in situ Lorentz microscopy (LM) as a function of the magnetic field. At remanence, defocused LM images showed the periodicity dependence of the magnetic states inside the lattice. A remarkable transition was observed in the type of domain structures as a function of p: for the large periodicities (p > 300 nm), conventional 90° and 180° domain walls were formed, whereas in small-period antidot arrays (p ≦ 160 nm) magnetic superdomain walls (SDWs) were nucleated to separate regions with different average magnetization direction, the so-called magnetic superdomains. In the SDW regime, a low-frequency Fourier filtering method was implemented to allow a quantitative analysis of the LM images by the transport of intensity equation method. In situ LM experiments under applied magnetic fields were performed to study the reversal magnetization process in a particular array (p = 160 nm), and clear differences were observed as a function of the magnetic field orientation. The switching process under magnetic fields parallel to the horizontal antidot rows occurs in two stages: the system first nucleates and propagates horizontal SDWs, parallel to the field. Then, at higher magnetic fields, vertical SDWs, perpendicular to the field, appear before saturation. When the magnetic field is applied at 45° with respect to the antidot rows, both horizontal and vertical SDWs are nucleated and propagated simultaneously. All the experiments were successfully correlated with micromagnetic simulations. The current study sheds new light on the magnetization reversal processes of antidot arrays and opens new possibilities of exploiting the potential of high-resolution in situ LM and new data analysis procedures to probe magnetization processes in nanomagnetism, particularly in periodic arrays of nanomagnets.

Degradation of the remanent ferromagnetic state under the action of ferroelectric relaxation processes in Co/(1−x)PMN-xPT/Co hybrids: Possible implications on cryogenic and room-temperature applications

Low-dimensional hybrid structures of heterogeneous constituents usually exhibit abnormal properties, a fact that makes such hybrids attractive for various cryogenic and room-temperature applications. Here, we studied Co/(1 − x)Pb(Mg1/3Nb2/3)O3-xPbTiO3/Co (Co/PMN-xPT/Co) with x = 0.29 and 0.30, specifically focusing on the evolution of the remanent ferromagnetic state, mrem of the Co outer layers in the whole temperature range from 300 K down to 10 K, upon application of an external electric field, Eex. We observed that mrem was vulnerable to degradation through the occurrence of electric field-induced magnetic instabilities (EMIs) that appeared only when Eex ≠ 0 kV/cm and were facilitated as Eex increases. However, EMIs completely ceased below a characteristic temperature Tces = 170 K even for the maximum |Eex| = 5 kV/cm applied in this work. A direct comparison of the magnetization data of the Co/PMN-xPT/Co hybrids reported here with the electromechanical properties of the parent PMN-xPT crystals plausibly indicates that EMIs are motivated by the coupling of the ferromagnetic domains of the Co outer layers with the ferroelectric domains of the PMN-xPT crystal. These results highlight the drawback of EMIs in relevant hybrids and delimit the temperature regime for the reliable operation of the Co/PMN-xPT/Co ones studied here.

Electric field modulation of ultra-high resonance frequency in obliquely deposited [Pb(Mg1/3Nb2/3)O3]0.68-[PbTiO3]0.32(011)/FeCoZr heterostructure for reconfigurable magnetoelectric microwave devices

The multiferroic heterostructure of FeCoZr/[Pb(Mg1/3Nb2/3)O3]0.68-[PbTiO3]0.32(011) (PMN-PT) prepared by oblique sputtering deposition technique shows a large electrical tunability of ultra-high ferromagnetic resonance frequency from 7.4 GHz to 12.3 GHz. Moreover, we experimentally demonstrate the possibility of realizing electrically reconfigurable magnetoelectric microwave devices with ultra-low power consumption by employing the heterostructure under different resetting electric fields through a reconfiguration process. In particular, the tunability of the FeCoZr/PMN-PT heterostructure from 8.2 GHz to 11.6 GHz can retain in a remanent state after releasing the resetting electric field. This suggests that the tunable microwave devices based on such heterostructures are permanently reconfigurable by simply using a trigger electric field double-pulse which requires much less energy than that of the conventional ones wherein an electric field needs to be constantly applied during operation.