Multidomain State Research Articles

The grain size effect on the magnetic properties in NiZn ferrite and the quality factor of the inductor

Polycrystalline ferrite materials with the chemical composition of Ni 0.49Zn 0.49Co 0.02Fe 1.90O x have been fabricated using the conventional ceramic sintering method. Grain sizes have been adjusted from ∼2.2 to ∼13.5 μm with changing sintering conditions. From the measurements of the complex permeability, it is suggested that the permeability is dominated only by the spin rotation at mono-domain state and both domain wall and spin rotation contribute at multi-domain state. At mono-domain state, the core loss has been drastically decreased similar to the other work. The measurement result for the loss angle indicates that the low loss state can be maintained up to the higher magnetic field with smaller grain size in spite of the mono-domain state. The simplified wire-wounded type inductors have been also fabricated and characterized. The results have shown that the inductor fabricated with the smaller grain size has a better performance in the quality value under relatively higher current.

Magnetic coupling of ferromagnetic stripe arrays: Analytical model for theα−β-phase coexistence regime of MnAs/GaAs(001)

We investigate the temperature-dependent hysteresis of the stripe state of MnAs thin films on GaAs(001) in the phase coexistence regime. The underlying magnetic domain structure is described employing an analytic model for stripe arrays with perpendicular anisotropy. In the framework of this model the magnetic properties of the MnAs stripe array can be unraveled as a combined effect of magnetostatic coupling of neighboring ferromagnetic stripes and the tendency to form antiparallel magnetic domains within the individual ferromagnetic stripes. The detailed analysis reveals the balance of demagnetization energy and domain-wall energy for the domain structure. It is capable to quantitatively predict the temperature dependency of the coercive field of MnAs thin films on GaAs(001) in the phase coexistence regime. Further, the analytic model allows for an understanding of the unusual magnetic reversal properties as a consequence of the temperature-driven geometrical variations in the stripe array. Here, it is the energy difference of the single and the multidomain states associated with the geometrical variations, which is the driving factor, rather than the temperature dependence of the magnetic properties themselves. Although the stripe array of MnAs thin films can be in an interstripe as well as in an intrastripe coupling state, the magnetization reversal is entirely determined by interstripe coupling.

Nano-meter-sized domain formation in lipid membranes observed by small angle neutron scattering

Using a contrast matching technique of small angle neutron scattering (SANS), we have investigated a phase separation to liquid-disordered and liquid-ordered phases on ternary small unilamellar vesicles (SUVs) composed of deuterated-saturated, hydrogenated-unsaturated phosphatidylcholine lipids and cholesterol, where the equilibrium size of these domains is constrained to less than 10nm by the system size. Below a miscibility temperature, we observed characteristic scattering profiles with a maximum, indicating the formation of nano-meter-sized domains on the SUVs. The observed profiles can be described by a multi-domain model rather than a mono-domain model. The nano-meter-sized domain is agitated by thermal fluctuations and eventually ruptured, which may result in the multi-domain state. The kinetically trapped nano-meter-sized domains grow to a mono-domain state by decreasing temperature. Furthermore, between the miscibility and disorder-order transition temperature of saturated lipid, the integrated SANS intensity increased slightly, indicating the formation of nano-meter-sized heterogeneity prior to the domain nucleation.

Controlling multidomain states to enable sub-10-nm magnetic force microscopy

The letter reports experimental data to demonstrate magnetic force microscopy (MFM) with sub-10-nm resolution under ambient conditions. To achieve this record high resolution, multidomain states in a nanomagnetic probe were controlled. Two demagnetized (multidomain) FePt (45/55) films sputtered on a silicon probe and separated by an 8 nm thick MgO layer were further annealed at temperature of 650 °C to trigger the high-anisotropy L10 phase. A field of above 2 T was applied to drive the probes into a saturated “single-domain” state. The multidomain probes were equivalently compared with state-of-the-art conventional MFM probes via comparative imaging of benchmark magnetic recording disks.

Three-dimensional micromagnetic simulations of multidomain bubble-state excitation spectrum in ferromagnetic cylindrical nanodots

The excitation spectrum of multidomain bubble states in cylindrical nanodots with a large perpendicular anisotropy has been investigated by means of three-dimensional micromagnetic simulations for various dot diameters. In a first step, the evolution of the zero-field susceptibility spectra as a function of the dot diameter is studied for bidomain bubble states. Increasing dot diameter leads to shifts of the resonance frequencies toward the low frequencies for the fundamental domain wall and domain modes, whereas the spectral positions of surface domain wall and domain modes are weakly affected. Second, the high-frequency response of a tridomain bubble state stabilized in larger dot diameters is analyzed. Dynamic interaction effects are revealed mainly through the identification of coupled domain-wall modes, the resonance frequencies of which depend on the relative domain-wall chiralities. Lastly, the magnetization dynamics of a metastable bidomain bubble state with a pair of vertical Bloch lines, each of them possessing a Bloch point, is addressed. In such a case, the presence of magnetic singularities leads to a splitting of the fundamental domain-wall mode into two resonance lines assigned to oscillations of domain-wall parts with different phase relations.

Strange Thermal Expansion of Ferroelectric TGS in the Cryogenic Temperature Region

Recently a strange temperature dependence of the volume thermal expansion coefficient of TGS crystal has been found in the cryogenic temperature region. Therefore an electric field effect on the simultaneous measurement of the permittivity and the thermal expansion was examined under consideration of difference of a ferroelectric domain structure. The strange feature of the volume thermal expansion coefficient below 10 K was recognized again in the measurement without poling and this feature disappeared in the measurement with poling. This strange thermal expansion without poling might occur because of freezing the interaction between each area in the multi-domain state.

Topological defects in antiferromagnetically coupled multilayers with perpendicular anisotropy

A rich variety of specific multidomain textures recently observed in antiferromagnetically coupled multilayers with perpendicular anisotropy include regular (equilibrium) multidomain states as well as different types of topological magnetic defects. Within a phenomenological theory we have classified and analyzed the possible magnetic defects in the antiferromagnetic ground state and determine their structures. The calculated magnetic phase diagrams show the existent regions for all types of magnetic defects. Experimental investigations of the remanent states (observed after different magnetic prehistory) in [Co/Pt]/Ru multilayers with wedged Co layers reveal a corresponding succession of different magnetic defect domain types.

Magnetic properties of Co/Pt multilayers on self-assembled particle arrays

A series of [Co(x)/Pt(0.8 nm)]8 multilayers with varying individual Co layer thickness was deposited onto self-assembled particle monolayers with particle sizes as small as 58 nm forming arrays of magnetic nanostructures. A maximal out-of-plane coercivity was observed for a Co layer thickness of 0.3 nm for all particle sizes, which decreases with further increasing Co layer thickness indicating a transition of the easy axis orientation from perpendicular to the film plane at about 0.8 nm Co layer thickness. While a single-domain state is the most favorable state after perpendicular demagnetization for a Co layer thickness of up to 0.4 nm for all particle sizes, greater Co layer thicknesses reveal a multidomain state. In addition, the angle dependent magnetization reversal behavior and the domain configurations of these magnetic nanostructures were investigated systematically. At the crossover thickness of 0.4 nm Co layer thickness, a two-domain configuration can be induced for 320 nm particles by applying a magnetic field under a critical angle of 75°.

Phenomenological theory of magnetization reversal in nanosystems with competing anisotropies

The interplay between intrinsic and surface/interface-induced magnetic anisotropies strongly influences magnetization processes in nanomagnetic systems. We develop a micromagnetic theory to describe the field-driven reorientation in nanomagnets with cubic and uniaxial anisotropies. Spin configurations in competing phases and parameters of accompanying multidomain states are calculated as functions of the applied field and the magnetic anisotropies. The constructed magnetic phase diagrams allow to classify different types of the magnetization reversal and to provide detailed analysis of the switching processes in magnetic nanostructures. The calculated magnetization profiles of isolated domain walls show that the equilibrium parameters of such walls are extremely sensitive to applied magnetic field and values of the competing anisotropies and can vary in a broad range. For nanolayers with perpendicular anisotropy the geometrical parameters of stripe domains have been calculated as functions of a bias field. The results are applied to analyze the magnetization processes as observed in various nanosystems with competing anisotropies, mainly, in diluted magnetic semiconductor films (Ga,Mn)As.

Magnetic structure and magnetoresistance of patterned epitaxial iron thin films: The influence of shape and magnetocrystalline anisotropy

A magnetic-force-microscopy investigation is conducted into the influence of the shape and magnetic anisotropy on the magnetic structure and the mode of magnetization reorientation in epitaxial iron thin films patterned by subtractive techniques. Magnetic anisotropy is found to have a strong influence on the magnetic structure. With an applied field directed along a specimen, the latter is in a single-domain state when oriented parallel to the easy axis of magnetization, and is in a multidomain state when oriented perpendicular to the easy axis, the domain magnetic moments being parallel to the easy axis in both cases. The magnetic structure appears as a streaky pattern. Magnetization reorientation proceeds by domain-wall motion in both cases. The tanks do not change the mechanism of magnetization reorientation in the rectangular part, yet they ensure a single-domain state at lower magnetic flux densities. The results should offer some scope for using epitaxial iron thin films of suitable shape and crystallographic orientation in spin-valve injectors or detectors.

Stripe domains and spin reorientation transition in Fe78B13Si9 thin films produced by rf sputtering

Magnetic thin films have been obtained by rf sputtering from an amorphous Fe78B13Si9 target. The samples have been produced with thickness t ranging in the interval 25–1000 nm. Microstructural investigations indicate that the films have different microstructures varying from fully amorphous to partially nanocrystalline with increasing t. Magnetic hysteresis loops have been measured by means of high-sensitive magnetometry. A tailorable spin reorientation transition (SRT) from in-plane single-domain-like to out-of-plane multidomain state with increasing film thickness was observed. Magnetic force microscopy images have been obtained for all samples indicating that for t≤80 nm the magnetization lies in the film plane. For larger thickness, a stripe domain pattern has been observed, indicating the presence of a magnetic anisotropy axis perpendicular to the film plane. In this work, SRT and stripe domain structure have been studied as a function of thickness and sample microstructure.

Linear field amplification for magnetoresistive sensors

In this article, we describe the fabrication and characterization of a spin valve (SV) magnetoresistive (MR) sensor, located in the gap of two magnetically soft flux guides (FGs) that enhance the sensor magnetic field sensitivity, while keeping in the sensor a quasilinear Barkhausen-noise-free response. Top pinned SV sensors were fabricated into stripes, having lengths of 100μm and widths of 2 and 3μm, by optical lithography and ion-milling etching. The FGs consisted of poles and yokes of an amorphous alloy of Co88.4Zr3.3Nb8.3, prepared by physical vapor deposition and were lithographically defined by a lift-off process. The SV sensor MR responses to applied uniform magnetic fields Ha, when either isolated or located in the gap of two types of FGs, were characterized in terms of the saturation field, coercive force, and sensitivity. The impact of the FG geometry in the magnetic field amplification and sensor response characteristics were studied. Magnetic force microscopy analysis was performed to identify the presence of multidomain states in the FGs and of a remanent field in their gap. SV sensors in the gap of FGs using long poles and having a sensing area of 1000μm2 exhibit a linear sensitivity of 50mV∕Oe in the field range of a couple of oersteds. The SV sensor in the gap of magnetically soft FGs exhibits enhanced hysteresis, characterized by a coercive force of approximately 1Oe. Two schemes are proposed to reduce the hysteresis in the sensor response.

Electron Holography for the Study of Magnetic Nanomaterials

Transmission electron microscopes fitted with field-emission guns (to provide coherent electron waves) can be adapted to record the magnetic fields within and surrounding nanoparticles or metal clusters, for example, the lines of force of a nanoferromagnet encapsulated within a multiwalled carbon nanotube. Whereas most chemists are aware that electron microscopy readily identifies crystallographic symmetries and phases, solves structures, and, in conjunction with electron energy-loss spectroscopy, yields valence states and electronic information of materials, relatively few know that it can also provide important quantitative information, with nanometer-scale spatial resolution, pertaining to such materials' magnetic properties. In this Account, with the aid of representative examples embracing solid-state chemistry, geochemistry, and bio-inorganic phenomena, we illustrate how off-axis electron holography affords deep insight into magnetic phenomena on the nanoscale. Specifically, we describe the unprecedented level of information available regarding the magnetic nature of magnetotactic bacteria, magnetic nanoparticle chains and chiral bracelets, and geochemically relevant phenomena involving exsolution (the un-mixing of two mineral phases, as in the magnetite-ulvöspinel system). It is, for example, possible to reveal vortices and multidomain states that have no net magnetization in minute blocks of magnetite. With the current burgeoning interest and activity in nanoscience and nanotechnology, our Account concludes with examples of some existing enigmas that electron holography, especially when augmented by the related technique of electron tomography, might play an important experimental role in resolving, such as the occurrence of ferromagnetism in nanocrystals of silver within carbon tubes and in clusters of alkali metals incarcerated within zeolites.

Theoretical analysis of magnetic force microscopy contrast in multidomain states of magnetic superlattices with perpendicular anisotropy

Recently synthesized magnetic multilayers with strong perpendicular anisotropy exhibit unique magnetic properties including the formation of specific multidomain states. In particular, antiferromagnetically coupled multilayers own rich phase diagrams that include various multidomain ground states. Analytical equations have been derived for the stray field components of these multidomain states in perpendicular multilayer systems. In particular, closed expressions for stray fields in the case of ferromagnetic and antiferromagnetic stripes are presented. The theoretical approach provides a basis for the analysis of magnetic force microscopy (MFM) images from this class of nanomagnetic systems. Peculiarities of the MFM contrast have been calculated for realistic tip models. These characteristic features in the MFM signals can be employed for the investigations of the different multidomain modes. The obtained results are applied for the analysis of multidomain modes that have been reported earlier in the literature from experiments on [Co/Cr]Ru superlattices.

Domains in Ultrathin Ferroelectric Films with Metallic and Semiconducting Electrodes

We discuss ferroelectric phase transitions into single- and multidomain states in very thin films using continuous theory. In a typical case of BaTiO3 film with SrRuO3 electrodes the homogeneous states remains ferroelectric down to 2.5 nm, same thickness as in ab-initio modeling, whereas the actual critical thickness is determined by the existence of the domains that may exist in films just 0.8 nm thick. Nonlinear screening by carriers in semiconducting electrodes could have made the phase transition first order, but this Batra transition in monodomain state does not happen since it is preempted by domain formation. The results do not depend on whether or not the screening carriers may be present in the ferroelectric itself.

Features of magnetic reversal of highly anisotropic uniaxial ferromagnets

Specificity of magnetization and magnetization reversal processes of highly anisotropic uniaxial ferromagnets, caused by the possibility of microvolumes of a material to exist in multidomain and single-domain states, is discussed. The influence of the demagnetization method on the behavior of the magnetization curves, thermal magnetization, and ambiguity of the shape of Henkel plots is shown by the example of the SmCo5 and Nd2Fe14B compounds.

Spin-polarized current versus stray field in a perpendicularly magnetized superconducting spin switch

In superconducting Co∕Pt–Nb–Co∕Pt multilayers with perpendicular magnetic anisotropy, the superconducting transition temperature Tc is considerably higher in the parallel (P) orientation of the two Co∕Pt magnetizations compared to the antiparallel (AP) orientation. Low temperature magnetic-force microscopy reveals that the individual ferromagnetic layers are uniformly magnetized in both configurations and do not exhibit a magnetic stray field arising from a multidomain state. We also demonstrate that the difference ΔTc=TcP−TcAP between both Tc values is enhanced at higher transport currents due to the increasing imbalance of spin-polarized charge carriers in the superconducting Nb layer. Hence, the spin switch can be controlled by the transport current in future superconducting devices.

The breakdown of the fingerprinting of vortices by hysteresis loops in circular multilayer ring arrays

Microscale single-layer ferromagnetic rings typically exhibit a magnetic vortex state at remanence, characterized by a flux-closed magnetic state with zero stray fields. Magnetic reversal in such systems yields a vanishing remanent magnetization. In contrast, the authors show that in individual layers in thin rings, which alternate magnetic and nonmagnetic materials (NiFe∕Cu∕Co), layer-resolved hysteresis loops, measured using x-ray resonant magnetic scattering, exhibit the characteristics of a vortex formation, although photoelectron emission microscopy and micromagnetic simulations clearly prove that multidomain states are formed. This result is of considerable importance for the development of pseudo-spin-valve-type structures for applications.

Prediction of ferroelectricity in BaTiO3∕SrTiO3 superlattices with domains

The phase transitions of superlattices into single- and multidomain states were studied using a mesoscale phase-field model incorporating structural inhomogeneity, micromechanics, and electrostatics. While the predictions of transition temperatures of BaTiO3∕SrTiO3 superlattices into multidomains show remarkably good, quantitative agreement with ultraviolet Raman spectroscopic and variable-temperature x-ray diffraction measurements, the single-domain assumption breaks down for superlattices in which the nonferroelectric layer thickness exceeds the characteristic domain size in the ferroelectric layers.

Magnetic confinement of the superconducting condensate in superconductor-ferromagnet hybrid composites

The influence of an inhomogeneous magnetic field on the magnetoresistance of thin Al films, used in different superconductor-ferromagnet hybrids, has been investigated. Two contrasting magnetic textures with out-of-plane magnetization are explored: namely, (i) a plain film in a multidomain state and (ii) an array of microsized dots. The stray fields of the ferromagnetic structures confine the superconducting condensate and, accordingly, modify the condition for the nucleation of superconductivity. By switching between different magnetic states of the ferromagnet, this confinement can be tuned at will, thereby reversibly changing the dependence of the critical temperature ${T}_{c}$ on an external magnetic field $H$. In particular, continuous evolution from a conventional linear ${T}_{c}(H)$ dependence with a single maximum to a reentrant superconducting phase boundary with multiple ${T}_{c}$ peaks has been demonstrated.