Ferromagnetic Domains BY D.J.CRAIK Lecturer in Chemistry, University of Nottingham AND R.S.TEBBLE Reader in Physics, University of Sheffield H с 1965 NORTH-HOLLAND PUBLISHING COMPANY-AMSTERDAM . Fig 9.63. The influence of spin on electron conductivity was invoked by Nevill Mott in 1936 [122], but remained practically uninvestigated, much less exploited, until the discovery of giant magnetoresistance (GMR) in 1988. Magnetic viscosity coefficient, normalized magnetization decay, thermal stability factor, and anisotropy field distribution of Fe–Co tape films were also found to depend on the particle size [194]. Also Read: Paramagnetic Materials. Next, we discuss the E-tuning of FMR in a composite with hexagonal ferrite and a ferroelectric. [2] He suggested that large number of atomic magnetic moments (typically 1012-1018)[citation needed] were aligned parallel. Note that it is made entirely of nonmagnetic materials. The curve of M(H, T) versus H for T < TC shown in Fig. A spintronic NOT-AND (NAND) gate. What energies contribute to the domain wall structure? However, the coupling strength with the magnetic medium in known DMS compounds is not sufficient to produce such an effect in bulk crystals. The physical entities are quantum dots. In magnetic materials, domains can be circular, square, irregular, elongated, and striped, all of which have varied sizes and dimensions. We investigate the scaling of the ground state energy and optimal domain patterns in thin ferromagnetic films with strong uniaxial anisotropy and the easy axis perpendicular to the film plane. Depending on the relative size of the particle and magnetic domains, two types of magnetic NPs can be distinguished. GMR and MTJ are important enablers of size reduction of ferromagnetic memory cells and hence the miniaturization of magnetic random access memory (MRAM), the limiting factor of which is not the ability to make small ferromagnetic islands (which must nevertheless be above the superparamagnetic size boundary, see Section 2.6) but the ability to sense minute magnetic fields. However this is not applicable to ferromagnets due to the variation of magnetization from domain to domain. This reduces some of the metal ions in the layer 4 and creates a conducting metal filament b continuing the path initiated by the conducting tip. As explained above a domain which is too big is unstable, and will divide into smaller domains. This strong (large) spin alignment leads to huge permeabilities: Material Relative Permeability µ r Nickel 250 Cobalt 600 Iron (pure) 4,000 Mumetal† 100,000 compare to paramagnetic metal: Aluminium ≈1 using the high depth resolution of PNR [260]. Ferromagnetism (along with the similar effect ferrimagnetism) is the strongest type and is responsible for the common phenomenon of magnetism in magnets encountered in everyday life. Download PDF Abstract: We show that the coupling between two ferromagnetic layers separated by a nonmagnetic spacer can be used to control the depinning of domain walls and induce unidirectional domain wall propagation. Now a positive voltage is applied to layer 5. The insets show the stripline device used for the measurements and shift in FMR frequency versus E. The A value for Zn2Y/PMN-PT is comparable to measured values for single crystal nickel ferrite/PMN-PT (Li et al., 2011). S2b, the red stars). When the latter is dominant (occurring for large enough separation), the configuration is unstable. DOI: 10.1038/nmat2961 Corpus ID: 205405308. Switching between them requires merely flipping spin without physically displacing the electrons. 3.50). A Dictionary of Physics. R. J. Taylor, A Large area domain viewer, Proceedings of SMM9, 1989, https://en.wikipedia.org/w/index.php?title=Magnetic_domain&oldid=990870847, Articles with unsourced statements from September 2011, Creative Commons Attribution-ShareAlike License, This page was last edited on 27 November 2020, at 00:12. In contrast, electronic charge-based devices have the fundamental shortcoming that charge is a scalar quantity possessing only magnitude. The electrical resistivity associated with ferromagnetic metal domain walls has been a subject of intensive study for many decades (Berger 1991, Cabrera and Falicov 1974). Leon Gunther, in Magnetic Properties of Fine Particles, 1992. In the Southalpine domain the Permian intrusive complexes of the Brixen, Ifinger and Kreuzberg granodiorite cover an area ... rocks contain small percentage of ferromagnetic minerals that _____ Werner F. THÖNY, Stefan WYHLIDAL, Wolfgang THÖNY, Peter TROPPER & Robert SCHOLGER become deformed and/or reorienta- ted, and are strained as a part of the whole rock. Download Article PDF. The coercive force JHC and the saturation magnetization as can be improved with acid treatment, values of jHe = 6 400 Oe and o-s = 70.7 emu/g are obtained. It also occurs in gadolinium and a few other rare-earth elements. This obviously depends on whether the trajectories are bent away from or toward the specimen surface. To exploit the giant magnetoresistance effect, layers a and c are ferromagnetic and layer b is a nonmagnetic metal. Single spin logic (SSL) is the spin analogy of single electron (charge) logic (Section 7.4.3). This has been investigated by Hoffmann et al. Weiss still had to explain the reason for the spontaneous alignment of atomic moments within a ferromagnetic material, and he came up with the so-called Weiss mean field. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction. optic Kerr effect (both methods in the time domain), and conventional ferromagnetic resonance (measured in the field domain) in terms of position and width of the ferromagnetic resonance. The contributions of the different internal energy factors described above is expressed by the free energy equation proposed by Lev Landau and Evgeny Lifshitz in 1935,[7] which forms the basis of the modern theory of magnetic domains. But a small enough domain will be stable and will not split, and this determines the size of the domains created in a material. It can be magnetized by subjecting it to an external magnetic field. For a ferromagnetic nanosystem, its domain What is the nature of hysteresis in multi-domain ferromagnetic materials? Microwave ME effects over 8–25 GHz were studied in bilayers of single crystal Y-type hexagonal ferrite Ba2Zn2Fe12O22 (Zn2Y) and polycrystalline PZT or single crystal PMN-PT (Tatarenko & Srinivasan, 2011). Magnetic NPs could be relevant in high-density magnetic recording, magnetic bioseparation, radio frequency and magnetic components, radar-absorbing composites, permanent magnets, magneto-rheological fluids, and magnetic fluid sensor applications. The labels signify: I, InAs; A, AlSb; G, GaSb. In most materials, each grain is big enough to contain several domains. α Magnetic domain structure is responsible for the magnetic behavior of ferromagnetic materials like iron, nickel, cobalt and their alloys, and ferrimagnetic materials like ferrite. Rather it is expected that the observed coercivity is a direct consequence of the reduced FM volume and increased amount of pinning sites due to the increased AF volume. The zero-field domain-mode ferromagnetic resonances (DM-FMRs) in the weakly nonlinear regime have been investigated for garnet films with a perpendicular anisotropy supporting parallel stripe domains by means of broadband microwave measurements, and analytical and numerical approaches. We discuss in detail the theoretical basis for the two-band model with spin- mixing which has been widely applied to the analysis of the transport properties of ferromagnetic metals. The magnetization at the point r (and r′) in the figure, at which the external magnetic field vanishes, is called the remnant magnetization Mr, and the magnetic field at points c and c′ at which the magnetization vanishes is called the coercive field Hc. (d) Further stability is achieved when the spin configuration form kind of vortex with four domains. Where Export. Furthermore, stability toward gravity settling of ferrofluid is achieved if the thermal energy is larger than the attractive magnetic energy [195]: For a magnetic field of Md = 4.46 × 105 A/m, H = 104 A/m, T = 298 K, the maximum particle diameter for which NPs are stable is d = 11.2 nm [196]. Applying an external magnetic field to the material can make the domain walls move, causing the domains aligned with the field to grow, and the opposing domains to shrink. The reason a piece of magnetic material such as iron spontaneously divides into separate domains, rather than exist in a state with magnetization in the same direction throughout the material, is to minimize its internal energy. These might be exploited to create memory devices, but they have the disadvantages of poor integratability and the necessity of using additional controlling transistors. A single strip in two dimensions and pinned at two inhomogeneities is considered. Contrasting values of the magnetic properties have been reported for bulk nickel (2 μm) and nickel NPs (10 nm) [190]. The ferromagnetic domain behavior was also investigated by performing field-dependent MFM imaging of the domain state after ZFC, as shown in Figure 2. Figure 7.19. (c) Relatively broad ferromagnetic domain walls are pinned onto narrow 90 ferroelectric boundaries. F: Metal Phjs.. Vol. Then the ion–carrier interaction cannot be described any more within the scheme of mean field approximation used in previous sections. If BSEs are considered, the so-called type-2 magnetic contrast occurs due to the action of the Lorentz force of the spontaneous induction B in ferromagnetic domains on the BSE trajectories. In another study on layered samples of Al-substituted nickel zinc ferrite and PZT, E-tuning of FMR was used to determine the strength of CME (Li, Zhou, et al., 2013). α Oxford University Press, 2009. A spin electronic interpretation of this resistance is possible which draws on the analogy between a ferromagnetic domain wall and a GMR trilayer (Gregg et al. Exchange length is an ambiguous term in nanomagnetism, which may be taken as the characteristic length scale defined by the exchange energy and the magnetostatic energy, or more practically by the exchange energy and the anisotropy energy. Here, we study the dynamics of labyrinth domain networks in ferromagnetic CoFe/Ni multilayers subject to a femtosecond optical pump and find an ultrafast domain dilation by 6% within 1.6 ps. A detailed argument for possible mechanisms including the AF domain size or interfacial spin structures is out of scope for this chapter. In the limit where the carrier spins traverse the wall with spin directions unaltered, the analogy with CPP transport in a GMR trilayer is complete. because the magnetic domain walls are pinned to the crys-tallographic 101 twin domain walls. Magnetic polarons can in principle exist in a mobile form analogous to dielectric polarons, where a carrier auto-localizes to minimize the energy of its interaction with dielectric medium. The first laboratory samples of MTJ structures (NiFe-Al2O3-Co) were demonstrated in 1995. This net magnetic moment arises from a two-dimensional ferromagnetic phase synthesized at the ferroelastic (orthorhombic) domain walls (DW), which nucleate to accommodate the huge epitaxial strain induced by the substrate, and thus, scales with the DW density [2]. 9.63(a)], we obtain a pair of two identical and parallel bar magnets, which are in contact with each other along the cut. By analogy with ferromagnetic memory, ferroelectric materials are being investigated for nonvolatile storage (nanocapacitor arrays). Spin has polarization, and is bistable in a magnetic field, (parallel or anti-parallel, which can represent the two logic states zero and one). Below the critical current, we get the static domain wall solution, which shows that the spin-polarized current cannot drive a domain wall moving continuously. The same can occur with an exciton due to its interaction with magnetic ions. where M0 is the saturation magnetization and v is the volume fraction for the piezoelectric phase. The high electric field across layer 3, which has the highest resistance, results in localized electrical breakdown to create a conducting tip a with an area of 10 nm2 or less. is the mean field constant. Advanced. A peak in coercivity is often observed below 100 nm. So instead, changing the direction of the magnetization induces tiny mechanical stresses in the material, requiring more energy to create the domain. Magnetic model: (a) AF and FM domains in epitaxial FePt3 (domains are not to scale). Box 653, 84105 Beer Sheva, Israel 2Laboratoire des Solides Irradiès, CNRS UMR 7642 & CEA/DSM/DRECAM, Ecole Polytechnique, 91128 Palaiseau, France A magnetic domain is a region within a magnetic material in which the magnetization is in a uniform direction. The spin-dependent scattering of the conduction electrons in the nonmagnetic layer is minimal, causing a small resistance of the material, when the magnetic moments of the neighboring layers are aligned in parallel, whereas for the antiparallel alignment the resistance is high. Layer 1 is a silicon substrate, layers 2 and 5 are platinum electrodes, layer 3 is a dielectric oxide (e.g., SiO2, Gd2O3), 2–20 nm thick; layer 4 is a solid electrolyte (ionic conductor), with a resistance about one tenth of that of layer 3, typically a metal-doped nonstoicheometric oxide (with oxygen vacancies) (e.g., MoO3−x:Cu, 0 ≤ x ≤ 1.5). This size depends on the balance of several energies within the material. 21, 541 – Published 1 October 1949 The gate voltage Vg manipulates the spins of the two-dimensional electron gas in the layer I below it. Both these systems have been studied using relaxation of magnetization (see articles by Barbara et al and by Tejada et al in this volume. But antiferromagnetic materials have a zero net magnetic moment. Ferromagnetic domain structure of La 0.78Ca 0.22MnO 3 single crystals G. Jung,1,2 V. Markovich,1 C. J. van der Beek,2 D. Mogilyansky,3 and Ya. 6. M Each grain is a little crystal, with the crystal lattices of separate grains oriented in random directions. 3.39). Finally, the domain wall dynamics along curved strips is also evaluated. For epoxy bonded Zn2Y–PZT the measured A = 1.2 MHz cm/kV, and it is enhanced by almost an order of magnitude to A ≈ 10 MHz cm/kV for eutectic bonded Zn2Y/PMN-PT. In the context of local variation of materials properties, a different system with high structural and chemical compatibility but different magnetic phases due to compositional modulation can be mentioned [330,331]. In contrast to multilayers with structural defects and imperfections concentrated at the interfaces, a homogeneous distribution of structural pinning sites can be assumed in the AF and FM regions and interfaces. This includes the formation of permanent magnets and the attraction of ferromagnetic materials to a magnetic field. In the case of CoFe2O4, TB increases from 100 to 350 K when particle size is increased from 4 to 9.5 nm [192]. We perform a path integral over Euclidean-time for (2) to do this, which is made equivalent to Imaginary-time in our formalism via an exact Wick-rotation [11][12][13]. Their observations may reflect manifestations of quantum nucleation of magnetization, for which an extension of CG was developed by Chudnovsky and the author [14]. At a sufficiently low temperature, the carrier will align the spins of ions within its range, forming a microscopic ferromagnetic domain called bound magnetic polaron (BMP). Electrons have spin as well as charge. Parallel spins have negative exchange energy (since J > 0) and positive dipolar energy (see Problem 4.26). The strength of ME interactions A = δH/E (or δf/H) were measured from data on resonance field shift δH or frequency shift δf in an electric field E. Studies on ME interactions were performed by placing the ferrite/PMN-PT bilayer on a microstripline transducer as shown in Figure 3.7. The grounded terminal Si is the spin injector and the terminal SC at a potential V is the spin collector. {\displaystyle H_{e}=\alpha \ M_{s}}. Next, we should require that experiment and theory should agree in the thermal activation regime. (b) AF/FM layering with FM domains in the AF layer. However, the best fit was achieved attributing the magnetization to the very bottom layers of the antiferromagnet in contact with the substrate. Based on the observations made with neutron scattering and complementary techniques, a magnetic model of the thin films can be constructed (Fig.   Subsequently, Charap [18] presented an improved theory of magnetic viscosity that took into account more rigourously mathematically the effect of the distribution of particle sizes. Hysteresis in the magnetization M versus magnetic field H of a ferromagnet. The fractional change in the remanent magnetization. Crosspoint cell arrays can be made according to this principle to create an addressable memory. Polar domain structure and vortex domain structure are two possible domain structures at the nanometer scale. 2. Off-axis electron holography is a related technique used to observe magnetic structures by detecting nanoscale magnetic fields. In recent years, E-tuning of FMR has been utilized for CME in composites with FeGaB films (Liu et al., 2013, 2011; Nan et al., 2013, 2012). J. Appl. Figure 3.50. So as the domains get smaller, the net energy saved by splitting decreases. The single-domain limit defining the critical size of magnetic NPs is provided by [191]. We have em-ployed the Borns approximation and the Matsubara’s Green’s function method to study the influence of the scattering of electron with the wall domain. Data were obtained on frequency shift in FMR when a static field E was applied to PZT or PMN-PT for the estimation of ME coefficient A. The present contribution will deal with the progress that has been achieved in the meantime. Maximum coercivity coincides with the development of multiple magnetic domains with particle sizes in the range of 100 nm. The robot’s body, composed of a homogeneous continuum of a soft polymer matrix with uniformly dispersed ferromagnetic microparticles, can be miniaturized below a few hundreds of micrometers in diameter, and the hydrogel skin reduces the friction by more than 10 times. 7.2 Domain structure In ferromagnetic materials, small regions with a particular overall spin orientation are termed domains. Below a critical size of 100 nm, Hc is proportional to d6[189]. Therefore, a domain wall requires extra energy, called the domain wall energy, which is proportional to the area of the wall. Within each domain, the local magnetization is saturated at Ms(T) for temperature T, but, in general, the direction of magnetization in different domains are not parallel. Data showing tuning of ferromagnetic resonance in a bilayer of single crystal Y-type hexagonal ferrite and PMN-PT. A linear relation between blocking temperature (TB) and particle size is observed [192]. First, the perpendicular ferromagnetic resonance (FMR) in the saturated state is considered as a … This interest in the system comes from the creation of novel structures and the potential insights that this gives to the physics of disorder and frustration using conventional soft magnetic thin films. Physical Theory of Ferromagnetic Domains Charles Kittel Rev. For the sample with S = 86%, the situation is reversed, in that FM domains are embedded in an AF continuum. Indeed, a hysteresis loop is observed in an array of single-domain FM NPs, but no hysteresis loop is observed in an SPM material [191]. We have discussed in some detail QTM in SD ferromagnetic particles. We suppose two stable configurations (positively or negatively curved with pinned ends) due to the action of a bistable potential. An additional way for the material to further reduce its magnetostatic energy is to form domains with magnetization at right angles to the other domains (diagram c, right), instead of just in opposing parallel directions. Particle size dependence of coercivity (Hc) of NP-based magnetic materials has been well documented [186–191]. Stoner applied Pierre Weiss’s molecular field idea to the free electron model. An important element in this construction is the structure of the boundary between two domains (referred to as domain wall or Bloch wall). There are few reports showing a drastic change in properties for ultrasmall NPs. Analytic solutions do not exist, and numerical solutions calculated by the finite element method are computationally intractable because of the large difference in scale between the domain size and the wall size. Very large magnetotransport effects (of the order of 600%) have been observed in ferromagnetic nanocontacts between oppositely magnetized domains of half-metallic ferromagnet (magnetite) (Versluijs et al. The most important requirement is to have a complete characterization of the system. How does domain wall thickness relate to the magnetic anisotropy constant and exchange integral? A spin electronic interpretation of this resistance is possible which draws on the analogy between a ferromagnetic domain wall and a GMR trilayer ( Gregg et al. The conductivity depends on the relative orientation of the electrode magnetizations and the tunnel magnetoresistance (TMR): it is low for parallel alignment of electrode magnetization and high in the opposite case. The exchange interaction which creates the magnetization is a force which tends to align nearby dipoles so they point in the same direction. The converse ME effect was reported for direct liquid injection-chemical vapor deposition (DLI-CVD) grown NFO films on (001)-single crystal lead zinc niobate-lead titanate (PZN-PT) or PMN-PT substrates (Li et al., 2011). The development of devices in which logical states are represented by spin. A sharp increase in the magnetic moment per atom is observed for particles containing less than 20 atoms. Size characteristics of magnetic NPs have a direct effect on the surface, magnetization, and magnetic relaxation properties. The ferrofluid arranges itself along magnetic domain walls, which have higher magnetic flux than the regions of the material located within domains. This phenomenon is observed in thin (a few nanometers) alternating layers (superlattices) of ferromagnetic and nonmagnetic metals (e.g., iron and chromium) (Figure 7.17). These results indicate that the antiferromagnetic coupling between the ferromagnetic layers mitigates the tilting of the walls, which suggest these systems to achieve efficient and highly- packed displacement of trains of walls for spintronics devices. Electrical resistivity of ferromagnetic nickel and iron based alloys A Fert and I A Campbell Laboratoire de Physique des Solidest, Universite de Paris-Sud, 91405 Orsay Received I December 1975 Abstract. However, an iron bar at room temperature is not magnetized, although TC for iron is about 1000K. The exchange interaction between localized spins favored a parallel (in ferromagnets) or an anti-parallel (in anti-ferromagnets) state of neighboring magnetic moments. The 180° domain wall in ferromagnetic and ferroelectric substances is considered over a broad temperature range. It is noteworthy that the discovery of GMR depended on the development of methods for making high-quality ultrathin films (Section 6.3.1). Download full text in PDF Download. = Thus, the critical domain size plays a critical role in defining the properties of magnetic NPs. Indeed, about a 10-fold increase in the atomic magnetic moment is measured when the number of atoms is reduced by a factor of 2 below 20 atoms. Spectra of spin-flip Raman scattering, measured on CdMnSe donor electrons in indicated configuration. e Alternatively, one can study the noise and AC susceptibility, which is a method used by the group at IBM, Yorktown that we will discuss in some detail later on in this paper. The device is still in a high resistance state because of the layer 4. The magnetic field sensitivity is even greater than for GMR. A more promising direction is resistive random access memory (RRAM). A modified Bitter technique has been incorporated into a widely used device, the Large Area Domain Viewer, which is particularly useful in the examination of grain-oriented silicon steels. Thomas Saerbeck, in Solid State Physics, 2014. Diagram for describing spin-controlled electron transport in a thin film multilayer. Spintronics, sometimes called magnetoelectronics, may be loosely defined as the technology of devices in which electron spin plays a role; it has three main directions now: The development of ultrasensitive magnetic sensors for reading magnetic memories. Current-Assisted Domain Wall Motion in Ferromagnetic Semiconductors To cite this article: Michihiko Yamanouchi et al 2006 Jpn. The reason for this discrepancy is related to the magnetic dipolar interactions between spins, which were so far neglected because they are much weaker than the exchange interaction (see Problem 9.47). Variation of coercivity with temperature of nanocrystalline magnetic materials has confirmed this description. Hysteresis and noise in ferromagnetic materials with parallel domain walls Benedetta Cerruti,1 Gianfranco Durin,2,3 and Stefano Zapperi3,4 1Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, Martí Franquès 1, Facultat de Física, 08028 Barcelona, Spain 2Istituto Nazionale di Ricerca Metrologica, strada delle Cacce 91, 10135 Torino, Italy The change in magnetic field causes the magnetic dipole molecules to change shape slightly, making the crystal lattice longer in one dimension and shorter in other dimensions. Both of them display an E-induced easy magnetization process. Figure 7.17. A theory of QTM in SD antiferromagnetic particles has recently been published by Barbara and Chudnovsky [15]. Edges of domains are Called domain ‘walls’. 10.10.2 shows that it decays exponentially with R because it is proportional to the overlap between atomic orbitals on different sites separated by R. Hence, dipolar interactions are expected to be relevant if the atoms are well separated, because they fall off as R−3. It is possible to show that an abrupt change of orientation between two domains is energy-costly, and a smooth change is preferred. α We have performed low-temperature scanning Hall probe microscopy on a ferromagnetic semiconductor (Ga0.957Mn0.043)As. The magnetic response of a composite to an applied electric field is termed converse ME effect, and the primary tools for studies on CME are measurements of magnetic hysteresis M versus H under E, tuning of FMR in E, and electric field control of magnetization or ferromagnetic domain switching by magnetic force microscopy. [3] When the magnetization of a piece of magnetic material is changed to a different direction, it causes a slight change in its shape. s Moreover, the magnetic chirality reverses in alternate FM domain walls. In this section, we discuss these tools for CME studies with two representative examples: M versus H for NFO/PZN-PT and FMR in a bilayer of single crystal Y-type hexagonal and PMN-PT (Li et al., 2011; Tatarenko & Srinivasan, 2011). Then the ion–carrier interaction cannot be described any more within the scheme of mean field approximation used in previous sections. The arrows and double-headed Evidence of ferromagnetic domains in the (La 0.757Dy 0.243) 0.7Ca 0.3MnO 3 perovskite Exchange interaction causes nearest neighbors to prefer antiparallel spins, but if there is a conflict, the global magnetic field biases the output to 1. To find the minimums a variational method is used, resulting in a set of nonlinear differential equations, called Brown's equations after William Fuller Brown Jr. We investigate the dynamics of a domain wall in a ferromagnetic nanowire with spin-transfer torque. The idea of BMP appears in the early papers of S. von Molnar (see review by Holtzberg et al. Using a nanoporous template, ferroelectric ceramic (e.g., lead zirconate titanate) can be deposited as nanoscale islands on a suitable metal (e.g., platinum). [10], Region of a magnetic material in which the magnetization has uniform direction, Magneto-optical images of different domain structures, Domain structure of an examplary meander domain (recorded using CMOS-MagView), Domain structure of an examplary magnetic bubble domain (recorded using CMOS-MagView). Ferromagnetic Domain Wall and Spiral Ground States in One-Dimensional Deformed Flat-Band Hubbard Model Makoto Homma and Chigak Itoi ∗ February 7, 2008 Abstract We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flat-band Hubbard model. Depending on the width of the nonmagnetic spacer layer, there can be a ferromagnetic or antiferromagnetic interaction between the magnetic layers, and the antiferromagnetic state of the magnetic layers can be transformed into the ferromagnetic state by an external magnetic field. Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013. Numerous ferrofluids, defined as colloids with a permanently magnetized single domain, have been developed and commercially used. Hence, magnetization of ferromagnetic materials below the Curie temperature involves the orientation of macroscopic domains by external magnetic fields. Since the measurement accuracy depends very much on the FMR line width, the technique in general is appropriate for bilayers consisting of single crystal platelets or epitaxial films of low-loss ferrites such as YIG, lithium ferrite, nickel ferrite, and hexagonal ferrites (Sun & Srinivasan, 2012). In: Advances in solid state physics.
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