Using the ferromagnetic resonance technique, a localized resonance mode was experimentally discovered in an array of out-of-plane magnetized nanosized circular dots with an aspect ratio L/R (thickness/radius) close to unity. The frequency of this mode is lower than the frequency of the main Herring-Kittel quasiuniform spin excitation mode. Micromagnetic modeling reproduces the measured dependencies of the resonance frequencies on magnetic field and confirms that the localized mode is a superposition of two modes localized at the top and bottom faces of the dot. An analytical model based on the Schr & ouml;dingerlike equation of magnetization dynamics was developed. This model accounts for the inhomogeneity of the demagnetizing field, predicts the presence of such a localized mode, and provides a good estimate of its frequency. Unlike the frequency of the main mode, which predominantly depends only on the aspect ratio of the dot, the frequency of the localized mode explicitly depends on the dot thickness. This offers an opportunity to solve the inverse problem of estimating the average dot sizes on the basis of the patterned film ferromagnetic resonance curves.

Analytical expression for a vortex magnetization curve is obtained involving higher order magnetic energy terms in the existing analytical model. Based on this approach we define a magnetic vortex approximating function for a cylindrical dot magnetized in-plane. Such fit function has only three input parameters to describe any measured or calculated vortex magnetization curve with high accuracy. These parameters can be expressed as a function of the aspect ratio of the cylindrical dot. We have successfully trained an artificial neural network (ANN) where the input is a set of magnetic and geometrical parameters of the dot and the output are three parameters of the approximating function. A neural network is quite compact (~200 neurons), and it predicts accurately magnetization curve of a magnetic vortex, even going beyond the range of the training data parameters. Such a fast method for predicting the magnetization curve can be used to quickly determine the magnetic response of a device based on a magnetic vortex and evaluate the linearity of the response over a given range of applied field.

A model of exchange bias in a polycrystalline bilayer based on thermal fluctuations was extended to account for an arbitrary magnetization angle of the ferromagnetic (FM) layer. It allows for a more accurate description of the thermally activated reversal of the Néel vector in antiferromagnetic (AFM) grains since the extended model takes into account the variation of barrier height resulting from the magnetization angle of the FM layer. Field-annealing (setting of the exchange bias) and further relaxation of the FM/AFM bilayer was simulated using a sequence of iterations based on this model. An array of AFM grains is generated based on a lognormal distribution of their volume. Chosen parameters of distribution are based on the fit to the experimentally measured temperature dependence of exchange bias in sputter-deposited CoFe/IrMn films. The angular deviation of the exchange bias and the degradation of its amplitude in an applied field, with relative angle varied from 0° to 180°, are calculated. Hysteresis of the exchange bias with field exposure is observed. A temperature–time ( $T$ – $\tau$ ) diagram of the deviation angle, predicting the stability of the exchange bias under specific temperature and time, is presented.

The impact of 400 keV Ar+ irradiation on the magnetic and electrical properties of in-plane magnetized magnetic tunnel junction (MTJ) stacks was investigated by ferromagnetic resonance, vibrating sample magnetometry and current-in-plane tunneling techniques. The ion fluences ranged from 10(12) cm(-2) 5 x 10(15) cm(-2) 10(14) cm(-2), the anisotropy of the Ta-capped FeCoB free layer was weakly modulated, following a decrease in the saturation magnetization. The tunnel magnetoresistance (TMR), along with the exchange-bias and the interlayer exchange coupling providing a stable magnetic configuration to the reference layer, decreased continuously. Above 10(14) cm(-2), a strong decrease in the saturation magnetization was accompanied by a loss of the magnetic coupling and of the TMR. We show there is an ion-fluence window where the modulation of magnetic anisotropy can occur while preserving a large TMR and stable magnetic configuration of the MTJ, and demonstrate that the layers surrounding the free layer play a decisive role in determining the trend of the magnetic anisotropy modulation resulting from the irradiation. Our results provide guidance for the tailoring of MTJ parameters via ion irradiation, which we propose as a potentially suitable technique for setting the magnetic easy-cone state in MTJ for attaining field-free, fast, and non-stochastic magnetization switching.

In this work, the effect of bombardment with high-energy ions on the parameters of magnetic tunnel junctions based on CoFeB / MgO, such as magnetic anisotropy, magnetoresistance, and the damping coefficient of magnetization precession, is investigated. The modeling of the ferromagnetic resonance spectra was carried out within the framework of the Smit-Beljers and Landau-Lifshitz-Gilbert formalisms. The ion fluence limit is established, below which a controlled modulation of the magnetic anisotropy is achieved while maintaining a high tunneling magnetoresistance and stable magnetic configuration of the transition

The influence of temperature, FeCoB layer thickness, and insertion of ultrathin metal spacers (Ta and W) on the magnetic anisotropy of MgO/FeCoB/MgO free layers has been explored by means of ferromagnetic resonance. The second-order contribution to the perpendicular magnetic anisotropy (PMA), stemming from the fluctuations of the first-order term, accounts for the onset of an easy-cone magnetic state in the course of the transition from the in-plane to out-of-plane magnetization. Since the second-order term is small, the easy-cone state is stable only within a narrow range of free-layer thicknesses and temperatures, where the interfacial first-order PMA term gets counterbalanced by the magnetostatic term. We have found that the insertion of metallic spacers in the middle of the FeCoB layer noticeably widens the range of thicknesses and temperatures for obtaining the easy-cone state. We show that the W spacer outperforms its Ta counterpart in this enhancement, albeit increasing the magnetization damping due to a higher degree of alloying with FeCoB. A physical mechanism of the easy-cone stabilization is proposed. It considers a variation of the local saturation magnetization (M-S) and, notably, Curie temperature (T-C) near the MgO/FeCoB interface versus the distance to the metal spacer (or the capping) layer. The larger M-S and T-C values near MgO provide more thermal stability to the first-order PMA (k(s1)), while the lower M-S and T-C ones near the spacer layer result in a faster drop of the magnetostatic term with temperature. As a result, the effective PMA field exhibits a thermal stabilization effect that can be exploited to stabilize the easy-cone anisotropy. Alongside the improved conditions for setting an easy cone in the MgO/FeCoB/MgO free layers, we demonstrate that an easy-cone configuration with an almost temperature-independent opening angle can be obtained using a MgO/FeCoB(1.6 nm)/Ta free layer.

Measured switching voltage-field diagrams of perpendicular magnetic tunnel junctions exhibit unexpected behavior at high voltages associated with significant heating of the storage layer. The boundaries deviate from the critical lines corresponding to the coercive field, which contrasts with the theoretically predicted behavior of a standard macrospin-based model. Combining recent experimental studies of the temperature dependence of spin polarization and perpendicular magnetic anisotropy, we are proposing a modified model. Our approach takes into account the Joule heating during the writing pulse, which reduces the spin polarization and the anisotropy, thereby reducing the spin torque efficiency and the coercive field during the switching. The numerical macrospin simulations based on this model are in agreement with our experimental measurements and consistent with the results derived from the linearization of Landau-Lifshitz-Gilbert equation.

We have used the ferromagnetic resonance in the X-band (9.37 GHz) to investigate the effect of 400 keV Ar+ irradiation on the perpendicular magnetic anisotropy (PMA) and Gilbert damping parameter, α, of double-MgO free layers designed for application in perpendicular magnetic tunnel junctions. The samples comprised a MgO/Fe72Co8B20/X(0.2 nm)/Fe72Co8B20/MgO layer stack, where X stands for an ultrathin Ta or W spacer. Samples with two different total FeCoB layer thicknesses, tFCB = 3.0 nm and tFCB = 2.6 nm, were irradiated with ion fluences ranging from 1012 cm−2 to 1016 cm−2. The effective first-order PMA field, BK1, decreased nearly linearly with the logarithm of the fluence for both FeCoB thicknesses and spacer elements. The decrease in BK1, which is likely caused by an ion-induced intermixing at the FeCoB/MgO interfaces, resulted in a reorientation of the magnetization of the free layers with tFCB = 2.6 nm, initially exhibiting a perpendicular easy-axis anisotropy. For intermediate fluences, 1013 cm−2 and 1014 cm−2, easy-cone states with different cone angles could be induced in the free layer with a W spacer. Importantly, no corresponding increase in the Gilbert damping was observed. This study shows that ion irradiation can be used to tune the easy-cone anisotropy in perpendicular magnetic tunnel junctions, which is interesting for spintronic applications such as spin-torque magnetic memory devices, oscillators, and sensors.

In the ongoing Big Data revolution, the semiconductor industry faces major issues associated to the energy cost and time delay of transferring data between the processor cores and the multiple levels of memory. Since the advent of the MOS transistor, the performance of microelectronic circuits has followed Moore's law, stating that their speed and density would double every 18 months. Today, this trend tends to get out of breath: the continuously decreasing size of devices and increasing operation frequency lead to critical power consumption and heating issues. While the microprocessor unit is running in the GHz range, the main external memory (DRAM) is very slow. To speed up operations, cache memories, mostly composed of SRAM (Static Random Access Memory), are inserted between the processor and DRAM to fill this so-called “memory gap”. SRAMs are very fast but have a large footprint, hence a large silicon cost, which limits the amount of on-chip memory that can be practically embedded on-chip. Furthermore, SRAM are volatile which means that they require to be constantly powered and thus consume energy to retain information. With the downscaling of SRAM, this has today become a major issue [1] as the CMOS transistor current leakage has led to a large increase in the static (e.g. standby) power consumption. Moreover, the sensitivity to process and environmental variation reduces the static noise margin of SRAM, limiting their downscaling. Finally, the growing number of access to caches has also led to a large rise in dynamic power consumption. As multicore processors cannot afford keeping more than a very small fraction of all cores active at any given moment, their performances are limited and their scaling is hitting a power wall. As pointed by the ITRS, one of the best solutions to stop this trend is the modification of the memory hierarchy by the integration of nonvolatility (NV) as a new feature of memory caches, which would immediately minimize static power as well as paving the way towards normally-off/instant-on computing. The development of an electrically addressable nonvolatile (e.g. zero-leakage) memory combining processor speed (Ghz), infinite endurance and a higher-than-SRAM density is a crucial step towards higher performance and more energy efficient computing platforms.

Magnetoresistive and magnetoresonance measurements carried out on patterned perpendicular magnetic tunnel junction pillars and full-sheet films reveal magnetic inhomogeneities of FeCoB free layer grown on MgO and coated with Ta. At low FeCoB thicknesses, the layer behaves as an ensemble of weakly coupled grains resulting in a decrease of the free-layer thermal stability. In contrast, for thicker layers, the grains become more strongly coupled but strong magnetic inhomogeneities remain, yielding the emergence and further increase of a second-order magnetic anisotropy term (similar to K(2eff)cos(4)0), eventually resulting in an easy-cone anisotropy. We show that the static and dynamic magnetic properties of such a free layer can be successfully described by a granular model with three thickness-dependent parameters: mean perpendicular anisotropy of the grains, grain-to-grain anisotropy distribution, and intergrain exchangelike coupling strength. Easy-cone anisotropy may help reduce the stochasticity of the spin transfer torque switching. However, it arises at intermediate values of the intergrain exchange coupling where the spin transfer torque (STT) switching efficiency is degraded, as shown by multimacrospin modeling. This is due to the excitation of exchange modes contributing weakly to the STT switching process while dissipating part of the STT energy.

Experimental measurements performed on MgO-based perpendicular magnetic tunnel junctions show a strong dependence of the stability voltage-field diagrams as a function of the direction of the magnetic field with respect to the plane of the sample. When the magnetic field is applied in-plane, systematic nonlinear phase boundaries are observed for various lateral sizes. The simulation results based on the phenomenological Landau-Lifshitz- Gilbert equation including the in-plane and out-of-plane spin transfer torques are consistent with the measurements if a second-order anisotropy contribution is considered. Furthermore, performing the stability analysis in linear approximation allowed us to analytically extract the critical switching voltage at zero temperature in the presence of an in-plane field. This study indicates that in the noncollinear geometry investigations are suitable to detect the presence of the second-order term in the anisotropy. Such higher order anisotropy term can yield an easy-cone anisotropy which reduces the thermal stability factor but allows for more reproducible spin transfer torque switching due to a reduced stochasticity of the switching. As a result, the energy per write event decreases much faster than the thermal stability factor as the second-order anisotropy becomes more negative. Easy-cone anisotropy can be useful for fast-switching spin transfer torque magnetic random access memories provided the thermal stability can be maintained above the required value for a given memory specification.

This chapter presents a theoretical basis of the anisotropic magnetoelectric (ME) effect in tri-layers of metglas and piezoelectric (PE) single crystals. The properties of various common PE and magnetostrictive substances are discussed, and arguments for the choice of the most appropriate materials are made. A linear description of the ME effects in terms of electric, magnetic and elastic material fields and material constants is presented. An averaging quasi-static method is used to illustrate the relation between the material constants, their anisotropy and the transversal direct ME voltage and charge coefficients. Subsequently, the aforementioned model is employed in the calculation of the maximum expected direct ME voltage coefficient for a series of tri-layered Metglas/Piezocrystal/Metglas composites as a function of the PE crystal orientation. The ME effects are shown to be strongly dependent on the crystal orientation, which supports the possibility of inducing large ME voltage coefficients in composites comprising lead-free PE single crystals such as LiNbO3, LiTaO3, alpha-GaPO4, a-quartz, langatate and langasite through the optimization of the crystal orientation.

This chapter describes an experimental technique, developed experimental setup and respective experimental study of the dynamic properties of direct magnetolelectric (ME) effect measured in metglas-piezocrystal laminates. We have prepared a variety of different magnetoelectric laminates by bonding magnetostrictive metglas foils onto single-crystalline substrates of LiNbO3 (LNO), GaPO4 (GPO) and PMN-PT. The measurements have been performed as a function of the crystal cut, magnitude and orientation of the magnetic bias field and the frequency of the modulation field. Despite much weaker PE coefficients of LNO and GPO, direct ME effects have been found to have comparative magnitudes in the samples based on them and on PMN-PT. Greatly enhanced ME coefficients in certain resonance modes are explored and their relations to the material properties of the crystals and the geometry of the composites are investigated. We demonstrate that control of the PE crystal's orientation can be successfully used in order to obtain almost any desired quasi-static and resonant anisotropic ME properties for some given application. Such unique features as chemical stability, linear piezoelectricity, thermal robustness open up a real perspective to use lead-free LNO and alpha-GPO based ME tri-layers, e.g., as vector magnetic field sensors working in a wide range of temperatures.

Hard-axis magnetoresistance loops were measured on perpendicular magnetic tunnel junction pillars of diameter ranging from 50 to 150 nm. By fitting these loops to an analytical model, the effective anisotropy fields in both free and reference layers were derived and their variations in temperature range between 340 K and 5 K were determined. It is found that a second-order anisotropy term of the form −K 2 cos 4 θ must be added to the conventional uniaxial –K 1 cos 2 θ term to explain the experimental data. This higher order contribution exists both in the free and reference layers. At T = 300 K, the estimated −K 2 /K 1 ratios are 0.1 and 0.24 for the free and reference layers, respectively. The ratio is more than doubled at low temperatures changing the ground state of the reference layer from “easy-axis” to “easy-cone” regime. The easy-cone regime has clear signatures in the shape of the hard-axis magnetoresistance loops. The existence of this higher order anisotropy was also confirmed by ferromagnetic resonance experiments on FeCoB/MgO sheet films. It is of interfacial nature and is believed to be due to spatial fluctuations at the nanoscale of the first order anisotropy parameter at the FeCoB/MgO interface.

A NdCo5 (37 nm)/Fe (22 nm) hard/soft bilayer was grown by pulsed laser deposition on a MgO (1 1 0) substrate, and investigated by vibrating sample magnetometry and ferromagnetic resonance (FMR). Due to the direct exchange coupling at the NdCo5/Fe interface, the spin reorientation transition (SRT) typical of NdCo5 is observed also in the bilayer by means of global magnetometry. Concerning the magnetization dynamics, the interlayer magnetic coupling is weak, thus allowing the identification of the FMR signals in the sample as those originating mainly from the individual responses of the Fe and NdCo5 layers. In the NdCo5 layer, the effective coupling field is negligible compared to the internal anisotropy, and the magnetization precession is similar to the one found in a NdCo5 single layer. In the magnetically soft Fe layer, however, the precession of the moments occurs in the exchange field stemming from the dynamically fixed NdCo5 layer, giving rise to a partial transfer of magnetic anisotropy from the latter and enabling us to follow the SRT of NdCo5 by measuring the Fe FMR peak field position. Controlling the anisotropy direction in the soft layer by making use of the SRT in the hard layer can find applications in future spintronic devices.

A numerical and experimental study of the anisotropy of the magnetoelectric (ME) response in tri-layered composites based on single-crystalline piezoelectrics has been carried out. Quasi-static and resonant direct ME measurements were performed on Metglas/Piezoelectric/Metglas tri-layered structures featuring thin foils of the magnetostrictive Metglas alloy and differently oriented piezocrystals of LiNbO3 (LNO) and GaPO4 (GPO). The transversal ME effects were found to be strongly dependent on the direction of the applied in-plane magnetic bias fields as well as the orientation of the crystals. Multiple peaks of the ME response were observed corresponding to different contour resonance modes of the piezocrystals. The largest ME coefficient of up to 249 V/(cm.Oe) was observed for a composite with a 41 degrees Y-cut LNO crystal at 323.1 kHz. In summary, we have shown that crystalline lead-free LNO and GPO can exhibit relatively large anisotropic ME effects in multilayers. The relations between the directional ME coupling and the material constants of the differently oriented piezocrystals were pinpointed. The precise control of this orientation should therefore allow one to engineer almost any desired quasi-static and resonant ME anisotropic properties for any specific application. (C) 2015 Elsevier Ltd. All rights reserved.

The spin wave dynamics in patterned magnetic nanostructures is under intensive study during the last two decades. On the one hand, this interest is generated by new physics that can be explored in such structures. On the other hand, with the development of nanolithography, patterned nanoelements and their arrays can be used in many practical applications (magnetic recording systems both as media and read-write heads, magnetic random access memory, and spin-torque oscillators just to name a few). In the present work the evolution of spin wave spectra of an array of non-interacting Permalloy submicron circular dots for the case of magnetic field deviation from the normal to the array plane have been studied by ferromagnetic resonance technique. It is shown that such symmetry violation leads to a splitting of spin-wave modes, and that the number of the split peaks depends on the mode number. A quantitative description of the observed spectra is given using a perturbation theory for small angles of field inclination from the symmetry direction. The obtained results give possibility to predict transformation of spin wave spectra depending on direction of the external magnetic field that can be important for spintronic and nanomagnetic applications.

The relative contributions of in-plane (damping-like) and out-of-plane (field-like) spin-transfer torques (STT) in the magnetization switching of out-of-plane magnetized magnetic tunnel junctions (pMTJ) has been theoretically analyzed using the transformed Landau-Lifshitz-Gilbert (LLG) equation with the STT terms. It is demonstrated that in a pMTJ structure obeying macrospin dynamics, the out-of-plane torque influences the precession frequency, but it does not contribute significantly to the STT switching process (in particular to the switching time and switching current density), which is mostly determined by the in-plane STT contribution. This conclusion is confirmed by finite temperature and finite writing pulse macrospin simulations of the current field switching diagrams. It contrasts with the case of STT switching in in-plane magnetized magnetic tunnel junction (MTJ) in which the field-like term also influences the switching critical current. This theoretical analysis was successfully applied to the interpretation of voltage field STT switching diagrams experimentally measured on pMTJ pillars 36 nm in diameter, which exhibit macrospin behavior. The physical nonequivalence of Landau and Gilbert dissipation terms in the presence of STT-induced dynamics is also discussed.

The glass system MgO-Al2O3-SiO2-FeOy has been mentioned as possible electrolyte for pyroelectrolysis of iron. This work was focused on the study of crystallization behaviour of the iron-containing Al-Mg-Si-O glass system under laser floating zone (LFZ) to identify expected changes occurring under freeze lining or other high temperature gradients at large industrial scale. Lower iron content and faster fibre growth were found favourable for the formation of isolated iron cations in the glass after cooling. The crystallization process, accompanied with separation of mullite and cordierite-type phases, is strongly affected by the formation of nanosized iron-containing clusters, confirmed by Mossbauer and EPR spectroscopies. LFZ method shows good prospects for studying crystallization/vitrification mechanisms in silicate-based glasses with additions of redox-active cations, by providing flexibility in tuning their oxidation state and attaining frozen-in conditions. (C) 2014 Elsevier B. V. All rights reserved.