We investigate equilibrium properties of an exchange-spring magnetic system constituted of a soft layer (e.g. Fe) of a given thickness on top of a hard magnetic layer (e.g. FePt). The magnetization profile M(z) as a function of the atomic position ranging from the bottom of the hard layer to the top of the soft layer is obtained in two cases with regard to the hard layer: i) in the case of a rigid interface (the FePt layer is a single layer), the profile is obtained analytically as the exact solution of a sine-Gordon equation with Cauchy's boundary conditions. Additional numerical simulations also confirm this result. Asymptotic expressions of M(z) show a linear behavior near the bottom and the top of the soft layer. In addition, a critical value of the number of atomic planes in the soft layer, that is necessary for the onset of spin deviations, is obtained in terms of the anisotropy and exchange coupling between the adjacent plane in the soft layer. ii) in the case of a relaxed interface (the FePt layer is a multilayer), the magnetization profile is obtained numerically for various Fe and FePt films thicknesses and applied field.
Microwave assisted magnetization reversal are studied in the bulk bilayer exchange coupled system. We investigate the nonlinear magnetization reversal dynamics in a perpendicular exchange spring media using Landau-Lifshitz equation. In the limit of the infinite thickness of the system, the propagation field leads the reversal of the system. The reduction of the switching field and the magnetization profile in the extended system are studied numerically. The possibility to study the dynamics analytically is discussed and an approximation where two P-modes are coupled by an interaction field is …
The depth profile of the intrinsic magnetic properties in an Fe/Sm-Co bilayer fabricated under nearly optimal spring-magnet conditions was determined by complementary studies of polarized neutron reflectometry and micromagnetic simulations. We found that at the Fe/Sm-Co interface the magnetic properties change gradually at the length scale of 8 nm. In this intermixed interfacial region, the saturation magnetization and magnetic anisotropy are lower and the exchange stiffness is higher than values estimated from the model based on a mixture of Fe and Sm-Co phases. Therefore, the intermixed inte…
The potential of exchange spring bilayers and graded media is reviewed. An analytical model for the optimization of graded media gives an optimal value of the magnetic polarization of Js = 0.8 T. The optimum design allows for thermally stable grains with grain diameters in the order of 3.3 nm, which supports ultra high density up to 5 to 10 Tbit per inch2. The switching field distribution is significantly reduced in bilayer media and graded media compared to single phase media. For the graded media the switching field distribution is reduced by about a factor of two. For bilayer media the mini…
Development of modern spintronic devices requires materials exhibiting specific magnetic effects. In this paper, we investigate a magnetization reversal mechanism in a [Co/Pdx]7/CoO/[Co/Pdy]7 thin-film composite where an antiferromagnet is sandwiched between a hard and a soft ferromagnets with different coercivities. The antiferromagnet/ferromagnet interfaces give rise to the exchange bias effect. The application of soft and hard ferromagnetic films causes exchange-spring-like behavior while the choice of the Co/Pd multilayers provides large out-of-plane magnetic anisotropy. We observed that t…
In this study we investigate the exchange coupling between the hard magnetic compound MnBi and the soft magnetic alloy FeCo including the interface structure between the two phases. Exchange spring MnBi-Fe$_x$Co$_{1-x}$ (x = 0.65 and 0.35) bilayers with various thicknesses of the soft magnetic layer were deposited onto quartz glass substrates in a DC magnetron sputtering unit from alloy targets. Magnetic measurements and density functional theory (DFT) calculations reveal that a Co-rich FeCo layer leads to more coherent exchange coupling. The optimum soft layer thickness is about 1 nm. In orde…
We report a large, quasi-reversible tunnel magnetoresistance in exchange-biased ferromagnetic semiconductor tunnel junctions wherein a soft ferromagnetic semiconductor (\gma) is exchange coupled to a hard ferromagnetic metal (MnAs). Our observations are consistent with the formation of a region of inhomogeneous magnetization (an "exchange spring") within the biased \gma layer. The distinctive tunneling anisotropic magnetoresistance of \gma produces a pronounced sensitivity of the magnetoresistance to the state of the exchange spring.
Motivated by manipulating the magnetic order of bilayer CrI$_3$, we carry out microscopic calculations to find the magnetic order and various magnetic domains of the system in the presence of an electric field. Making use of density functional simulations, a spin model Hamiltonian is introduced consisting of isotropic exchange couplings, Dzyaloshinskii-Moriya (DM) interaction, and on-site magnetic anisotropy. The spin dynamics of two well-known states of bilayer CrI$_3$, low temperature (LT) and high temperature (HT) phases, are obtained by solving the Landau-Lifshitz-Gilbert equation. We show…
Double layer graphene is a gapless semiconductor which develops a finite gap when the layers are placed at different electrostatic potentials. We study, within the tight-biding approximation, the electronic properties of the gaped graphene bilayer in the presence of disorder, perpendicular magnetic field, and transverse electric field. We show that the gap is rather stable in the presence of diagonal disorder. We compute the cyclotron effective mass in the semi-classical approximation, valid at low magnetic fields. Landau level formation is clearly seen in zigzag and armchair ribbons of the ga…
We studied the magnetoresistance of normal metal (NM)/ferromagnet (FM) bilayers in the linear and nonlinear (current-dependent) regimes and compared it with the amplitude of the spin-orbit torques and thermally induced electric fields. Our experiments reveal that the magnetoresistance of the heavy NM/Co bilayers (NM = Ta, W, Pt) is phenomenologically similar to the spin Hall magnetoresistance (SMR) of YIG/Pt, but has a much larger anisotropy, of the order of 0.5%, which increases with the atomic number of the NM. This SMR-like behavior is absent in light NM/Co bilayers (NM = Ti, Cu), which pre…
In this work, we present an experimental study of spin mediated enhanced negative magnetoresistance in Ni80Fe20 (50 nm)/p-Si (350 nm) bilayer. The resistance measurement shows a reduction of ~2.5% for the bilayer specimen as compared to 1.3% for Ni80Fe20 (50 nm) on oxide specimen for an out-of-plane applied magnetic field of 3T. In the Ni80Fe20-only film, the negative magnetoresistance behavior is attributed to anisotropic magnetoresistance. We propose that spin polarization due to spin-Hall effect is the underlying cause of the enhanced negative magnetoresistance observed in the bilayer. Sili…
Current-induced spin-orbit torques in Co$_2$FeAl/Pt ultrathin bilayers are studied using a magnetoresistive harmonic response technique, which distinguishes the dampinglike and fieldlike contributions. The presence of a temperature-dependent magnetic proximity effect is observed through the anomalous Hall and anisotropic magnetoresistances, which are enhanced at low temperatures for thin platinum thicknesses. The fieldlike torque efficiency decreases steadily as the temperature is lowered for all Pt thicknesses studied, which we propose is related to the influence of the magnetic proximity eff…
We have studied the spin Hall magnetoresistance (SMR), the magnetoresistance within the plane transverse to the current flow, of Pt/Co bilayers. We find that the SMR increases with increasing Co thickness: the effective spin Hall angle for bilayers with thick Co exceeds the reported values of Pt when a conventional drift-diffusion model is used. An extended model including spin transport within the Co layer cannot account for the large SMR. To identify its origin, contributions from other sources are studied. For most bilayers, the SMR increases with decreasing temperature and increasing magne…
In this letter we report a direct observation of a magnetic proximity effect in an amorphous thin film exchange-spring magnet by the use of neutron reflectometry. The exchange-spring magnet is a trilayer consisting of two ferromagnetic layers with high $T_c$'s separated by a ferromagnetic layer, which is engineered to have a significantly lower $T_c$ than the embedding layers. This enables us to measure magnetization depth profiles at which the low $T_c$ material is in a ferromagnetic or paramagnetic state, while the embedding layers are ferromagnetic. A clear proximity effect is observed 7 K …
We analyze the experimentally obtained spin-current-related magnetoresistance in epitaxial Pt/Co bilayers by using a drift-diffusion model that incorporates both bulk spin Hall effect and interfacial Rashba-Edelstein effect (REE). The magnetoresistance analysis yields, for the Pt/Co interface, a temperature-independent Rashba parameter in the order of 1e-11 eV m that agrees with theoretical calculations, along with an effective interfacial REE thickness of several angstroms which is in overall consistency with our previous spin-orbit torque analysis. In particular, our results suggest that bot…
X-ray magnetic circular dichroism at the Er M4,5 edge is used to study the switching behavior of the hard ErFe2 layers in an epitaxial [ErFe2(70Å)/YFe2 (150Å)]{\times}25 exchange-spring superlattice. Magnetic hysteresis loops for the Er magnetization, at temperatures T < 200 K, reveal a switching behavior with a single type of irreversible switch corresponding to vertical exchange spring states. Experiments at T > 200 K reveal a crossover to a regime with two types of switching processes. Computational modelling for this system gives a semi-quantitative agreement with the experiment and reveal…
Magnetization and magnetoresistance measurements are reported for antiferromagnetically coupled DyFe$_2$/YFe$_2$ multilayers in fields up to 23 T. We demonstrate that the formation of short exchange springs (~ 2 nm) in the magnetically soft YFe$_2$ layers results in a giant magneto-resistance as high as 32% in the spring region. It is shown that both the magnitude of the effect, and its dependence on magnetic field, are in good agreement with the theory of Levy and Zhang for giant magnetoresistance due to domain wall like structures.
Magnetization and magnetic microstructure of top soft magnetic layer (Fe), which is exchange spring coupled to bottom hard magnetic layer ($L1_0$ FePt) is studied using high resolution Kerr microscopy. When the sample (FePt/Fe) is at remanent condition of hard magnetic layer, considerable shifting of Fe layer hysteresis loop from centre i.e., exchange bias phenomena is observed. It is observed that one can tune the magnitude of exchange bias shift by reaching the remanent state from different saturating fields ($H_{SAT}$) and also by varying the angle between measuring field and $H_{SAT}$. The…
The magnetization behaviour of the soft Cobalt Ferrite-hard Strontium Ferrite nanocomposite is tuned from the non exchange spring nature to the exchange spring nature, by controlling the particle size of the soft Cobalt Ferrite in the Cobalt Ferrite: Strontium Ferrite (1:8) nanocomposite. The relative strength of the interaction governing the magnetization process in the nanocomposites is investigated using Henkel plot and First Order Reversal Curve (FORC) method. The FORC method has been utilized to understand the magnetization reversal behaviour as well as the extent of the irreversible magn…
We report on the magnetization depth profile of a hybrid exchange spring system in which a Co/Pd multilayer with perpendicular anisotropy is coupled to a CoFeB thin film with in-plane anisotropy. The competition between these two orthogonal anisotropies promotes a strong depth dependence of the magnetization orientation. The angle of the magnetization vector is sensitive both to the strength of the individual anisotropies and to the local exchange constant, and is thus tunable by changing the thickness of the CoFeB layer and by substituting Ni for Pd in one layer of the Co/Pd stack. The result…
We report two effects that lead to a reduction of the switching field distribution in exchange spring media. The first effect relies on a subtle mechanism of the interplay between exchange coupling between soft and hard layers and anisotropy that allows significant reduction of the switching field distribution in exchange spring media. This effect reduces the switching field distribution by about 30% compared to single-phase media. A second effect is that due to the improved thermal stability of exchange spring media over single-phase media, thermal fluctuation leads to reduced fundamental tra…
We explore the moiré magnon bands in twisted bilayer magnets with next-nearest neighboring Dzyaloshinskii-Moriya interactions, assuming that the out-of-plane collinear magnetic order is preserved under weak interlayer coupling. By calculating the magnonic band structures and the topological Chern numbers for four representative cases, we find that (i) the valley moiré bands are extremely flat over a wide range of continuous twist angles; (ii) the topological Chern numbers of the lowest few flat bands vary significantly with the twist angle; and (iii) the lowest few topological flat bands in bi…
We report the first magnetic-field-dependent Raman scattering studies on Pb(Zr,Ti)O3-CoFe2O4 bilayer multiferroic system. The phonon frequencies of the nano-bilayers obviously change with magnetic field, which is absent in the single Pb(Zr,Ti)O3 films. The magnetostriction of the CoFe2O4 layer generates stress mechanically transferred to the Pb(Zr,Ti)O3 layer, resulting in the mode changes. The observed magnetic-field-induced softening of the soft mode in the Pb(Zr,Ti)O3 layer bears a striking resemblance to direct magnetoelectric output in the bilayers, providing evidence for stress-mediated …
We predict the emergence of spin Hall magnetoresistance in a magnetic bilayer composed of a normal metal adjacent to an antiferromagnet. Based on a recently derived drift-diffusion equation, we show that the resistance of the bilayer depends on the relative angle between the direction transverse to the current flow and the Néel order parameter. Although this effect presents striking similarities with the spin Hall magnetoresistance recently reported in ferromagnetic bilayers, in the present case its physical origin is attributed to the anisotropic spin relaxation of itinerant spins in the anti…
We describe a systematic study of the exchange coupling between a magnetically hard metallic ferromagnet (MnAs) and a magnetically soft ferromagnetic semiconductor (GaMnAs) in bilayer and trilayer heterostructures. An exchange spring model of MnAs/GaMnAs bilayers accounts for the variation of the exchange bias field with layer thickness and composition. We also present evidence for hole-mediated interlayer exchange coupling in MnAs/p-GaAs/\GaMnAs trilayers and study the dependence of the exchange bias field on the thickness of the spacer layer.
We carefully investigated the ferromagnetic coupling in the as-grown and annealed ferromagnetic semiconductor GaMnAs/AlGaMnAs bilayer devices. We observed that the magnetic interaction between the two layers strongly affects the magnetoresistance of the GaMnAs layer with applying out of plane magnetic field. After low temperature annealing, the magnetic easy axis of the AlGaMnAs layer switches from out of plane into in-plane and the interlayer coupling efficiency is reduced from up to 0.6 to less than 0.4. However, the magnetic coupling penetration depth for the annealed device is twice that o…
We present a comprehensive study on the magnetization reversal in Fe/NiFe bilayer system by alternating the order of the magnetic layers. All the samples show growth-induced uniaxial magnetic anisotropy due to oblique angle deposition technique. Strong interfacial exchange coupling between the Fe and NiFe layers leads to the single-phase hysteresis loops in the bilayer system. The strength of coupling being dependent on the interface changes upon alternating the order of magnetic layers. The magnetic parameters such as coercivity HC, and anisotropy field HK become almost doubled when NiFe laye…
This paper describes a model for magnetization reversal in polycrystalline Ferromagnetic/Antiferromagnetic exchange biased bilayers. We assume that the exchange energy can be expanded into cosine power series. We show that it is possible to fit experimental asymmetric shape of hysteresis loops in exchange biased bilayer for any direction of the applied field. The hysteresis asymmetry is discussed in terms of energy considerations. An angle beta is introduced to quantify the easy axis dispersion of AF grains.
Magnetization reversal in exchange-spring magnet films has been investigated by a First Order Reversal Curve (FORC) technique and vector magnetometry. In Fe/epitaxial-SmCo films, the reversal proceeds by a reversible rotation of the Fe soft layer, followed by an irreversible switching of the SmCo hard layer. The switching fields are clearly manifested by separate steps in both longitudinal and transverse hysteresis loops, as well as sharp boundaries in the FORC distribution. In FeNi/polycrystalline-FePt films, particularly with thin FeNi, the switching fields are masked by the smooth and step-…
The properties of antiferromagnetic ferromagnetic bilayer have been studied using self-consistent mean-field approximation for Heisenberg Hamiltonian. The perpendicular exchange coupling has been revealed in a bilayer with a compensated interface. For a uniform antiferromagnetic film a symmetrical hysteresis loop has been calculated, because the transverse instability develops within the antiferromagnetic film at certain critical value of external magnetic field. On the other hand, shifted hysteresis loop with a finite exchange bias field has been obtained for a non-uniform antiferromagnetic f…
The spin Hall magnetoresistance (SMR) and anomalous Hall effect (AHE) are observed in a Cr2O3/Ta structure. The structural and surface morphology of Cr2O3/Ta bilayers have been investigated. Temperature dependence of longitudinal and transverse resistances measurements confirm the relationship between SMR and AHE signals in Cr2O3/Ta structure. By means of temperature dependent magnetoresistance measurements, the physical origin of SMR in the Cr2O3/Ta structure is revealed, and the contribution to the SMR from the spin current generated by AHE has been proved. The so-called boundary magnetizati…
The spin structure of exchange-coupled MnBi:Co-Fe bilayers is investigated by X-ray magnetic circular dichroism (XMCD), polarized neutron reflectometry (PNR), and micromagnetic simu-lations. The purpose of the present research is two-fold. First, the current search for new permanent-magnet materials includes hard-soft nanocomposites, and the analysis of coercivity mechanisms in these structures is an important aspect of this quest. Second, topological micro-magnetic structures such as skyrmions have recently become of intense fundamental and applied research, for example in the context of spin…
To date, magnetic proximity effect (MPE) has only been conclusively observed in ferromagnet (FM) based systems. We report the observation of anomalous Hall effect and anisotropic magnetoresistance in angular dependent magnetoresistance (ADMR) measurements in Pt on antiferromagnetic (AF) $α$-Fe$_2$O$_3$(0001) epitaxial films at 10 K, which provide evidence for the MPE. The Néel order of $α$-Fe$_2$O$_3$ and the induced magnetization in Pt show a unique ADMR compared with all other FM and AF systems. A macrospin response model is established and can explain the AF spin configuration and all main …
The exchange bias at ferromagnetic/antiferromagnetic interfaces strongly depends upon the state of antiferromagnetic (AF) layer which, due to strong magnetoelastic coupling, is sensitive to mechanical stresses. In the present paper we consider magnetoelastic effects that arise at FM/AF interface due to lattice misfit and magnetic ordering. We show how magnetostriction affects mutual orientation of AF and FM vectors and easy-axis direction in thin AF layer. The results obtained could be used for tailoring exchange biased systems.
Strong ferromagnetic interlayer exchange couplings $J$ in perpendicularly magnetized systems are becoming increasingly desirable for applications. We study whether ferromagnetic interlayer exchange couplings can be measured by a combination of broadband ferromagnetic resonance methods and magnetometry hysteresis loops. For this we model the switching and the eigenexcitations in bilayer systems comprising a soft layer coupled to a thicker harder layer that possesses higher perpendicular magnetic anisotropy. For large $J >0$ the switching fields are essentially independent of $J$ but the frequen…
The periodic deviations of ferromagnetic and antiferromagnetic spins from corresponding uniform configurations are shown to be energetically favorable close to a compensated interface of ferromagnetic antiferromagnetic bilayer. The amplitude of the deviations decreases exponentially into the film volumes as a function of a coordinate perpendicular to the interface. The interaction energy is found to be proportional to a square of a scalar product of unit ferromagnetic and antiferromagnetic vectors.
A modified effective field model was developed to quantitatively interpret the angular dependent magnetization reversal processes in exchange biased Fe/IrMn bilayers. Several kinds of multi-step loops with distinct magnetization reversal routes were observed for the samples measured at various field orientations. Two types of angular dependent switching fields are observed and their transitions are investigated, which are found to be driven by both Fe and IrMn layer thicknesses. Our modified effective field model can nicely describe all the switching field behaviors including the critical effe…
By performing angle-resolved photoemission spectroscopy of the bilayer colossal magnetoresistive (CMR) manganite, $La_{2-2x}Sr_{1+2x}Mn_{2}O_{7}$, we provide the complete mapping of the Fermi level spectral weight topology. Clear and unambiguous bilayer splitting of the in-plane 3d$_{x^2-y^2}$ band, mapped throughout the Brillouin zone, and the full mapping of the 3d$_{3z^2-r^2}$ band are reported. Peculiar doping and temperature dependencies of these bands imply that as transition from the ferromagnetic metallic phase approaches, either as a function of doping or temperature, coherence along …
We report on a temperature-driven reversible change of the in-plane magnetic anisotropy of V$_2$O$_3$/Ni bilayers. This is caused by the rhombohedral to monoclinic structural phase transition of V$_2$O$_3$ at $T_C$ = 160 K. The in-plane magnetic anisotropy is uniaxial above $T_C$, but as the bilayer is cooled through the structural phase transition, a secondary magnetic easy axis emerges. Ferromagnetic resonance measurements show that this change in magnetic anisotropy is reversible with temperature. We identify two structural properties of the V$_2$O$_3$/Ni bilayers affecting the in-plane mag…
We optimize the recording medium for heat-assisted magnetic recording by using a high/low $T_{\mathrm{c}}$ bilayer structure to reduce AC and DC noise. Compared to a former work, small Gilbert damping $α=0.02$ is considered for the FePt like hard magnetic material. Atomistic simulations are performed for a cylindrical recording grain with diameter $d=5\,$nm and height $h=8\,$nm. Different soft magnetic material compositions are tested and the amount of hard and soft magnetic material is optimized. The results show that for a soft magnetic material with $α_{\mathrm{SM}}=0.1$ and $J_{ij,\mathrm{…
Epitaxial bilayers of ferromagnetic La2/3Ca1/3MnO3 (LCMO) and superconducting YBa2Cu3O7-d (YBCO) have been grown on single-crystalline SrTiO3 (STO) substrates by pulsed laser deposition. The Manganese magnetization profile across the FM layer has been determined with high spatial resolution at low temperatures by X-ray resonant magnetic reflectivity (XRMR). It is found that not only the adjacent superconductor but also the substrate underneath influences the magnetization of the LCMO film at the interfaces at low temperatures. Both effects can be investigated individually by XRMR.
We present an ab-initio density function theory to investigate the electronic and magnetic structures of the bilayer graphene with intercalated atoms C, N, and O. The intercalated atom although initially positioned at the middle site of the bilayer interval will finally be adsorbed to one graphene layer. Both N and O atoms favor the bridge site (i.e. above the carbon-carbon bonding of the lower graphene layer), while the C atom prefers the hollow site (i.e. just above a carbon atom of the lower graphene layer and simultaneously below the center of a carbon hexagon of the upper layer). Concerni…
The influence of random interlayer exchange on the phase states of the simplest magnetic heterostructure consisting of two ferromagnetic Ising layers with large interaction radius is studied. It is shown that such system can exist in three magnetic phases: ferromagnetic, antiferromagnetic and ferrimagnetic. The possible phase diagrams and temperature dependencies of thermodynamic parameters are described. The regions of existence of the magnetic phases in external magnetic field are determined at zero temperature.
We experimentally study magnetization aging in a thin-film NiO/Permalloy bilayer. Aging characteristics are nearly independent of temperature below the exchange bias blocking temperature, but rapidly vary above it. The dependence on the magnetic history qualitatively changes across this temperature. The observed behaviors are consistent with the spin glass transition at the exchange bias blocking temperature, with significant implications for magnetism and magnetoelectronic phenomena in antiferromagnet/ferromagnet bilayers.
