Interlayer Coupling Constant Research Articles

Static and dynamical behaviour of magnetically coupled Co/Cu/CoFeB trilayers

Engineering the magnetic behaviour of stacks of ferromagnetic and non-magnetic thin films is mainly controlled by the anisotropy of individual layers plus the interlayer exchange coupling constant. Then, Co/Cu/CoFeB trilayers with different Cu layer thicknesses, tCu, were fabricated by sputtering. The effects of tCu on the magnetization reversal processes, the interlayer coupling, FMR frequencies and damping parameters were investigated. The analysis of the hysteresis loops have demonstrated how the two ferromagnetic films can be strongly coupled and behave like a single system for tCu ≤ 3 nm, or like two almost independent or uncoupled layers for tCu ≥ 3 nm. It is shown that the interlayer coupling is at the origin of the observed two FMR resonance modes: the acoustic and the optic modes. Particularly, the resonance frequency of the optic mode is very sensitive to the interlayer coupling constant and high resonance frequencies can be achieved (over 25 GHz) for ferromagnetically coupled Co/CoFeB bilayers with interlayer exchange coupling Jeff = (2.7 ± 0.8) erg/cm2. However, the technological application of such high resonance frequencies of the optic mode can be limited by the increase in the damping parameter mainly due to the spin-pumping effect.

Fluctuation Conductivity in MOD-Derived YBCO Thin Films

Normal-state properties of some epitaxial YBa2Cu3O7-δ thin films which were derived from the metal-organic deposition route were studied through the context of Aslamazov and Larkin theory of fluctuation conductivity. Six samples with various superconducting properties were selected for this purpose. Resistivity vs. temperature analysis showed that the general normal-state behavior of the samples can be described by 3D, 2D, and 1D Aslamazov and Larkin model of fluctuation conductivity. Samples with the higher superconducting transition temperatures showed the higher Josephson interlayer coupling. Moreover, a linear behavior has been found between Josephson interlayer coupling constant and critical current density. In addition, fitting excess conductivity with Lawrence-Doniach (LD) and Maki-Thompson (MT) models revealed that the LD term dominates in 3D region near the superconducting transition. However, the MT term gains an important role in 2D region far away superconducting transition.

Magnetic Properties and Spin-Wave Excitations in Co/Mn Multilayers

Co/Mn multilayers were prepared using evaporation technique under ultra-high vacuum conditions and their structural and magnetic properties were studied. The temperature dependence of the spontaneous magnetization [Formula: see text] was recorded for different cobalt layer thickness ([Formula: see text]) ranging from 19[Formula: see text]Å to 70[Formula: see text]Å. Bloch’s law describes satisfactory the thermal change of magnetization for all samples. In addition, the change of the spin-wave (SW) parameter [Formula: see text] versus [Formula: see text] was discussed. The torque magnetometry was utilized to extract the effective anisotropy ([Formula: see text]) and the interlayer coupling constant ([Formula: see text]) was determined from the in-plan M–H loops. An updated model based on SW theory was applied to describe the [Formula: see text] variation and to calculate the approximate values of exchange interactions for samples with different Co-layer thicknesses.

Dynamic Phenomena in Mixed Spin-1 and Spin-1/2 Ising Bilayer System: Effective-Field Theory Based on Glauber Type Stochastic Dynamics

The dynamic compensation and dynamic hysteresis features of the mixed bilayer Ising system (MBIS) consist of spin-1 and spin-1/2 on a bilayer square lattice and have been studied extensively with the use of the effective-field theory and Glauber type stochastic dynamic. Firstly, the thermal variations of the total magnetization were investigated in order to find the compensation types of the MBIS. The six compensation types were found to be the Q-, R-, P-, N-, S-, and L-types. Then, the effects of the temperature, interlayer coupling constant, crystal field, and oscillating field frequency on the dynamic magnetic hysteresis properties were widely studied.

Realizing Broadband Transparency via Manipulating the Hybrid Coupling Modes in Metasurfaces for High‐Efficiency Metalens

AbstractMetasurfaces with locally controlled phase discontinuity are promising for novel manipulations of the optical fields. However, the high insert loss at off‐resonance frequencies and narrow operation band of the resonant metasurface lead to the common low efficiency, obstructing it from practical applications. Here, it is shown that a broadband transparent metasurface, made of three‐layer complementary square ring resonator (CSRR) arrays, can be employed for high‐efficiency and broadband beam manipulation. The nonuniform metasurface can be optimized with high transmittance (above 90%) while maintaining full range (from 0 to 2π) phase modulation by adjusting the geometric parameters of the CSRR on the middle layer. The physical insight can be understood with a coupled oscillator model, it is found that the interlayer coupling constant is the key factor to realize phase modulation with high efficiency. A transmittance metalens with long focal depth in broadband is experimentally demonstrated as an example, the measured transmission efficiency is higher than 80%. The developed broadband wavefront engineering elements can be employed for high‐performance, miniaturized and superior environmental suitability sensing, imaging, and communication system.

Magnetic Properties and Electronic Structure of Ni/C Multilayer Films

The magnetic properties of Ni/C multilayers were investigated using vibrating sample magnetometer and ferromagnetic resonance (FMR). Spin wave resonances were seen in FMR and the spin wave was found to be sustained through whole layers. The interlayer coupling constant was small pointing out a weak exchange coupling between Ni films through C spacers. The FMR linewidth, in parallel geometry, of the uniform mode decreases with the increase in Ni thickness from 30 to 300 A which can be understood by considering interfacial effects. The magnetization decreases with decreasing Ni thickness due to the structural imperfections associated with the presence of Ni1−xCx alloys at the interface. Density functional theory (DFT) has been performed to shed light on the decrease in magnetic moment at the interfaces.

The annealing effect on memory state stability and interlayer coupling in perpendicular magnetic tunnel junctions with ultrathin MgO barrier

Abstract Perpendicular magnetic tunnel junctions (p-MTJs) attract great interest because of their excellent performance in spin-transfer-torque magnetic random access memories (STT-MRAMs). The annealing process is critical to achieve the required structural and magnetic properties, therefore obtaining high perpendicular tunneling magnetoresistance (p-TMR) and lower switching current. In this work, the CoFeB/MgO/CoFeB-based p-TMR stack was prepared and a high p-TMR value of 155.9% was obtained from CIPT. The p-MTJs were patterned with pillar sizes ranging from 50 nm to 1000 nm and were annealed upon different annealing temperatures (TA) of 300 and 340 °C. The resistance at parallel (RP) and antiparallel (RAP) state in p-MTJs was obtained upon the application of a ±30 mT perpendicular magnetic field, where the angle of magnetization between storage and reference layer at memory state, θP and θAP, were derived from the P and AP resistance ratios with and without magnetic field. The condition θP = θAP of about 63.5° was found in as-deposited samples, indicating a ferromagnetic interlayer coupling between storage and reference layers, where θP = 0° and θAP = 180° at TA = 300 °C and 340 °C demonstrate a stable memory state. The stability of the resistance state was modeled by considering the evolution of effective perpendicular magnetic anisotropy (Keff) and interlayer coupling constant (J), showing a method to evaluate the ratio of Keff/J via the memory state resistance characterization, where the Keff/J of about −1.26 was obtained in our as-deposited samples. Our study assesses the effect of TA on the θP and θAP and supplies the method to enhance the stability through the optimization of perpendicular magnetic anisotropy and interlayer coupling, so to better control the performance of p-MTJ-based STT-MRAMs.

Measurements of Gilbert damping parameter α for CoPt-based and CoFe-based films for magnetic recording applications

Time-resolved MOKE (TRMOKE) and Q-band ferromagnetic resonance (FMR) are used to evaluate the damping parameter α and the magnetic anisotropy field (where K is the uniaxial anisotropy constant and is the saturation magnetization) of CoPtX–Y and CoPtX (where X is non-magnetic element and Y denotes oxide(s)) granular alloys with perpendicular magnetic anisotropy and variable Co/Pt atomic ratio R. It is found that α monotonically increases in the range of 0.03–0.07 with decreasing R in the range of 2.5–5.5. By comparing the CoPtX films sputter-deposited in Ar and in Ar+O2 atmosphere, it is found that α is less sensitive than HK to the presence of non-magnetic additives (Cr, B) in the grain core. This suggests that α is much less sensitive than K to perturbations of d-electron band structure. FMR and TRMOKE are also used to evaluate α of magnetically soft CoFeX alloys. It is shown that adding 2 at.% Tb to CoFeX leads to an increase of α from 0.012 (undoped case) to 0.048, and a negative shift of the resonance field which is linearly dependent on the RF frequency. This effect, similar to that previously reported on Tb-doped NiFe films, is attributed to the highly anisotropic Tb 4f–5d exchange coupling. A synthetic-antiferromagnetic trilayer CoFeX (7 nm)/Ru (0.8 nm)/CoFeX (7 nm) is investigated by FMR. The interlayer RKKY coupling constant, evaluated from the frequency shift between the acoustic (symmetric) and optic (antisymmetric) resonance modes is JEX = 0.11 erg cm−2. The α value corresponding to the acoustic mode (0.016) matches that of a single-layer CoFeX film whereas the optic mode shows a higher α (0.0265). This is interpreted to be a consequence of spin-pumping through the Ru interlayer. The evaluated spin mixing conductance for the CoFeX/Ru interface is = 22.5 nm−2.

Magnetic Properties and Electronic Structure of Co/Zr Multilayers

We investigate the magnetic and electronic properties of Co/Zr multilayers with an emphasis on the interfacial effects. The saturation magnetization, coercivity, and uniaxial anisotropy depend significantly on Co thickness. Spin-wave resonance modes were observed, and the change of resonant field as a function of mode number (n) obeys the so-called n2 law. The interlayer coupling constant was determined. The electronic properties of the interfacial alloys were studied using the WIEN2k code, employing the density functional theory. Calculations describe satisfactorily the observed magnetic behaviour. The influence of pressure on the magnetic properties of the interfacial Co1−xZrx alloys was investigated in which we demonstrate that the ferromagnetism is altered by pressure.

Dynamic Magnetic Hysteresis Behaviors in a Mixed Spin (3/2, 2) Bilayer System with Different Crystal-Field Interactions

Dynamic magnetic hysteresis (DMH) behaviors of the mixed spin-3/2 and spin-2 Ising bilayer system with different crystal-field interactions on a two-layer square lattice is studied by the use of dynamic mean field calculations based on the Glauber-type stochastic. The hysteresis loops are obtained for different reduced temperatures (T), magnetic field amplitudes (h), frequencies (w) and interlayer coupling constants (J3). Influences of the T, h, w and J3 on the DMH properties are investigated. We also study the temperature, frequency and interlayer coupling interaction dependence of the coercive field and remanent magnetization. We compare our results with some theoretical and experimental works and observe a quantitatively good agreement with some theoretical and experimental results.

Anisotropic magnetization relaxation in ferromagnetic multilayers with variable interlayer exchange coupling

The FMR linewidth and its anisotropy in F$_1$/f/F$_2$/AF multilayers, where spacer f has a low Curie point compared to the strongly ferromagnetic F$_1$ and F$_2$, is investigated. The role of the interlayer exchange coupling in magnetization relaxation is determined experimentally by varying the thickness of the spacer. It is shown that stronger interlayer coupling via thinner spacers enhances the microwave energy exchange between the outer ferromagnetic layers, with the magnetization of F$_2$ exchange-dragged by the resonance precession in F$_1$. A weaker mirror effect is also observed: the magnetization of F$_1$ can be exchange-dragged by the precession in F$_2$, which leads to anti-damping and narrower FMR linewidths. A theory is developed to model the measured data, which allows separating various contributions to the magnetic relaxation in the system. Key physical parameters, such as the interlayer coupling constant, in-plane anisotropy of the FMR linewidth, dispersion of the magnetic anisotropy fields are quantified. These results should be useful for designing high-speed magnetic nanodevices based on thermally-assisted switching.

Spin-1 and -2 bilayer Bethe lattice: A Monte Carlo study

The magnetic behaviors of bilayer with spin-1 and 2 Ising model on the Bethe lattice are investigated using the Monte Carlo simulations. The thermal magnetizations, the magnetic susceptibilities and the transition temperature of the bilayer spin-1 and 2 on the Bethe lattice are studied for different values of crystal field and intralayer coupling constants of the two layers and interlayer coupling constant between the layers. The thermal and magnetic hysteresis cycles are given for different values of the crystal field, for different temperatures and for different exchange interactions.

Size effect on magnetic properties of a nano-graphene bilayer structure: A Monte Carlo study

In this paper we use the Monte Carlo simulations to investigate the magnetic properties of an Ising ferromagnetic–antiferromagnetic model. The system is based on a nano-graphene structure-like bilayer with two bloc sizes: N=24 and 42 spins. For each size N, the upper layer A is formed with spin −3/2, whereas the lower layer B is composed of spin −5/2. We only consider the first nearest-neighbor interactions between the sites i and j. The magnetic properties are studied, in the absence as well as in the presence of a crystal magnetic field, and an external magnetic field. The increasing temperature and crystal field as well as the inter-layer coupling constant, are also studied for this system sizes N=24 and 42 spins. The zero-field-cooled and the field cooled magnetization behaviors are investigated for different values of external magnetic field and a fixed value of exchange interaction between the two blocs. The magnetizations as well as the magnetic susceptibilities versus the temperature are used in order to obtain blocking temperature.The saturation magnetization and coercive field are also obtained for the two sizes of the studied system. It is found that the blocking temperature decreases on increasing the crystal magnetic field and/or the external magnetic field, for a fixed system size. On the other hand, it is found that the blocking temperature increases on increasing the system size from N=24 to 42 spins, for fixed values of external and the crystal magnetic fields.

Synthesis and Physical Properties of K4[Fe(C5O5)2(H2O)2](HC5O5)2·4H2O (C5O52–= Croconate): A Rare Example of Ferromagnetic Coupling via H-bonds

The reaction of the croconate dianion (C(5)O(5))(2-) with a Fe(III) salt has led, unexpectedly, to the formation of the first example of a discrete Fe(II)-croconate complex without additional coligands, K(4)[Fe(C(5)O(5))(2)(H(2)O)(2)](HC(5)O(5))(2)·4H(2)O (1). 1 crystallizes in the monoclinic P2(1)/c space group and presents discrete octahedral Fe(II) complexes coordinated by two chelating C(5)O(5)(2-) anions in the equatorial plane and two trans axial water molecules. The structure can be viewed as formed by alternating layers of trans-diaquabis(croconato)ferrate(II) complexes and layers containing the monoprotonated croconate anions, HC(5)O(5)(-), and noncoordinated water molecules. Both kinds of layers are directly connected through a hydrogen bond between an oxygen atom of the coordinated dianion and the protonated oxygen atom of the noncoordinated croconate monoanion. A H-bond network is also formed between the coordinated water molecule and one oxygen atom of the coordinated croconate. This H-bond can be classified as strong-moderate being the O···O bond distance (2.771(2) Å) typical of moderate H-bonds and the O-H···O bond angle (174(3)°) typical of strong ones. This H-bond interaction leads to a quadratic regular layer where each [Fe(C(5)O(5))(2)(H(2)O)(2)](2-) anion is connected to its four neighbors in the plane through four equivalent H-bonds. From the magnetic point of view, these connections lead to an S = 2 quadratic layer. The magnetic properties of 1 have been reproduced with a 2D square lattice model for S = 2 ions with g = 2.027(2) and J = 4.59(3) cm(-1). This model reproduces quite satisfactorily its magnetic properties but only above the maximum. A better fit is obtained by considering an additional antiferromagnetic weak interlayer coupling constant (j) through a molecular field approximation with g = 2.071(7), J = 2.94(7) cm(-1), and j = -0.045(2) cm(-1) (the Hamiltonian is written as H = -JS(i)S(j)). Although this second model might still be improved since there is also an extra contribution due to the presence of ZFS in the Fe(II) ions, it confirms the presence of weak ferromagnetic Fe-Fe interactions through H-bonds in compound 1 which represents one of the rare examples of ferromagnetic coupling via H-bonds.

Magnetic Properties and Electronic Structure of Ni81Fe19/Zr Multilayer Films

Magnetic properties of NiFe/Zr multilayer films, prepared by DC magnetron sputtering, have been studied by vibrating sample magnetometer and ferromagnetic resonance (FMR). Spin-wave resonances were observed in Ni81Fe19/Zr multilayer films in FMR experiments, and the spin wave was found to be sustained by both the whole films. Estimated small interlayer coupling constant shows weak exchange coupling effect between NiFe layers across Zr spacers. The FMR linewidth, in parallel geometry, of the uniform mode was found to increase with decreasing NiFe thickness (20 A ≤ \(t_{\mathrm{NiFe}}\) ≤ 120 A) indicating that it corresponds to an interfacial effect. In addition, electronic and magnetic properties of multilayers are investigated by self-consistent ab initio calculations based on Korringa–Kohn–Rostocker (KKR). Spin polarized within the framework of the Coherent Potential Approximation (CPA) is considered for calculations.

Analytical Study of Low-Field Diffusive Transport in Highly Asymmetric Bilayer Graphene Nanoribbon

We present a simplified theory of carrier backscattering coefficient in a twofold degenerate asymmetric bilayer graphene nanoribbon (BGN) under the application of a low static electric field. We show that for a highly asymmetric BGN (Δ = γ), the density of states in the lower subband increases more that of the upper, in which Δ and γ are the gap and the interlayer coupling constant, respectively. We also demonstrate that under the acoustic phonon scattering regime, the formation of two distinct sets of energy subbands signatures a quantized transmission coefficient as a function of ribbon width and provides an extremely low carrier reflection coefficient for a better Landauer conductance even at room temperature. The well-known result for the ballistic condition has been obtained as a special case of the present analysis under certain limiting conditions which forms an indirect validation of our theoretical formalism.

Diffusive Thermoelectric Power in Highly Asymmetric Bilayer Graphene Nanoribbons

We present a simplified theoretical analysis of diffusive thermoelectric power (TEP) in a highly asymmetric bilayer graphene nanoribbon (BGN) within the framework of the tight binding formalism. BGN possesses two sets of subbands, the upper and the lower. We have shown that, for a highly asymmetric BGN (Δ = γ, where Δ and γ are the gap and interlayer coupling constant, respectively), the density of states in the lower set of subbands increases compared with the upper. The effect of ribbon width on the TEP under the aforementioned phonon scattering regime has also been quantitatively shown. The TEP exhibits an oscillatory dependence on ribbon width. Reflection coefficients of the carriers in both the upper and lower subbands have been treated in detail. Results of the ballistic formalism have been obtained as a special case in the present analyses under certain limiting conditions, forming an indirect validation of our theoretical formulations.

Spin-Wave Excitations in Evaporated Co/Pt Multilayers

The magnetic behavior of evaporated Co/Nb multilayers has been investigated by magnetic measurements and ferromagnetic resonance (FMR). The modes of spin-wave (S-W) resonances were observed in some Co/Nb multilayers in FMR measurements. So, the S-Ws were sustained by the whole layers and propagated through the Nb layers. The dependence of the mode number n on the resonance field Hres is following the n2 law. As a result, the interlayer coupling constant (JI) was determined. A S-W theory has been applied to explain the variation of the magnetization versus temperature and hence to estimate the approximate values of the bulk exchange interaction (Jb) and interface exchange interaction (Jint) for various Co/Nb multilayers.

Determination of magnetic anisotropies, interlayer coupling, and magnetization relaxation in FeCoB/Cr/FeCoB

We studied magnetic anisotropic properties, interlayer coupling, and spin wave relaxation in ten periods of CoFeB/Cr/CoFeB films grown on seed layers of Cu with a Co:Fe:B composition ratio of 2:2:1. The measurements were taken in samples with 50 Å layers of CoFeB using the ferromagnetic resonance technique. The thickness of the Cr interlayers was varied from 4 to 40 Å for understanding the mechanisms of interlayer coupling. We investigated the magnetic anisotropy parameters by rotating the sample with respect to the microwave magnetic field from in plane to perpendicular to the plane. We identify both the acoustic branch and the optical branch in the spin wave resonance spectra. The effective interlayer coupling constant and the out-of-plane anisotropy show an oscillatory change, while the uniaxial in-plane anisotropy increases monotonically with increasing the thickness of the spacing layers. Moreover, we show that the spin wave relaxation can be optimized by adjusting the interlayer exchange interactions.

THE CRYSTAL FIELD EFFECTS ON THE PHASE DIAGRAMS OF THE SPIN-2 BILAYER BETHE LATTICE

The bilayer spin-2 Ising model on the Bethe lattice is investigated by taking into account the intralayer coupling constants of the two layers J1 and J2, interlayer coupling constant between the layers J3 and crystal field interaction Δ by using the exact recursion equations in a pairwise approach. The ground state (GS) phase diagrams of the model are obtained on the (J2/|J1|, J3/q|J1|) planes for given Δ values and on the (Δ/qJ, J3/qJ) plane when J1 = J2 = J, and thus 33 distinct GS configurations are found. The temperature-dependent phase diagrams are obtained for J1 > 0, J2 > 0, and for J3 > 0 or J3 < 0 on the (kT/J1, J3/J1) planes for given Δ/qJ1 and J2/J1 and on the (Δ/J, kT/J) plane for given J3/J when J1 = J2 = J for the coordination number q = 3. It was found that the system exhibits both first- and second-order phase transitions and tricritical points. The paramagnetic phases are also classified by studying the thermal variations of the quadrupolar moments.