Interlayer Exchange 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.

Influence of Nanosize Effect and Non-Magnetic Dilution on Interlayer Exchange Coupling in Fe–Cr/Cr Nanostructures

Magnetic properties of multilayered [Fe–Cr/Cr]×8 nanostructures with the interlayer exchange coupling of the antiferromagnetic type and without the interlayer coupling have been studied. The values of the saturation magnetization and the interlayer exchange coupling constant are shown to strongly depend on the thickness and non-magnetic dilution of the Fe–Cr layers. It is found that those parameters differently affect the interlayer exchange coupling, which is explained by an interplay between the size effect (the thickness of the Fe–Cr layers) and the magnetic polarization of the Fe–Cr/Cr interfaces depending on the Fe concentration.

Readable High-Speed Racetrack Memory Based on an Antiferromagnetically Coupled Soft/Hard Magnetic Bilayer.

The current-induced domain wall (DW) motion in a racetrack memory with a synthetic antiferromagnets (SAFs) structure has attracted attention because of the ultrahigh velocity of the DW. However, since there is little stray field due to the zero net magnetization in a pair of antiferromagnetically (AFM) coupled domains, how to read the information stored in the pair of domains is still challenging. In the present work, we propose a readable SAF racetrack memory composed of two ferromagnetic (FM) layers with distinct uniaxial-anisotropy constants. As a result, a region of staggered domains formed between two neighboring DWs in the two layers. In this region, there is a parallel alignment of the moments in the two FM layers. This parallel magnetization is readable and can be exploited to label the structure of the nearby AFM-coupled domains for the racetrack with DWs moving in a fixed direction. This function can be realized by connecting a Schmitt Trigger to a sensor for reading. The stability and the length of the staggered region can be well-tuned by changing the magnetic parameters, such as the interlayer exchange coupling constants, the Dzyaloshinskii–Moriya interaction (DMI) constants, and the uniaxial-anisotropy constants of the two FM layers, in a range that is experimentally achievable.

Time domain magnetization dynamics study to estimate interlayer exchange coupling constant in Nd-Fe-B/Ni80Fe20 films

Interlayer exchange coupling (Jex) between a hard magnetic Nd-Fe-B layer and a soft magnetic Ni80Fe20 layer is studied by means of time-resolved magneto-optical Kerr effect (TRMOKE) microscope. Whereas a single 16 nm thick Nd-Fe-B layer without Ni80Fe20 showed high coercivity of μ0Hc = 2 T and resonance frequency of fr = 161 GHz at external bias magnetic field of μ0Hb = 2 T due to the high anisotropy field, those of the bi-layer Nd-Fe-B (16 nm)/Ni80Fe20 (5 nm) are dramatically reduced to μ0Hc = 1.34 T and fr = 74.4 GHz. When the Nd-Fe-B and Ni80Fe20 are separated by a 1 nm thick non-magnetic Mo layer, by contrast, the coercivity recovered partially to μ0Hc = 1.9 T but the frequency further reduced to fr = 63.4 GHz. We derived Jex based on a simple macrospin model, whose value reduced from 3.9 ± 0.1 mJ/m2 for the bi-layer without the Mo layer to 0.1 ± 0.1 mJ/m2 with the Mo layer. The reduction in Jex suggested that the interlayer exchange decoupling between the Nd-Fe-B and the Ni80Fe20 layers was responsible to the recovery of μ0Hc and the reduction of fr by the insertion of the non-magnetic layer. We successfully estimated the interlayer exchange coupling constant in the hard/soft magnetic bilayer system by TRMOKE and macrospin-modeling, which had been previously difficult because of its high anisotropy and high coercivity. This method is applicable also to the quantitative estimation of the intergranular exchange coupling.

Investigation of Magnetic Properties of Multilayer Thin Films with Spin-Wave Resonance

A theory has been developed to simulate spin-wave resonance (SWR) modes in the multilayer systems consisting of alternate magnetic and nonmagnetic layers. An equation of motion of magnetization with Gilbert-type damping parameter for simulating SWR modes was used. It has been realized that the theory developed for the magnetic multilayer films is suitable to study the spin dynamics and extract various magnetic parameters. It has been shown that SWR modes strongly depend on an effective magnetic anisotropy constant (K eff), interlayer exchange coupling constant (A 12) and effective magnetization (M eff). The nature of the effective magnetic anisotropy and interlayer exchange coupling constants has been investigated by using the developed SWR theory in detail. The separation between optic and acoustic modes strongly depends on the magnitude of the interlayer exchange coupling constant, whereas the relative position of the acoustic and optic modes depends on the sign of $A_{12}$ . With increasing the interlayer exchange coupling constant, the resonance field of the optic mode decreases (increases) for ferromagnetic (antiferromagnetic) coupling. When the effective magnetic anisotropy constant increases, the resonance field of the acoustic and optic modes increases for both the ferromagnetic and antiferromagnetic couplings. The increasing of the effective magnetization results in decreasing of the resonance field of SWR mode at parallel geometry, whereas that of SWR mode increases at the perpendicular geometry. The results are compatible to the other theories and experimental results.

Interface Dzyaloshinskii-Moriya interaction in the interlayer antiferromagnetic-exchange coupled Pt/CoFeB/Ru/CoFeB systems

Interfacial Dzyaloshinskii-Moriya interaction (iDMI) in interlayer exchange coupled (IEC) Pt/Co$_{20}$Fe$_{60}$B$_{20}$(1.12 nm)/Ru/Co$_{20}$Fe$_{60}$B$_{20}$(1.12 nm) systems have been studied theoretically and experimentally. Vibrating sample magnetometer has been used to measure their magnetization at saturation and their interlayer exchange coupling constants. These latter are found to be of an antiferromagnetic nature for the investigated Ru range thickness (0.5-1 nm). Their dynamic magnetic properties were studied using Brillouin light scattering (BLS) technique. The BLS measurements reveal pronounced non-reciprocal spin waves propagation. In contrast to the calculations for symmetrical IEC CoFeB layers, this experimental nonreciprocity is Ru thickness and thus coupling strength dependent. Therefore, to explain the experimental behaviour, a theoretical model based on the perpendicular interface anisotropy difference between the bottom and top CoFeB layers has been developed. We show that the Ru thickness dependence of the spin wave non-reciprocity is well reproduced by considering a constant iDMI and different perpendicular interfacial anisotropy fields between the top and bottom CoFeB layers. This anisotropy difference has been confirmed by the investigation of the CoFeB thickness dependence of effective magnetization of Pt/CoFeB/Ru and Ru/CoFeB/MgO individual layers, where a linear behaviour has been observed.

Interlayer exchange coupling, dipolar coupling and magnetoresistance in Fe/MgO/Fe trilayers with a subnanometer MgO barrier

Fe/MgO/Fe trilayers with a subnanometer MgO tunnel barrier were grown by molecular beam epitaxy. Longitudinal magnetooptic Kerr effect measurements confirmed the existence of the antiferromagnetic interlayer exchange coupling (IEC) between the Fe layers for 2Å<dMgO<6Å. The coupling was enhanced for the trilayer grown on a homoepitaxial MgO buffer layer, and its IEC constant was estimated to be −3.3erg/cm2 at a MgO thickness of 2.7Å. After magnetic characterization, the sample was patterned into circular-shaped pillars with diameters ranging from 200nm to 520nm. We showed that the dipolar coupling that appeared after the nanofabrication process modified the effective coupling between layers, and we determined dependence of the dipolar coupling on the pillar diameter. Finally, magnetoresistance (MR) was measured as a function of MgO thickness (dMgO), and a non-zero MR was found for the MgO as thin as 3.4Å. Extrapolation of the MR (dMgO) dependence to MR=0 allowed us to determine the length of the pinholes in our sample, which was estimated to be (3.2±0.5)Å.

Standing Spin Waves in Ultrathin Magnetic Films: A Method to Test for Layer-Dependent Exchange Coupling

We introduce a method to test theoretical models for the layer dependence of exchange coupling constants in ultrathin magnetic films. The method is based on the observation of high-energy and high-momentum standing spin wave modes using high-resolution electron energy loss spectroscopy. Experimental data are presented for 5-8 layers of fcc cobalt deposited on Cu(100). The power of the method is illustrated by comparison to two theoretical studies predicting rather different results concerning the ratio of the interlayer and intralayer exchange coupling constants near the surface. Only the theory with a large interlayer coupling shows sufficient energy spreading in the layer dependence of the dispersion curves to match the experimental data. We furthermore discuss the reason for the surprising success of the simple nearest-neighbor Heisenberg model with a single exchange constant matched to experiment.

Effect of layer thickness ratio on magnetization reversal process in stacked media with high coercivity

Effect of thickness ratio and interlayer exchange coupling on time-evolutional magnetization reversal process in stacked media with high coercivity was investigated by utilizing micromagnetic simulation. Regardless of the layer thickness ratio, for each stacked medium the magnetization reversal process is divided into three regions, namely the spin-flop rotation, the incoherent rotation and the coherent rotation along with increase of the interlayer exchange coupling constant A interlayer . In order to get the incoherent rotation region which is suitable for the recording media, it is required that the A interlayer is between about 1.3×10 -7 and 2.2×10 -7 erg/cm for the media with the layer thickness ratio of 1 : 3 and 3 : 1, and that one is between about 1.8×10 -7 and 2.5×10 -7 erg/cm for the media with the ratio near 1 : 1.

Ferromagnetic resonance studies of exchange coupled ultrathin Py/Cr/Py trilayers

Magnetic properties of ultrathin Py/Cr/Py trilayers have been investigated as a function of Cr spacer layer thickness by using ferromagnetic resonance (FMR) and vibrating sample magnetometer (VSM) techniques. The Cr spacer layer thickness was increased from 4 to 40 Å with 1 Å steps to determine the dependence of interlayer exchange coupling between ferromagnetic layers on the spacer layer thickness. Two strong and well resolved peaks were observed which correspond to a strong (acoustic) and weak (optic) modes of magnetization precession in the effective dc field due to the exciting external microwave field as the external dc field orientation comes close to the film normal. The separation of the two modes in the field axis depends on the thickness of Cr spacer layer. An interchange in the relative positions of the acoustic and optic modes has been observed for a particular thickness of Cr spacer layer as well. A computer program for magnetically exchange coupled N magnetic layers was written to simulate the experimental FMR spectra and to obtain the magnetic parameters of ultrathin Py/Cr/Py trilayers. FMR data have been analyzed from every aspect by using this program and interlayer exchange coupling constant was calculated for the prepared structures. It was found that the relative position of the peaks depends on the nature (sign) of the interlayer exchange coupling between ferromagnetic layers through Cr spacer layer. In Py/Cr/Py trilayers, strength of the interlayer exchange coupling constant oscillates and changes its sign with Cr spacer layer thickness with a period of about 11 Å.

Magnetic structure and interlayer exchange coupling in spring magnets—studied via nuclear resonant scattering

Magnetic properties of FePt/Ag/Fe and FePt/Pd/Fe layer systems, prepared by magnetron sputtering, were investigated using the nuclear resonant forward scattering of synchrotron radiation. This technique allows the accurate determination of magnetic hyperfine field orientations by using an extremely thin 57Fe probe layer suitably embedded within the soft magnetic layer. From an evaluation of these measurements within a one-dimensional micromagnetic model, the interlayer exchange coupling constants between the magnetically hard (FePt) and soft (Fe) layers were determined as function of the Ag and Pd interlayer thickness. The interlayer thickness dependence of the bilinear coupling constants provides evidence for the superposition of Ruderman–Kittel–Kasuya–Yoshida coupling and a magnetostatic interaction between the magnetic layers.

Interlayer exchange coupling in perovskite-type magnetic trilayers

The interlayer exchange coupling constant of ferromagnetic trilayers made of perovskite oxides has been calculated by using a tight-binding model for ${e}_{g}$ orbitals of Mn and Ni ions in $\mathrm{La}\mathrm{Ba}\mathrm{Mn}{\mathrm{O}}_{3}∕\mathrm{La}\mathrm{Ni}{\mathrm{O}}_{3}∕\mathrm{La}\mathrm{Ba}\mathrm{Mn}{\mathrm{O}}_{3}$. We show that the extended ${e}_{g}$ band model, which includes the second nearest neighbor hoppings, reproduces experimental results well for suitable settings of the Fermi level. However, both oscillation period and intensity are shown to be sensitive to the position of the Fermi level. The results may be examined experimentally by replacing La with Sr or Ca to alter the electron number in $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_{3}$.

Analysis of thermal stability enhancement in double layer antiferromagnetically coupled media

In this article, we present a combined analytical analysis along with micromagnetic simulations on the thermal stability of double layer longitudinal media with antiferromagnetic exchange coupling (AFC). The thermal stability enhancement in double layer AFC media is characterized quantitatively and comparisons with the performance of conventional single layer longitudinal media are made. It has been found that the thermal stability enhancement of the AFC media over a single layer media with the same medium coercivity can be achieved by optimizing the interlayer exchange coupling. The effective grain volume gain is found to be approximately V1+0.4V2, where V1 and V2 are the grain volumes of the top and bottom layers, respectively. Increasing V2 requires a larger interlayer exchange coupling constant.

4f–3d exchange coupling in Gd/X/Co (X=Pt, Cr) multilayers

We have studied the interlayer exchange coupling between Gd and Co through Pt and Cr spacers in a series of multilayers. Magnetization curves have been analyzed with a model, taking into account bilinear and biquadratic interlayer exchange couplings between Gd and Co. The interlayer exchange coupling constants have been determined as a function of the Pt or Cr spacer layer thickness.

Recording characteristics and thermal stability of AFC thin film media

We present a micromagnetic and analytical analysis of double layer media with antiferromagnetic exchange coupling. It has been found that in order to achieve good recording performance, strong interlayer exchange coupling and large thickness ratio are desired. When the thickness of the bottom layer is small, thermal activation assists the bottom layer to switch, which requires a smaller interlayer exchange coupling constant. Thermal stability of double layer AFC media has also been investigated in comparison to single layer media in the case of strong and weak interlayer exchange coupling.

Spin-wave resonance in ferromagnetic coupled Co/Cu multilayers

FMR experiments have been performed on [Co(50 Å)/Cu(4 Å)] 20 multilayers at room temperature by using an X-band ESR spectrometer and a series of spin-wave modes have been observed when an external field was perpendicular to the film plane. We have analyzed these spin-wave modes by spin-wave resonance theory of multilayers and obtained the interlayer exchange coupling constant.

Oscillatory interlayer exchange coupling of Co/Ru and permalloy / Ru multilayers investigated by Brillouin light scattering

We have determined the absolute value of the interlayer exchange coupling constant A 12 of sputtered Co/Ru and permalloy/Ru multilayers using Brillouin light scattering. The spin wave frequencies and therefore A 12 are found to oscillate as a function of the Ru layer thickness in both multilayer systems with a period of 11.5å. The amplitudes of the oscillations in A 12 are found to be smaller by a factor of 2 in permalloy/Ru compared to Co/Ru, which scales with the smaller saturation magnetization in permalloy. Contrary to the Co/Ru system we found evidence for a short period oscillation in permalloy/Ru. Detailed calculations show that the spin-wave frequency oscillations result from the canting of layer magnetizations in the antiferromagnetic coupling regimes.

Exchange coupling of ferromagnetic layers across nonmagnetic interlayers

In order to obtain the interlayer exchange coupling constant A 12 asa function of the interlayer thickness d 0 in magnetic sandwich structures we have measured the frequencies of the low lying spin wave modes by means of Brillouin light scattering. A computer fit is then applied which yields values for A 12. This way we have determined A 12 as a function of d 0 for Fe/Cu, Fe/Ag, Fe/Au, Fe/V, Co/Pt, Co/Cu and Co/Y. Generally A 12 decreases exponentially with increasing d 0. In some cases we find an interesting dependence on the growth conditions, like e.g. crystallinity. Interlayers with good epitaxial growth decouple faster than polycrystalline ones. We report also on an experimental method which we have developed to facilitate these experiments: for the investigation of A 12 as a function of d 0 we use sandwich structures with wedge formed interlayers. A whole range of d 0 can then be studied on one sample.

Spin wave resonance study of exchange-coupled Ni 80Fe 20 double layers separated by thin interlayers of Cu, Cr and Pd

We have performed ferromagnetic resonance measurements on thin polycrystalline Ni 80Fe 20 (permalloy) double layers with interlayers of Cu, Cr and Pd. Furthermore, a mathematical model is presented, which allows a calculation of resonance fields in the parallel configuration. Comparison of the calculated and measured resonance field values yields an interlayer exchange coupling constant A 12 as a function of interlayer thickness d. We observe exponential dependencies of A 12 on d for Cr, Cu and Pd interlayers with the strongest decay for Cr. Additionally, we present FMR measurements and calculations for a Ni 80Fe 20/Cr/Co heterostructure layer system.

Theoretical analysis of double-halide superexchange in layered solids of the compounds[NH3(CH2)nNH3]CuBr4withn=3 and 4

Recently, interlayer exchange-coupling constants in solids of compounds $[\mathrm{N}{\mathrm{H}}_{3}{(\mathrm{C}{\mathrm{H}}_{2})}_{n}\mathrm{N}{\mathrm{H}}_{3}]\mathrm{Cu}{\mathrm{Br}}_{4}$, with $n=3 \mathrm{and} 4$, have been measured by Drumheller et al. Following our earlier theoretical analysis of such compounds with Cl instead of Br for $n=2\ensuremath{-}5$, and one ClBr mixed compound for $n=2$, we apply a four-center, six-electron model to calculate these coupling parameters, assuming a double-halide Cu\char22{}Br\char22{}Br\char22{}Cu superexchange unit. Excellent agreement with the experimental values is obtained. Nonlinearity of the superexchange bridge for $n=4$ is found to be essential to obtain the correct value for the coupling parameter. We perform similar calculations on a layered structure with a Co\char22{}double-oxygen\char22{}Co bridge.