Biquadratic Exchange Coupling Research Articles

Magnetization dynamics in layered systems with coexisting bilinear and biquadratic interlayer exchange coupling

Important aspects of exchange-coupled magnetic layered structures are related to the noncollinear arrangement of sublayer magnetizations which can arise from competition between bilinear (BL) and biquadratic (BQ) interlayer exchange coupling (IEC). In this work, the influence of coexisting BL and BQ IEC of different strengths on magnetization precession in layered systems is investigated both experimentally and theoretically. Laser-induced magnetization precession has been studied in the $\text{Fe/Si}({d}_{\text{Si}}$) multilayers (MLS) as a function of the amplitude ($H$) and orientation angle (${\ensuremath{\theta}}_{H}$) of external magnetic field using time-resolved magneto-optical Kerr (TRMOKE) effect. Strongly changing characters of precession frequency dependencies $\ensuremath{\omega}(H,{\ensuremath{\theta}}_{H})$ for Fe sublayer thickness ${d}_{\text{Fe}}=3$ nm and Si spacer-layer thicknesses (${d}_{\text{Si}}$) varying in the range of 0.9--2.4 nm have been observed. Analytical formulas for acoustic and optic mode dispersion relations with coexisting BL and BQ IEC, scaled by ${J}_{1}$ and ${J}_{2}$ parameters, respectively, for the in-plane effective magnetic anisotropy and arbitrary magnetic field direction were derived, and very good agreement with the experimentally observed frequency dependencies has been obtained. It is shown that BQ coexisting with BL IEC significantly influences on the magnitude and form of dispersion relations. From analytical formula derived, it follows that zero-field optical mode frequency tends to zero as $|{J}_{1}|$ approaches $2{J}_{2}$. The acoustic and optic mode-crossing effect has been observed and it is found that values of crossing fields and frequency gaps strongly increase as ${\ensuremath{\theta}}_{H}$ angles decrease and depend on relative BL and BQ IEC strengths. The BL IEC is of ferromagnetic type with ${J}_{1}\ensuremath{\approx}1.6$ mJ/${\mathrm{m}}^{2}$ for the MLS with ${d}_{\text{Si}}=0.9$ nm, and changes to antiferromagnetic one with ${J}_{1}\ensuremath{\approx}\ensuremath{-}0.9$ mJ/${\mathrm{m}}^{2}$ for the MLS with ${d}_{\text{Si}}=1.4$ nm, while the ${J}_{2}$ parameter of BQ IEC decreases from 1.8 to 1.0 mJ/${\mathrm{m}}^{2}$. The coupling strengths decrease by one to two orders of magnitude for the sample with ${d}_{\text{Si}}=2.4$ nm, but both mode frequencies are still observed and well reproduced by the theory. It is shown that ${J}_{1}$ and ${J}_{2}$ parameters obtained in the TRMOKE experiment coincide within the estimated error bars with the determined from independent measurements of magnetization processes in the static magneto-optical Kerr effect and interpreted with the use of analytical formulas derived. Numerical solutions of coupled Landau-Lifshitz-Gilbert (LLG) equations for acoustic and optic modes, with inclusion of BL IEC, intrinsic Gilbert damping, and spin-pumping damping terms, and extended to include BQ IEC, were performed and fitted to experimental data. It is shown that determined effective damping coefficients on $H$ and ${\ensuremath{\theta}}_{H}$ dependencies for acoustic and optic modes are very well simulated with the use of LLG equation solutions with Gilbert damping, spin-pumping-damping--related effective spin-mixing conductance, and spin-diffusion length parameters included. The dependencies of the parameters on ${d}_{\text{Si}}$ spacer-layer thickness are discussed and compared with available data for other systems.

Ultra-wide-band millimeter-wave generator using spin torque oscillator with strong interlayer exchange couplings

Recent increased development interest in millimeter-wave oscillator devices has necessitated realization of small oscillators with high frequency, wide frequency tunability, and room-temperature operation. Spin-torque oscillators (STOs) are fascinating candidates for such applications because of their nanometer size and suitability for room-temperature operation. However, their oscillation frequency and tunable range are limited to the order of 100 MHz–10 GHz. Here, we propose use of bilinear (J1) and biquadratic (J2) interlayer exchange couplings between ferromagnets in STOs to overcome these problems. The bilinear coupling contributes to oscillation frequency enhancement, whereas the biquadratic coupling facilitates frequency tunability via a current. Using micromagnetic simulation with parameters estimated from a material with small saturation magnetization, for J1 = 0 and J2 = − 1.0 mJ/m2, respectively, we find that the STO exhibits high frequency from 23 to 576 GHz and that its tunability reaches 61 GHz/(1011 A/m2) for current densities of − 0.5 to − 9.5 × 1011 A/m2. An analytical theory based on the macrospin model is also developed, which exhibits good quantitative agreement with the micromagnetic simulations. These results introduce new possibilities for spintronics applications in high-frequency devices such as next-generation mobile communications.

Thermally robust synthetic antiferromagnetic fixed layers containing FeCoB for use in STT-MRAM devices

In this work we measure the bilinear and biquadratic interlayer exchange coupling, J1 and J2, for several different synthetic antiferromagnetic structures containing FeCoB both before and after annealing at 350°C, with Ru spacer layers ranging in thicknesses from 0.4 to 1 nm. We show that when FeCoB is on top of the Ru spacer layer, in a Co/Ru/FeCoB trilayer structure, it is able to maintain antiferromagnetic coupling after annealing at 350°C, for Ru spacer layer thicknesses of 1 nm or less. This is in contrast to coupling in FeCoB/Ru/FeCoB trilayer structures that becomes strongly ferromagnetically coupled after annealing above 300°C. This difference is thought to be caused by boron diffusion into the spacer layer, which in turn enhances the diffusion of magnetic atoms into the spacer layer. We also show that coupling in a FeCoB/Co/Ru/FeCo/FeCoB structure remains AFC after annealing at 350°C, for Ru spacer layer thicknesses of 0.8 nm or less. This is thought to be caused by the Co and FeCo layers acting as diffusion barriers and reducing the diffusion of boron into the Ru spacer layer during the annealing process. We also show that, in a Co/Ru/Co trilayer structure, J1 can be increased in magnitude by replacing the top Co layer with FeCo, for spacer layer thicknesses of 0.5 nm or less. After these samples have been annealed at 350°C, the replacement of the top Co layer with FeCo was found to result in a two fold increase in the magnitude of J1, for Ru spacer layer thicknesses of 0.5 nm or less.

Coexistence of non-Fermi liquid behavior and biquadratic exchange coupling in La-substituted CeGe: Nonlinear susceptibility and DFT+DMFT study

Studies connected with the investigations of non-Fermi liquid (NFL) systems continue to attract interest in condensed matter physics community. Understanding the anomalous physical properties exhibited by such systems and its related electronic structures is one of the central research topics in this area. In this context, Ce-based and Ce-site diluted (with non-magnetic ions) compounds provide a fertile playground. Here, we present a detailed study of non-linear DC susceptibility and combined density functional theory plus dynamical mean field theory (DFT+DMFT) on Ce0.24La0.76Ge. Theoretical investigation of 4f partial density of states, local susceptibility and self-energy demonstrates the presence of NFL behavior which is associated with fluctuating local moments. Non-linear DC susceptibility studies on this compound reveal that the transition from NFL state to the new phase is due to development of the bi-quadratic exchange coupling and it obeys the non-linear susceptibility scaling. Under the application of magnetic fields, local moments interact spatially through conduction electrons resulting in magnetic fluctuations. Our studies point to the fact that the origin of the observed bi-quadratic exchange coupling is due to the spatial magnetic fluctuations.

Effects of interlayer and bi-quadratic exchange coupling on layered triangular lattice antiferromagnets

The magnetic field evolution of ground spin states of the stacked planar triangular antiferromagnet with antiferromagnetic interlayer interaction Jc is explored using a minimal 3D classical Heisenberg model. A bi-quadratic coupling is also used to mimic the effect of spin fluctuations (Zhitomirsky 2015 J. Phys.: Conf. Ser. 592 012110) which are known to stabilize the magnetization plateau. A single ion anisotropy is included and states with a magnetic field applied in the ab plane and along the c axis are determined. For -plane, an additional new state, in contrast to 2D model (Zhitomirsky 2015 J. Phys.: Conf. Ser. 592 012110), is obtained with weak interlayer interaction, while the magnetization plateau vanishes at large Jc and other new states with z components of spins emerge. For -axis, an extra state, compared with 2D model, is obtained with a weak interlayer interaction. When Jc is large enough, only the state corresponding to the Umbrella phase in 2D model exits.

Devlin-like approach to a spin-1 transverse XY model with biquadratic exchange and single-ion anisotropy

The effect of the biquadratic exchange interaction on the phase diagram of a d-dimensional spin-1 transverse XY model with easy-axis single-ion anisotropy is studied by employing the Devlin-like two-time Green functions framework. The chain of equations of motion is closed adopting the random phase approximation for the exchange higher order Green functions and treating exactly the crystal-field anisotropy terms. For short-range interactions and d > 2, analytical estimates and numerical calculations predict a reentrant behavior of the critical lines close to the magnetic-field-induced quantum critical point for appropriate values of the single-ion anisotropy parameter and suitable combinations of the bilinear and biquadratic exchange couplings. Remarkably, increasing the biquadratic exchange reduces or destroies the reentrant character of the quantum critical lines, in qualitative agreement with the findings of the Anderson-Callen-like strategy. In our formalism, the easy-plane anisotropy case can be studied similarly but the phase diagram and the quantum critical scenario do not present any reentrant phenomena.

Origin of biquadratic interlayer exchange coupling in Co2MnSi-based current-perpendicular-to-plane pseudo spin valves

We fabricated current-perpendicular-to-plane pseudo spin valves (CPP PSVs) having Co2MnαSi0.82 electrodes with various Mn compositions, α, and an Ag spacer and investigated the strength of biquadratic interlayer exchange coupling (90° coupling) in the CPP PSVs by comparing magnetoresistance characteristics and spin-transfer-torque induced magnetization switching characteristics. We experimentally found that (a) the strength of the 90° coupling increased as α increased, (b) it was weakened by insertion of an ultrathin CoFe layer between Co2MnSi (CMS) and the Ag spacer, resulting in the suppression of the 90° coupling at 290 K, and (c) it strongly depended on temperature. These results clarify that the Mn atoms diffused into an Ag spacer with paramagnetic character are the origin of the 90° coupling in CMS-based CPP PSVs.

Spin wave propagation spectra in Octonacci one-dimensional magnonic quasicrystals

In this paper, we study spin wave propagation in quasiperiodic magnonic superlattices that follow the so-called Octonacci quasiperiodic sequence, where the N-th stage can be obtained through the recurrence rule SN=SN-1SN-2SN-1, for N⩾3, and starting with S1=A and S2=B. The multilayered magnonic nanostructure is composed of two simple cubic ferromagnetic materials, labeled A and B, which interact through bilinear and biquadratic exchange couplings at their interfaces. The ferromagnetic materials are described by the Heisenberg model, and a transfer matrix treatment is employed, with the calculations performed for the exchange-dominated regime, taking the random phase approximation (RPA) into account. The obtained numerical results show the effects of both (i) the Octonacci quasiperiodic sequence and (ii) the biquadratic exchange coupling on the band structure and transmission spectra of spin waves. Comparisons are also performed with the spectra found in other periodic and quasiperiodic structures.

Antiferromagnetic coupling and impurity effects at junctions betweenFe3O4and Fe(001) layers

We investigated the strong antiferromagnetic (AF) interlayer exchange coupling (IEC) at junctions between Fe(001) and ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}(001)$ epitaxial films and the effects of an insertion layer of Mn or Co. In addition, we developed a nonlinear least-squares-fit technique to analyze the details of the magnetization processes and to distill the IEC constants. The analyses were performed by taking into account bilinear and biquadratic exchange couplings with a twisted magnetization state. The fitting results suggest the existence of significant distributions in bilinear and/or biquadratic IECs, which can originate from nonuniform stacking of atoms at the interface. The insertion of a Co layer with a thickness in the range of zero to two monolayers between the ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}(001)$ and the Fe(001) layers significantly affects the magnetic-hysteresis (M-H) processes, whereas the insertion of a Mn layer does not. A quantitative fitting analysis of M-H curves suggests that the inserted thin Mn layer does not affect the AF-IEC significantly, whereas the Co layer suppresses the AF coupling and in fact is preferable for achieving ferromagnetic coupling, which is consistent with the tendency predicted by our theoretical model regarding impurity effects for the IEC of $\mathrm{Fe}/{\mathrm{Fe}}_{3}{\mathrm{O}}_{4}(001)$.

The phase diagrams with influence of biquadratic exchange coupling on martensitic–austenitic transformations for core–surface nanoparticles

Recently, origin of the martensite–austenite transitions in core–surface type magnetic nanoparticles has been investigated theoretically and it has been indicated that repulsive biquadratic exchange coupling (K<0.0) causes the coexisting martensite and austenite phases. In the present paper, the phase diagrams of homogeneous and composite nanoparticles in the kBT/J0−D/J0 plane are studied for the presence and absence of attractive biquadratic exchange interaction in addition to repulsive biquadratic exchange interaction. Significant changes in the phase diagram points are discussed in the presence of martensitic and austenitic transformations. Four regions in the phase diagrams are found as second-order, martensitic–austenitic, TCid and first-order phase transition regimes.

Interlayer coupling inNi80Fe20/Ru/Ni80Fe20multilayer films: Ferromagnetic resonance experiments and theory

We present a systematic study of the static and dynamic magnetization behavior of interlayer-coupled ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$(200 \AA{})/Ru(${t}_{\mathrm{Ru}}$)/${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$(100 \AA{}) trilayers as a function of the Ru spacer layer thickness ${t}_{\mathrm{Ru}}$. As ${t}_{\mathrm{Ru}}$ was varied in the range from 0 to 15.8 \AA{}, we observe a strong antiferromagnetic (AFM) exchange coupling between the two ferromagnetic (FM) layers for ${t}_{\mathrm{Ru}}$ = 5 \AA{}, which becomes weak for ${t}_{\mathrm{Ru}}$ = 10 \AA{}. For ${t}_{\mathrm{Ru}}$ = 14.1 \AA{}, the coupled magnetic system changes from AFM to FM ordering. Using broadband ferromagnetic resonance spectroscopy, we have probed the effects of the different coupling mechanisms on both the acoustic and optic magnetic modes. We found that the biquadratic exchange coupling has a negligible effect compared to Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange coupling, while the uniaxial anisotropy at the ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$/Ru interfaces also plays an important role in determining the behaviors of the modes. A mode anticrossing phenomenon is observed when the RKKY exchange interaction term is above a critical value. A theoretical framework developed is in very good agreement with our experimental results.

A Monte Carlo study of the spin-1 Blume–Emery–Griffiths phase diagrams within biquadratic exchange anisotropy

The effect of the bi-quadratic exchange coupling anisotropy on the phase diagram of the spin-1 Blume–Emery–Griffiths model on simple-cubic lattice is investigated using mean field theory (MFT) and Monte Carlo simulation (MC). It is found that the anisotropy of the biquadratic coupling favors the stability of the ferromagnetic phase. By decreasing the parallel and/or perpendicular bi-quadratic coupling, the ferrimagnetic and the antiquadrupolar phases broaden in contrast, the ferromagnetic and the disordered phases become narrow. The behavior of magnetization and quadrupolar moment as a function of temperature is also computed, especially in the ferrimagnetic phase.

Spin-state crossover model for the magnetism of iron pnictides.

We propose a minimal model describing magnetic behavior of Fe-based superconductors. The key ingredient of the model is a dynamical mixing of quasidegenerate spin states of Fe(2+) ion by intersite electron hoppings, resulting in an effective local spin S(eff). The moments S(eff) tend to form singlet pairs and may condense into a spin nematic phase due to the emergent biquadratic exchange couplings. The long-range ordered part m of S(eff) varies widely, 0 ≤ m ≤ S(eff), but magnon spectra are universal and scale with S(eff), resolving the puzzle of large but fluctuating Fe moments. Unusual temperature dependences of a local moment and spin susceptibility are also explained.

Topology and Origin of Effective Spin Meron Pairs in Ferromagnetic Multilayer Elements

We report on pairs of converging-diverging spin vortices in Co/Rh/NiFe trilayer disks. The lateral magnetization distribution of these effective spin merons is directly imaged by means of element-selective x-ray microscopy. By this method, both the divergence and circulation states of the individual layers are identified to be antisymmetric. Reversal measurements on corresponding continuous films reveal that biquadratic interlayer exchange coupling is the cause for the effective meron pair formation. Moreover, their three-dimensional magnetization structure is determined by micromagnetic simulations. Interestingly, the magnetic induction aligns along a flux-closing torus. This toroidal topology enforces a symmetry break, which links the core polarities to the divergence configuration.

Doping-induced metallicity and coexistence of magnetic subsystems in [formula omitted

Electronic structure calculations are used to analyze the electronic and magnetic properties in K2Fe4+xSe5. Fe atoms can be divided into two distinct groups. The x=0 (parent) compound forms an insulating, collinear, local moment phase with high Néel temperature. We show that large biquadratic exchange coupling and exchange-elastic interactions stabilize the magnetic order. For x>0 the additional Fe atoms fill vacancy sites. They form impurity bands for small x, which broaden as x increases. They determine the states at the Fermi level and may be viewed as a magnetic subsystem separate from the host. Spin fluctuations are prevalent because magnetic interactions between the ‘defect’ and the ‘parent’ atoms are relatively weak, while chemical fluctuations are prevalent for low x. Fluctuations of either type lead to the formation of a weakly metallic state. The unusual coexistence of the two magnetic subsystems offers a new perspective as to how superconductivity and strong antiferromagnetism can coexist. We argue that spin fluctuations of the impurity subsystem share common features with the Fe-pnictide superconductors.

Specular and off-specular polarized neutron reflectometry of canted magnetic domains in loose spin coupled CuMn/Co multilayers

Specular and off-specular polarized neutron reflectometry of strong biquadratic coupling in a Cu${}_{0.94}$Mn${}_{0.06}$/Co multilayer is presented. Detailed analysis of the reflectivity via the distorted-wave Born approximation reveals a formation of on average $\ensuremath{\langle}\ifmmode\pm\else\textpm\fi{}$30${}^{\ensuremath{\circ}}\ensuremath{\rangle}$ canted lateral magnetic domains. Domains with mean width of 0.43 $\ensuremath{\mu}$m extend throughout the multilayer structure and magnetization alternates in the sign of the canting with subsequent layers. Temperature and field dependence of the magnetic structure are evaluated and included in the magnetic model, which is used to deduce bilinear and biquadratic interlayer exchange coupling energies.

Bi-quadratic interlayer exchange coupling in Co2MnSi/Ag/Co2MnSi pseudo spin-valve

Bi-quadratic interlayer exchange coupling is found below 100 K in a Co2MnSi/Ag/Co2MnSi current-perpendicular-to-plane pseudo spin valves. The bi-quadratic coupling constant J2 was estimated to be ∼−0.30 erg/cm2 at 5 K and the strong temperature dependence of the coupling strength points its likely origin to the “loose spin” model. Application of current of ∼2 × 107 A/cm2 below 100 K leads to an increase in the magnetoresistance (MR), indicating current induced antiparallel alignment of the two magnetic layers. These results strongly suggest that the presence of the bi-quadratic interlayer exchange coupling causes the reduction of the magnetoresistance at low temperature and illustrates the importance of understanding the influence of interlayer exchange coupling on magnetization configuration in magnetic nanostructures.

Manifold domain structure of double films with perpendicular magnetic anisotropy

We present epitaxial structures made of twin nickel blocks with perpendicular magnetic anisotropy separated by a copper layer which, for some values of this interleaving layer, show domain structures with four levels of contrast in magnetic force microscopy images. This manifold domain structure implies that the magnetization in the Ni blocks, in addition to the parallel orientation, undergoes a non-collinear configuration with respect to each other. To explain this result we consider a magnetoelastic domain structure with M in the plane that can elude the clamping done by the substrate with an average strain of −42 × 10−6 (≈70% of the bulk value). Thus, the out-of-plane anisotropy is balanced and a biquadratic exchange coupling can stabilize the non-collinear domain configurations between the Ni blocks.

Exchange Coupling in Synthetic Antiferromagnetic Multilayers for Magnetic Write Head

Fine tuning of exchange coupling constants was demonstrated in synthetic antiferromagnetic multilayers consisting of three ferromagnetic layers and two spacer layers. The effects of interfacial roughness on both the bilinear and biquadratic exchange coupling constants were studied. A model was developed to simulate the behavior of such synthetic antiferromagnetic multilayer system. Detailed exchange coupling constants, both bilinear and biquadratic, were extracted from experimental data by using the model and compared for different samples.

The structure dependence of exchange bias in ferromagnetic / antiferromagnetic bilayers

The structure dependence of exchange bias in ferromagnetic/antiferromagnetic (FM/AF) bilayers has been investigated in detail by extending Slonczewski's 'proximity magnetism' idea. Here three important parameters are discussed for FM/AF bilayers, i.e. interfacial bilinear exchange coupling J1, interfacial biquadratic (spin-flop) exchange coupling J2 and antiferromagnetic layer thickness tAF. The results show that both the occurrence and the variety of the exchange bias strongly depend on the above parameters. More importantly, the small spin-flop exchange coupling may result in an exchange bias without the interfacial bilinear exchange coupling. However, in general, the spin-flop exchange coupling cannot result in the exchange bias. The corresponding critical parameters in which the exchange bias will occur or approach saturation are also presented.