Effective Magnetoelastic Coupling Research Articles

Magnetoelastic coupling for Fe–Ga thin films epitaxially grown on different substrates

This paper reports the systematic study on the structure, magnetic properties and magnetoelastic properties for the Fe100−x Ga x (001) thin films epitaxially grown on the different substrates of GaAs(001) and MgO(001) using the sputtering technique. The alloy composition dependence of effective magnetoelastic coupling coefficient B eff along the FeGa [110] direction indicated that the largest magnetoelastic coupling was obtained for the Fe–Ga layer with x = 30 grown on the MgO substrate, which was evaluated to be B eff = − 9.4 × 107 erg cm−3. Considering the results of structural analysis and magnetization measurement, the different crystallite sizes depending on the kind of substrate may give rise to the different magnetoelastic coupling strengths between the Fe–Ga layers on the MgO and the GaAs. The magnetostriction along the Fe–Ga [111] direction λ 111 was also estimated with the assumption of plausible elastic property of Fe–Ga, and showed the values comparable to the reported value of bulk Fe–Ga. This means the large magnetostriction can be obtained even for the Fe–Ga thin films epitaxially grown not only on the GaAs(001) but also on the MgO(001). The findings in this work will give a guideline for designing spintronic applications with a Fe–Ga layer exhibiting a large magnetoelastic coupling.

Magnon-polaron formation in XXZ quantum Heisenberg chains

We study the formation of magnon-polaron excitations and the consequences of different time scales between the magnon and lattice dynamics. The spin-spin interactions along the 1D lattice are ruled by a Heisenberg Hamiltonian in the anisotropic form XXZ, in which each spin exhibits a vibrational degree of freedom around its equilibrium position. By considering a magnetoelastic coupling as a linear function of the relative displacement between nearest-neighbor spins, results provide an original framework for achieving a hybridized state of magnon-polaron. Such state is characterized by high cooperation between the underlying excitations, where the traveling or stationary formation of magnon-polaron depends on the effective magnetoelastic coupling. A systematic investigation reveals the critical amount of the magnon-lattice interaction ($\chi_c$) necessary to emergence of the stationary magnon-polaron quasi-particle. Different characteristic time scales of the magnon and the vibrational dynamics unveiled the threshold between the two regimes, as well as a limiting value of critical magnetoelastic interaction, above which the magnon velocity no longer interferes at the critical magnetoelastic coupling capable of inducing the stationary regime.

Ferromagnetic Resonance and Elastic Vibrations in Epitaxial Yttrium Iron Garnet Films

The ferromagnetic resonance (FMR) spectra of epitaxial yttrium iron garnet films are experimentally studied. The field dependences of the FR frequency are used to determine the effective fields induced by the first and second anisotropy constants and the effective uniaxial anisotropy field. The FMR frequency and linewidth are found to increase in the fields lower than 8 Oe applied in the bismuth-containing film plane. This increase is related to the formation of a nonuniform magnetization distribution, which is supported by a direct magnetooptical observation. The FMR spectra are found to be modulated by a set of narrow lines, the amplitude of which is proportional to the FMR signal intensity. The frequency position of the lines is independent of the magnitude and direction of a dc magnetic field. This modulation is shown to be associated with the resonance excitation of transverse elastic vibration modes. The effective magnetoelastic coupling parameter and the linewidth of the elastic vibrations excited by resonance pumping are estimated.

Extended x-ray absorption fine structure spectroscopy of stretched magnetic films on flexible substrate

This study investigates element-specific atomic distances and strains in ferromagnetic (FM) nano-thin films deposited on a flexible substrate, which can be modulated by stretching the substrate. Extended x-ray absorption fine structure (EXAFS) spectroscopy was used for the experiments. Both in-plane tensile and out-of-plane compressive strains were investigated by applying %-order tensile strains to the substrate. The atomic distance changes induced by stretching the substrate were quantitatively discussed by considering the Poisson compression, crystalline orientations of the FM metals, and polarization in the EXAFS measurement. Consequently, the ratio of strain transfer from the flexible substrate to the FM layers was estimated to be about 30% and 60% in Co and Fe nano-thin films, respectively. The strain transfer in Co films with different Co or Pt underlayer thicknesses was also measured. The results are compared with the thickness dependence of the effective magnetoelastic coupling constant, which represents the magnitude of the inverse magnetostriction effect. Although the strain transfer partially contributes to the thickness dependence, the difference in the Co lattice constant is suggested to have a significant influence on the effective magnetoelastic coupling constant.

Stress-induced large anisotropy field modulation in Ni films deposited on a flexible substrate

A tensile strain on the order of a few percent was created in Ni thin films deposited on a flexible polyethylene naphthalate substrate, and the strain-induced change in the magnetic anisotropy was investigated. The magnetic easy axis was reversibly switched by 90° by the application of the stress. The easy axis was orthogonal to the applied stress. The in-plane saturation magnetic field or the uniaxial magnetic anisotropy energy changed linearly in reaction to the applied tensile strain up to a strain of 2.3%. Moreover, a large difference in the saturation magnetic field up to ∼0.3 T, which corresponds to a change in the magnetic anisotropy energy of ∼7 × 104 J/m3, was realized. The effective magnetoelastic coupling constant was almost independent of the thickness of Ni.

Nonlinear magnetoelastic coupling of epitaxial layers of Fe, Co, and Ni on Ir(100)

The effective magnetoelastic coefficients ${B}_{i}^{\text{eff}}$ are measured for epitaxial layers of Fe, Co, and Ni on Ir(100). Mechanical stress during film growth and stress during magnetization processes are measured directly by the optical cantilever curvature technique. Our results indicate that the effective magnetoelastic coupling coefficients ${B}_{1}^{\text{eff}}$ and ${B}_{2}^{\text{eff}}$ of Fe, Ni, and Co deviate from the respective bulk values, and we propose that strain may play an important role for this nonbulklike magnetoelastic behavior. The impact of the magnetoelastic coupling on the magnetic anisotropy is explored by magneto-optic Kerr effect measurements. The measurements reveal that the easy magnetization axis is in plane for Fe and Co layers on Ir(100). It changes from out of plane to in plane for Ni at about 15 monolayer with increasing film thickness. This spin reorientation transition can be well described by the measured magnetoelastic coupling coefficients. The result of nonbulklike magnetoelastic coupling is discussed in view of recent theoretical work on the calculation of magnetoelastic coupling in strained systems.

Dispersion of the sound velocity in iron borate under nuclear magnetoacoustic resonance

The frequency dependence of the velocity of coupled magnetoelastic waves in the weak ferromagnet FeBO3 is investigated experimentally and theoretically. An anomalous frequency dependence of the transverse sound velocity is observed for a single-domain sample under conditions of nuclear magnetoacoustic resonance, when the frequency of sound excited in the sample is close to the NMR frequency of Fe57 nuclei. It is shown that the observed dependence is associated with a considerable effect of nonequilibrium states of the nuclear spin system on the renormalization of elastic constants due to effective magnetoelastic coupling.

Relativistic spin-polarized theory of magnetoelastic coupling and magnetic anisotropy strain dependence: Application to Co/Cu(001)

A self-consistent relativistic spin-polarized version of the total-energy full-potential linearized-augmented-plane-wave (FLAPW) method is developed on the basis of a second-variation treatment of the spin-orbit coupling (SOC). As illustration, the method is applied to determine the magnetoelastic coupling, orbital magnetic moment anisotropy and magnetic anisotropy energy (MAE) of a Co overlayer on Cu(001). The MAE (-0.36 meV) calculated at the equilibrium overlayer/substrate distance is in good agreement with experiment. As discovered earlier by Wu and Freeman, we find a linear dependence of the MAE on the overlayer/substrate distance. The calculated positive effective magnetoelastic coupling coefficient (1.13 meV) is caused by a positive surface magnetoelastic anisotropy (0.23 meV). This causes a negative magnetostriction coefficient ${\ensuremath{\lambda}}_{001}=\ensuremath{-}5.20\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and an isotropic magnetostriction coefficient ${\ensuremath{\lambda}}_{s}=\ensuremath{-}5.65\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ that is in very good agreement with previous studies based on a perturbative SOC treatment.

Microstructure and magnetoelastic coupling coefficients in thin NiFe and Ni films

The effective magnetoelastic (ME) coupling coefficients Beff of polycrystalline Ni79Fe21 and Ni films have been reported as functions of thickness t. Beff was observed to have a thickness-independent bulk term, Bb, and a thickness-dependent surface term, Bs/t consistent with the Néel model. For thickness below 50 Å the surface term is important; it can change the sign of the effective ME coupling constant and dramatically increase its magnitude. We expect that the surface ME coupling we observe in polycrystalline thin films may be a combination of the intrinsic Néel surface effect and extrinsic microstructure effects. Our transmission electron microscopy, Auger depth profiling, and atomic force microscopy rule out film discontinuity and compositional gradients as significant sources of the surface ME effect.

Evidence for strong surface magnetoelastic anisotropy in epitaxial Cu/Ni/Cu(001) sandwiches.

Measurements of effective magnetic anisotropy energy of epitaxial Cu/Ni/Cu(001) sandwiches are analyzed as a function of Ni film thickness $h$. The magnetization easy axis is perpendicular to the films for $20<h<140$ \AA{}. The magnetic anisotropy is best described by inclusion in the effective anisotropy energy of the strain-dependent magnetic surface anisotropy term, predicted by the strain-dependent N\'eel model, along with the usual magnetostatic, magnetocrystalline, and bulk magnetoelastic energies. The surface magnetocrystalline and surface magnetoelastic anisotropy energies of the Ni/Cu(001) interface are determined to be +0.9 erg/${\mathrm{cm}}^{2}$ and -52 erg/${\mathrm{cm}}^{2}$, respectively. The effective magnetoelastic coupling coefficient (bulk plus surface) of Cu/Ni/Cu(001) is predicted to change sign at $h=80$ \AA{}. The two observed magnetization easy-axis reversals are also well described by this model.

Perpendicular magnetic anisotropy, domains, and misfit strain in epitaxial Ni/Cu1-xNix/Cu/Si (001) thin films.

We have investigated the magnetic anisotropy in epitaxial Ni/${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ni}}_{\mathit{x}}$/Cu/Si (001) thin films (0x50%) as a function of Ni thickness h and alloy substrate composition. Also the average in-plane biaxial strain ${\mathit{e}}_{0}$(h) in Ni/Cu (001) (x=0) was measured ex situ versus Ni thickness using optical interferometry. We observed that the preferred direction of magnetization is perpendicular to the films over an exceptionally broad Ni thickness range for films kept under UHV: 10 \AA{}h60 \AA{} in Ni/Cu (001); 20 \AA{}h40 \AA{} in Ni/${\mathrm{Cu}}_{60}$${\mathrm{Ni}}_{40}$/Cu (001). We have also studied the perpendicular magnetic anisotropy by magnetic force microscopy and observed a complex domain pattern characterized by two length scales and very strong contrast. We have analyzed our results using a phenomenological model that includes the bulk magnetoelastic anisotropy energy (${\mathit{B}}^{\mathit{b}}$${\mathit{e}}_{0}$) and both the surface magnetocrystalline (${\mathit{K}}^{\mathit{s}}$/h) and the surface magnetoelastic (${\mathit{B}}^{\mathit{s}}$${\mathit{e}}_{0}$/h) anisotropy energies. Our analysis yields the magnetic surface energies ${\mathit{K}}^{\mathit{s}}$ and ${\mathit{B}}^{\mathit{s}}$ of the vacuum/Ni (001) and Ni/Cu (001) interfaces. The origin of the strong perpendicular magnetic anisotropy lies in the surface energy ${\mathit{K}}^{\mathit{s}}$ corresponding to the Ni/Cu (001) interface and the bulk magnetoelastic anisotropy energy. The surface magnetoelastic anisotropy energy ${\mathit{B}}^{\mathit{s}}$${\mathit{e}}_{0}$ favors an in-plane magnetization. The effective magnetoelastic coupling coefficient depends strongly on h for h\ensuremath{\le}150 \AA{} and changes sign near h\ensuremath{\approxeq}28 \AA{}. The two observed in-plane to out-of-plane magnetization easy-axis transition thicknesses are predicted by our pheomenological model. The lower magnetization easy-axis transition is not due to the onset of misfit dislocations at the Ni/Cu interface.

Giant surface magnetostriction in polycrystalline Ni and NiFe films

We have measured the effective magnetoelastic coupling coefficients, Beff, of polycrystalline NiFe/Ag/Si, NiFe/Cu/Si, and Ni/SiO2/Si films in situ as functions of magnetic layer thickness over the range from 1.5 to 50 nm using magneto-optic Kerr effect and applied static strain. The Beff’s agree well with bulk values at large thicknesses but take on anomalously large values for thicknesses below about 5 nm. The data are well fit by a Néel model, Beff=Bbulk+Bsurf/(t−t0), where t0 may be related to intermixing at the interface with the substrate (verified by Auger depth profiling). These data suggest that the surface conditions are of enhanced importance in controlling magnetic properties, particularly anisotropy, permeability, and noise, even in films whose compositions are nominally of zero magnetostriction.

Parallel Pumping of Europium and Yttrium Iron Garnets at Low Temperatures

The spin-wave dispersion and relaxation properties as well as magnetoelastic and elastic properties of europium iron garnet (EuIG) and yttrium iron garnet (YIG) are measured at low temperatures and at about 17 Gc/sec using the parallel-pump technique. ${\mathrm{Eu}}^{3+}$ ions have unusual magnetic and relaxation characteristics in large exchange fields, and the effect of these ions on the spin-wave spectrum of the iron lattice is of interest. Also, the large effective magnetoelastic coupling constant of EuIG along [111] should have a marked effect on the character of the threshold curve as well as the magnon-phonon interaction notch. We find that the spin-wave linewidth of YIG is less than that of EuIG and that the three-magnon confluence process does not account quantitatively for the $k$-dependent linewidth at low temperatures. The exchange constant of EuIG is predicted quite well from the known magnetic properties of the ${\mathrm{Eu}}^{3+}$ ion and its expected effect on the spin-wave spectrum of the iron lattice. The large magnetoelastic coupling constant of EuIG along [111] makes the threshold curve quite anomalous. It shifts the longitudinal notch to higher $k$ values, yielding an erroneously high exchange constant. Also, the shear-wave notch is absent, possibly because the spin-wave instability merges smoothly into the elastic-wave instability. Along [100], the coupling constant of EuIG is much smaller and a normal threshold curve is obtained. For YIG, the magnetoelastic coupling constants derived from parallel-pump measurements are significantly higher than those obtained from strain-gauge measurements. This might be due to the lower temperature at which the parallel-pump measurements were done. For EuIG, the agreement between the two kinds of measurements was reasonably good. The elastic $Q$ increases with decreasing temperature for both garnets and is larger for YIG than for EuIG, as expected.