Thickness-Dependent Gilbert Damping and Soft Magnetism in Metal/Co-Fe-B/Metal Sandwich Structure.

The achievement of the low Gilbert damping parameter in spin dynamic modulation is attractive for spintronic devices with low energy consumption and high speed. Metallic ferromagnetic alloy Co-Fe-B is a possible candidate due to its high compatibility with spintronic technologies. Here, we report thickness-dependent damping and soft magnetism in Co-Fe-B films sandwiched between two non-magnetic layers with Co-Fe-B films up to 50 nm thick. A non-monotonic variation of Co-Fe-B film damping with thickness is observed, which is in contrast to previously reported monotonic trends. The minimum damping and the corresponding Co-Fe-B thickness vary significantly among the different non-magnetic layer series, indicating that the structure selection significantly alters the relative contributions of various damping mechanisms. Thus, we developed a quantitative method to distinguish intrinsic from extrinsic damping via ferromagnetic resonance measurements of thickness-dependent damping rather than the traditional numerical calculation method. By separating extrinsic and intrinsic damping, each mechanism affecting the total damping of Co-Fe-B films in sandwich structures is analyzed in detail. Our findings have revealed that the thickness-dependent damping measurement is an effective tool for quantitatively investigating different damping mechanisms. This investigation provides an understanding of underlying mechanisms and opens up avenues for achieving low damping in Co-Fe-B alloy film, which is beneficial for the applications in spintronic devices design and optimization.

Theory of tensorial Gilbert damping in antiferromagnets.

Although the magnetic Gilbert damping was considered as a scalar quantity in micromagnetic and atomistic spin simulations, recent investigations show that the Gilbert damping parameter is a tensor. Here, we investigate the effect of anisotropic and chiral damping in one-sublattice ferromagnets and two-sublattice antiferromagnets. We employ linear response theory to calculate the susceptibility with the damping tensor and determine the ferromagnetic and antiferromagnetic resonance frequencies together with the effective damping. Our results show that apart from the scalar Gilbert damping, the antisymmetric chiral damping has a significant contribution to the spin dynamics that it breaks the antiparallel alignment of two sublattices in antiferromagnets even in the absence of an applied field. To this end, we also compare the tensorial damping and cross-sublattice scalar damping in antiferromagnets.

Temperature Evolution of Magnon Propagation Length in Tm3Fe5O12 Thin Films: Roles of Magnetic Anisotropy and Gilbert Damping.

The magnon propagation length, ⟨ξ⟩, of a ferro-/ferrimagnet (FM) is one of the key factors that controls the generation and propagation of thermally driven magnonic spin current in FM/heavy metal (HM) bilayer based spincaloritronic devices. For the development of a complete physical picture of thermally driven magnon transport in FM/HM bilayers over a wide temperature range, it is of utmost importance to understand the respective roles of temperature-dependent Gilbert damping (α) and effective magnetic anisotropy (Keff) in controlling the temperature evolution of ⟨ξ⟩. Here, we report a comprehensive investigation of the temperature-dependent longitudinal spin Seebeck effect (LSSE), radio frequency transverse susceptibility, and broad-band ferromagnetic resonance measurements on Tm3Fe5O12 (TmIG)/Pt bilayers grown on different substrates. We observe a significant drop in the LSSE voltage below 200 K independent of TmIG film thickness and substrate choice. This is attributed to the noticeable increases in effective magnetic anisotropy field, HKeff (∝Keff) and α that occur within the same temperature range. From the TmIG thickness dependence of the LSSE voltage, we determined the temperature dependence of ⟨ξ⟩ and highlighted its correlation with the temperature-dependent HKeff and α in TmIG/Pt bilayers, which will be beneficial for the development of rare-earth iron garnet based efficient spincaloritronic nanodevices.

A Strategy for Enhancing Perpendicular Magnetic Anisotropy in Yttrium Iron Garnet Films.

In future information storage and processing, magnonics is one of the most promising candidates to replace traditional microelectronics. Yttrium iron garnet (YIG) films with perpendicular magnetic anisotropy (PMA) have aroused widespread interest in magnonics. Obtaining strong PMA in a thick YIG film with a small lattice mismatch (η) has been fascinating but challenging. Here, a novel strategy is proposed to reduce the required minimum strain value for producing PMA and increase the maximum thickness for maintaining PMA in YIG films by slight oxygen deficiency. Strong PMA is achieved in the YIG film with an η of only 0.4% and a film thickness up to 60 nm, representing the strongest PMA for such a small η reported so far. Combining transmission electron microscopy analyses, magnetic measurements, and a theoretical model, it is demonstrated that the enhancement of PMA physically originates from the reduction of saturation magnetization and the increase of magnetostriction coefficient induced by oxygen deficiency. The Gilbert damping values of the 60-nm-thick YIG films with PMA are on the order of 10-4. This strategy improves the flexibility for the practical applications of YIG-based magnonic devices and provides promising insights for the theoretical understanding and the experimental enhancement of PMA in garnet films.

Large Thermo-Spin Effects in Heusler Alloy-Based Spin Gapless Semiconductor Thin Films.

Recently, Heusler alloy-based spin gapless semiconductors (SGSs) with high Curie temperature (TC) and sizable spin polarization have emerged as potential candidates for tunable spintronic applications. We report comprehensive investigation of the temperature-dependent ANE and intrinsic longitudinal spin Seebeck effect (LSSE) in CoFeCrGa thin films grown on MgO substrates. Our findings show that the anomalous Nernst coefficient for the MgO/CoFeCrGa (95 nm) film is ≈1.86 µV K-1 at room temperature, which is nearly 2 orders of magnitude higher than that of the bulk polycrystalline sample of CoFeCrGa (≈0.018 µV K-1) and almost 3 orders of magnitude higher than that of the half-metallic ferromagnet La1-xNaxMnO3 (≈0.005 µV K-1) but comparable to that of the magnetic Weyl semimetal Co2MnGa thin film (≈2-3 µV K-1). Furthermore, the LSSE coefficient for our MgO/CoFeCrGa (95 nm)/Pt (5 nm) heterostructure is ≈20.5 nV K-1 Ω-1 at room temperature, which is twice larger than that of the half-metallic ferromagnetic La0.7Sr0.3MnO3 thin films (≈9 nV K-1 Ω-1). We show that both ANE and LSSE coefficients follow identical temperature dependences and exhibit a maximum at ≈225 K, which is understood as the combined effects of inelastic magnon scatterings and reduced magnon population at low temperatures. Our analyses not only indicate that the extrinsic skew scattering is the dominating mechanism for ANE in these films but also provide critical insights into the functional form of the observed temperature-dependent LSSE at low temperatures. Furthermore, by employing radio frequency transverse susceptibility and broad-band ferromagnetic resonance in combination with the LSSE measurements, we establish a correlation among the observed LSSE signal, magnetic anisotropy, and Gilbert damping of the CoFeCrGa thin films, which will be beneficial for fabricating tunable and highly efficient Heusler alloy-based spin caloritronic nanodevices.

Emergent Magnonic Materials: Challenges and Opportunities.

Advances in information technology are hindered by energy dissipation from Joule losses associated with charge transport. In contrast, the process of information based on spin waves propagation (magnons) in magnetic materials is dissipationless. Low damping of spin wave excitations is essential to control the propagation length of magnons. Ferrimagnetic Y3Fe5O12 garnets (YIG) exhibit the lowest magnetic damping constants. However, to attain the lowest damping constant, epitaxial growth of YIG on single crystal substrates of Gd3Ga5O12 at elevated temperatures is required, which hinders their CMOS integration in electronic devices. Furthermore, their low saturation magnetization and magnetocrystalline anisotropy are challenging for nanoscale device applications. In the search for alternative material systems, polycrystalline ferromagnetic Co25Fe75 alloy films and ferrimagnetic spinel ferrites, such as MgAl0.5Fe1.5O4 (MAFO), have emerged as potential candidates. Their damping constants are comparable, although they are at least one order of magnitude higher than YIG's. However, Co25Fe75 alloy thin film growth is CMOS compatible, and its magnon diffusion length is 20× longer than in MAFO. In addition, MAFO requires epitaxial growth on lattice-matched MgAl2O4 substrates. We discuss the material properties that control the Gilbert damping constant in CoxFe1-x alloys and MAFO and conclude that CoxFe1-x alloy thin films bring us closer to the realization of the exploitation of spin waves for magnonics.

Role of SSW on thermal-gradient induced domain-wall dynamics.

We study the thermal gradient (TG) induced domain wall (DW) dynamics in a uniaxial nanowire in the framework of the Stochastic-Landau-Lifshitz-Gilbert equation. TG drives the DW in a certain direction, and DW (linear and rotational) velocities increase with TG linearly, which can be explained by the magnonic angular momentum transfer to the DW. Interestingly, from Gilbert damping dependence of DW dynamics for fixed TG, we find that the DW velocity is significantly smaller even for lower damping, and DW velocity increases with damping (for a certain range of damping) and reaches a maximal value for critical damping which is contrary to our usual desire. This can be attributed to the formation of standing spin wave (SSW) modes (from the superposition of the spin waves and their reflection) together with travelling spin wave (TSW) modes. SSW does not carry any net energy/momentum to the DW, while TSW does. Dampingαcompels the spin current polarization to align with the local spin, which reduces the magnon propagation length and thusαhinders to generate SSWs, and contrarily the number of TSWs increases, which leads to the increment of DW speed with damping. For a similar reason, we observe that DW velocity increases with nanowire length and becomes saturated to maximal value for a certain length. Therefore, these findings may enhance the fundamental understanding as well as provide a way of utilizing the Joule heat in the spintronics (e.g. racetrack memory) devices.

Electric and Magnetic Tuning of Gilbert Damping Constant in LSMO/PMN-PT(011) Heterostructure.

Electric field control of magnetodynamics in magnetoelectric (ME) heterostructures has been the subject of recent interest due to its fundamental complexity and promising applications in room temperature devices. The present work focuses on the tuning of magnetodynamic parameters of epitaxially grown ferromagnetic (FM) La0.7Sr0.3MnO3(LSMO) on a ferro(piezo)electric (FE) Pb(Mg0.33Nb0.67)O3-PbTiO3(PMN-PT) single crystal substrate. The uniaxial magnetic anisotropy of LSMO on PMN-PT confirms the ME coupling at the FM/FE heterointerface. The magnitude of the Gilbert damping constant (α) of this uniaxial LSMO film measured along the hard magnetic axis is significantly small compared to the easy axis. Furthermore, a marked decrease in the α values of LSMO at positive and negative electrical remanence of PMN-PT is observed, which is interpreted in the framework of strain induced spin dependent electronic structure. The present results clearly encourage the prospects of electric field controlled magnetodynamics, thereby realising the room temperature spin-wave based device applications with ultra-low power consumption.

Magnetic Damping and Dzyaloshinskii-Moriya Interactions in Pt/Co2FeAl/MgO Systems Grown on Si and MgO Substrates.

Spin-pumping-induced damping and interfacial Dzyaloshinskii-Moriya interaction (iDMI) have been studied in Pt/Co2FeAl/MgO systems grown on Si or MgO substrates as a function of Pt and Co2FeAl (CFA) thicknesses. For this, we combined vibrating sample magnetometry (VSM), microstrip ferromagnetic resonance (MS-FMR), and Brillouin light scattering (BLS). VSM measurements of the magnetic moment at saturation per unit area revealed the absence of a magnetic dead layer in both systems, with a higher magnetization at saturation obtained for CFA grown on MgO. The key parameters governing the spin-dependent transport through the Pt/CFA interface, including the spin mixing conductance and the spin diffusion length, have been determined from the CFA and the Pt thickness dependence of the damping. BLS has been used to measure the spin wave non-reciprocity via the frequency mismatch between the Stokes and anti-Stokes lines. iDMI has been separated from the contribution of the interface perpendicular anisotropy difference between Pt/CFA and CFA/MgO. Our investigation revealed that both iDMI strength and spin pumping efficiency are higher for CFA-based systems grown on MgO due to its epitaxial growth confirmed by MS-FMR measurements of the in-plane magnetic anisotropy. This suggests that CFA grown on MgO could be a promising material candidate as a spin injection source via spin pumping and for other spintronic applications.

Generalization of the Landau-Lifshitz-Gilbert equation by multi-body contributions to Gilbert damping for non-collinear magnets.

We propose a systematic and sequential expansion of the Landau-Lifshitz-Gilbert equation utilizing the dependence of the Gilbert damping tensor on the angle between magnetic moments, which arises from multi-body scattering processes. The tensor consists of a damping-like term and a correction to the gyromagnetic ratio. Based on electronic structure theory, both terms are shown to depend on e.g. the scalar, anisotropic, vector-chiral and scalar-chiral products of magnetic moments:ei⋅ej, (nij⋅ei)(nij⋅ej),nij⋅ (ei×ej),(ei⋅ej)2,ei⋅ (ej×ek) …, where some terms are subjected to the spin-orbit fieldnijin first and second order. We explore the magnitude of the different contributions using both the Alexander-Anderson model and time-dependent density functional theory in magnetic adatoms and dimers deposited on Au(111) surface.

Structural Phase-Dependent Giant Interfacial Spin Transparency in W/CoFeB Thin-Film Heterostructures.

Pure spin current has transformed the research field of conventional spintronics due to its various advantages, including energy efficiency. An efficient mechanism for generation of pure spin current is spin pumping, and high effective spin-mixing conductance (Geff) and interfacial spin transparency (T) are essential for its higher efficiency. By employing the time-resolved magneto-optical Kerr effect technique, we report here a giant value of T in substrate/W (t)/Co20Fe60B20 (d)/SiO2 (2 nm) thin-film heterostructures in the beta-tungsten (ß-W) phase. We extract the spin diffusion length of W and spin-mixing conductance of the W/CoFeB interface from the variation of damping as a function of W and CoFeB thickness. This leads to a value of T = 0.81 ± 0.03 for the ß-W/CoFeB interface. A stark variation of Geff and T with the thickness of the W layer is obtained in accordance with the structural phase transition and resistivity variation of W with its thickness. Effects such as spin memory loss and two-magnon scattering are found to have minor contributions to damping modulation in comparison to the spin pumping effect which is reconfirmed from the unchanged damping constant with the variation of Cu spacer layer thickness inserted between W and CoFeB. The giant interfacial spin transparency and its strong dependence on crystal structures of W will be important for future spin-orbitronic devices based on pure spin current.

Effects of Interfacial Oxidization on Magnetic Damping and Spin-Orbit Torques.

We investigate the effects of interfacial oxidation on the perpendicular magnetic anisotropy, magnetic damping, and spin-orbit torques in heavy-metal (Pt)/ferromagnet (Co or NiFe)/capping (MgO/Ta, HfOx, or TaN) structures. At room temperature, the capping materials influence the effective surface magnetic anisotropy energy density, which is associated with the formation of interfacial magnetic oxides. The magnetic damping parameter of Co is considerably influenced by the capping material (especially MgO) while that of NiFe is not. This is possibly due to extra magnetic damping via spin-pumping process across the Co/CoO interface and incoherent magnon generation (spin fluctuation) developed in the antiferromagnetic CoO. It is also observed that both antidamping and field-like spin-orbit torque efficiencies vary with the capping material in the thickness ranges we examined. Our results reveal the crucial role of interfacial oxides on the perpendicular magnetic anisotropy, magnetic damping, and spin-orbit torques.

Drag effect induced large anisotropic damping behavior in magnetic thin films with strong magnetic anisotropy.

The determination of intrinsic Gilbert damping is one of the central interests in the field of spintronics. However, some external factors in magnetic films tend to play a remarkable role in the magnetization dynamics. Here, we present a comprehensive study of the magnetic relaxation in ferromagnetic films with various in-plane magnetic anisotropy via ferromagnetic resonance technique. We find that the magnetic drag effect can result in the resonant linewidth broadening and the nonlinear dependence of linewidth on frequency stemming from field-magnetization misalignment. As a result, this could lead to the imprecise extraction of the key dynamic parameter-Gilbert damping and cause the confusing behaviors of ultra-low and anisotropic damping in thin films and multi-layers with high magnetic anisotropy. Our results provide a crucial way for the accurately quantitative estimation of the Gilbert damping in spintronics measurements.

Characterizing the Magnetic Interfacial Coupling of the Fe/FeGe Heterostructure by Ferromagnetic Resonance.

We characterize the magnetic interfacial coupling of the Fe/FeGe heterostructure and its influence on the magnetic damping via ferromagnetic resonance in the temperature range of 200-300 K. When the temperature is below the critical temperature of FeGe, the interfacial coupling rises. The strength of the magnetic interfacial coupling is determined as a function of the temperature and reaches up to 0.194 erg/cm2 at 200 K. Meanwhile, the Gilbert damping of the Fe layer is enhanced from 0.035 at 300 K to 0.050 at 200 K. The enhancement is linearly proportional to the strength of magnetic interfacial coupling. We attribute the enhancement to the interfacial coupling that transfers spin angular momentum from Fe to FeGe via the exchange interaction. Our results reveal that the interfacial coupling is an effective approach to inject spin current into the chiral spin texture.

Engineering Co2 MnAlx Si1- x Heusler Compounds as a Model System to Correlate Spin Polarization, Intrinsic Gilbert Damping, and Ultrafast Demagnetization.

Engineering of magnetic materials for developing better spintronic applications relies on the control of two key parameters: the spin polarization and the Gilbert damping, responsible for the spin angular momentum dissipation. Both of them are expected to affect the ultrafast magnetization dynamics occurring on the femtosecond timescale. Here, engineered Co2 MnAlx Si1- x Heusler compounds are used to adjust the degree of spin polarization at the Fermi energy, P, from 60% to 100% and to investigate how they correlate with the damping. It is experimentally demonstrated that the damping decreases when increasing the spin polarization from 1.1 × 10-3 for Co2 MnAl with 63% spin polarization to an ultralow value of 4.6 × 10-4 for the half-metallic ferromagnet Co2 MnSi. This allows the investigation of the relation between these two parameters and the ultrafast demagnetization time characterizing the loss of magnetization occurring after femtosecond laser pulse excitation. The demagnetization time is observed to be inversely proportional to 1 - P and, as a consequence, to the magnetic damping, which can be attributed to the similarity of the spin angular momentum dissipation processes responsible for these two effects. Altogether, the high-quality Heusler compounds allow control over the band structure and therefore the channel for spin angular momentum dissipation.

Effect of oblique versus normal deposition orientation on the properties of perpendicularly magnetized L10 FePd thin films.

Materials such as L10 Fe-based alloys with perpendicular magnetic anisotropy derived from crystal structure have the potential to deliver higher thermal stability of magnetic memory elements compared to materials whose anisotropy is derived from surfaces and interfaces. A number of processing parameters enable control of the quality and texture of L10 FePd among them, including substrate, deposition temperature, pressure and seed and buffer layer. The angle of inclination between the substrate and the sputtering target can also impact the texture of L10 crystallization of sputtered Fe-Pd and magnetic properties of the derived thin films. This study examines the difference between FePd layers that have been magnetron sputter deposited on Cr(15 nm)/Pt, Ir, or Ru(4 nm)/FePd (8 nm)/Ru(2 nm)/Ta(3 nm) substrate layers at an oblique angle (30° tilt from the sputtering target) versus normal incidence (target facing the substrate). X-ray diffraction, ferromagnetic resonance spectroscopy and vibrating sample magnetometry were used to compare the degree of L10 order and static and dynamic properties of films deposited under both conditions. The films grown using the oblique orientation exhibit a stronger degree of L10 orientation, a larger magnetic anisotropy energy and a lower Gilbert damping, on all three buffer layers.

Effect of CoFe dusting layer and annealing on the magnetic properties of sputtered Ta/W/CoFeB/CoFe/MgO layer structures.

We explored the effect of a CoFe wedge inserted as a dusting layer (0.2 nm-0.4 nm thick) at the CoFeB/MgO interface of a sputtered Ta(2 nm)/W(3 nm)/CoFeB(0.9 nm)/MgO(3 nm)/Ta(2 nm) film-a typical structure for spin-orbit torque devices. Films were annealed at temperatures varying between 300 °C and 400 °C in an argon environment. Ferromagnetic resonance studies and vibrating sample magnetometry measurements were carried out to estimate the effective anisotropy field, the Gilbert damping, the saturation magnetization and the dead layer thickness as a function of the CoFe thickness and across several annealing temperatures. While the as-deposited films present only easy-plane anisotropy, a transition along the wedge from in-plane to out-of-plane was observed across several annealing temperatures, with evidence of a spin-reorientation transition separating the two regions.

Ultralow Damping in Nanometer-Thick Epitaxial Spinel Ferrite Thin Films.

Pure spin currents, unaccompanied by dissipative charge flow, are essential for realizing energy-efficient nanomagnetic information and communications devices. Thin-film magnetic insulators have been identified as promising materials for spin-current technology because they are thought to exhibit lower damping compared with their metallic counterparts. However, insulating behavior is not a sufficient requirement for low damping, as evidenced by the very limited options for low-damping insulators. Here, we demonstrate a new class of nanometer-thick ultralow-damping insulating thin films based on design criteria that minimize orbital angular momentum and structural disorder. Specifically, we show ultralow damping in <20 nm thick spinel-structure magnesium aluminum ferrite (MAFO), in which magnetization arises from Fe3+ ions with zero orbital angular momentum. These epitaxial MAFO thin films exhibit a Gilbert damping parameter of ∼0.0015 and negligible inhomogeneous linewidth broadening, resulting in narrow half width at half-maximum linewidths of ∼0.6 mT around 10 GHz. Our findings offer an attractive thin-film platform for enabling integrated insulating spintronics.

Enhancing the Spin-Orbit Coupling in Fe3O4 Epitaxial Thin Films by Interface Engineering.

By analyzing the in-plane angular dependence of ferromagnetic resonance linewidth, we show that the Gilbert damping constant in ultrathin Fe3O4 epitaxial films on GaAs substrate can be enhanced by thickness reduction and oxygen vacancies in the interface. At the same time, the uniaxial magnetic anisotropy due to the interface effect becomes significant. Using the element-specific technique of X-ray magnetic circular dichroism, we find that the orbital-to-spin moment ratio increases with decreasing film thickness, in full agreement with the increase in the Gilbert damping obtained for these ultrathin single-crystal films. Combined with the first-principle calculations, the results suggest that the bonding with Fe and Ga or As ions and the ionic distortion near the interface, as well as the FeO defects and oxygen vacancies, may increase the spin-orbit coupling in ultrathin Fe3O4 epitaxial films and in turn provide an enhanced damping.

Selective Tuning of Gilbert Damping in Spin-Valve Trilayer by Insertion of Rare-Earth Nanolayers.

Selective tuning of the Gilbert damping constant, α, in a NiFe/Cu/FeCo spin-valve trilayer has been achieved by inserting different rare-earth nanolayers adjacent to the ferromagnetic layers. Frequency dependent analysis of the ferromagnetic resonances shows that the initially small magnitude of α in the NiFe and FeCo layers is improved by Tb and Gd insertions to various amounts. Using the element-specific technique of X-ray magnetic circular dichroism, we find that the observed increase in α can be attributed primarily to the orbital moment enhancement of Ni and Co, rather than that of Fe. The amplitude of the enhancement depends on the specific rare-earth element, as well as on the lattice and electronic band structure of the transition metals. Our results demonstrate an effective way for individual control of the magnetization dynamics in the different layers of the spin-valve sandwich structures, which will be important for practical applications in high-frequency spintronic devices.