Experimental Investigation of Temperature-Dependent Gilbert Damping in Permalloy Thin Films

Ferromagnetic resonance measurement with frequency modulation down to 2 K

Ferromagnetic resonance (FMR) spectroscopy is a powerful technique to study the precessional dynamics of magnetization in thin film heterostructures. It provides valuable information about the mechanisms of exchange bias, spin angular momentum transfer across interfaces, and excitation of magnons. A key desirable feature of FMR spectrometers is the capability to study magnetization dynamics over a wide phase space of temperature (T), frequency (f), and magnetic field (B). The design, fabrication, and testing of such a spectrometer, which uses frequency modulation techniques for improved detection of microwave absorption, reduces heat load in the cryostat and allows simultaneous measurements of inverse spin Hall effect (ISHE) induced dc voltages, is described in this paper. The apparatus is based on a 2-port transmitted microwave signal measurement using a grounded co-planar waveguide. The input radio frequency (RF) signal, frequency modulated at a tunable f-band, excites spin precession in the sample, and the attenuated RF signal is measured phase sensitively. The sample stage, inserted in the bore of a superconducting solenoid, allows magnetic field and temperature variability of 0 to ±5 T and 2-310 K, respectively. We demonstrate the working of this Cryo-FMR and ISHE spectrometer on thin films of Ni80Fe20 and Fe60Co20B20 over a wide T, B, and f phase space.

Simulation study of the Gilbert damping in Ni80Fe20/Nd bilayers: comparison with experiments

We present an experimental and computational investigation the Neodymium thickness dependence of the effective damping constant (αeff) inNi80Fe20/Neodymium (Py/Nd) bilayers. The computational results show that the magnetic damping is strongly dependent on the thickness of Nd, which is in agreement with experimental data. Self consistent solutions of the spin accumulation model and the local magnetisation were used in the simulations. It was not possible to obtain agreement with experiment under the assumption of an enhanced damping in a single Py monolayer. Instead, it was found that the enhanced damping due to spin pumping needed to be spread across two monolayers of Py. This is suggested to arise from interface mixing. Subsequently, the temperature dependence of the effective damping was investigated. It is found that, with increasing temperature, the influence of thermally-induced spin fluctuations on magnetic damping becomes stronger with increasing Nd thickness.

Direct and Inverse Spin Splitting Effects in Altermagnetic RuO2

Recently, the altermagnetic materials with spin splitting effect (SSE), have drawn significant attention due to their potential to the flexible control of the spin polarization by the Néel vector. Here, the direct and inverse altermagnetic SSE (ASSE) in the (101)-oriented RuO2 film with the tilted Néel vector are reported. First, the spin torque along the x-, y-, and z-axis is detected from the spin torque-induced ferromagnetic resonance (ST-FMR), and the z-spin torque emerges when the electric current is along the [010] direction, showing the anisotropic spin splitting of RuO2. Further, the current-induced modulation of damping is used to quantify the damping-like torque efficiency (ξDL) in RuO2/Py, and an anisotropic ξDL is obtained and maximized for the current along the [010] direction, which increases with the reduction of the temperature, indicating the present of ASSE. Next, by way of spin pumping measurement, the inverse altermagnetic spin splitting effect (IASSE) is studied, which also shows a crystal direction-dependent anisotropic behavior and temperature-dependent behavior. This work gives a comprehensive study of the direct and inverse ASSE effects in the altermagnetic RuO2, inspiring future altermagnetic materials and devices with flexible control of spin polarization.

Parametric magnon transduction to spin qubits

The integration of heterogeneous modular units for building large-scale quantum networks requires engineering mechanisms that allow suitable transduction of quantum information. Magnon-based transducers are especially attractive due to their wide range of interactions and rich nonlinear dynamics, but most of the work to date has focused on linear magnon transduction in the traditional system composed of yttrium iron garnet and diamond, two materials with difficult integrability into wafer-scale quantum circuits. In this work, we present a different approach by using wafer-compatible materials to engineer a hybrid transducer that exploits magnon nonlinearities in a magnetic microdisc to address quantum spin defects in silicon carbide. The resulting interaction scheme points to the unique transduction behavior that can be obtained when complementing quantum systems with nonlinear magnonics.

Nonlinear features of the superconductor-ferromagnet-superconductor φ0 Josephson junction in the ferromagnetic resonance region

We demonstrate the manifestations of nonlinear features in magnetic dynamics and I-V characteristics of a φ₀ Josephson junction in the ferromagnetic resonance region. We show that at small values of the system parameters damping, spin-orbit interaction, and Josephson-to-magnetic energy ratio, the magnetic dynamics is reduced to the dynamics of a scalar Duffing oscillator driven by the Josephson oscillations. The role of the increasing superconducting current in the resonance region is clarified. Shifting of the ferromagnetic resonant frequency and the reversal of its damping dependence due to nonlinearity are demonstrated by the full Landau-Lifshitz-Gilbert-Josephson system of equations and in its different approximations. Finally, we demonstrate the negative differential resistance in the I-V characteristics and its correlation with the fold-over effect.

A short-circuited coplanar waveguide for low-temperature single-port ferromagnetic resonance spectroscopy setup to probe the magnetic properties of ferromagnetic thin films

A coplanar waveguide shorted in one end is proposed, designed, and implemented successfully to measure the properties of magnetic thin films as a part of the vector network analyzer ferromagnetic resonance (FMR) spectroscopy setup. Its simple structure, potential applications, and easy installation inside the cryostat chamber made it advantageous especially for low-temperature measurements. It provides a wide band of frequencies in the gigahertz range essential for FMR measurements. Our spectroscopy setup with a short-circuited coplanar waveguide has been used to extract the Gilbert damping coefficient and effective magnetization values for standard ferromagnetic thin films, such as Permalloy (Py) and Cobalt (Co). The thickness and temperature-dependent studies of those magnetic parameters have also been done here for the afore-mentioned magnetic samples.

Suppression of spin rectification effects in spin pumping experiments

Spin pumping (SP) is a well-established method to generate pure spin currents allowing efficient spin injection into metals and semiconductors avoiding the problem of impedance mismatch. However, to disentangle pure spin currents from parasitic effects due to spin rectification effects (SRE) is a difficult task that is seriously hampering further developments. Here we propose a simple method that allows suppressing SRE contribution to inverse spin Hall effect (ISHE) voltage signal avoiding long and tedious angle-dependent measurements. We show an experimental study in the well-known Py/Pt system by using a coplanar waveguide (CPW). Results obtained demonstrate that the sign and size of the measured transverse voltage signal depends on the width of the sample along the CPW active line. A progressive reduction of this width evidences that SRE contribution to the measured transverse voltage signal becomes negligibly small for sample width below 200 μm. A numerical solution of the Maxwell equations in the CPW-sample setup, by using the Landau-Lifshitz equation with the Gilbert damping term (LLG) as the constitutive equation of the media, and with the proper set of boundary conditions, confirms the obtained experimental results.

Giant oscillatory Gilbert damping in superconductor/ferromagnet/superconductor junctions

Interfaces between materials with differently ordered phases present unique opportunities for exotic physical properties, especially the interplay between ferromagnetism and superconductivity in the ferromagnet/superconductor heterostructures. The investigation of zero- and π-junctions has been of particular interest for both fundamental physical science and emerging technologies. Here, we report the experimental observation of giant oscillatory Gilbert damping in the superconducting niobium/nickel-iron/niobium junctions with respect to the nickel-iron thickness. This observation suggests an unconventional spin pumping and relaxation via zero-energy Andreev bound states that exist not only in the niobium/nickel-iron/niobium π-junctions but also in the niobium/nickel-iron/niobium zero-junctions. Our findings could be important for further exploring the exotic physical properties of ferromagnet/superconductor heterostructures and potential applications of ferromagnet π-junctions in quantum computing, such as half-quantum flux qubits.

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, HfO_x, 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.

Spin-Wave Dynamics and Symmetry Breaking in an Artificial Spin Ice

Artificial spin ices are periodic arrangements of interacting nanomagnets which allow investigating emergent phenomena in the presence of geometric frustration. Recently, it has been shown that artificial spin ices can be used as building blocks for creating functional materials, such as magnonic crystals. We investigate the magnetization dynamics in a system exhibiting anisotropic magnetostatic interactions owing to locally broken structural inversion symmetry. We find a rich spin-wave spectrum and investigate its evolution in an external magnetic field. We determine the evolution of individual modes, from building blocks up to larger arrays, highlighting the role of symmetry breaking in defining the mode profiles. Moreover, we demonstrate that the mode spectra exhibit signatures of long-range interactions in the system. These results contribute to the understanding of magnetization dynamics in spin ices beyond the kagome and square ice geometries and are relevant for the realization of reconfigurable magnonic crystals based on spin ices.

Element-Specific Detection of Sub-Nanosecond Spin-Transfer Torque in a Nanomagnet Ensemble

Spin currents can exert spin-transfer torques on magnetic systems even in the limit of vanishingly small net magnetization, as recently shown for antiferromagnets. Here, we experimentally show that a spin-transfer torque is operative in a macroscopic ensemble of weakly interacting, randomly magnetized Co nanomagnets. We employ element- and time-resolved X-ray ferromagnetic resonance (XFMR) spectroscopy to directly detect subnanosecond dynamics of the Co nanomagnets, excited into precession with cone angle ≳0.003° by an oscillating spin current. XFMR measurements reveal that as the net moment of the ensemble decreases, the strength of the spin-transfer torque increases relative to those of magnetic field torques. Our findings point to spin-transfer torque as an effective way to manipulate the state of nanomagnet ensembles at subnanosecond time scales.

Ferromagnetic resonance studies of strain tuned Bi:YIG films

Bismuth-doped Yttrium iron garnet (Bi:YIG) thin films known for large magneto-optical activity with low losses still need to get probed for its magnetization dynamics. We demonstrate a controlled tuning of magnetocrystalline anisotropy in Bi-doped Y₃Fe₅O₁₂ (Bi:YIG) films of high crystalline quality using growth induced epitaxial strain on [1 1 1]-oriented Gd₃Ga₅O₁₂ (GGG) substrate. We optimize a growth protocol to get thick highly-strained epitaxial films showing large magneto-crystalline anisotropy, compare to thin films prepared using a different protocol. Ferromagnetic resonance measurements establish a linear dependence of the out-of-plane uniaxial anisotropy on the strain induced rhombohedral distortion of Bi:YIG lattice. Interestingly, the enhancement in the magnetoelastic constant due to an optimum substitution of Bi³⁺ ions with strong spin orbit coupling does not strongly affect the precessional damping (∼[Formula: see text]). Large magneto-optical activity, reasonably low damping, large magnetocrystalline anisotropy and large magnetoelastic coupling in Bi:YIG are the properties that may help Bi:YIG emerge as a possible material for photo-magnonics and other spintronics applications.

Another view on Gilbert damping in two-dimensional ferromagnets

A keen interest towards technological implications of spin-orbit driven magnetization dynamics requests a proper theoretical description, especially in the context of a microscopic framework, to be developed. Indeed, magnetization dynamics is so far approached within Landau-Lifshitz-Gilbert equation which characterizes torques on magnetization on purely phenomenological grounds. Particularly, spin-orbit coupling does not respect spin conservation, leading thus to angular momentum transfer to lattice and damping as a result. This mechanism is accounted by the Gilbert damping torque which describes relaxation of the magnetization to equilibrium. In this study we work out a microscopic Kubo-Středa formula for the components of the Gilbert damping tensor and apply the elaborated formalism to a two-dimensional Rashba ferromagnet in the weak disorder limit. We show that an exact analytical expression corresponding to the Gilbert damping parameter manifests linear dependence on the scattering rate and retains the constant value up to room temperature when no vibrational degrees of freedom are present in the system. We argue that the methodology developed in this paper can be safely applied to bilayers made of non- and ferromagnetic metals, e.g., CoPt.

Effect of Sharp Diameter Geometrical Modulation on the Magnetization Reversal of Bi-Segmented FeNi Nanowires

Controlling functional properties of matter and combining them for engineering a functional device is, nowadays, a common direction of the scientific community. For instance, heterogeneous magnetic nanostructures can make use of different types of geometrical and compositional modulations to achieve the control of the magnetization reversal along with the nano-entities and, thus, enable the fabrication of spintronic, magnetic data storage, and sensing devices, among others. In this work, diameter-modulated FeNi nanowires are fabricated paying special effort to obtain sharp transition regions between two segments of different diameters (from about 450 nm to 120 nm), enabling precise control over the magnetic behavior of the sample. Micromagnetic simulations performed on single bi-segmented nanowires predict a double step magnetization reversal where the wide segment magnetization switches near 16 kA/m through a vortex domain wall, while at 40 kA/m the magnetization of the narrow segment is reversed through a corkscrew-like mechanism. Finally, these results are confirmed with magneto-optic Kerr effect measurements at the transition of isolated bi-segmented nanowires. Furthermore, macroscopic vibrating sample magnetometry is used to demonstrate that the magnetic decoupling of nanowire segments is the main phenomenon occurring over the entire fabricated nanowires.

Dirac surface state-modulated spin dynamics in a ferrimagnetic insulator at room temperature

This work demonstrates markedly modified spin dynamics of magnetic insulator (MI) by the spin momentum-locked Dirac surface states of the adjacent topological insulator (TI), which can be harnessed for spintronic applications. As the Bi concentration x is systematically tuned in 5-nm-thick (Bi _x Sb_1-x )₂Te₃ TI films, the weight of the surface relative to bulk states peaks at x = 0.32 when the chemical potential approaches the Dirac point. At this concentration, the Gilbert damping constant of the precessing magnetization in 10-nm-thick Y₃Fe₅O₁₂ MI films in the MI/TI heterostructures is enhanced by an order of magnitude, the largest among all concentrations. In addition, the MI acquires additional strong magnetic anisotropy that favors the in-plane orientation with similar Bi concentration dependence. These extraordinary effects of the Dirac surface states distinguish TI from other materials such as heavy metals in modulating spin dynamics of the neighboring magnetic layer.

Optical conversion of pure spin currents in hybrid molecular devices

Carbon-based molecules offer unparalleled potential for THz and optical devices controlled by pure spin currents: a low-dissipation flow of electronic spins with no net charge displacement. However, the research so far has been focused on the electrical conversion of the spin imbalance, where molecular materials are used to mimic their crystalline counterparts. Here, we use spin currents to access the molecular dynamics and optical properties of a fullerene layer. The spin mixing conductance across Py/C60 interfaces is increased by 10% (5 × 1018 m-2) under optical irradiation. Measurements show up to a 30% higher light absorbance and a factor of 2 larger photoemission during spin pumping. We also observe a 0.15 THz slowdown and a narrowing of the vibrational peaks. The effects are attributed to changes in the non-radiative damping and energy transfer. This opens new research paths in hybrid magneto-molecular optoelectronics, and the optical detection of spin physics in these materials.Carbon-based molecules could prove useful in terahertz and optical devices controlled by pure spin currents. Here, conversely, the authors use spin currents to probe molecular dynamics and enhance the optical response of a fullerene layer, enabling hybrid magneto-molecular optoelectronic devices.

Capping Layer (CL) Induced Antidamping in CL/Py/β-W System (CL: Al, β-Ta, Cu, β-W)

For achieving ultrafast switching speed and minimizing dissipation losses, the spin-based data storage device requires a control on effective damping (α_eff) of nanomagnetic bits. Incorporation of interfacial antidamping spin orbit torque (SOT) in spintronic devices therefore has high prospects for enhancing their performance efficiency. Clear evidence of such an interfacial antidamping is found in Al capped Py(15 nm)/β-W(t_W)/Si (Py = Ni₈₁Fe₁₉ and t_W = thickness of β-W), which is in contrast to the increase of α_eff (i.e., damping) usually associated with spin pumping as seen in Py(15 nm)/β-W(t_W)/Si system. Because of spin pumping, the interfacial spin mixing conductance (g^↑↓) at Py/β-W interface and spin diffusion length (λ_SD) of β-W are found to be 1.63(±0.02) × 10¹⁸ m^-2 (1.44(±0.02) × 10¹⁸ m^-2) and 1.42(±0.19) nm (1.00(±0.10) nm) for Py(15 nm)/β-W(t_W)/Si (β-W(t_W)/Py(15 nm)/Si) bilayer systems. Other different nonmagnetic capping layers (CL), namely, β-W(2 nm), Cu(2 nm), and β-Ta(2,3,4 nm) were also grown over the same Py(15 nm)/β-W(t_W). However, antidamping is seen only in β-Ta(2,3 nm)/Py(15 nm)/β-W(t_W)/Si. This decrease in α_eff is attributed to the interfacial Rashba like SOT generated by nonequilibrium spin accumulation subsequent to the spin pumping. Contrary to this, when interlayer positions of Py(15 nm) and β-W(t_W) is interchanged irrespective of the fixed top nonmagnetic layer, an increase of α_eff is observed, which is ascribed to spin pumping from Py to β-W layer.

Tunable magnetization and damping of sputter-deposited, exchange coupled Py|Fe bilayers

We report on magnetic damping of exchange coupled, polycrystalline Py(Ni₈₀Fe₂₀)|Fe and Fe|Py bilayers, prepared by sputter-deposition on an amorphous 3 nm Ta seed layer. FMR measurements are performed on varying thicknesses of the individual Py and Fe layers while keeping the total bilayer structure thickness fixed. When Fe is grown directly on Ta, there is large magnetic inhomogeneity and damping. However, when a Py layer is deposited between Fe and Ta, both the magnetic inhomogeneity and damping significantly decrease even if Fe is covered by Ta. The intrinsic damping of the Ta|Py|Fe film can be further lowered by increasing the Fe to Py ratio. SQUID measurements show a linear increase in saturation magnetization with increasing ratio of Fe to Py. A combination of in-plane and out-of-plane X-ray diffraction measurements show that Py is textured along the 〈111〉 directions and Fe is textured along the 〈110〉, with Fe texture significantly improving if it is deposited on Ta|Py instead of Ta. By improving the texture of Fe by introducing a thin Py layer between Fe and Ta, one can grow Fe thin films with zero in-plane anisotropy, tunable magnetic moment, and low magnetic damping, approaching that of the best single crystal Fe.

Observation of inverse Edelstein effect in Rashba-split 2DEG between SrTiO3 and LaAlO3 at room temperature

The Rashba physics has been intensively studied in the field of spin orbitronics for the purpose of searching novel physical properties and the ferromagnetic (FM) magnetization switching for technological applications. We report our observation of the inverse Edelstein effect up to room temperature in the Rashba-split two-dimensional electron gas (2DEG) between two insulating oxides, SrTiO3 and LaAlO3, with the LaAlO3 layer thickness from 3 to 40 unit cells (UC). We further demonstrate that the spin voltage could be markedly manipulated by electric field effect for the 2DEG between SrTiO3 and 3-UC LaAlO3. These results demonstrate that the Rashba-split 2DEG at the complex oxide interface can be used for efficient charge-and-spin conversion at room temperature for the generation and detection of spin current.