Magnetoelasticity of Co25Fe75 thin films

Abstract

We investigate the magnetoelastic properties of Co₂₅Fe₇₅ and Co₁₀Fe₉₀ thin films by measuring the mechanical properties of a doubly clamped string resonator covered with multilayer stacks containing these films. For the magnetostrictive constants, we find λ _{Co25 Fe75} = (-20.68 ± 0.25) × 10^-6 and λ _{Co10 Fe90} = (-9.80 ± 0.12) × 10^-6 at room temperature, in contrast to the positive magnetostriction previously found in bulk CoFe crystals. Co₂₅Fe₇₅ thin films unite low damping and sizable magnetostriction and are thus a prime candidate for micromechanical magnonic applications, such as sensors and hybrid phonon-magnon systems.

FIG. 1.

Schematic of doubly clamped Si₃N₄ nanostring covered with a CoFe layer stack on top (black) and an interferometric readout setup. The string is supported by posts etched from the silicon substrate (grey). The whole sample is mounted on a piezoactuator (red). Φ is the angle between the external magnetic field and the x-direction (along the string), and Θ denotes the angle between the x-direction and the magnetization direction in the CoFe film. The layer stack with Ta(3 nm) and Cu(3 nm) seed and capping layers is the same as used in Ref. . The CoFe layer thickness varied for different alloy ratios. To extract the resonance frequency of the oop mechanical motion of the string, the amplitude of a reflected laser beam is measured with a photodiode and analyzed with a VNA.

FIG. 2.

Mechanical response of the fundamental mode of a 25 µm long nanostring as a function of external field direction Φ at µ₀ = H = 950 mT. (a) shows the frequency dependent photovoltage as a function of external magnetic field direction and drive frequency, this is a direct measure for the mechanical amplitude of the string. (b) shows the extracted resonance frequencies at specific field directions. The inset in (b) shows a slice from (a) at Φ = 153° and the fit to a Lorentzian line shape (red line) used to extract the resonance frequency. Error bars are fit errors.

FIG. 3.

Global fit to magnetization direction dependent resonance frequencies of strings with different lengths covered with the Co₂₅Fe₇₅ stack. The resonance frequencies of the strings with a length of 25 µm (diamonds), 35 µm (triangles), 50.8 µm (hexagons), and 51.2 µm (circles) length were globally fit using Eqs. (1) and (2) (red lines). Fit errors are within the size of the data symbols. In (b), the deviation ΔΩ_m = Ω₀ – Ω_fit is plotted vs Φ. The residuals are nonzero for all the strings; however, no clear systematics are apparent.

FIG. 4.

Magnetostrictive and magnetoelastic constants for the two Co_1—x Fe_x alloys and pure metals (Co and Fe) for reference. Circles show the magnetostrictive contant (λ_||) on the left scale, while diamonds (red) depict the corresponding magnetoelastic constant (b) on the right scale. The star shaped data points correspond to literature values from Refs. and . Uncertainties in the alloy composition (±2%) are represented by the symbol size for the Co₂₅Fe₇₅ and Co₁₀Fe₉₀ compounds, uncertainties in the values of λ_|| and b are given in the text.

FIG. 5.

Result of a numeric finite element simulation of the eigenfrequency and mode shape of a L = 25 µm nanostring, alike to what is shown in Fig. 2. Using the same material and geometry parameters as in the experiment, as well as the experimentally obtained prestress (σ₀ = 458 MPa), the resonance frequency and the mode shape were simulated. Giving a resonance frequency of Ω_simu = 7.373 MHz and the mode-shape of an undisturbed oop oscillation.

FIG. 6.

(a) Sketch of the FMR measurement setup: The sample is positioned on the center conductor of a coplanar waveguide (CPW) with the CoFe facing the CPW. The CPW is connected to a microwave source on one side and to a microwave diode and a lock-in amplifier at the other. An external magnetic field is applied [(c) and (d)] in-plane or [(e) and ( f )] out-of-plane. (b) Exemplary field-swept FMR measurement at f = 20 GHz ut-of-plane. (b) Exemplary field-swept FMR measurement at f = 20 GHz for Co₁₀Fe₉₀ with the external field applied in-plane. Frequency dependence of the ip (oop) resonance field H_res [(c) and (e)] and full width half maximum ΔH [(d) and ( f )] of the FMR spectra obtained from 20 nm Co₁₀Fe₉₀ (red) and 10 nm Co₂₅Fe₇₅ (blue) grown on top of a Si₃N₄ substrate. The solid lines are fits to the data.