High frequency voltage-induced ferromagnetic resonance in magnetic tunnel junctions

TL;DR

This paper investigates voltage-induced ferromagnetic resonance in magnetic tunnel junctions with a tungsten buffer, demonstrating control over magnetic properties and achieving resonance frequencies above 30 GHz through optimized structures.

Contribution

It introduces an optimized MTJ structure enabling high-frequency V-FMR and combines experimental analysis with macrospin modeling for detailed magnetic property characterization.

Findings

V-FMR observed at frequencies over 30 GHz

PMA energy controlled by layer thickness and annealing

Magnetization damping characterized through modeling

Abstract

Voltage-induced ferromagnetic resonance (V-FMR) in magnetic tunnel junctions (MTJs) with a W buffer is investigated. Perpendicular magnetic anisotropy (PMA) energy is controlled by both thickness of a CoFeB free layer deposited directly on the W buffer and a post-annealing process at different temperatures. The PMA energy as well as the magnetization damping are determined by analysing field-dependent FMR signals in different field geometries. An optimized MTJ structure enabled excitation of V-FMR at frequencies exceeding 30 GHz. The macrospin modelling is used to analyse the field- and angular-dependence of the V-FMR signal and to support experimental magnetization damping extraction.

Tables

Table 1. Table 1: PMA energies of samples with different t CoFeB subscript 𝑡 CoFeB t_{\mathrm{CoFeB}} after annealing at increasing temperatures. Values of K PMA subscript 𝐾 PMA K_{\mathrm{PMA}} in bold indicate samples with perpendicular effective anisotropy.

	$t_{\mathrm{CoFeB}}$ = 0.9 nm	$t_{\mathrm{CoFeB}}$ = 1.2 nm
$T_A$ (∘C)	$K_{\mathrm{PMA}}$ (MJ/m3)	$K_{\mathrm{PMA}}$ (MJ/m3)
as dep.	0.5	0.4
200	0.7	0.6
250	1.04	0.8
300	1.19	0.95
350	1.51	1.12

Equations

$$\Delta H=\frac{4\pi \alpha }{\gamma }f+\Delta H_0$$

$$\begin{array}{r}{V}_{\text{mix}}=V_{S1}\frac{\Delta H_1^2}{(H-H_{r1}{)}^2+\Delta H_1^2}\\ +V_{A1}\frac{(H-H_{r1})\Delta H_1}{(H-H_{r1}{)}^2+\Delta H_1^2}\\ +V_{S2}\frac{\Delta H_2^2}{(H-H_{r2}{)}^2+\Delta H_2^2}\\ +V_{A2}\frac{(H-H_{r2})\Delta H_2}{(H-H_{r2}{)}^2+\Delta H_2^2}\end{array}$$

Full text

I Introduction

Magnetic multilayer structures are commonly utilized as key elements of magnetic field sensors tumanski_thin_2001 and magnetic random access memories bhatti_spintronics_2017 . A stack structure similar to the one used in existing applications and related physical mechanisms, such as magnetoresistance effect and spin-transfer-torque (STT), can be used for future microwave solutions, for example spin torque oscillators chen_sto_review_2015 or microwave detectors skowronski_microwave_2016 . One of the main drawbacks of the existing technologies is a relatively high current used in the STT-based devices. In order to reduce the power consumption of such devices, a few alternative solutions have been proposed, including spin-orbit torque liu_spin-torque_2012 ; miron_current-driven_2010 and electric-field controlled magnetism weisheit_electric_2007 ; Miwa_perpendicular_2018 . The latter typically requires structures with relatively thick insulators for application of a significant electric-field at the insulator/ferromagnet interface.

Recently, a few different mechanisms have been proposed to maximize the effect of an electric field on magnetic properties of materials, including diluted magnetic semiconductors chiba_magnetization_2008 , nitride semiconductors sztenkiel_stretching_2016 , charge migration in multilayers bauer_electric_2012 and voltage controlled magnetic anisotropy (VCMA) in metallic thin films maruyama_large_2009 . It has been already presented that, by utilizing the VCMA effect, driving the magnetization into a precession at several GHz is possible zhu_voltage-induced_2012 , which is promising for high-frequency devices.

In this work we present studies on CoFeB/MgO/ CoFeB-based MTJs deposited on a W buffer skowronski_underlayer_2015 ; chang_electric_2017 . Using a relatively thin CoFeB bottom free layer and different annealing temperatures, high perpendicular magnetic anisotropy (PMA) energies of up to 1.5 MJ/m3 are achieved, which, in turn, enables voltage-induced ferromagnetic resonance (V-FMR) excitation at frequencies exceeding 30 GHz. In addition, the V-FMR measurements in combination with vector network analyser ferromagnetic resonance (VNA-FMR) investigation bilzer_study_2006 ; glowinski_coplanar_2014 were used to determine the magnetization damping in the discussed multilayers.

II Experiment

Multilayers of the following structure: W(5)/ CoFeB($t_{\mathrm{CoFeB}}$)/ MgO(1.8)/ CoFeB(5)/ Ta(5)/ Ru(5)/ Pt(2) (thickness in nm) were deposited using magnetron sputtering in a similar conditions to Ref. skowronski_perpendicular_2015 . Two thicknesses of the free layer, i.e., $t_{\mathrm{CoFeB}}$ = 0.9 and 1.2 nm, were investigated. After the deposition process, magnetic properties were determined with VNA-FMR in 10 $\times$ 10 mm samples by analysing the frequency vs. perpendicular magnetic field dependence using the Kittel relation $f$ = $\gamma$/(2$\pi$)$\sqrt{BH}$, where $H$ is the external magnetic field and $B$ is the magnetic field induction. Measurements were repeated after subsequent sample annealing in high-vacuum furnace at $T_{\mathrm{A}}$ = 200, 250, 300 and 350∘C. Independently, the same multilayers were fabricated into pillars of 2 $\times$ 4 $\mu$m2 using electron-beam lithography and ion-beam milling for transport measurements. The transport properties were measured in a probe station that enabled sample rotation at azimuth ($\theta$) and polar ($\phi$) angle with respect to the sample plane, in a magnetic field of up to 1 T with a broadband electrical contact. Both quasi-static (resistance vs. magnetic field) and dynamic measurements (DC mixing voltage vs. magnetic field) were performed using a two-point method.

III Results and discussion

First, we focus on the wafer-level investigation using VNA-FMR. Resonance frequency ($f$) vs. perpendicular magnetic field curves of samples with different thicknesses of the free layer ($t_{\mathrm{CoFeB}}$ = 0.9 and 1.2 nm) are presented in Fig. 1. Experimental points were modelled using the Kittel relation with a CoFeB saturation magnetization value of $\mu_{0}M_{S}$ = 1.6 T skowronski_underlayer_2015 . The PMA energies ($K_{\mathrm{PMA}}$) resulting from fits to the model are gathered in Table 1. Assuming an infinite-plane sample configuration, the demagnetization energy density $K_{\mathrm{D}}$ = $\mu_{0}M_{\mathrm{S}}^{2}$/2 = 1.02 MJ/m3, resulting in an effective perpendicular anisotropy for the sample with $t_{\mathrm{CoFeB}}$ = 0.9 nm for $T_{\mathrm{A}}$ $\geq$ 250∘C and for sample with $t_{\mathrm{CoFeB}}$ = 1.2 nm for $T_{\mathrm{A}}$ $>$ 300∘C. The PMA energy of the sample with $t_{\mathrm{CoFeB}}$ = 0.9 nm annealed at $T_{\mathrm{A}}$ = 350∘C evaluated from the TMR dependence on the magnetic field applied in the sample plane skowronski_perpendicular_2015 is K = 1.47 MJ/m3, which is in good agreement with the values obtained from VNA-FMR.

From the same type of measurements, the free layer magnetization damping ($\alpha$) was calculated from the linewidth ($\Delta H$) vs. $f$ slope according to the following Eq.;

[TABLE]

where $\gamma$ = 1.76$\times$1011 Hz/T is the gyromagnetic ratio and $\Delta H_{0}$ is the inhomogeneous broadening shaw_resolving_2014 . An example of the $\Delta H$ vs. $f$ dependence for the sample with $t_{\mathrm{CoFeB}}$ = 1.2 nm annealed at $T_{\mathrm{A}}$ = 300∘C is presented in Fig. 2(a). The calculated $\alpha$ for all samples is presented in Fig. 2(c). The values obtained for the sample with $t_{\mathrm{CoFeB}}$ = 1.2 nm agree well with the W/CoFeB sample of similar thickness reported in Ref. couet_impact_2017 . One can also note a tendency of $\alpha$ to increase with decreasing thickness of CoFeB swindells_spin_2019 .

Next, we move on to the transport measurement on the fabricated sample. The crystallization process of CoFeB (initiated from the MgO tunnel barrier) starts after annealing at 250∘C yuasa_giant_2007 . Therefore, we begin the analysis of the V-FMR signal for the samples annealed at this temperatures. The tunnelling magnetoresistance ratio of the fabricated MTJ reaches 40% (measured between an orthogonal and parallel CoFeB magnetization orientations) and the resistance-area product is around $RA$ = 40 kOhm*$\mu$m2. Figure 3(a-i) presents DC voltage (a result of a small AC current mixing with resistance change originating from the VCMA) $V_{\mathrm{mix}}$ as a function of the magnetic field applied at an angle $\theta$ = 60∘ from the sample plane. The resonance peak at higher (smaller) field originates from the free (reference) layer. This dependence was modelled using a sum of two symmetric and asymmetric Lorentz curves:

[TABLE]

where $H_{\mathrm{r1}}$ ($H_{\mathrm{r2}}$) is the resonance field of the free (reference) layer at a given $f$, $V_{\mathrm{S1}}$ and $V_{\mathrm{A1}}$ ($V_{\mathrm{S2}}$ and $V_{\mathrm{A2}}$) are the amplitudes of the symmetric and antisymmetric Lorentz functions of the free (reference) layer and $\Delta H_{1}$ ($\Delta H_{2}$) is the linewidth of the free (reference) layer. Fitting the $\Delta H_{1}$ and $\Delta H_{2}$ vs. $f$ dependence enabled us to calculate the damping of the free and the reference layers independently - Fig. 3(j-k). The results agree well with $\alpha$ obtained using the VNA-FMR method and are included in Fig. 2(c).

Within the limit of the available magnetic field of up to 1 T, for the MTJ annealed at 250∘C the maximum resonance signal was measured for around $f$ = 20 GHz, depending on the magnetic field configuration bonetti_spin_2009 . In order to increase the resonance frequency, the fabricated sample was further annealed at 300∘C, which enhanced the PMA energy. The V-FMR signal measured at a nearly perpendicular field ($\theta$ = 85∘) is presented in Fig. 4(a-i). A much better signal-to-noise ratio was obtained for an azimuth angle $\phi$ = 0∘, resulting in a symmetric lineshape, contrary to the signal presented in Fig. 3(a-i), where $\phi$ = 90∘ resulted in an asymmetric signal. In the general case, the lineshape depends on the angle of the free layer magnetization vector projection on the sample plane and the reference layer magnetization, which, in our case is defined along the $y$ axis (Fig. 3(l)) nozaki_electric-field-induced_2012 . We also note that, contrary to the previous studies of V-FMR in MTJs shiota_high_2014 ; kanai_electric_2014 , the lineshape is only little affected by the bias voltage ($V_{\mathrm{B}}$), which is due to strong PMA in our devices - Fig. 4(j-n). Therefore, magnetic anisotropy changes induced by static bias voltage are weak comparing to high PMA energy.

To understand the angular dependence of the V-FMR and to confirm the magnetization damping analysis, the macrospin simulations were performed. We used Landau-Lifshitz-Gilbert equation, where voltage excitation was modelled as sinusoidal changes of $K_{\mathrm{PMA}}$. This, in turn, contributes an alternating term to the effective field, which determines magnetization dynamics. Afterwards, MTJ resistance is calculated and multiplied by the assumed leakage current associated with the applied voltage, resulting in $V_{\mathrm{mix}}$, in the same way as in the experimental procedure. We used a similar approach previously in V-FMR spin diode effect modelled using micromagnetic simulations frankowski_perpendicular_2017 .

The simulated dependence of the linewidth vs. $f$ for different $K_{\mathrm{PMA}}$ is depicted in Fig. 2(b). A strong deviation from the linear dependence is observed for high $K_{\mathrm{PMA}}$, which is a result of a significant non-collinear direction of the magnetic field and magnetization in this case presented in Fig. 2(d). At the same time, magnetic fields sufficient to saturate the sample would increase the effective field to the level where the VCMA excitation would no longer be strong enough to induce significant magnetization dynamics frankowski_perpendicular_2017 . Therefore, we limit the V-FMR investigation to samples annealed at 250 and 300∘C.

IV Summary

In conclusion, ferromagnetic resonance in W/CoFeB/MgO/CoFeB was investigated by means of wafer-level vector network analyser FMR and voltage-induced FMR in patterned devices. Both the CoFeB thickness and the thermal treatment influence magnetic anisotropy, which reaches a value of 1.5 MJ/m3, which is well above demagnetizing energy. Resonance signals from both the reference and the free layer are analysed, allowing for magnetization damping determination. For thin CoFeB free layers the damping between 0.01 and 0.02 was measured, independent on annealing conditions, which is approximately double of the thicker reference layer damping. V-FMR in the MTJ annealed at 300 ∘C is measured up to a high value of $f$ = 31 GHz.

Acknowledgments

We would like to thank prof. Tomasz Stobiecki, prof. Sławomir Gruszczyński and dr. Sławomir Ziętek for a fruitful discussions and technical assistance in the measurements. This work was supported by the National Science Centre, Poland, grant No. LIDER/467/L-6/14/NCBR/2015 by the Polish National Centre for Research and Development. M.F. acknowledges grant Preludium UMO-2015/17/N/ST3/02276 from National Science Center, Poland. Microfabrication was performed at Academic Centre for Materials and Nanotechnology of AGH University. Numerical calculations were supported by PL-GRID infrastructure.