Magnetoresistive detection of spin waves

Abstract

We explore a detection method for spin waves consisting in integrating a magnetoresistive sensor on a magnonic waveguide. When subjected to the stray magnetic field generated by the spin wave, the relative orientation of the magnetizations of the two magnetic layers in the sensor oscillates in time, resulting in an electrical resistance change according to the so-called giant magnetoresistance effect. Upon application of an appropriate current bias, this variation of resistance translates into a sizable microwave voltage. At the submicrometer scale explored here, this signal is about 50 times larger than the one extracted from conventional inductive measurements of spin waves for comparable detection areas. Moreover, this detection scheme is expected to scale very favorably down to the nanometer size relevant for future magnon-based data processing architectures.

Fig. 1.. MR detection of spin waves.

(A) Working principle. In orange, the waveguide in which a spin wave propagates. In gray, the soft (free) layer with its magnetization oscillating around its equilibrium state (dashed line) due to the dipole stray fields generated by the spin wave (dashed arrows). In green, the hard (reference) layer supposed unperturbed by the spin wave. (B) Annotated scanning electron microscopy picture of a typical measured sample. Left: The exciting microwave antenna (yellow), connected to port 1 of the vector network analyzer. Right: The sensor in which the gray center part is the MR detection area. The sensor is connected to port 2 of the vector network analyzer. In orange, the Ni₈₀Fe₂₀ waveguide covering the excitation antenna and the sensor. (C) Typical spin-wave signal. The graph shows the real part of the mutual impedance from port 1 to port 2 for a $+I_{\text{DC}}$ and a $-I_{\text{DC}}$ bias, dashed blue and solid magenta lines, respectively, with $\mid I_{\text{DC}}\mid =1.5$ mA.

Fig. 2.. Analysis of the measured mutual inductance.

(A) Inductive contribution $\mathrm{\Sigma }{Z}_{21}$ to the mutual impedance. Real part (blue dashed curve), imaginary part (red curve), and modulus (black dotted curve). (B) MR contribution $\mathrm{\Delta }{Z}_{21}$ to the mutual impedance. Real part (blue dashed curve), imaginary part (red curve), and modulus (black dotted curve). (C) Real part of the MR signal measured for several applied external fields, ${\mathrm{\mu }}_0{H}_0=20$ , 40, and 60 mT (blue dashed, magenta and black dotted curves, respectively). (D) Experimental (black squares and black dots) and theoretical (blue and red lines) estimates of the resonance frequency and group velocity of spin waves (see method of extraction in the Results).

Fig. 3.. Micromagnetic simulation of the system.

(A) Cross-sectional sketch of the layout of the simulation containing the exciting antenna (yellow structure) represented with its Ørsted field, the Permalloy slab (orange) in which a spin wave propagates at a wave vector $\mathbf{k}$ , and the GMR stack (green and gray). (B) Real part (blue dashed curve), imaginary part (red curve), and modulus (black dotted curve) of the response function ${\mathrm{\Phi }}_{\mathit{xx}}$ relating the oscillation of the free layer to the excitation provided by the microwave antenna. This function provides a numerical equivalent of the transmission spectrum measured in the device. Magnetic field is ${\mathrm{\mu }}_0{H}_0=20$ mT. Other magnetic parameters and dimensions are given in Materials and Methods. (C) Visualization of simulated spin wave and free-layer oscillations for a microwave frequency of 6.06 GHz [corresponding to the maximum of the modulus in (B)]. The color map shows a snapshot of the normalized in-plane component of the dynamic magnetization $m_x$ . For easier visualization, the dynamic magnetization in the GMR stack has been multiplied by a factor of 5. Note the interrupted y scale allowing one to visualize both the magnonic waveguide and the GMR stack despite their large vertical separation.