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A Tunable Magneto-Acoustic Oscillator with Low Phase Noise

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A Tunable Magneto-Acoustic Oscillator with Low Phase Noise A tunable magneto-acoustic oscillator with low phase noise A. Litvinenko,1, ∗ R. Khymyn,2 V. Tyberkevych,3 V. Tikhonov,1 A. Slavin,3 and S. Nikitov1, 4, 5 1Laboratory of metamaterials, Saratov State University, 410012, Saratov, Russia. 2Department of Physics, University of Gothenburg, 412 96, Gothenburg, Sweden. 3Department of Physics, Oakland University, 48309, Rochester, Michigan, USA. 4Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, 125009, Moscow, Russia. 5Moscow Institute of Physics and Technology (National Research University), 141700, Dolgoprudny, Moscow Region, Russia. (Dated: November 17, 2020) A frequency-tunable low phase noise magneto-acoustic resonator is developed on the base of a parallel-plate straight-edge bilayer consisting of a yttrium-iron garnet (YIG) layer grown on a substrate of a gallium-gadolinium garnet(GGG). When a YIG/GGG sample forms an ideal parallel plate, it supports a series of high-quality-factor acoustic modes standing along the plate thickness. Due to the magnetostriction of the YIG layer the ferromagnetic resonance (FMR) mode of the YIG layer can strongly interact with the acoustic thickness modes of the YIG/GGG structure, when the modes' frequencies match. A particular acoustic thickness mode used for the resonance excitations of the hybrid magneto-acoustic oscillations in a YIG/GGG bilayer is chosen by the YIG layer FMR frequency, which can be tuned by the variation of the external bias magnetic field. A composite magneto-acoustic oscillator, which includes an FMR-based resonance pre-selector, is developed to guarantee satisfaction of the Barkhausen criteria for a single-acoustic-mode oscillation regime. The developed low phase noise composite magneto-acoustic oscillator can be tuned from 0.84 GHz to 1 GHz with an increment of about 4.8 MHz (frequency distance between the adjacent acoustic thickness modes in a YIG/GGG parallel plate), and demonstrates the phase noise of -116 dBc/Hz at the offset frequency of 10 KHz. PACS numbers: 85.75.-d, 05.45.Xt, 75.40.Gb, 75.47.-m, 84.30.Qi: I. INTRODUCTION significantly reduce the close-in phase noise, the far-out phase noise still remains determined by the intrinsic pa- One of the most important tasks in the modern com- rameters of the used VCO. munication and radar technology is the development of The phase noise of an oscillator can be estimated using reference oscillators with low phase noise, as the low level an empirical Leeson's equation[4]: of phase noise translates into a high level of frequency 2 F kT !0 !c stability necessary for the improved device performance. L(∆!) = 10log 1+ 1+ (1) 2P 2Q∆! ∆! Also, in digital communication systems phase noise af- s fects the system bit-error rate, and, therefore, the speed where !0 is the oscillator central (or "carrier") frequency, of data processing. In radar applications, lowering the ∆! | is the ”offset” frequency, Ps { is the signal power, phase noise leads to the increase of a radar range and F { is the noise factor of the oscillator active element, sensitivity, as it allows to detect a signal reflected from k { is the Boltzmann constant, T { is the ambient abso- the target with a lower power level. lute temperature, Q { is the unloaded resonator quality In many common applications, reference or local tun- factor, and !c { is the flicker corner frequency [4]. As it able oscillators are based on the yttrium-iron garnet follows from the Leeson's equation (1), both the "close- (YIG) resonators, because the frequency of a ferromag- in" and the "far-out" levels of the phase noise of an os- netic resonance (FMR) in YIG can be easily tuned cillator are, mainly, determined by the quality factor of over a decade by applied bias magnetic field. Also an resonator used in the oscillator. YIG resonators biased by powerful permanent magnets Thus, the enhancement of the resonator Q-factor is could have rather high resonance frequencies lying in the a key element in the development of new reference GHz frequency range, and demonstrate a relatively low oscillators for information and signal processing[5{8]. arXiv:2011.07648v1 [physics.app-ph] 15 Nov 2020 linewidth, and, therefore, a relatively low level of the This goal, in principle, can be achieved by using res- phase noise, especially at the reasonably large offset fre- onators with low energy losses, such as dielectric[9], quencies from the carrier. Another common method to optoelectronic[10], acoustic[11], and magnetic oscillators reduce the oscillator phase noise is to use voltage con- [12] or the combinations of these oscillator types[13]. trolled oscillators (VCO) stabilized with a phase locked The highest Q-factor, so far, is found in optoelectronic loop (PLL) [1{3], but, although this technique allows to and dielectric resonators, but, unfortunately, these res- onator types are, usually, rather bulky and have insuffi- cient thermal stability of their resonance frequency. An alternative is to use the solid-state acoustic resonators ∗ Currently with Spintec, France. Correspondence to: Litvi- that can demonstrate Q-factors that are much higher [email protected] than in magnetic YIG magnetic resonators, while having 2 FIG. 1. a) Scheme of the a simple one-port reflection-based MAR , which was experimentally characterized using a vector network analyzer (VNA); b) Thickness distributions of the magnetic FMR mode and standing acoustic modes in the YIG/GGG bilayer sample; c) S11-parameters of the one-port MAR at different values of the perpendicular-to-plane magnetic bias field. sizes that are much smaller than the sizes of dielectric uration presented in Fig. 1 the whole YIG/GGG struc- and optoelectronic resonators. Unfortunately, the purely ture acts as an effective high-overtone bulk acoustic res- acoustic resonators are not tunable. onator (HBAR)[11, 36, 37]. Note, that HBARs among all A compromise solution would be to use hybrid the known acoustic resonators demonstrate the highest 14 magneto-acoustic resonators (MAR) that can support Q-factor (up to 10 ), making the proposed YIG/GGG hybrid magneto-elastic oscillation modes that combine a MAR design well-suited for the realization of low phase high quality factor of the purely acoustic modes with the noise local oscillators. In this work, using the results excellent tunability of the magnetic modes. It was shown of theoretical analysis of the magneto-acoustic interac- in 1950s-60s that YIG has a considerable magnetostric- tion and experimental parameters of the YIG/GGG epi- tion constant[14], and that magneto-elastic waves of the taxial parallel-plate structures, we design a novel tun- GHz frequency range can be efficiently excited in mag- able magneto-acoustic oscillator that has a level of phase netic layered films and hetero-structures [15{22]. In the noise, that is much lower than in conventional magnetic 1980s the technological progress in the liquid-phase epi- oscillators based only on the FMR mode of a YIG film. taxy resulted in the development of high-quality (FMR linewidth below 0.5 Oe) YIG films grown on the (al- most lattice-matched) mono-crystalline gadolinium gal- II. MAGNETO-ACOUSTIC RESONATOR WITH lium garnet (GGG) substrates. It was also demonstrated A HIGH Q-FACTOR that magnetic oscillations excited in YIG through magne- tostriction can effectively excite standing acoustic thick- The scheme of the YIG/GGG MAR is shown in the ness modes in the whole YIG-GGG garnet structure, be- Fig. 1(a). It consists of a parallel-plate straight-edge rect- cause the sound velocities in YIG and GGG are almost angular resonator cut from a monocrystalline epitaxial equal [23{26]. The interest to magneto-acoustic effects YIG/GGG bilayer magnetized to saturation perpendicu- in garnet hetero-structures has been recently revived in a lar to its plane by a bias magnetic field H0, and excited number of papers where YIG-GGG structures were used by a strip-line antenna connected to a vector network an- either in the transmission line configuration [27{29] or alyzer (VNA). The YIG film in the bilayer has the static with ZnO acoustical transducers which were used for a magnetization 4πMs = 1740 Gs , the FMR linewidth broad-band excitation of acoustic modes in these struc- ∆H0 = 0.5 Oe and the thickness of 9.75 µm, and the tures [30{33]. in-plane sizes of 2x2 mm2. The thickness of the GGG Below, we show that a traditional parallel-plate layer is 364 µm. straight-edge YIG/GGG resonator can be successfully A signal of a given frequency f from the strip-line an- used as a tunable high-Q-factor magneto-acoustic res- tenna excites the FMR mode in the YIG layer (uniform onance element of a local oscillator with a low phase along the YIG film thickness) corresponding to a partic- noise. YIG/GGG films were previously used as hy- ular magnitude of the bias perpendicular bias magnetic brid magneto-acoustic resonators (MAR)[34, 35], where field H0. The FMR mode of the YIG resonator is coupled the YIG film served as an effective, narrow-band and through the YIG magnetostriction to the standing thick- frequency-tunable transducer which can selectively excite ness acoustic modes of the YIG/GGG hetero-structure, an acoustic thickness standing mode of the YIG/GGG and by simultaneous variation of the excitation frequency structure, having a desirable frequency. In the config- f and the bias magnetic field H0 it is possible to align any 3 of the discrete thickness acoustic modes of the YIG/GGG the FMR mode in the absence of the magneto-elastic in- hetero-structure with the YIG resonator FMR frequency teraction Hac = 0. Similarly, we represent the dynamic given by the Kittel formula: acoustic displacement, using the known profiles of the acoustic thickness eigenmodes of the YIG-GGG struc- f = γ(H0 − µ0Ms); (2) ture: where γ = 28:3 GHz/T - is a gyromagnetic ratio of YIG.
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