3418 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 54, NO. 12, DECEMBER 2007 Efficiency of Spin-Wave Bus for Information Transmission Alexander Khitun, Dmitri E. Nikonov, SeniorMember,IEEE, Mingqiang Bao, Member,IEEE, Kosmas Galatsis, and Kang L. Wang, Fellow,IEEE Abstract—We compare the transport parameters such as signal attenuation and signal velocity for a spin-wave bus and a conven- tional electronic transmission line. The spin-wave bus is inferior to the traditional metal interconnects in all figures-of-merit. The realization of integrated spin-wave-based logic circuits will require spin amplifiers to provide gain. Index Terms—Magnetic circuits, magnetic films, magnetostatic surface waves, transmission lines. I T HAS recently been proposed to use spin waves as a physi- cal mechanism for information transmission and processing [1]–[3]. A bit of information can be encoded into the phase of the spin wave (e.g., two relative phases of “0” and “π” may be used to represent two logic states 1 and 0, respectively). The data processing in the circuit is accomplished by manipulating the relative phases of the propagating spin waves. Magnetic films can be used as a spin conduit media for wave propagation, or otherwise referred to as the spin-wave bus. In this paper, we discuss two important characteristics of the spin-wave bus: 1) signal propagation speed and 2) signal attenuation. The speed of signal propagation is defined by the spin- wave group velocity, whereas the dissipation power is defined by the spin-wave damping. To explore the efficiency of the spin-wave bus, we estimate the transport characteristics of the ferromagnetic spin waveguide and compare them with those of a conventional electronic transmission line with the same dimensions. In Fig. 1(a), we have schematically shown the general view of a microstrip and the spin-wave bus. The mi- crostrip consists of a conductive substrate (ground plane), a dielectric layer, and a signal conductor on the top. The dielectric layer has thickness t and relative permittivity ε r , and the signal conductor has thickness d and width w. The spin-wave bus consists of a ferromagnetic wire on top of a nonmagnetic in- sulating substrate, which has the same dimensions as the signal Manuscript received September 7, 2007. This work was supported in part by the Focus Center Research Program Center on Functional Engineered Nano Architectonics (FENA) and in part by the Nanoelectronics Research Initiative, Western Institute of Nanoelectronics (WIN). The review of this brief was arranged by Editor S. Datta. A. Khitun, M. Bao, K. Galatsis, and K. L. Wang are with the Device Research Laboratory, Department of Electrical Engineering, FENA, University of California, Los Angeles, Los Angeles, CA 90095-1594 USA, and also with WIN, University of California, Los Angeles, Los Angeles, CA 90095- 1594 USA (e-mail: ahit@ee.ucla.edu). D. E. Nikonov is with the Technology and Manufacturing Group, Intel Corporation, Santa Clara, CA 95054 USA. Digital Object Identifier 10.1109/TED.2007.908898 conductor (w = 0.2 mm, d = 0.1 mm, and t = 10 μm). Signal propagation in both cases can be represented as a superposition of two waves traveling in opposite directions along with the microstrip or the spin-wave bus. The amplitude of the signal can be expressed as follows: A(z,t)= A 1 e -κz cos(ωt - βz)+ A 2 e κz cos(ωt + βz) (1) where κ represents the attenuation, and β defines the signal velocity ν = ω/β. For numerical assets on the spin-wave bus, we use the analytical formula for spin-wave dispersion in a finite-size ferromagnetic film [4], which is given by ω =  ω H (ω H + ω M )+ ω 2 M 4 (1 - exp -2kd )  1/2 (2) where d is the thickness of the ferromagnetic film, ω H = γH 0 , ω M = γ 4πM s ,γ is the gyromagnetic ratio, and H 0 is the external magnetic field at which film magnetization saturates at M s . We estimate the spin-wave attenuation κ =(τν ) -1 , where τ =(2πγαM s ) -1 is the relaxation time and α is the Gilbert damping coefficient. In our numerical simulations, we used an experimentally found Gilbert coefficient of α = 0.0097 from [5], and the material characteristics for NiFe, i.e., γ = 19.91 × 10 6 rad/s Oe, 4πM s = 10 kG, and H 0 = 200 Oe, are taken from the literature [6], [7]. Signal attenuation in the microstrip transmission line is estimated by the RLC model described in [8], and the following formulas for the transport coefficients were used: κ = R 2  2C/L  1 +  1 + ω 2 c ω 2  1/2  -1/2 β = ω  LC/2  1 +  1 + ω 2 c ω 2  1/2  1/2 (3) where ω c = R/L, R is the resistance per unit length, L is the inductance per unit length, and C is the capacitance per unit length. To consider the skin effect, we use the closed-form formulas that are found in [9]. The resistance and inductance per unit length in the high-frequency region asymptotically behave as follows [9]: R ′ (f ) → R ′ ∞ (f )= R ′ ∞ (f i )  f/f i L ′ (f ) → L ′ ∞ + R ′ ∞ (f )/ω (4) 0018-9383/$25.00 © 2007 IEEE