Measurement of nonlinear frequency shift coefficient in spin-torque oscillators based on MgO tunnel junctions

Abstract

The nonlinear frequency shift coefficient, which represents the strength of the transformation of amplitude fluctuations into phase fluctuations of an oscillator, is measured for MgO-based spintorque oscillators by analyzing the current dependence of the power spectrum. We have observed that linewidth against inverse normalized power plots show linear behavior below and above the oscillation threshold as predicted by the analytical theories for spin-torque oscillators. The magnitude of the coefficient is determined from the ratio of the linear slopes. Small magnitude of the coefficient (∼ 3) has been obtained for the device exhibiting narrow linewidth (∼ 10 MHz) at high bias current.Spin-torque oscillators (STOs) emit a microwave signal. The signal originates in magnetization oscillations excited by bias dc current in a magnetoresistive (MR) device 1,2 . In recent years, extensive studies have been carried out on STOs because they are a promising candidate for an on-chip microwave oscillator 3,4 . One of the important properties of an STO is its frequency nonlinearity, i.e., a frequency depends on an oscillation amplitude 5,6 . Due to the property, the frequency of STO is tunable only by changing bias dc current, which is generally considered to be an advantage for applications. The nonlinearity is, however, a disadvantage of STO when thermal fluctuations are taken into account. According to the analytical theory of Kim et al. 7 , amplitude fluctuations are transformed into phase fluctuations because of the nonlinearity, resulting in spectrum linewidth broadening. The linewidth is a measure of the phase stability of oscillation and it is preferable that it be narrow. Estimating quantitatively the nonlinearity, which determines the device performances, is therefore a key subject for further developments of STOs. According to the recent theories 7,8,9,10,11,12 , the quantity representing the degree of the nonlinearity is the normalized dimensionless nonlinear frequency shift coefficient ν (regarding the definition of the coefficient, see, e.g., Eq. (7) It is theoretically known that the coefficient ν has various values depending on magnetic environments and damping 10,11,12 . In general, the coefficient ν also depends on bias current 10,12 . Considering that the variation of ν with bias current is small in the range near threshold, we treat ν as a constant independent of bias current.First, we demonstrate numerically how large the coefficient ν is in typical STOs. A calculation example of ν at the threshold in a planar device with uniaxial anisotropy is shown in Fig. 1, representing the dependence on the magnitude and the angle of an in-plane external magnetic field. The calculation is performed by the method The parameters chosen are an uniaxial anisotropy field H k = 200 Oe, a demagnetizing field 4πMs = 8000 Oe, the Gilbert damping αG = 0.01, and the nonlinearity of damping 13 q1 = 3. In the notation used here, positive and negative ν denotes the red and blue frequency shift, respectively. described in Ref. 11 ...

Direct experimental measurement of phase-amplitude coupling in spin torque oscillators

“…It was predicted that the value of can be both positive or negative, resulting in blueshift or redshift of the frequency and its value depends on the applied field magnitude and orientation. 10,18 One previous study of the nonlin-ear coefficient extracted from the linewidth dependence on the inverse power 10 found such small values for between 2.5 and 3 for a free layer mode with similar linewidth. For the SAF mode studied here, the frequency only slightly depends on the voltage, hence was expected to be small.…”

“…So far, attempts to measure the nonlinear coefficients has been restricted to frequency domain spectral measurements, despite the greater performance of time-domain techniques. [10][11][12][13][14] In this work we report time domain measurements of the microwave voltage noise related to a spin-torque induced oscillation of the synthetic antiferromagnetic ͑SAF͒ layer of a MgO MTJ nanopillar. 15 We observe that the signal is affected by both phase and amplitude noise.…”

Spin transfer nano-oscillators

“…87 For high current regime, the linewidth is not only related to the thermal fluctuations, but an additional intrinsic linewidth is present due to the chaotization of the magnetization trajectory 20,46 as also observed in recent experimental works. 75,[88][89][90] In addition, for real STNO devices the micromagnetic effects caused by devices edges, defects or inhomogeneous current injections are sources of nonuniform precession and thereby of linewidth broadening.…”

Quasilinear spin-torque nano-oscillator via enhanced negative feedback of power fluctuations

“…where p is the instantaneous normalized power (which may fluctuate away from 0 p ), 0 2 / N df dp   is the agility of the STNO (assumed to be independent of I, except through p 0 (I ) ), and the total damping ( , ) ( This NLAO analysis indicates that ∆f is minimized when both E 0 is maximized and  is minimized, with ideally   1, which leads to strategies [17,18,19] for the reduction of  through the application of either an in-plane hard axis or an out-of-plane magnetic field, Experiments [20,21,22,23,24,25,26] …”