Triple mode-jumping in a spin torque oscillator

Triple Mode-Jumping in a Spin Torque Oscillator

Anders J. Eklund

, Sohrab R. Sani

, S. Majid Mohseni

, Johan Persson

, B. Gunnar Malm

and Johan ˚ Akerman

∗

School of Information and Communication Technology

KTH Royal Institute of Technology, Electrum 229, 164 40 Kista, Sweden

†

NanOsc AB, Electrum 205, 164 40 Kista, Sweden

‡

Department of Physics, University of Gothenburg, 405 30 Gothenburg, Sweden

Abstract—In a nano-contact Co/Cu/NiFe spin torque oscillator, mode-jumping between up to three frequencies within 22.5–

24.0 GHz is electrically observed in the time domain. The measurements reveal toggling between two states with differing oscillation amplitude, of which the low-amplitude state is further divided into two rapidly alternating modes. Analysis of the mode dwell time statistics and the total time spent in each mode is carried out, and it is found that in both aspects the balance between the modes is greatly altered with the DC drive current.

I. I

The spin torque oscillator (STO) [1] is a highly tunable nano-scale spintronic device capable of generating radio fre- quency (RF) signals in the range from a few hundred MHz up to the high microwave and low millimeter wave bands [2]. Due to its high and highly tunable frequency as well as the ability of high modulation rates [3], it is a compelling device for future RF communication applications and high-speed, highly sensitive data read-out of magnetic hard disk bit patterns [4] as well as within magnonics [5] as a source of locally generated spin waves [6], [7].

The device consists of two ferromagnetic (FM) metallic thin films separated by a nonmagnetic spacer layer. An elec- trical current flowing perpendicularly through the film stack becomes spin polarized by the local magnetizations of the FM layers and experiences an electrical resistance which is depen- dent on the relative angle between them. This is known as giant magnetoresistance (GMR); the resistance is at its lowest when the magnetizations are parallel and gradually increases with the angle until the anti-parallel state is reached. Since the electron spin (angular momentum) direction is changed when entering the second FM, the second FM effectively exerts a torque on the electrons. Through Newton’s 3rd law, the magnetization of the second FM is thus subject to an equal and opposite reaction torque, known as spin transfer torque, which can be utilized to change the magnetization direction of the material. In the STO, spin transfer torque is used to destabilize the magnetization of a ’free’ FM layer and excite it into precession similar to ferromagnetic resonance (FMR) [8], [9]. In a more detailed view, the excitation takes place in the form of different spin wave modes [10], one of which is the propagating spin wave mode [11]. This mode is interesting not only from the point

This work was supported by the Swedish Foundation for Strategic Research (SSF), the Swedish Research Council (VR) under contract 2009-4190, and the Knut and Alice Wallenberg Foundation. Johan ˚Akerman is a Royal Swedish Academy of Sciences Research Fellow supported by a grant from KAW.

of view of magnonics but also because of its high frequency stability and its nature to (in most conditions) blue shift with the magnitude of the DC drive current, thereby attaining the otherwise more inaccessible frequencies well above the FMR frequency of the free layer material.

As a function of the DC drive current, STOs generally exhibit nonlinearities in the generated frequency [12]. The non- linearities occur between linear ’plateaus’ which are submodes of the propagating mode, but the origin of these submodes is unknown. In order to suppress the nonlinearities, which apart from complicating the STO operation also generally reduce the frequency stability, the underlying submodes need to be better understood. In this work, we will demonstrate how one or two additional, higher-frequency, submodes can be excited within a range of operating points.

II. M

The sample used in this study is a nano-contact STO, with the GMR film stack specified as Co(5.5)/Cu(5)/Ni

Fe

(3) (thicknesses in nm). The DC drive current is injected per- pendicularly into the films by means of a 100 nm diameter, electron-beam lithography defined circular opening in the insulating SiO

, filled with Cu. Details of the fabrication process can be found in [13]. The nano-contact is connected to the signal line of an on-chip ground-signal-ground (GSG) coplanar waveguide, with its ground lines connected to the bottom of the film stack. The waveguide was contacted with a 0–40 GHz GSG microwave probe. To excite the propagating spin wave mode with high frequency stability and electrical output power, the sample was placed in an applied magnetic field B

= 1.0 T directed with an angle θ

= 70

out of the film plane.

A 0–40 GHz bias-T was used to separate out the AC voltage GMR signal from the DC biasing current IDC (sup- plied by a Keithley 6221 current source). The AC signal was fed to a 0.1–26.5 GHz rated low-noise amplifier (LNA) with 45 dB gain and a 3.3 dB noise figure and first measured with a spectrum analyzer (Rohde & Schwarz FSU 67). Time- domain measurements were carried out by down-mixing the AC signal using a 4–40 GHz mixer with 5.5 dB conversion loss to a 0–4 GHz intermediate frequency (IF) band. The down-mixing reference microwave signal with frequency fLO was supplied by an Agilent E8257D signal generator with negligible phase noise. The lower-frequency part of the IF signal was then further amplified using a 0–2.5 GHz LNA (gain 37.5 dB, noise figure 3.9 dB) in order to be recorded on

ICNF2013 978-1-4799-0671-0/13/$31.00 c 2013 IEEE

DC current (mA)

Frequency (GHz)

10 15 20 25

19 20 21 22 23 24 25

(a)

DC current (mA)

Frequency (GHz)

20 21 22 23 24 25

21.5 22 22.5 23 23.5 24 24.5

dB over noise

0 5 10 15 20

(b)

Fig. 1. Power spectral density with spectrum analyzer settings (a) RBW = 2 MHz, VBW = 10 kHz, tsweep = 0.8 s, average over 5 consecutive sweeps (full sweep frequency range 0 – 30 GHz not displayed) and (b) RBW = 5 MHz, VBW = 10 Hz, tsweep = 60 s, single sweep (full sweep frequency range displayed).

The color scale is identical for both figures.

a real-time digital oscilloscope (LeCroy WaveMaster 825Zi) utilizing an electrical bandwidth limiter at 3 GHz and sampling rate 10 GS/s. With this setup, the measurement bandwidth was limited primarily by the IF LNA to 2.5 GHz, positioned such that the investigated STO signals were well within the range (fLO, fLO + 2.5 GHz). For each of the three operating points selected for time-domain investigation, a total of 40 consecutive 12.8 ms long timetraces were recorded and stored for post-processing.

III. D

A

For observation of the frequency vs time in the recorded timetraces we utilized short-time Fourier transformation (STFT) [14], where the waveform is divided into segments of equal length which are then individually Fourier transformed.

Compared to utilizing pure time-domain analysis (of e.g. the time between the waveform peaks), STFT is less affected by the inevitable electrical measurement background noise and also effectively handles the representation of eventual simultaneous frequencies. Caution is required when selecting the STFT segment length, since this length sets the time resolution. Ultimately, the segment length should be kept as short as possible in order to be able to observe the most rapid frequency changes in the signal, but by using a shorter segment the frequency resolution decreases (following the time-frequency uncertainty principle [14]) making nearby frequencies unseparable. Whenever the STFT of one waveform segment indicates several ’simultaneous’ frequencies, it might always be that the signal is rapidly shifting between the different frequencies during the envelope of the segment. In the current study, we found nonsimultaneity and a reasonable frequency resolution using a segment length of 10 ns. To reduce effects of the periodic boundary conditions of the transform, we used a regular Hamming windowing function, and we denote the segment length as twindow. We utilize half- overlapping segments, thus retrieving one STFT point every twindow/2.

Once we have concluded nonsimultaneity of the involved frequencies, we ascribe each segment to one of their respective frequency bands and extract the dwell time of each individual frequency pulse. In order to decrease the number of ’false’

pulses we require the length of each pulse to be longer than one single STFT point (i.e. minimum length being 10 ns).

Whenever a pulse of length one STFT point is detected, it is dismissed and its length is appended to the previous pulse. The dwell times are plotted in histograms, and due to the large dif- ferences in timescales associated with the different modes, we utilize logarithmic bin widths. We compensate for the unevenly distributed range of discrete measurable lengths by dividing each bin by its number of possible length values and multiply by the bin width and STFT point density (2/twindow). For comparison, one example of an uncompensated histogram for RF 3 is given in Fig. 2d. The plotted histograms contain the count values from the entire 512 ms (40*12.8) of available data for each operating point, and the total time distribution is given within parenthesis as percentage values.

IV. D

The power spectral density as measured with the spectrum analyzer using our routine settings is shown in Fig. 1a. Below IDC = 17 mA, we observe two of the previously mentioned linear plateus, joined by a smooth nonlinearity around 12 mA.

Within 17–21 mA there is more nonlinearity, and the single mode is accompanied by an extremely wide tail which narrows down until the onset of two additional, higher frequency modes takes place at IDC = 21.5 mA. The signal graininess within 21.5–25.0 mA occurs due to the STO changing its frequency on a timescale comparable to the sweep time, tsweep. In order to properly capture the long-time behavior, we set up a considerably slower measurement with the result shown in Fig. 1b. Due to the differing slopes of the two new modes, they intersect at 23.5 mA and merge into a single higher-frequency mode. This mode appears to degrade (while the original mode is again strengthened) as the current is increased further to 25 mA. Currents higher than 25 mA injected into identical devices have shown to irreversibly change the oscillation characteristics (through heating and possibly electromigration) and were thus avoided for the sample investigated in this work.

We first direct attention to the time-domain behavior at

IDC = 22.5 mA, in the center of the triple-mode current

range. The STFT in Fig. 2a clearly shows how the oscillation

changes on a timescale of milliseconds between a state with

Time (ms)

Frequency (GHz)

0 1 2 3 4 5

22.5 23 23.5

(a)

Time (µs)

Frequency (GHz)

96.3 96.4 96.5 96.6

22.5 23 23.5

(b)

0 1 2 3 4 5

−1

−0.5 0 0.5 1

Time (ms)

AC voltage (V)

(c)

10

10

10

10

10

10

10

10

Dwell time (s)

Count (1)

RF 3 (31.4 %) RF 2 (21.8 %) RF 2&3 (53.2 %) RF 1 (46.8 %) RF 3 uncompensated

(d)

Fig. 2. Time-domain measurement at IDC = 22.5 mA. (a) STFT, twindow = 10 µs. (b) STFT, twindow = 10 ns. (c) AC voltage as recorded (i.e. without compensation for the gain of the transmission line). (d) Dwell time distribution.

only the lowest RF (RF 1) and a second state containing the two higher frequencies (RF 2, RF 3). Furthermore, the jumping is accompanied by distinct shifts in the oscillation amplitude, as shown in Fig. 2c where there is a striking correlation with the two-state alternation; the single-frequency state of RF 1 having the higher amplitude. The same relation with higher RF 1 amplitude is also found for the two additional time-domain investigated operating points of IDC = 21.0 mA and 25.0 mA.

One possible explanation could be the theoretically well known dependence of the magnetization precession frequency on the precession amplitude [15], which is however contradicted by comparing the voltages of RF 2 for IDC = 21.0 mA and RF 1 for IDC = 25.0 mA, which both have a frequency close to 23 GHz. The voltages VRMS are 0.19 V and 0.38 V, respectively, and since they are differing by a factor of two for the same frequency we conclude that the amplitude difference between the modes is not a consequence of the STO amplitude- frequency relation. Instead, we view the amplitude difference primarily as a consequence of the different modes representing independent solutions for the magnetization trajectory.

The dwell time distribution in Fig 2d shows that the pulses of RF 2 on average are slightly shorter than for RF 3 and that both favour lengths down towards our minimum measurable value of 10 ns. RF 1 and the double state of RF 2&3, on the other hand, have dwell times in the order of 1 µs – 1 ms.

A portion of the RF 2&3 blocks has the same dwell time as characteristic for RF 2 and 3 individually, and a closer

investigation (not presented here) shows that a clear majority of these are single RF 2 pulses enclosed with RF 1 — providing a clear indication that the modes of RF 2 and RF 1 are closer to each other in the magnetization precession phase space than RF 3 and RF 1.

At IDC = 21.0 mA, just before the two higher-frequency modes rise above the noise floor in the spectrum analyzer, the time-domain measurement (Fig. 3a) reveals that the three frequencies are indeed already present. The dynamics is, though, quantitatively different with RF 3 having shorter dwell times (on the limit of detectability) and being much more sporadic in relation to RF 2. The double-RF state here occupies not more than 2.5 % of the total time (in contrast to 53.2 % at IDC = 22.5 mA) and from Fig. 3b we also note that the double-RF state exists during considerably shorter times than the single-RF, RF 1 state. Finally, at IDC = 25.0 mA, the STFT (Fig. 3c) only resolves one single frequency in the former double-frequency state, with the temporal statistics shown in Fig. 3d. We note that the dwell time distributions are now rather similar to each other, with RF 1 pulses being shorter than for the lower biasing currents.

V. C

A wide-band, highly sensitive electrical time-domain mea-

surement technique was used to observe the real-time dy-

namics of a GMR nano-contact STO and demonstrate the

Time (µs)

Frequency (GHz)

882.4 882.5 882.6 882.7 882.8 882.9 883 22

22.5 23 23.5 24

(a)

10

10

10

10

10

10

10

10

Dwell time (s)

Count (1)

RF 3 (0.2 %) RF 2 (2.3 %) RF 2&3 (2.5 %) RF 1 (97.5 %)

(b)

Time (µs)

Frequency (GHz)

107.6 107.7 107.8 107.9 108 108.1 108.2 23

23.5 24 24.5 25

(c)

10

10

10

10

10

10

10

10

Dwell time (s)

Count (1)

RF 2 (27.4 %) RF 1 (72.6 %)

(d)

Fig. 3. Time-domain measurement STFT (twindow = 10 ns) and dwell time distribution at (a)–(b); IDC = 21.0 mA and (c)–(d); IDC = 25.0 mA.

occurence of mode-jumping between frequencies in this sys- tem. The measurements reveal mode-jumping between two and three frequencies in a two-state pattern, involving timescales down to tens of nanoseconds and up to milliseconds. The mode balance is drastically changed with the bias current.

Furthermore, a pronounced amplitude difference between the two involved states indicates that their respective precessional magnetization orbits are qualitatively different from the theo- retical predictions based on a one-to-one amplitude-frequency relationship. To our knowledge, this type of oscillation dynam- ics is rarely found in any experimental system and highlights the complexity of the magnetization precession in STOs.

R

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