was shown to be negligible [92]. The difference in linewidth of a sample with graphene and one without graphene can be used to estimate the real part of the effective spin-mixing conductance [222,223]
g↑↓= 4πMsdF M
gµB
αP y/Gr− αP y
, (6.3)
where dF Mis the thickness of the ferromagnetic Py layer. The imaginary part of the spin mixing conductance can be neglected since it is much smaller than the real part for metallic ferromagnets [222]. The spin-mixing conductance is a measure of the efficiency of the spin injection and was here estimated to be 2 × 1020m−2 using Ms = 0.96 T as extracted above, dF M = 30 nm and a literature value of g = 2 [212]. The value of the effective spin-mixing conduc-tance extracted here is substantially larger (roughly one order of magnitude) than previously reported in similar Py/graphene systems [92,93]. The spin mixing conductance is an important figure of merit if one wants to investigate the spin transport properties of the graphene channel as discussed below.
6.4. Inverse spin Hall voltage
In the section above clear indication of spin pumping into graphene is shown based on the broadening of the FMR in samples where graphene is present.
In order to investigate spin transport in graphene, a spin current js can be detected with a Pt electrode placed at a distance L (600 nm for device A and 700 nm for device B) from the Py pad, see also Fig. 6.2. The charge current jc due to the inverse spin-Hall effect can be detected as a voltage in an open-circuit configuration. This voltage changes sign if the direction of the spin polarization σ is reversed (jc∼ σ × js, see also section1.4), while σ is simply controlled by the external field H. The voltage due to the inverse spin-Hall effect follows the line shape of the FMR and is therefore described by a Lorentzian.
Here, the voltage U at the Pt electrode was measured with a lock-in techni-que employing magnetic field modulation (µ0dH ∼2.75 mT) at a frequency of 377 Hz. This technique has the advantage that it is more sensitive and not affected by thermal voltages that can drift over the long time scales of the me-asurements. Therefore, we recorded dU/µ0dHas a function of frequency and magnetic field as shown in Fig.6.5(a). The signal follows the FMR condition, which is indicated by red dots. The slight discrepancy at larger frequencies can be explained by sample to sample variation as the FMR condition was extracted from a different sample. Fig.6.5(b) shows dU/µ0dHas a function of magnetic field and reveals the expected lineshape of a derivative of a Lorent-zian. Similar results were obtained for sample B, shown in Fig.6.5(c). The voltage at the Pt electrode shows for all frequencies the expected symmetry in magnetic field as one can easily see in Fig.6.5(a).
6. Spin pumping into graphene
50
0
-50 µ0H (mT)
8 7 6 5 4 3 2
f (GHz)
-200 -150 -100 -50
0 50 100 150 dU/µ0dH (µV/T)
(a) sample A
-50 0 50
dU/µ0dH (µV/T)
(b) sample A @ 4.10GHz
16 12 8
4 -40 -20 0 20 40
µ0H (mT)
sample B @ 3.65GHz
Figure 6.5. Inverse spin Hall voltage at Pt electrode: (a) shows the voltage measured at the platinum electrode as a function of magnetic field and frequency for sample A. The superimposed red dots mark the position of the FMR condition extracted from a measurement of S11 of a different sample.
(b) shows the cut indicated in (a) and a cut from sample B. The signal clearly shows the mirror symmetry with respect to zero magnetic field. In the case of sample B, the data points around zero magnetic field were removed due to technical limitations.
120
6.4. Inverse spin Hall voltage
As motivated above, a magnetic field modulation based measurement techni-que has its advantages when it comes to sensitivity and influences by spurious effects. However, it can itself lead to a background signal, which we would like to discuss in this paragraph. The small modulation of the magnetic field induces a voltage in the wires connecting the sample to the voltage amplifiers.
This voltage depends on the magnetic field due to a field dependent modula-tion amplitude given by the magnet set-up. This is a result of a non-linear current to field conversion of the magnet set-up used here. In order to remove this background, the voltage at the Pt electrode was once measured with the microwave source turned on and once with the microwave source turned off.
The difference of these two measurements is shown in Fig.6.5and used in the following analysis.
6.4.1. Influence of spurious effects
It is well known that several spurious effects can appear in spin pumping experiments [223]. Since the voltage at the Pt electrode is measured at low frequency, these effects can either arise due to thermal gradients in the sample or due to RF rectification effects (down mixing).
The effect of thermal voltages can most likely be excluded since the voltage is measured in a field modulation technique that is only sensitive to voltages that depend on the external magnetic field. Therefore, only charge currents within the Py pad could give rise to a magnetic field dependent voltage. However, thermal gradients in the Py pads, creating a charge current within the Py pads, are highly unlikely since a homogeneous RF absorption is expected. We therefore rule out any contributions from thermal effects.
The measurement set-up presented above are only sensitive to voltages that develop in x direction. As far as we know, only the AHE can contribute to a rectification effects that lead to a potential gradient along this direction. The AHE was included into the analysis and its contribution could be quantified due to a different lineshape. The contribution was found to be small and only weakly dependent on RF power.
6.4.2. Power dependence of the voltage at the Pt electrode
The voltage due to the inverse spin Hall effect at the Pt electrode should scale linearly with applied RF power (js∼ h2RF). In order to extract the dependence on RF power, the measured dU/µ0dHwas fitted with a model containing the signal originating from the inverse spin Hall effect and from the anomalous Hall effect [116]:
U(H) = UISHE
γ2
(H − HF M R)2+ γ2 + UAHE −2γ (H − HF M R)
(H − HF M R)2+ γ2. (6.4)
6. Spin pumping into graphene
Here, UISHEand UAHErepresent the amplitudes of the contribution of the ISHE and the AHE to the signal. HF M Ris the field at which the FMR condi-tions is met and γ describes the width of the resonance, as earlier described.
Contributions due to the AHE can be expected since RF eddy currents are induced by the RF magnetic field in the Py pads. These currents flow in the y-z plane in the permalloy and in combination with a varying magnetization in the x-z plane an anomalous Hall voltage (a Hall voltage proportional to the magnetization) can be expected to appear. This voltage will consist of a component at twice the frequency and of a down mixed DC component along the x direction.
Power dependence was performed on sample B and a fit at 8.9 mW is shown in the inset in Fig. 6.6. The contribution due to the ISHE is much larger than the contribution due to the AHE for any microwave power investigated.
Both contributions scale linearly with power as indicated by the solid lines that are guide to the eyes. The linear scaling with power is expected for both contributions.
Figure 6.6. Power dependence of the voltage at the Pt electrode:
The contribution of the ISHE and the AHE to the voltage at the Pt electrode are shown as a function of microwave power individually. The inset shows an actual measurement with a fit to Eq.6.4. Both contributions scale linearly with power as indicated by the red and blue lines that are guides to the eye.