Supplementary material: Nature Nanotechnology NNANO D

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1 Supplementary material: Nature Nanotechnology NNANO D Coercivities of the Co and Ni layers in the nanowire spin valves In the tri-layered structures used in this work, it is unfortunately not possible to measure the coercivities of the cobalt and nickel layers separately. The Ni is electrodeposited within the pores, while the Co is evaporated on top. Since the amount of Co is much more than the amount of Ni, the Co signal completely swamps the Ni signal in magnetization measurements. However, we had individually measured the coercivities of nickel and cobalt nanowires in the past 9, 13. For nickel, ref. [9] reported a maximum coercivity of 950 Oe at room temperature for nanowires of diameter 18 nm and it decreased to 600 Oe for wider nanowires of 21 nm diameter. Since coercivity increases with decreasing temperature 13, a value of 800 Oe is quite possible in our 50- nm diameter nanowires at 1.9 K. The coercivity of cobalt nanowires has been studied extensively in ref. [13]. The coercivity of 22 nm diameter wires was found to be > 1600 Oe at room temperature, so that the coercivity of 50 nm wires can quite likely be 1800 Oe at the low temperature of 1.9 K. Thus, the leading and trailing edges of the peaks occurring in the magnetoresistance shown in Fig. 2 occur at fields that we can reasonably expect to be the coercive fields of the ferromagnetic contacts. Why the magnetoresistance peaks cannot be caused by the AMR effect and must be due to the spin valve effect The resistivity of bulk Co and Ni is ~ 10-6 Ω-m. Because they are in pores, we will concede that the resistivities increase somewhat because of additional surface roughness scattering. Therefore, we will assume that the resistivities are 10-5 Ω-m (this is what was assumed in, for example, 1

2 Ansermet, J-Ph. Perpendicular transport of spin polarized electrons through magnetic nanostructures. J. Phys: Condens. Matt., 10, 6027 (1998).). Because the Co and Ni layers are ~500 nm thick, and the pore diameter is 50 nm, the resistance of each ferromagnetic layer in a single pore is ~ 2.5 kω. Since the contact area of our samples is 1 mm 2 and the nanowire density is 2x10 10 cm -2, the contact pads cover about 2x10 8 wires in parallel. Therefore the contribution of the ferromagnetic contacts to the total resistance of the sample is 2.5 kω/(2 x 10 8 ) = 12.5 µω. If we become even more conservative and assume that only 1% of the wires are electrically accessed, then the contribution of the ferromagnets to the total sample resistance is 1.25 mω. Meanwhile, the peak height is 2 Ω. This peak is more than three orders of magnitude larger than the total resistance of the ferromagnets and therefore cannot originate from AMR effects that affect only the resistance of the ferromagnets. Therefore, this peak must come about from a change in the resistance of the organic and can only be a spin valve peak. Calculation of drift mobility in nanowire Alq 3 The reported drift mobility in Alq 3 is given by the relation 28 : 2 µ ( E) = µ exp[ α 1/ ] (S-1) 0 E where µ 0 and α are constants and E is the electric field. Ref. [28] reports µ 0 = cm 2 /Vsec, and α = 10-2 (cm/v) 1/2 in the bulk or thin-film organic. In order to determine the electric field E in the organic, we proceed as follows. The voltage over the nanowires can be estimated from the measured resistance and the current using Ohm s law: V = IR = 10 µa x 1520 Ω = 15.2 mv. Since the Alq 3 layer (in the first set) is nominally 33 nm 2

3 wide, the average electric field across it is 15.2 mv/33 nm = 4.6 kv/cm. Using this value in Equation (S-1), we estimate that the carrier mobility in the thin-film organic is 2 x x 10-9 cm 2 /V-sec. In nanowires, the mobility is expected to be lower. Elliott has derived a relation between the spin relaxation time τ s and the momentum relaxation time τ m which Yafet has shown to be temperature independent [Yafet, Y., in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic, New York, 1963), Vol. 14.]: τ m τ s E g (S-2) Here is the spin orbit interaction strength in the band where the carrier resides (in our case the LUMO band) and E g is the energy gap to the nearest band (in our case the HOMO-LUMO gap). The spin relaxation time is τ s (T) = λ 2 T /D s (T) where D s (T) is the spin diffusion coefficient 17. There is some question about whether the spin diffusion coefficient D s (T) and the charge diffusion coefficient D(T) are the same [Pramanik, S., Bandyopadhyay, S. and Cahay, M. unpublished], but this is mostly pertinent to when the spin relaxation mechanism is D yakonov- Perel. For the Elliott-Yafet mechanism, spin relaxation is tied to momentum relaxation and therefore D s (T) D(T). Therefore, τ s (T) = λ 2 T /D(T) = m * λ 2 T /(ktτ m ), where D(T) is the temperature dependent diffusion coefficient related to the mobility by the Einstein relation and m * is the effective mass. Using the above, Equation (S-2) can be recast as (τ 2 mkt/m * λ 2 T ) /E g. Since neither nor E g is affected by confinement in a nanowire, we can posit that at any temperature τ τ λ = (S-3) thin film thin film m T nanowire nanowire m λt 3

4 Since we found that the spin relaxation time is suppressed tenfold in a nanowire compared to the value in thin films, we conclude that the momentum relaxation time (and hence the mobility) must also be suppressed tenfold in a nanowire. Therefore, our mobility is 2 x x cm 2 /V-sec. Relative insensitivity of the spin diffusion length to spin flip at the interfaces of the organic and the ferromagnets Spin flip at the interface between the injecting ferromagnet and the organic (first interface) will reduce the spin polarization from P 1 to P 1 /α 1. Spin flip at the interface between the organic and the detecting ferromagnet (second interface) will reduce the spin polarization from P 2 to P 2 /α 2. Referring back to Equation (1) in the main text, the product P 1 P 2 will be replaced by P 1 P 2 /α 1 α 2. The modified Equation (1) will be: 2( PP / η) e ( d d0 )/ λt R = 1 2 (S-4) ( d d0 )/ T R 1 λ ( PP 1 2/ η) e We have re-calculated λ T from Equation (S-4) for various values of α 1 and α 2. We plot below the re-calculated λ T as a function of η = α 1 α 2 for P 1 = 42%, P 2 = 34% and d-d 0 = 33 nm. Even if we assume a large spin relaxation at either interface (α 1 =α 2 = 2), λ T changes from 5.5 nm to 7.5 nm, which is less than 50% change, not an order of magnitude change. Therefore, λ T is not particularly sensitive to spin flip at the ferromagnet/organic interfaces in our samples. 4

5 Fig. S-1: Spin diffusion length λ T, calculated from modified Equation (1), as a function of η = α 1 α 2. Importance of long spin relaxation time in opto-spintronics It is often claimed that organic light emitting diodes (OLEDs) will capture 50% of the display market by 2015, since these are inexpensive compared to semiconductor (inorganic) LEDs, and can be produced on flexible substrates. The OLED consists of a p-n junction diode, just like an inorganic LED, with one difference: the p-type region is a hole transport layer and the n-type region is an electron transport layer. Alq 3 is an important electron transport layer used in OLEDs. In OLEDs, the electron-hole pairs form excitons which recombine to produce photons or light. Because of the valley degeneracies in the HOMO level of organic molecules, 75% of the excitons formed are triplets and 25% are singlets. Only the singlets recombine radiatively to produce photons, while the triplets recombine non-radiatively to produce phonons and are 5

6 wasted. Therefore, the maximum efficiency is limited to 25%. This can be changed if we inject spin polarized carriers into the electron and hole transport layers to produce only singlets. In that case, the maximum efficiency can be 100%, resulting in brighter OLEDs. There is already some experimental evidence for this [ref. 27]. For all this to happen, it will be necessary that the spin relaxation time exceed the exciton lifetime (or radiative recombination time) considerably. That will ensure that the singlets remain as singlets until they recombine. For this purpose, long spin relaxation times are very desirable. This paper shows that long spin relaxation times are indeed possible in optically active organics like Alq 3. Atomic force micrograph of the porous anodic alumina film used to produce the nanowire spin valve structures Fig: S-2: Atomic force micrograph of the porous anodic alumina film used to fabricate the nanowire spin valve structures. The dark areas are the pores (50 nm diameter) and the surrounding light areas are alumina. 6