5 Results and Discussion-Conventional Ferromagnet:
6.1 Fe/Nb system
6.1.3 Fe/Nb interface resistance by CPP measurement
In this section, we investigated the electron transport properties of interface between ferromagnet and superconductor with current flowing perpendicular to plan (CPP) at 4.2 K in Fe/Nb multilayers. When the bulk scattering is negligible in a ballistic contact, the transport properties are directly connected to the probabilities of scattering at the interface. In a ferromagnet with different numbers of spin-up and spin-down conduction channels, only a fraction of the majority channels can be Andreev reflected. However, experimental studies of F/S contacts in the diffusive limit are more intriguing and are more complex in unconventional proximity effects.
[9] The resistance can either decrease or increase when cooling from above the critical temperature of superconductor. [10-12]Transport properties are governed by interplay between spin accumulation close to the interface and the Andreev reflection at the interface.
Each sample has N Fe/Nb repeated bilayers plus one layer of Fe, indicated as (Fe/Nb)N/Fe. The superconducting energy gap ∆ of Nb is smaller than the energy of the exchange fields in Fe by several orders of magnitude. Thus, the conventional proximity effect in ferromagnetic metals is negligible. All changes induced by the contact to a superconductor depended on the properties of the interface itself.
From the results of Section 6.1.1, the sputtered bulk Nb has a superconducting transition temperature of TC = 9.2 K. When Nb films are sandwiched between fixed Fe thickness, TC decreases with decreasing Nb thickness. We have deduced the
Nbcrit 34
d ≈ nm from the analysis of our experimental data within the Radović’s model under the single mode approximation.[13, 14]This means when Nb thickness is thinner than dNbcrit ≈ 34nm, Nb is always normal, otherwise the Nb could become
superconductor in Fe/Nb multilayers based on the phase diagram of Fig. 6.3.
In the present CPP experiment, two series of samples were made with Nb thickness fixed at 15 and 80 nm separately, Fe thickness fixed at 20nm, and increasing numbers of bilayers. Plots of the product of the sample area A and total resistance RT
against bilayer number N are given in Fig. 6.5. The unit area CPP resistance ART is linearly proportional to the number of bilayers for both Nb thicknesses. The dash lines in Fig. 6.5 are least–squares fit to each set of data. Shukla et al.[15]calculated the interlayer exchange coupling between Fe layers when separated by Nb space layers, using a self-consistent full-potential linear augmented plane-wave (FLAPW) method.
They observed an oscillating exchange coupling as a function of Nb spacer thickness with a period of 0.6 nm. However, we found that the Fe layer was not coupled across Nb in the Fe/Nb multilayer thin film with Nb thickness varied from 0.5 nm to 4 nm.
[16] Since there is no antiferromagnetic coupling of Fe through Nb film, a one-band model could be applied. Therefore, the linear behavior of AR against N can be described as
for normal Nb. Here t is the thickness,ρ is the resistivity, and RFe/Nb(NM),(S) is the interface resistance between Fe and Nb layers for normal and superconducting states, respectively. According to individual fit, the equation is easy to be simplified as
1 2
ART =C +C N for normal Nb and ART =(N+1)C1 for superconducting Nb, with
1 2 Fe/Nb( )S Fe Fe
C = AR +ρ t and C2 =2ARFe/Nb(NM) +ρFe Fet +ρNb Nbt . Similar analysis on Co/Nb multilayers has been presented in Chapter 3. [17] There is mutual uncertainty between C1 and C2. We can perform a global fit to all data simultaneously since the
two sets of data share the same parameters. As shown in Fig. 6.5, the straight line gives C1=7.1 1.3 ± fΩ m2 and C2 =5.2 0.6 ± fΩ m2 . The specific unit area resistance of one pair of interfaces can be derived to be
2 / ( )
2ARFe Nb S =5.9 0.3± fΩ m and 2ARFe Nb NM/ ( ) =2.8 0.4± fΩ m2 by putting bulk resistivities 6.2 Ω μ cm and 8 Ω μ cm for 500 nm thick Fe and Nb at 10 K into Eq.
(6.6). and Eq. (6.7). From the Pippard’s model of partial quenching of Andreev reflection by impurities in the superconductor, the residual (S/NM) boundary resistance can be written as 2AR∝ρs al , where ( )
a 2 S
l = π ξ is the extinction length in S of the electron evanescent wave from NM, ξS is the intrinsic coherence length in S, and ρs is the bulk resistivity when S is in the normal state just above Tc. [18, 19]
The value 2ARCo / Nb( )S =6.3 0.9± fΩ m2 for Co/Nb multilayer reported in Chapter
5 [17] is close to 2ARFe/Nb( )S =5.9 0.3± f mΩ 2 for Fe/Nb multilayer. This is expected from Pippard’s model due to that AR is only proportional to the coherence length and resistivity in superconductor film.
Instead of using bulk resistivity, we also varied the Fe and Nb thickness while the numbers of bilayers were fixed at 6 and 12, respectively, to treat the CPP resistivities as fitting parameters. The CPP resistance is linearly proportional to the thickness for both Fe layer and Nb layer. Using one-band model, the linear behavior of AR against thickness can be written as
for varying Nb thickness (dNb) with Fe thickness fixed at 20 nm. As shown in Figure
6.6(a) and (b), individual linear least-square fits of AR versus dFe and dNb samples yield a slope ρFe of 6.2 Ω μ cmand ρNbof 12 Ω μ cm, respectively. However, all the above equations share the same parameters. Therefore, we can perform a global fit to all data simultaneously to reduce the deviation. We can rewrite
Eq. (6.3) as ART =g1+Ng2+(N+1)t gFe 3 +Nt gNb 3, Eq. (6.4) as ART =(N+1)g1+(N+1)t gFe 3,
Eq. (6.5) as ART =g1+6g2+7d gFe 3 + 6t gNb 3, and
Eq (6.6) as ART =g1+12g2+13t gFe 3 + 6d gNb 3.
Here g1 is the2ARFe/Nb( )S , g2 is the 2ARFe/Nb(NM), g3 is the ρFe, and g4 is the ρNb. The results in Table 6.1 are two-parameter and four-parameter best fit values by using global fit. From the studies of transport properties of normal metal-superconductor (NM/S) structures, it is established that the difference between the superconducting and normal state conductance (δG G= NM S/ −GNM N/ ) is negative for large NM/S interface resistance (RNM/S) and changes sign with decreasing RNM/S. [20] In Table 6.1, we can find the 2ARFe/Nb( )S is larger than 2ARFe/Nb(NM) . The spin accumulation causes an additional voltage drop across the interface due to reduced spin transport into S. Therefore, the interface resistance of the F/S system should be larger than that of the F/NM system. We also observed that the CPP resistivity of Nb is bigger than bulk resistivity. This probably shows that the conduction electron scattering at grain boundaries is the main scattering process in our sputtered samples.
Figure 6.5: Specific resistance, ART, versus bilayer number N of two sets of samples with Nb thicknesses fixed at 15 nm and 80 nm, respectively. The dashed lines are linear least square fits to individual sets. The solid lines are global fit for two parameters and dash dot lines are global fit for four parameters to two sets of data simultaneously.
0 2 4 6 8 10 12 14
0 20 40 60 80 100
120 Nb superconducting state Nb normal state
individual Fit
global Fit (two parameter) global Fit (four parameter)
N
AR
T( f Ω m
2)
Figure 6.6: (a) Specific resistance, ART, versus Fe thickness with Nb thickness fixed at 15 nm and N=6. (b) Specific resistance, ART, versus Nb thickness with Fe thickness fixed at 20 nm and N=12. The dashed lines are linear least square fits to individual sets. The solid lines are global fit for four parameters to the data simultaneously.
0 20 40 60 80
0 20 40 60 80
dFe
individual Fit
global Fit (four parameter)
AR
T( f Ω m
2)
dFe(nm) (a)
0 3 6 9 12 15 18 21 24 27
0 20 40 60 80
dNb
individual Fit
global Fit (four parameter)
AR
T( f Ω m
2)
dNb(nm)
(b)
Table 6.1: The best derived values and parameters for the Fe/Nb multilayers