Andreev experiments on superconductor/ferromagnet point contacts

Andreev reflection is a smart tool to investigate the spin polarization P of the current through point contacts between a superconductor and a ferromagnet. We compare different models to extract P from experimental data and investigate the dependence of P on different contact parameters.

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Дата:	2013
Автори:	Bouvron, S., Stokmaier, M., Marz, M., Goll, G.
Формат:	Стаття
Мова:	English
Опубліковано:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2013
Назва видання:	Физика низких температур
Теми:	К 75-летию со дня рождения И. К. Янсона
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/118230
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Цитувати:	Andreev experiments on superconductor/ferromagnet point contacts / S. Bouvron, M. Stokmaier, M. Marz, G. Goll // Физика низких температур. — 2013. — Т. 39, № 3. — С. 354–359. — Бібліогр.: 32 назв. — англ.

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spelling	irk-123456789-1182302017-05-30T03:02:54Z Andreev experiments on superconductor/ferromagnet point contacts Bouvron, S. Stokmaier, M. Marz, M. Goll, G. К 75-летию со дня рождения И. К. Янсона Andreev reflection is a smart tool to investigate the spin polarization P of the current through point contacts between a superconductor and a ferromagnet. We compare different models to extract P from experimental data and investigate the dependence of P on different contact parameters. 2013 Article Andreev experiments on superconductor/ferromagnet point contacts / S. Bouvron, M. Stokmaier, M. Marz, G. Goll // Физика низких температур. — 2013. — Т. 39, № 3. — С. 354–359. — Бібліогр.: 32 назв. — англ. 0132-6414 PACS: 72.25.Ba, 73.23.–b, 73.63.Rt, 74.78.Na, 81.07.Lk http://dspace.nbuv.gov.ua/handle/123456789/118230 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	К 75-летию со дня рождения И. К. Янсона К 75-летию со дня рождения И. К. Янсона
spellingShingle	К 75-летию со дня рождения И. К. Янсона К 75-летию со дня рождения И. К. Янсона Bouvron, S. Stokmaier, M. Marz, M. Goll, G. Andreev experiments on superconductor/ferromagnet point contacts Физика низких температур
description	Andreev reflection is a smart tool to investigate the spin polarization P of the current through point contacts between a superconductor and a ferromagnet. We compare different models to extract P from experimental data and investigate the dependence of P on different contact parameters.
format	Article
author	Bouvron, S. Stokmaier, M. Marz, M. Goll, G.
author_facet	Bouvron, S. Stokmaier, M. Marz, M. Goll, G.
author_sort	Bouvron, S.
title	Andreev experiments on superconductor/ferromagnet point contacts
title_short	Andreev experiments on superconductor/ferromagnet point contacts
title_full	Andreev experiments on superconductor/ferromagnet point contacts
title_fullStr	Andreev experiments on superconductor/ferromagnet point contacts
title_full_unstemmed	Andreev experiments on superconductor/ferromagnet point contacts
title_sort	andreev experiments on superconductor/ferromagnet point contacts
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2013
topic_facet	К 75-летию со дня рождения И. К. Янсона
url	http://dspace.nbuv.gov.ua/handle/123456789/118230
citation_txt	Andreev experiments on superconductor/ferromagnet point contacts / S. Bouvron, M. Stokmaier, M. Marz, G. Goll // Физика низких температур. — 2013. — Т. 39, № 3. — С. 354–359. — Бібліогр.: 32 назв. — англ.
series	Физика низких температур
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first_indexed	2025-07-08T13:35:43Z
last_indexed	2025-07-08T13:35:43Z
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fulltext	© S. Bouvron, M. Stokmaier, M. Marz, and G. Goll, 2013 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3, pp. 354–359 Andreev experiments on superconductor/ferromagnet point contacts S. Bouvron, M. Stokmaier, and M. Marz Physikalisches Institut, Karlsruher Institut für Technologie (KIT), 76131 Karlsruhe, Germany G. Goll Physikalisches Institut and DFG-Zentrum für Funktionelle Nanostrukturen, Karlsruher Institut für Technologie (KIT), 76131 Karlsruhe, Germany E-mail: gernot.goll@kit.edu Received December 5, 2012 Andreev reflection is a smart tool to investigate the spin polarization P of the current through point contacts between a superconductor and a ferromagnet. We compare different models to extract P from experimental data and investigate the dependence of P on different contact parameters. PACS: 72.25.Ba Spin polarized transport in metals; 73.23.–b Electronic transport in mesoscopic systems; 73.63.Rt Nanoscale contacts; 74.78.Na Mesoscopic and nanoscale systems; 81.07.Lk Nanocontacts. Keywords: Andreev reflection, spin polarization, point contacts. Following the pioneering work of Igor Yanson and his group at the Institute for Low Temperature Physics and Engineering of the Ukrainian Academy of Sciences (ILTPE NASU) on tiny metallic contacts between two metal electrodes [1], point-contact spectroscopy (PCS) has become a powerful method to study the interactions of ballistic electrons with other excitations in metals [2]. The interpretation of the observed characteristics in point- contact (PC) spectra is usually difficult. These difficulties are frequently inherent in the fabrication of point contacts. In many cases contacts are made by the needle-anvil or shear technique in which two sharpened metal pieces are brought into a gentle touch until a conductive contact is formed. Those contacts are microscopically not well-de- fined with respect to contact size, geometry, and structure of the metallic nanobridge, and with respect to the local electronic parameters such as the mean free path in the immediate contact region. The only control parameter is the contact resistance, and hence, it is challenging to iden- tify the relevant transport regime free of doubt. Usually Sharvin's [3] or Wexler's [4] formulae for the ballistic and diffusive transport regime, respectively, are used to infer a PC size estimate from the measured PC resistance. Only recently [5], direct scanning electron microscopy (SEM) measurements of the nanocontact size of nanostructured point contacts allowed for the first time a direct compari- son with theoretical models for contact-size estimates of heterocontacts. The semiclassical models yield reasonable values for the PC radius a as long as the correct transport regime is determined by taking into account the local trans- port parameters of the individual contact. Of course, this requires a careful characterization of the samples with res- pect to the local resistivity and the local mean free path. Among the rich variety of solid-state problems investi- gated by point-contact spectroscopy the study of super- conductor–metal contacts contributes a significant portion. Nowadays point-contact spectroscopy is an important tool to explore the symmetry and nodal structure of the energy gap Δ of conventional and unconventional superconduc- tors [6]. When the temperature is lowered below the super- conducting transition temperature cT of the superconduct- ing electrode of a superconductor (S) / normal metal (N) Present address: Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany. ** Present address: Institute for Nuclear and Energy Technologies (IKET), Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany. Andreev experiments on superconductor/ferromagnet point contacts Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 355 point-contact Andreev reflection [7] of charge carriers at the S/N interface occurs. Andreev reflection leads to min- ima at /V eΔ≈ ± in the differential resistance /dV dI as a function of applied bias V, i.e., maxima in the corre- sponding conductance curves ( ) = ( / )( )G V dI dV V , and thus allows determination of the gap size, also while vary- ing temperature and magnetic field, respectively [8,9]. A new pitch came into the field when Andreev reflec- tion was used to extract the spin polarization P of the current through superconductor/ferromagnet (F) point con- tacts [10,11]. Knowledge of the spin polarization of possi- ble materials for spin-electronic devices is a key issue for spintronics [12]. An efficient spin injection is of central importance for utilizing the spin degree of freedom as a new functionality in spin-electronic devices. The spin po- larization P of ferromagnets can be measured by various techniques including photoemission [13], spin-dependent tunnelling [14], and point-contact Andreev reflection (PCAR) [15]. For a quantitative analysis of the results, however, one has to be aware of the different nature of the quantities measured by each technique. The spin polariza- tion, defined by the difference of spin-up and spin-down density-of-states, is typically measured with spin-polarized photoemission while the spin polarization of the transport current is obtained, e.g., in PCAR experiments [16], which in turn is distinctly different from the spin polarization of the density-of-states resulting from tunneling experiments [14]. An issue of considerable importance is how the spin polarization obtained by Andreev reflection is related to the ferromagnet's bulk spin polarization [17]. Already a variety of materials have been investigated including the ferromagnetic elements Fe, Co, and Ni and several alloys mainly with Al, Nb, or Pb as a supercon- ducting counter electrode [10,11,18–23]. However, differ- ent models [10,11,24–26] describing the transport through S/F interfaces yielded varying values for P, also depend- ing on the contact fabrication and the transport regime [27], an issue that is not yet understood in detail [28]. In the following, we want to review the main ideas of two most prominent models shortly and compare the results of both to the same set of experimental data obtained on nano- structured Al/Fe contacts [23]. The theoretical analysis of most S/F point-contact ex- periments has been carried out in the spirit of the Blonder– Tinkham–Klapwijk (BTK) theory [9] for Andreev reflec- tion at an interface between N and classical S with spin- singlet pairing. This is the coherent process by which an electron from N enters S and a hole of opposite spin is ret- ro-reflected, creating a spin-singlet Cooper pair in S. Pos- sible ordinary reflection at the S/F interface barrier is parametrized by a phenomenological parameter, the barrier strength Z . The sensitivity of the Andreev process to the spin of the carriers originates from the conservation of the spin direction at the interface. Consequently, when there is an imbalance in the number of spin-up and spin-down elec- trons at the Fermi level, as it is the case in the spin- polarized situation of a ferromagnetic metal, this leads to a reduction of the Andreev reflection probability [15]. An- dreev reflection is limited by the minority carriers of the metal. In the simpliest approach applied for the analysis of several experiments [10,18–21,24], the total current I through the constriction is decomposed into a fully unpolarized part (1 ) uP I− ′ for which Andreev reflection is allowed and into a fully polarized part pP I′ for which Andreev reflection is zero, = (1 ) .u pI P I P I− +′ ′ The weighting factor P′ determines the spin polarization of the ferromagnet. In the following we will refer to this model as the dispartment model. Consequentially, the con- ductance SFG is also decomposed into two parts: = (1 ) ( ) ( )SF u pG P G V P G V− +′ ′ with , , , ( , )( ) = [1 ( , ) ( , )]u p u p u p df E V TG V A E Z B E Z dE dV ∞ −∞ − + −∫ , where uG denotes the conductance, uA the Andreev re- flection probability, and uB the normal reflection proba- bility of the fully unpolarized channel, and pG , pA , and pB denote the corresponding quantities of the fully polar- ized channel. Both contributions are derived in the BTK formalism and following expressions for the zero- temperature conductances uG and pG are obtained [25]: \| \| <E Δ \| \| >E Δ =0\| ( )u TG E 2 2 2 2 2(1 ) (1 2 )Z β β + + + 2 2 1 2Z β β+ + =0\| ( )p TG E 0 2 2 4 (1 ) 4Z β β+ + with 2 2= / \| \|E Eβ Δ − . Despite the attractive simplicity of the BTK formalism it has been shown [17,27] that application of the BTK for- malism (even in its generalized form [25]) has certain drawbacks and enforces several assumptions for the analy- sis. This has mainly to do with the problem to determine P′ and Z independently. The physical reason is that both lead to a reduction of the Andreev current and diminish the conductance change in = /G dI dV . The model fails to distinguish whether it is high P or high Z that causes the depression of conductance at small bias. This problem is evaded by applying a different theoretical approach [26]. S. Bouvron, M. Stokmaier, M. Marz, and G. Goll 356 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 Cuevas and coworkers [22,26] developed a model based on quasiclassical Green functions. The central quan- tities of the model are two transmission coefficients 2 , ,= \| \|tτ↑ ↓ ↑ ↓ . Therefore, we will refer to this model as the -τ τ↓↑ -model throughout this paper. The transmission coefficients contain all microscopic properties relevant for the transport through the constriction, i.e., they account for the majority- and minority-spin bands in the ferromagnet, the electronic structure of the superconductor, and the in- terface. ,t↑ ↓ and 1/2 , ,= (1 )r τ↑ ↓ ↑ ↓− are the spin-dependent transmission and reflection amplitudes, respectively, enter- ing the normal-state scattering matrix Ŝ which supple- ments the boundary conditions of the theory. Of course, the restriction to a single conduction channel per spin direction is a rough simplification of the point contact, but it is final- ly justified by the agreement with the experiment [22,23]. Following the calculation by Cuevas and coworkers the spin-dependent current through the S/F point contact can be separated in two spin contributions, =SFI I I↓↑ + and each contribution can be written in its BTK form [9] = [ ( ) ( )][1 ( ) ( )] ,eI d f eV f A B hσ σ σε ε ε ε ε ∞ −∞ − − + −∫ where ( )f E is the Fermi function, ( )Aσ ε and ( )Bσ ε are the spin-dependent Andreev reflection and normal reflec- tion probabilities, respectively, and =σ ↑ or ↓ . ( )Aσ ε ( ( ))Bσ ε is calculated from the spin-dependent transmis- sion (reflection) amplitudes, and finally, the zero- temperature conductance of the S/F contact adopts the form 2 22 2 2 2 , (1 ) 4 ( / )4= ( ) 1 ( / ) , > [(1 ) (1 ) 1 ( / ) ] SF eV r r r r eVeG h eV eV r r r r eV τ τ Δ Δ τ τ τ τ τ τ Δ Δ Δ ↓↑ ↓ ↓↑ ↑ ↓ ↓ ↓↑ ↑ ↑ ↓ ↓↑ ↑ ⎧ ≤⎪ + −⎪⎪ ⎨ + + − −⎪ ⎪ − + + −⎪⎩ while the normal-state conductance is given by 2 = ( ) .N eG h τ τ↓↑ + It is obvious that the Andreev spectra are determined by a set of three free parameters τ↑ , τ↓ , and Δ . The current spin polarization P in this model is defined by \| \| =P τ τ τ τ ↓↑ ↓↑ − + and can be determined from the fit parameters of an exper- imental Andreev spectrum. We note, that this expression is symmetric with respect to τ↑ and τ↓ , therefore, one can- not assign a transmission coefficient to the majority or mi- nority charge carriers in the ferromagnet. However, we expect the high transmissive coefficient τ↓ to correspond to the minority electrons. In the absence of spin polariza- tion, i.e., = 0P for a N/S contact with =τ τ↓↑ , above formulae reduce to the well-known BTK result [9]. Figure 1 displays a set of normalized conductance curves for = 0.02 cT T , = 0.99τ↓ , and = 0.99τ↑ , 0.53, 0.42, 0.33, 0.25, and 0.17 which equals = 0P , 0.3, 0.4, 0.5, 0.6, 0.7 from top to bottom. The shape of each spec- trum is unambiguously determined by a set of τ↑ , τ↓ . For = 0P (top curve) the curve reproduces the well-known BTK result where Andreev reflection causes a doubling of the normal-state conductance for energies <eV Δ . We note that the characteristic double-peak feature at \| \| =eV Δ caused by the reduction of the conductance at low bias originates from a small fraction of charge carriers ordinari- ly reflected at an interface barrier. In the case of two spin- dependent transport channels it is intuitive to consider the high-transmittive spin channel to get a measure for the fraction of charge carriers ordinarily reflected at the inter- face barrier. From the transmission coefficients 2= 1/ (1 )Zτ↓ ↓+ one derives 1/2= ((1 ) / )Z τ τ↓ ↓ ↓− . For the upper curve which corresponds to the unpolarized BTK case one gets = 0.1Z↓ as the parameter equivalent to the BTK interface parameter Z . While the shape of the spectra is unambiguously deter- mined by a set of τ↑ , τ↓ , the spectra for same polarization can look quite different. Figure 2 shows four curves calcu- lated for different sets of τ↑ , τ↓ which all result in = 0.4P . The calculations have been performed for a finite temperature = 0.22 cT T . The high-transmission spin- channel seems to be decisive whether the curve shape ap- pears more point-contact-like or more tunnelling-like. Before we compare curves calculated by both models, let us first check the validity of the fitting procedure. For this purpose we measured point-contact spectra of S/N point contacts in a 4He cryostat down to = 1.4T K and Fig. 1. Normalized differential conductance / NG G vs. /eV Δ . The curves are calculated with the -τ τ↓↑ -model (see text) for different polarizations at = 0.02 cT T . For clarity, the curves are shifted successively upwards by 0.2 units. Andreev experiments on superconductor/ferromagnet point contacts Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 357 fitted them with both models. The PCs have been estab- lished in the edge-to-edge configuration with a sharpened Pb electrode and a normal-metal electrode made from Cu or Pt. Therefore, for both fits we expect 0P P= =′ . Fig- ures 3(a) and (b) show the experimental data together with the fits according to the -τ τ↓↑ -model [26] (dashed line) and the dispartment model [25] (solid line). In both cases we got almost perfect agreement with the data. For the Pb/Cu contact with = 2.7R Ω measured at = 1.4T K (upper panel) we obtained 0 = ( = 0)TΔ Δ = 1.38 meV, = = 0.814τ τ↓↑ as parameters for the -τ τ↓↑ -model, and 0 = 1.38Δ meV, = 0.475Z , = 0.011P′ for the dispart- ment model. For the Pb/Pt contact with = 7.5R Ω measu- red at = 2.1T K (lower panel) the parameters are 0 = 1.48Δ meV, 0/ = 0.10Γ Δ , = 0.811τ↑ , = 0.819τ↓ for the -τ τ↓↑ -model, and 0 = 1.42Δ meV, 0/ = 0.10Γ Δ , = 0.488Z , = 0.015P′ for the dispartment model. In both cases we found within the experimental error a good agreement of 0P P≈ ≈′ as expected for these non- magnetic metals. The energy gap of Pb determined from the fits coincides fairly good to the gap value reported in literature [29]. We note that a small broadening of the Pb/Pt spectra caused by inelastic scattering in the contact region is accounted for by introducing the Dynes [30] pa- rameter Γ which is of the order of 5–10% of 0Δ . In the next step we compare curves calculated with the simple dispartment model to those calculated with the -τ τ↓↑ -model for nominal same polarization =P P′. Fig- ure 4 displays a set of normalized conductance curves cal- culated for = 0.1T K, = = 0P P′ , 0.2, 0.4, 0.6, 0.8, and 1, and = 0.3Z for the dispartment model, and = 0.917τ↓ for the -τ τ↓↑ -model, respectively, which corresponds to 1/2= [(1 ) / ] = 0.3Z τ τ↓ ↓ ↓− . In the extreme case = = 0P P′ which describes a S/N contact the calculations perfectly agree with each other, as well as for the other extreme case = = 1P P′ which describes a halfmetallic S/F contact. For the latter, there is only a small difference in the vicinity of the coherence peaks at \| / \| = 1eV Δ . However, at interme- diate values with increasing polarization the Andreev sig- nal is much faster suppressed for the dispartment model Fig. 3. (Color online) Point-contact spectra of S/N contacts to- gether with fits according to Martin–Rodero et al. [26] (dashed line) and Mazin et al. [25] (solid line). (a) Pb/Cu contact at 1.4 K with = 2.7R Ω. (b) Pb/Pt contact at 2.1 K with = 7.5R Ω. For the fit parameters see text. ––44 ––44 ––33 ––33 ––22 ––22 ––11 ––11 00 00 11 11 22 22 33 33 44 44 VV, mV, mV VV, mV, mV (a)(a)Pb/CuPb/Cu 1.81.8 1.61.6 1.41.4 1.21.2 1.01.0 1.71.7 1.61.6 1.51.5 1.41.4 1.31.3 1.21.2 1.11.1 1.01.0 Pb/PtPb/Pt (b)(b) G /G G /G NN G /G G /G NN Fig. 2. Normalized differential conductance / NG G vs. /eV Δ . The curves are calculated with the -τ τ↓↑ -model (see text) for the same polarization = 0.4P at = 0.22 cT T . For clarity, the curves are shifted successively upwards by 0.4 units. 2.52.5 2.02.0 1.51.5 1.01.0 0.50.5 00 ττupup ττdowdownn ––66 ––44 ––22 00 22 44 66 eVeV//ΔΔ G /G G /G NN 0.420.42 0.990.99 0.39 0.90.39 0.9 0.26 0.60.26 0.6 0.13 0.30.13 0.3 PP = 0.4= 0.4 Fig. 4. (Color online) Comparison of Andreev spectra with = 0P , 0.2, 0.4, 0.6, 0.8, and 1 calculated according to the -τ τ↓↑ -model (black lines) and the dispartment model (red lines). For clarity, the curves are shifted successively downwards by 0.4 units. PP = 0%= 0% PP = 20%= 20% PP = 40%= 40% PP = 60%= 60% PP = 80%= 80% PP = 100%= 100% eVeV//ΔΔ ––44 ––22 00 22 44––33 ––11 11 33 22 11 00 G /G G /G NN S. Bouvron, M. Stokmaier, M. Marz, and G. Goll 358 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 than for the -τ τ↓↑ -model. Our comparison discloses a notable difference of both quantities which makes ques- tionable a contrasting juxtaposition of P and P′ values de- rived from the analysis of experimental data by one of the- se models. In order to illustrate this difference on experimental da- ta we used both models to fit the same set of data measured on Al/Fe nanostructured point contacts [23]. The PCs were fabricated by structuring a hole of 5–10 nm diameter with electron-beam lithography and subsequent reactive ion etching into a 50-nm thick Si3N4 membrane, evaporating on one side a 200 nm Al layer, and on the other side a 12 nm thick Fe layer and a Cu layer of thickness Cu = 188d nm as a low-ohmic electrode [31]. Figure 5 displays the normalized conductance spectra of six differ- ent nanostructured PCs with contact resistances between 2.7 and 24.2 Ω measured in a dilution refrigerator at = 0.1T K together with fitting curves calculated with the -τ τ↓↑ -model (a) and the dispartment model (b). Both models perfectly describe the data, minor deviations are observed only at \| / \| 1eV Δ ≈ where the experimental curves are more rounded probably caused by a leveling-off of the electron temperature due to heating by electromag- netic stray fields or a small pair-breaking effect by Fe. The corresponding fit parameters are listed in Table 1. Within an uncertainty of 1% the same gap value 0Δ is found for both models, however, there is a notable difference in the Z parameter, which is a factor 2–3 higher in the dispartment model, and the spin polarization P′ which is lower. Although the origin of Z is not clear at all, in both models it subsumes all ordinary reflection of charge carri- ers that occurs at the interface for = = 0P P′ , e.g., reflec- tion caused by an insulating interface layer, lattice imper- fections, Fermi velocity mismatch, etc. For P and > 0P′ Fig. 5. (Color online) Point-contact spectra of Al/Fe contacts at 0.1 K together with fits according to the -τ τ↓↑ -model (a) and according to the dispartment model (b). Table 1. Fit parameters 0Δ , τ↑ , and τ↓ of the -τ τ↓↑ -model and 0Δ , Z , and P′ of the dispartment model for conductance spec- tra of nanostructured Al/Fe point contacts. From the transmission coefficients τ↑ and τ↓ the interface barrier Z↓ and the current spin polarization P have been calculated. Sample No. ,NR Ω 0Δ , meV τ↑ τ↓ Z↓ P 0Δ , meV Z P′ 1 2.68 0.174 0.371 0.983 0.132 0.452 0.176 0.337 0.396 2 6.98 0.175 0.362 0.984 0.128 0.460 0.176 0.338 0.407 3 7.29 0.157 0.349 0.993 0.083 0.480 0.158 0.272 0.444 4 9.59 0.190 0.361 0.984 0.128 0.463 0.191 0.342 0.407 5 18.4 0.166 0.348 0.997 0.054 0.482 0.168 0.218 0.497 6 24.2 0.174 0.343 0.994 0.078 0.487 0.174 0.262 0.494 Andreev experiments on superconductor/ferromagnet point contacts Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 359 the situation is less apparent. The physical reason is that Z and P′ both lead to a reduction of the Andreev current. The dispartment model obviously fails to distinguish whether a high-spin polarization or a high barrier causes the depression whereas for the -τ τ↓↑ -model as per defini- tion only the conductance channel not affected by the sup- pression of Andreev reflection due to polarization is con- sidered to determine ordinary reflection. Another important aspect is that the previously reported dependence of the spin polarization on the contact size [23] is robust against the model used to extract P. Independent- ly of the model there is a clear reduction of the spin polari- zation with decreasing contact resistance NR , i.e., increas- ing contact radius a. The reduction of P has been allo- cated as being due to spin-orbit scattering in the contact region with a constant scattering length so modelled by a simple exponential decay [23], 0( ) = exp ( / )soP a P a− . A spin-orbit scattering length = 255so nm has been ob- tained for the analysis with the -τ τ↓↑ -model. The same systematic trend of ( )P a′ is found for the dispartment model albeit with a lower value for so . For small contacts both models result in almost the same spin polarization. In summary, we have discussed possible reasons for the scatter of polarization values found for the spin polariza- tion measured by Andreev reflection in point-contact ex- periments. We showed that the scatter is partially caused by the models used to extract the spin polarization from the data, and partially caused by intrinsic mechanisms like the spin-orbit scattering in the contact region. The authors thank H. v. Löhneysen for stimulating dis- cussions and continuous support of the point-contact re- search at the Physikalisches Institut. G.G. acknowledges the fruitful and long-lasting collaboration over almost two decades with Igor Yanson who brought him into touch with point-contact spectroscopy during a sabbatical stay at Karlsruhe. Igor Yanson was a exceptionally gifted teacher and outstanding scientist. We acknowledge the financial support provided within the DFG-Center for Functional Nanostructures. 1. I.K. Yanson, Zh. Eksp. Teor. Fiz. 66, 1035 (1974) [Sov. Phys. 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Andreev experiments on superconductor/ferromagnet point contacts

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