Transition from skew-scattering to side jump in Co sub-mono-layers on the surface of K.

Transcription

1 Transition from skew-scattering to side jump in Co sub-mono-layers on the surface of K. Gerd Bergmann Department of Physics and Astronomy, Univ. South.California Los Angeles, CA , USA Abstract The anomalous Hall resistance (AHR) is measured for a K film which is covered with sub-mono-layers of Co ranging from 0.01 to 1 atomic layers. The AHR of single Co atoms has a negative sign while clusters of Co have a positive sign. The amplitude of the AHE per atom for low coverages of Co is larger by a factor 500 than for a mono-layer. This suggests different mechanisms for the AHR, skewscattering for single atoms and side-jump for larger clusters or monolayers. The Co filmisthencoveredwithpbuptoacoverageofone mono-layer. The Pb coverage enhances the AHR by a factor of 20. This suggests the presence of a spin current in the Pb layer which yields a large AHR due to the large spin-orbit scattering of the Pb. PACS: Ba, Ak, Mk In ferromagnetic metals and metals with magnetic impurities one observes two contributions to the Hall resistance, (i) the normal Hall resistance and (ii) the anomalous Hall resistance (AHR) which is caused by the interaction of the conduction electron spin with the magnetic moments of the sample. In a ferromagnet one expresses the AHR either as the product of an anomalous Hall constant R s times the magnetization (in z-direction) or as a resistance R 0 yx which one obtains by back extrapolation of the (linear) high field Hall curve. The anomalous Hall effect was already observed by Hall a century ago [1]. However, theoretically it is a rather complicated problem. There are two main mechanisms discussed in the literature, (a) skew-scattering and (b) side-jump. The first models of skew-scattering were developed by Karpulus 1

2 and Luttinger [2] and Smit [3], while the side-jump was invented by Berger [4]. Experimentally the AHR has been studied intensively [5], [6], [7], [8]. As an experimental tool the AHR has been very valuable to investigate the magnetic behavior of thin films. Due to its importance in spin-tronics, the AHR has been intensively studied in recent years (for further references see [9]). Recently an additional mechanism has been under discussion which is connected with the Berry phase and believed to occur even in the absence of any scattering (see for example [10]). Here we restrict the discussion to the skew-scattering and the side-jump. It is often suggested that skew-scattering dominates in metals with dilute magnetic impurities and side-jump dominates in ferromagnetic metals and alloys. The two mechanisms have different dependences on the mean free path of the conduction electrons. However, investigation by changing the mean free path of the electrons has a number of difficulties: (i) There are spin up and spin down conduction electrons in the metal with magnetic moments. They generally contribute differently to the conductance (mean free path) and to the AHR. (ii) A change in the mean free path will also change the scattering potential of the magnetic moments which complicates the analysis and is generally ignored. Our group recently investigated the AHR of thin amorphous Fe films by separating the scattering mechanism and the propagation of the conduction electrons [11]. This was achieved by preparing sandwiches of a ferromagnet with a short mean free path and a non-magnetic metal with a large mean free path. The interaction of the moments with the conduction electrons occured in the ferromagnet which was not altered during the experiment. The propagation occured in the non-magnetic metal whose thickness and mean free path were increased during the experiment. The result of our investigation was that the AHR in the ferromagnetic Fe is due to the sidejump. In the present paper we investigate the transition from dilute magnetic impurities to a ferromagnetic mono-layer by preparing a sandwich of K and Co. The Co is condensed on top of the K and its coverage is changed in the range of 0.01 atomic layers (the dilute case) to a mono-layer (the ferromagnetic case). We observe a dramatic change of the AHR as a function of the coverage. Afterwards we cover the Co film with sub-mono-layers of Pb. ThePbatomsarestrongspin-orbitscatterers. The author s group recently investigated the effect of spin-orbit scatterers in the presence of spin currents theoretically [12] and experimentally [13]. 2

3 In the experiment a K film with a thickness of 6.1nm and a resistance of 73.4Ω is quench condensed at helium temperature onto a quartz plate in a vacuum better than Torr. Then the K film is covered in many steps with 0.01, 0.02, 0.04, 0.07, 0.1, 0.2, 0.39, 0.67 and 0.96 atomic layers of Co. After each evaporation the film is annealed, the first film to 40K and the following films to 35K. The Hall curve of each film a measured in the field range 7T < B < +7T at a temperature of 6.5K. The Hall resistance is composed of the normal Hall resistance which is linear in the magnetic field and an anomalous contribution Ryx ahe. AlreadythepureKfilm has a small anomalous Hall resistance (AHR). But it is very small compared with the AHR of the Co at the K surface. In Fig.1a the AHR is plotted for the different Co coverages. Fig.1a: The AHR of a K film with different coverages of Co as a function of the magnetic field B. It can be seen that the AHR of the pure K is very small compared to the Co contribution and can be ignored in the present discussion. The AHR for small Co coverages is negative and its amplitude increases with the coverage up to a coverage of 0.04 atomic layers of Co. For larger Co coverages the amplitude decreases (see Fig.1b). 3

4 Fig.1b: The AHR of the K/Co film of Fig.1 for Co coverages of 0.2, 0.39 and 0.96 at.lay. At a coverage of 0.2 atomic layers the AHR shows a positive AHR at low fields which reverses at higher fields. For the Co coverages of 0.39 to 0.96 atomic layers the AHR is positive. Its amplitude increases slightly with increasing coverage. It has the opposite sign than for small Co coverages. In Fig.2 the amplitude of the AHR is plotted versus the Co coverage. While the amplitude for 0.01 atomic layers of Co is 0.15Ω the amplitude for 0.96 atomic layers is Ω. This means that the small and large coverages have not only opposite sign but that the magnitude of the AHR per atom is afactorof500 larger for small coverage than for the large coverage of about a mono-layer. Fig.2:TheamplitudeoftheAHR as a function of the Co coverage. 4

5 In the next step the Co is covered with sub-mono-layers of Pb. Fig.3 shows the AHR of the K/Co/Pb film for different Pb coverages. Fig.3: The AHR of the K/Co/Pb film with different coverages of Pb as a function of the magnetic field B. The AHR increases with the Pb coverage. In Fig.4 the amplitude of the AHR is plotted as a function of the Pb coverage. Fig.4:TheamplitudeoftheAHR of the K/Co/Pb film as a function of the thickness of the Pb coverage. The shapes of the AHR curves for the K/Co/Pb film are similar. In Fig.5 the AHR of the film for different Pb coverages is normalized to the value one at B =7T. One recognizes that they fall on a single curve. It should be mentioned that the K/Co curve is not included. It has a stronger change of 5

6 slope around the field of 1T. Fig.5: The AHR curves of Fig.4 normalized to 1.0 at the field B =7T. The resistance of the film increased with the coverage of the original K film. In Fig.6 the change of R xx is shown as a function of the Co and Pb coverage. Fig.6: The resistance R xx of the K film as a function of the Co and Pb coverage. The experimental results show a number of interesting features. The amplitude of the AHR for Co on top of the K film is roughly linear for small Co coverages and has a maximum between 0.04 and 0.07 atomic layers of Co. ThissuggeststhatsingleCoatomshave adifferent contribution to the AHR than pairs or larger clusters. For six nearest neighbors on the surface the probability to form pairs is about 6p where p is the probability that a surface place is occupied. For a coverage of.05 atomic layers one has p =.05 and the probability that a Co atom is part of a pair is 0.3. From 6

7 the change in the sign of the AHR we conclude that single Co atoms have a negative AHR while larger cluster possess a positive AHR. (The sign of pairs might lie somewhere in between). Therefore the behavior of the AHR asafunctionofthecocoverageyieldsastrongargumentthatthecoatoms do not propagate on the surface, that for sufficiently small coverage the Co atoms remain single. The next interesting observation is the huge factor between the AHR per atom for dilute Co surface impurities and a mono-layer of Co. A factor of 500 is not just a quantitative difference but signals a qualitatively different mechanism. The large magnitude of the AHR for dilute Co surface impurities suggests strongly that the skew-scattering mechanism is at work. For skew-scattering the AHR is proportional to the electronic mean free path. With increasing Co coverage the resistance increases and for a mono-layer of Co it is larger by a factor of about 2.5 than for the pure Co film. Still this factor of 2.5 in the mean free path is tiny compared to the factor of 500 in the observed AHR per Co atom. However, for the side-jump one expects a much smaller AHR because its contribution is roughly smaller by the factor y/l than the skew-scattering ( y is the length of the side jump as introduced by Berger and l is the mean free path of the conduction electrons). Our observation agrees well with the perception that for dilute magnetic impurities "skew-scattering" is the dominant mechanism and for (disordered) bulk ferromagnetic metals the "side-jump" is dominant. Finally we turn to the effect of the Pb coverage on top of the Co layer. There are two important observations: (i) The shape of the AHR curve changes and (ii) the amplitude of the AHR increases roughly by a factor 20 from the K/Co film to the final K/Co/Pb film. One may expect that the direct contact between the Co and the Pb changes the "band"-structure of the Co mono-layer. That such an effect is present one can deduce from thefactthattheshapeoftheahrforthek/cofilm looks slightly more ferromagnetic than the shape of the K/Co/Pb films. But this change happens already for the smallest Pb coverage of 0.01 atomic layers. All the AHR curves for the K/Co/Pb series look alike as Fig.5 demonstrates. The rounding of the AHR curves suggests that the magnetic moments feel a smaller mean field. Of course, it is out of the question that the Pb coverage increases the magnetization of the Co atoms by a factor of 20. At the present time we see two possible explanations for the increase of the AHR with the Pb coverage: (i) The Pb somehow changes the band-structure of the Co mono-layer so that the skew-scattering mechanism becomes again 7

8 activated. (ii) The Co magnetic moments introduce a different mean free path for the spin up and down electrons. As a consequence the current through the film has different contributions from spin up and down electrons, i.e., the current has a non-zero spin current component. Pb as a strong spin-orbit scatterer scatters the spin up and down electrons asymmetrically sidewards. If the number of spin up and down electrons is equal then the side scattering cancels out. However, for a spin-current a contribution to the AHR remains. It is proportional to the polarization of the current (j j ) / (j + j ) and the anomalous Hall scattering cross section σ xy of the Pb impurity. The author has calculated the anomalous Hall scattering cross section σ xy for a spin-orbit scatterer in terms of the Friedel phase shifts. If someone performs a first principle calculation of the phase shift of Pb one can use the Pb impurities as a gauge to measure the polarization of a spin current. Presently the author favors the explanation that the increase of the AHR with the Pb coverage is due to a spin current in the presence of the Co mono-layer. In conclusion we observed the AHR in a K film which is covered with submono-layers of Co ranging from 0.01 to 1 atomic layers. The AHR for very dilute Co atoms is negative while for coverage of 0.2 atomic layers and more the AHR is positive. The analysis of the AHR shows that the Co atoms do not cluster for small Co coverages. Furthermore the amplitude of the AHE per atom for low coverages of Co is larger by a factor 500 than for a monolayer. This suggests different mechanisms for the AHR, skew-scattering for single atoms and side-jump for larger clusters or mono-layers. The Co film is covered with Pb up to a coverage of one mono-layer. The Pb coverage enhances the AHR by a factor of 20. This suggests the presence of a spin current in the Pb layer which yields a large AHR due to the large spin-orbit scattering of the Pb. Acknowledgment: The research was supported by NSF Grant No. DMR References [1] E.H.Hall, Philos.Mag. 12, 157 (1881), 8

9 [2] R.Karpulus and J.M.Luttinger, Phys.Rev. 95,1154 (1954), Hall effect in ferromagnets [3] J.Smit, Physica 16, 612 (1951), [4] L.Berger, Phys.Rev. B2, 4559 (1970), Side jump mechanism for the Hall effect of ferromagnets [5] K.Rhie, D.G.Naugle, O.Beom hoan and J.T.Markert, Phys.Rev. B48, (1993), Side-jump effect in paramagnetic amorphous metals [6] J.Stankiewicz, L.Morellon, P.A.Algarabel, and M.R.Ibarra, Phys.Rev. B61, (2000), Hall effect in Gd5(Si1.8Ge2.2) [7] P.Khatua, A.K.Majumdar, A.F.Hebard, and D.Temple, Phys.Rev. B68, (2003), Extraordinary Hall effect in Fe-Cr giant magnetoresistive multilayers [8] Wei-Li Lee, S.Watauchi, V.L.Miller, R.J.Cava, N.P.Ong, Science 303, 1647 (2004), Dissipationless Anomalous Hall Current in the Ferromagnetic Spinel CuCr2Se(4-x)Brx [9] A.Crépieux and P.Bruno, Phys.Rev. B64, (2001), Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation [10] Y. Yao, L.Kleinman, A. H. MacDonald, J.Sinova, T. Jungwirth, D.Wang, E.Wang and Q.Niu, Phys. Rev. Lett. 92, (2004), First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe 9

10 [11] G.Bergmann, and Manjiang Zhang, subm. to Phys.Rev.Lett., The anomalous Hall effect in ferromagnetic Fe: Skew-scattering or sidejump? [12] G.Bergmann, Phys.Rev. B63, (2001), Spin-orbit scatterer as an experimental tool to measure spin currents [13] G.Bergmann and F.Song, Phys.Rev. B70, R (2004), Induced spin currents in alkali films 10