PHYSICAL REVIEW B VOLUME 57, NUMBER 5 1 FEBRUARY 1998-I Giant magnetoresistance in Fe1 xCox /Cr 001... trilayers C. T. Yu, K. Westerholt, K. Theis-Bro¨hl, V. Leiner, Th. Zeidler, and H. Zabel Institut fu¨r Experimentalphysik/Festko¨rperphysik, Ruhr-Universita¨t Bochum, D-44780 Bochum, Germany Received 12 June 1997 We have investigated the magnetic and magnetotransport properties of wedge-shaped Fe1 xCox /Cr/Fe1 xCox trilayers grown by molecular-beam epitaxy on Al2O3 (1 1¯02) substrates with the Co concentration x ranging from 0 to 0.2. A completely antiferromagnetic AFM coupling with zero remanence is obtained in both pure Fe/Cr and alloy Fe1 xCox /Cr samples at a Cr thickness of about 10 Å. The giant magnetoresistance GMR of the AFM coupled Fe/Cr trilayer is about 5.5% at low temperatures. With increas- ing Co concentration, the GMR effect, / s , decreases drastically, having an amplitude of only 0.7% at x 0.2. In the pure Fe/Cr trilayer, there is a strong reduction of the GMR effect with increasing temperature. In contrast, the GMR of the samples with alloy magnetic layers is only weakly temperature dependent because of an increase of the net change of the magnetoresistance, , with temperature. The strong decrease of the GMR effect in the alloy trilayers is tentatively ascribed to the possible loss of the band matching of the minority-spin band, which is important in the Fe/Cr superlattice. The temperature dependence of at finite temperatures can well be interpreted by introducing a positive linear temperature term together with a negative quadratic term, which are attributed to spin-dependent electron-phonon scattering and spin-flip electron-magnon scatter- ing, respectively. S0163-1829 98 04905-4 I. INTRODUCTION nates from spin asymmetry in the scattering time. Actually there is ample experimental evidence that the spin asymme- Since the discovery of the giant magnetoresistance try of the interface scattering is the dominant contribution to GMR in magnetic multilayers,1 the origin of the phenom- the GMR effect in magnetic multilayers.20 Assuming single enon has been extensively discussed and it is usually under- Cr impurities as scatters in the Fe/Cr interfaces a strong stood in terms of spin-dependent scattering of conduction asymmetry in the scattering time for the spin-up and spin- electrons at the interfaces or within the magnetic layers.2 The down electron actually has been predicted.21 interface scattering is believed to be dominant in CIP-GMR The systematic study of magnetic alloy multilayers, al- current in the plane , and CPP-GMR current perpendicular though being rather scarce in the literature, can give infor- to the plane is more sensitive to bulk scattering.3 Concern- mation on the mechanism of the GMR effect. Inomato and ing the amplitude of the GMR effect in different multilayers, Saito have shown22 that the GMR of Co/Cu can be enhanced the mechanisms involved are still subject of discussion.4 In by alloying Co with a small amount of Fe, but the addition of Fe/Cr superlattices the GMR effect can reach values of more than 200% when the superlattice consists of thin magnetic Ni in Co 1 xNix/Cu multilayers was shown to decrease the layers with sharp interfaces.5 On the contrary, only a very GMR.23 The study of Fe1 xCrx /Cr multilayers24 revealed an small value of less than 1% of the GMR has been achieved increase of the GMR at low Cr concentrations. These results in antiferromagnetically AFM coupled Co/Cr super- have been regarded as an indication that scattering at the lattices.6,7 random magnetic potential at the interface is the main scat- Theoretical calculations9,10 considering both spin- tering process for the GMR.25 dependent scattering11­13 and spin-polarized electron The main goal of the present investigation is a systematic bands14,15 in the layered structure revealed that there are two study of the change of the GMR effect in antiferromagneti- main contributions to the GMR effect. First, the polarized cally coupled Fe1 xCox /Cr/Fe1 xCox alloy trilayers. To our band structure in conjunction with any spin-independent knowledge, this alloy multilayer has not been reported yet in scattering process can produce a large GMR effect, if the the literature. In addition to introducing Co point defect scat- Fermi velocities and/or the Fermi surfaces for the minority tering, it is expected in a rigid-band picture that the addition and majority electrons are different.10,16 In order to obtain a of Co will fill the majority band of Fe and change the ex- very large GMR effect it seems that for one of the spin change splitting. This should eventually destroy the match- directions the band structure of the ferromagnetic layer and ing between the minority-spin band of the Fe and Cr bands, the spacer layer should be similar, i.e., the density of states at and induce a corresponding change of the GMR effect. Fermi level, the position and dispersion of the electron bands The paper is organized as follows. In Sec. II the sample should be nearly identical band matching effect17,18 . For the preparation and the experimental methods are described. In two systems with exceptionally large amplitudes of the GMR Sec. III we present the main results concerning magne- effect namely Fe/Cr Refs. 1,5 and Co/Cu,19 this situation is totransport, magnetic, and structural properties. Discussions realized for the minority-spin band and the majority-spin about the GMR effect of the Fe1 xCox /Cr/Fe1 xCox trilay- band, respectively.18 ers and its temperature dependence are given in Sec. IV, the The second main contribution to the GMR effect origi- conclusion is provided in Sec. V. 0163-1829/98/57 5 /2955 8 /$15.00 57 2955 © 1998 The American Physical Society 2956 C. T. YU et al. 57 II. EXPERIMENTAL METHODS For the determination of the alloy composition, we used Using molecular-beam epitaxy MBE we have grown electron microprobe analysis in a wavelength dispersive Fe mode, which allows the determination of the relative compo- 1 xCox /Cr/Fe1 xCox trilayers with a wedge-shaped Cr in- sition of Fe and Co to a much higher resolution than using terlayer on Al2O3(11¯02) substrates with a Cr 001 and a the energy-dispersive mode. Nb 001 buffer layer. The growth of Nb on sapphire is well The interlayer exchange coupling properties of the trilay- established and can be described by the following epitaxial ers were characterized by magnetic hysteresis loops mea- relation:26 sured via the magneto-optical Kerr effect MOKE in a scan mode. For measuring the in-plane component of the magne- Al2O3 Nb tization, a longitudinal configuration with an incidence angle of about 45° was chosen. The MOKE signal was determined 112¯0 1 1¯0 using a Faraday modulation technique.28 The rather high modulation amplitude and the use of lock-in techniques pro- 0001 111 vides an angular resolution of better than 10 4degrees.28 Hysteresis loops were measured in scan steps of 1 mm for 1¯100 112¯ . magnetic fields along both 100 and 110 of the trilayers. For the measurements of the magnetoresistance, a con- The Cr 110 exactly aligns with Nb 110 . All samples ventional four-probe method was employed with the current were prepared in a conventional UHV chamber RIBER, in the plane CIP and the magnetic field applied parallel to EVA32 designed for metal epitaxy. The base pressure of the the film surface. The specimen studied here were cut from system is about 4 10 9Pa and the working pressure is bet- the wedge-shaped sample with a width of about 2 mm along ter than 2 10 8Pa. The sapphire substrates have a miscut of the wedge direction . For better electrical contacts four gold less than 1.5°. After chemical etching and rinsing, the sub- stripes were sputtered onto the surface of the specimen. Sil- strates were transferred into the introduction chamber and ver glue was used to contact the specimen with gold wires of annealed at 500 °C. Afterwards the substrate was annealed 0.05 mm in diameter. For measurements at room temperature again at 1100 °C for 1 h in the preparation chamber. Prior to about 296 K and liquid-nitrogen temperature 77 K , the the growth of the trilayer, a Nb buffer layer of about 100 magnetic field was generated by an electromagnet and con- Å was first grown at 900 °C and then annealed at 950 °C for trolled by calibrated Hall sensor, whereas for measurements 30 min in order to achieve a single-crystal growth of Cr and at liquid-helium temperatures, a superconducting solenoid Fe was used. All resistivity measurements were made using an 1 xCox in the bcc 001 direction. Then a Cr buffer layer of about 100 Å was grown at 450 °C, followed by an an- ac-lock-in technique, providing a resolution of 10 5. For nealing step at 750 °C for 30 min. The measurements at liquid nitrogen and room temperature, Fe whole traces of the magnetoresistance loops were taken. In 1 xCox /Cr/Fe1 xCox trilayer was grown at a substrate temperature of 300 °C. A Cr caplayer of about 50 Å was the following, the magnetoresistance ratio is defined relative finally grown to prevent the trilayer from oxidation. Both Fe to the resistivity or resistance at saturation fields ( s) as and Cr were evaporated from effusion cells. The deposition (H) s / s 100%. rate was 0.2 Å/s for Fe and 0.16 Å/s for Cr. Co was evapo- rated by an electron gun with a rate of about 0.02 Å/s, as III. RESULTS monitored by an optical rate controller. The Fe1 xCox alloy layers were prepared by a simultaneous evaporation of Fe Figure 1 shows typical small-angle x-ray-reflectivity spec- and Co. tra of the Fe1 xCox /Cr/Fe1 xCox wedge-shaped trilayers The nominal thickness of the magnetic Fe1 xCox layers is with different Cr thicknesses. The open circles represent the about 30 Å , the wedge-shaped Cr spacer ranges from about experimental data and the solid lines are fits to the data using 4.5 to 13 Å with a gradient of 0.16 Å/mm on average over a modified Parratt formalism including root-mean-square the whole 50 mm long substrates. In the present study we roughness parameters for all interfaces and the surface.27 have grown a series of samples with the alloy composition The interference fringes are due to the finite thickness of the ranging from x 0 to x 0.2. films. The insets of the figures reproduce the electron-density The layered structure of the films was characterized by profile normal to the film surface, which is obtained from the small-angle x-ray reflectivity scans together with quantitative fit and denoted by 2 with 2 ( 2/ )r0 n(Z f).29,27 electron microprobe analysis. A medium resolution double- Here is the wavelength of the radiation, r0 is the classical axis diffractometer equipped with a graphite monochromator electron radius, Z is the atomic form factor, f is a disper- was used for the x-ray-scattering experiments. For the con- sion correction, and n is the density of atoms. finement of the Cu K beam size, a horizontal slit of 0.15 The thickness and roughness parameters resulting from mm in width was used together with vertical slits of 0.2 mm. the fit in Fig. 1 are given in Table I. Starting from the surface For determination of the Cr wedge thickness, we usually the sample consists of a roughly 20 Å thick oxide surface measured the sample at 3 different positions along the layer, a Cr top layer of about 46 Å, the trilayer comprising wedge. The experimental data were fitted using a modified two 30 Å thick Fe0.80Co0.20 layers with a wedge-shaped Cr Parratt formalism incorporating random thickness fluctua- spacer in between, a Cr buffer layer of 102 Å and a Nb tions at the interfaces.27 For confirming the in-plane crystal buffer layer of 62 Å on the average. The Cr wedge has a orientation, grazing incidence x-ray-scattering techniques lateral thickness gradient of about 0.157 Å/mm with 4.3 Å at were used. the thin end and 12.2 Å at the thick end of the sample, 57 GIANT MAGNETORESISTANCE IN Fe 2957 1 xCox /Cr(001) . . . TABLE II. Structure parameters of Fe1 xCox /Cr trilayers on the AFM coupling position, as derived from small-angle x-ray- reflectivity measurments. D denotes the thickness of individual layer. D Å x 0 x 0.03 x 0.05 x 0.10 x 0.20 Oxide 18.7 17.2 16.0 21.0 21.0 Cr 31.5 48.2 29.5 29.7 45.6 Fe1 xCox 23.6 37 34.3 30.1 30.2 Cr 9.8 10.0 10.5 9.6 9.8 Fe1 xCox 23.7 37.7 34.8 31.3 31.6 Cr 71.9 121.5 108.2 101.9 102.4 Nb 58.0 92.8 89.6 74.7 62.0 FIG. 1. X-ray reflectivity spectra for an Fe0.8Co0.2 /Cr/Fe0.8Co0.2 trilayer with a Cr overlayer, a Cr and a Nb buffer layer on sapphire pling starts to become noticeable. For a Cr thickness of about substrates. The scans in I, II, and III were measured from sample 10 Å, completely antiferromagnetic coupling is realized as positions that are about 5, 25, and 45 mm away from the thin side of indicated by a zero remanence. It should be mentioned that a 50 mm long sample. The solid lines are the fits to the data points over a large region of the wedge-shaped samples a mixture using a modified Parratt formalism. The insets of the figures show of bilinear and biquadratic coupling is present.30 The biqua- the electron-density profile resulting from the fit. dratic term can be modeled in terms of conventional non- corresponding to a change of about 1 monolayer of Cr per 9 Heisenberg exchange coupling J2(S1*S2)2. For different Co mm. The interfacial roughness for the individual layer are in concentrations the coupling properties with respect to Cr the range of 1.2­4.6 Å. Similar measurements of small-angle thicknesses are hardly influenced, except for a change of the x-ray reflectivity have been taken for all samples of the amplitude of the coupling constant. A complete antiferro- present study with the Co concentration x 0, 0.03, 0.05, magnetic coupling is observed at dCr 10 Å in all samples. and 0.10. The structural parameters for all samples studied It should be noted that the first antiferromagnetic maximum here are summarized in Table II. is at 9­10 Å in both Fe/Cr and Co/Cr superlattices. Thus we For the determination of the interlayer exchange coupling do not expect a large variation of the position of the first in the Fe maximum with alloying. The representative hysteresis loops 1 xCox /Cr/Fe1 xCox trilayers with varying Cr thicknesses and Co composition, extensive investigations of for this position of all Fe1 xCox /Cr/Fe1 xCox trilayers are the magnetic hysteresis loops have been made along both the sketched on the right panel in Fig. 4. A detailed interpreta- hard and easy axis, respectively. Figure 2 displays the tion of the coupling properties with respect to Cr thickness normalized remanent magnetization as a function of and Co content will be given elsewhere.30 the wedge-shaped Cr thicknesses for the sample The GMR effect in magnetic trilayers is usually quite Fe small compared to that of multilayers,31 because trilayers 0.80Co0.20 /Cr/Fe0.80Co0.20 as an example. The insets show four representative hysteresis loops measured along the 100 possess less interfaces than multilayers. Therefore, the usual axis. For a Cr thickness less than about 5.2 Å, the hysteresis loop shows only ferromagnetic coupling with a high rema- nence. With increasing Cr thickness antiferromagnetic cou- TABLE I. Structure parameters resulting from simulation of the small-angle x-ray reflectivity using a modified Parratt model for sample Fe0.8Co0.2 /Cr/Fe0.8Co0.2 . D and denote the thickness of each layer and roughness at each interface or surface, respectively. Position I, II, and III correspond to a distance about 5, 25, and 45 mm away from the thin end of a 50 mm long sample. I II III D Å D Å D Å Oxide 20.0 1.7 21.6 1.0 21.0 1.0 Cr 45.7 7.4 45.5 7.9 45.6 7.1 Fe0.80Co0.20 30.1 4.0 30.7 4.4 30.0 2.9 FIG. 2. Normalized remanent magnetization as a function of Cr Cr 5.2 4.6 8.1 4.3 11.2 1.2 thicknesses dCr for the sample Fe0.8Co0.2 /Cr/Fe0.8Co0.2 obtained Fe0.80Co0.20 31.6 2.3 32.1 3.3 31.2 2.6 from magnetization loops measured by MOKE. The insets show Crbuffer 101.3 1.0 103.1 2.1 102.8 1.3 four representative loops for different Cr thickness regimes. A com- Nbbuffer 61.4 3.0 62.9 2.8 61.8 1.8 pletely antiferromagnetic coupling occurs at about 10 Å. The upper Al2O3 2.7 2.4 2.5 x axis gives the actual position of each measurement along wedge- shaped sample. 2958 C. T. YU et al. 57 FIG. 3. Magnetoresistance curves measured in different con- FIG. 4. Magnetoresistance curves for Fe figurations with the current parallel, perpendicular, and in 45° to the 1 xCox /Cr/Fe1 xCox trilayers with different Co concentrations at room temperature and magnetic field for samples Fe0.95Co0.05 /Cr with different Cr thick- 77 K, with the external field applied along the hard axis 110 of the nesses: a dCr 5.2 Å with ferromagnetic coupling; b dCr 10.5 films in longitudinal configuration. The related magnetic hysteresis Å with antiferromagnetic coupling. The insets of the figures show loops obtained from MOKE at room temperature are plotted on the the magnetic hysteresis loops. For both longitudinal and transverse right panel. configurations, the field is applied along 110 axes. For 45°, the field is along 100 axes. temperature and 77 K. All MR curves shown in this figure anisotropic magnetoresistance AMR , which depends on the were measured in a longitudinal configuration with the mag- relative orientation between magnetization and sensing cur- netic field applied along the 110 direction of the film. From rent, must be considered, particularly when the Cr thickness this figure it can be seen that at low fields all MR curves is not in the range of complete antialignment of the submag- show an apparent jump. This is a typical feature of MR netizations. For clarifying the AMR effect we have measured curves with cubic symmetry when the magnetic field is ap- the magnetoresistance in different configurations with re- plied along 110 axis.33 From energy considerations, it cor- spect to the angle between the current and the external field. responds to a magnetic phase transition from an antialigned In Fig. 3, we show the anisotropic magnetoresistance state allowing only coherent spin rotation to a state with the curves for two typical samples of Fe submagnetizations M 0.95Co0.05 /Cr trilayers 1 and M 2 lying in directions symmetri- with ferromagnetic coupling a and antiferromagnetic cou- cal to the external field direction 110 . At higher fields the pling b , respectively. The insets of the figures show the MR ratio shows a nearly linear variation with the magnetic corresponding hysteresis loops. The magnetoresistance field and a well defined saturation field. This feature implies curves are measured in longitudinal configuration, transverse that the influence arising from magnetic disorder at the inter- configuration, and in 45° configuration i.e., the magnetic face due to roughness is negligible, thus indicating the high field was applied at 45° to the current . For the ferromagneti- quality of the films. cally coupled sample the upper panel of Fig. 3 , only the The MR ratio as a function of the Co concentration x is AMR is observed. For the longitudinal and transverse con- plotted in Fig. 5. For the pure Fe/Cr/Fe trilayer, the MR ratio figuration, the magnetoresistance shows positive or negative is about 5 and 2 % at 77 K and room temperature, respec- slope with the magnetic field, as expected. The AMR effect is ascribed to the spin-orbit interaction and depends upon the angle between the current and the magnetization as cos2 .32 Therefore, for the measurement in 45° the AMR effect is eliminated approximately as actually seen in the figure. The typical magnetoresistance curves for the antiferromagneti- cally coupled sample are shown in the lower panel of the same figure. Owing to the AMR effect, the magnetoresis- tance measured in transverse and longitudinal configuration shows a small reduced and enhanced amplitude, respectively. For all trilayers studied here, the variation of magnetoresis- tance due to the AMR effect is on the order of 0.1% and thus about an order of magnitude lower than the GMR effect. For the antiferromagnetically coupled samples discussed below, the magnetoresistance is dominated by the GMR effect. FIG. 5. MR ratio as a function of Co concentration for In Fig. 4, we show the MR curves for the AFM coupled Fe1 xCox /Cr/Fe1 xCox trilayers at 77 K and room temperature. position of the Fe1 xCox /Cr/Fe1 xCox trilayers at room The drawn lines are a guide to the eye. 57 GIANT MAGNETORESISTANCE IN Fe 2959 1 xCox /Cr(001) . . . FIG. 7. MR ratio for different Fe1 xCox /Cr trilayers as function of temperature. The lines are a guide to the eye. FIG. 6. Upper panel: the extrapolated residual resistivity of the Fe1 xCox /Cr/Fe1 xCox trilayers as function of x. Lower panel: GMR effect in the Fe1 xCox /Cr/Fe1 xCox trilayers in more normalized resistivity of the Fe1 xCox /Cr trilayers as function of detail, we have plotted the temperature dependence of the net temperature. change of the magnetoresistance in a saturation field and tively. This strong temperature dependence of the GMR ef- zero field over the temperature regime between 77 K and fect is consistent with previous reports for Fe/Cr multilayers room temperature Fig. 8 . In this figure, the net change of in the literature.34 With adding Co the GMR effect decreases the magnetoresistance is normalized by the value at 77 K. drastically and rapidly. Quite surprisingly, even for a small The temperature dependence of changes qualitatively concentration of 3 at. % Co, the GMR effect is strongly sup- when adding Co. For the Fe/Cr trilayer, decreases mo- pressed with an MR ratio of only 1.1 and 0.6 % at 77 and notonously with increasing temperature. For all the alloy 296 K, respectively. With further increase of the Co concen- Fe1 xCox /Cr/Fe1 xCox trilayers there is a clear increase of tration, the change of the MR ratio is much weaker. with increasing temperature up to about 200 K, followed At the first sight, one might assume that the concentration by a slight decrease of for higher temperatures. Thus, the dependence of the GMR effect in Fig. 5 could simply be observed weak temperature dependence of the MR ratio in explained by disorder scattering in the alloy system. How- the trilayers with alloy magnetic layer in Fig. 7 is due to an ever, from Fig. 6, one can see that the residual resistivity for unusual increase of with temperature. individual samples is irregular with respect to the Co con- centration, indicating that the alloy disorder scattering is not IV. DISCUSSION the main contribution to the total resistivity of the films. This The main result of the present paper is the strong decrease is easy to understand considering the real structure of the of the GMR effect in Fe film. As described above, the film consists of eight individual 1 xCox /Cr/Fe1 xCox trilayers, com- bined with a qualitative change of the temperature depen- layers with eight interfaces, the magnetic trilayer only has a dence of the GMR effect even at Co concentrations as low as thickness of about 70 Å compared to a total thickness of 3 at. %. For higher Co concentrations the further change of about 230 Å for the film. In a resistor array model, the the GMR is only moderate. We will first discuss the change trilayer only contributes about 30% of the conductivity and of the amplitude of the GMR and then come to a discussion the main contribution to the residual resistivity 0 comes of the temperature dependence. from the interface scattering. The influence of disorder scat- tering in the alloy layer arising from Co point defects, which enters into the GMR by adding to the residual resistivity at saturation field s is not important in these films. The drop of the GMR effect at low Co concentrations must have another origin. In contrast to the strong reduction of the GMR effect with temperature in Fe/Cr, the alloy Fe1 xCox /Cr/Fe1 xCox trilayers exhibit a much weaker temperature dependence see Figs. 4 and 5 . For the samples with x 0.03, 0.05, and 0.1 the MR ratio decrease slightly between 77 K and room tem- perature, for the sample with x 0.2 the MR ratio at 77 K and room temperature is nearly identical. The temperature dependence of the MR ratio for different Co concentration is displayed in Fig. 7. For pure Fe/Cr the GMR effect is strongly temperature dependent. For the alloy trilayers, how- ever, the MR ratio is only weakly affected by the tempera- FIG. 8. Normalized net change of magnetoresistance in a ture. saturation field for different Fe1 xCox /Cr/Fe1 xCox trilayers. The In order to characterize the temperature dependence of the lines are the fits to the experimental data. 2960 C. T. YU et al. 57 A. The origin of the decrease of the GMR effect TABLE III. Fitting parameters from the simulation of the net We first stress that the strong decrease of the GMR in change of magnetoresistance as a function of temperature by (T) a bT cT2 for different Fe Fe 1 xCox /Cr/Fe1 xCox trilay- 1 xCox /Cr at low Co-concentration seems to be specific ers. For details, see main text. for this alloy system since it has not been observed in other systems like Fe1 xCrx /Cr, Co1 xFex /Cu, and Samples a b c Co1 xNix /Cu. First one might assume that this concentration dependence is due to the loss of band matching for the MBE812 (x 0) 9.93e-1 5.11e-4 4.86e-6 minority-spin band with alloying. As mentioned in the intro- MBE886 (x 0.03) 1.05e-1 1.34e-2 3.17e-5 duction, in the Fe MBE841 (x 0.05) 7.24e-2 1.36e-2 3.29e-5 1 xCox alloy the majority-spin band is ex- pected to be filled up with increasing x. Here it is helpful to MBE837 (x 0.10) 4.64e-1 8.64e-3 2.04e-5 refer to the Slater-Pauling curve as a guide, which shows an MBE832 (x 0.20) 5.69e-2 1.47e-2 3.21e-5 increase of the magnetic moment in Fe1 xCox with Co con- centration up to x 0.3.35 Regarding the density of states for scattering for the two spin channels can be spin dependent. the majority band of Fe,8 one finds that for filling up the The electron-phonon scattering rate in Boltzmann theory is majority band of Fe only about 5% electrons/Fe atoms are given by40 required. Thus, the increase of the magnetic moment up to 30 at. % Co is mainly due to a change of the exchange split- 2 I2 ting . The change of certainly will change the matching 1 k T. 1 behavior between the Cr bands and the minority band of cN F B M 2 Fe1 xCox . If the Cr band lies between the spin-up and spin- down bands of the Fe with the spin-dependent density of states N ( ), the 1 xCox alloy, step potential barriers ( ) F exist for both spin directions. In addition, the band structure mean-square phonon frequency 2 , and the electron- itself may undergo modifications on alloying with Co.36 Both phonon matrix element I2 , which is also spin dependent. ( ) variations can destroy the matching feature and thus dimin- If, as for the case of bulk Co,8 the density of states N ( ) ish the disparity between the potential barriers encountered F and N ( ) are very different, the electron-phonon scattering by the majority and minority spins at the interfaces. This F rate for the two spin channels can be different. might lead to a reduction of the spin asymmetry in the scat- The electron-magnon scattering usually plays a more im- tering at the Fe1 xCox /Cr interfaces. portant role at higher temperatures. It was shown37 that the However, it seems questionable that only 3 at. % of Co in magnon scattering in antiferromagnetically coupled Fe/Cr Fe can cause a definite modification of the band matching superlattices follows a T 2 law well below the Curie tempera- behavior in Fe/Cr, resulting in the strong reduction of the ture. GMR effect observed experimentally. The fact that a low Approximately, neglecting temperature-dependent elec- concentration of Co in Fe can modify the GMR so strongly tron-electron scattering, the net change of the magnetoresis- suggests that point-defect scattering on Co atoms is very tance at a given temperature can be written as important. For Fe/Cr, a strong asymmetry of scattering by Cr impurities in Fe exists.21 The addition of Co to Fe causes a T partial compensation of the spin-dependent scattering of Cr 0 p T m T . 2 impurities, because Co impurities in Fe lead to an opposite Here spin asymmetry of the scattering.16 This compensation effect 0 denotes the primary part of the ground-state GMR effect related to elastic scattering, which is assumed to will certainly reduce the GMR effect. be temperature independent; p is the influence arising from possible spin-dependent phonon scattering; m(T) represents the influence coming from electron-magnon scat- B. Temperature dependence of the GMR tering which causes spin flip and should yield a negative As shown in Fig. 6, the temperature dependence of the effect on the GMR. MR ratio is quite different for the pure Fe/Cr trilayers and for According to the above assumption, we have fitted (T) films with alloy magnetic layers. The strong reduction of the by a second-order polynomial function. The fitting results are GMR effect with increasing temperature is consistent with plotted in Fig. 8 as broken lines with the fitting parameters previous reports in Fe/Cr superlattices,34,37 and is interpreted listed in Table III. The fit to the experimental data is good by electron-magnon scattering or significant spin fluctuations with a negative quadratic term and a positive linear term, as of local spins,39 causing spin mixing. In comparison, a less expected. This indicates that a common physical effect domi- significant temperature dependence of the GMR effect was nates (T) in all samples studied here. The positive con- reported for the Co/Cu superlattice,38 and attributed to stant of the phonon term implies that phonon scattering does weaker spin fluctuations in Co.39 indeed contribute to the magnetoresistance. The negative At finite temperature the inelastic temperature-dependent constant in the quadratic term for both Fe/Cr and scattering mainly originates from electron-phonon scattering Fe1 xCox /Cr samples is consistent with a destructive influ- and electron-magnon scattering. Within the two-current ence on the GMR effect from electron-magnon scattering. model, the electron-magnon scattering leads to a mixing of The observation of the anomalous temperature dependence the two spin channels, thus reducing the magnetoresistance of the magnetoresistance in the alloy Fe1 xCox /Cr trilayers effect. The electron-phonon scattering, however, does not in- is just due to the fact that phonon scattering dominates over volve spin-flip processes. Therefore, the electron-phonon the magnon scattering up to temperatures of about 200 K. 57 GIANT MAGNETORESISTANCE IN Fe 2961 1 xCox /Cr(001) . . . The spin-dependent scattering by phonons can only be ob- properties of the trilayers have been investigated by x-ray- served if the primary GMR effect in the ground state is mod- reflectivity measurements, MOKE techniques and magne- erate and the effect from electron-magnon scattering is not toresistance measurements. For the pure Fe/Cr trilayer, we too strong. As a result of the spin-dependent phonon scatter- observed a GMR effect of about 5.5% at low temperatures. ing, the magnetoresistance may be enhanced with in- Adding small amounts of Co, the GMR decreases drastically creasing temperature, as actually observed in all alloy trilay- with an amplitude of only 0.7% at x 0.2. In contrast to the ers. pure Fe/Cr trilayer, which shows a strong reduction of the For the Fe/Cr trilayer, the dominant temperature effect of GMR effect with increasing temperature, the GMR of the the magnetoresistance may come from magnons or spin samples with FeCo alloy magnetic layer is weakly tempera- fluctuation at the interface, which causes spin mixing of the ture dependent because the net change of the magnetoresis- two electron channels. The spin-dependent phonon scattering tance increases with temperature. The strong decrease of part is less significant because of the comparable density of the GMR effect with Co concentration is tentatively inter- states DOS at the Fermi level for spin-up and spin-down preted in terms of a band matching effect, which is important electrons in Fe.8 With adding Co the majority band will be for the GMR in Fe/Cr. The unusual temperature dependence filled up, and the asymmetry of the DOS at the Fermi level of magnetoresistance in Fe1 xCox /Cr trilayer with alloy will increase. This, unambiguously, enhances the spin- magnetic layers is ascribed to an interplay between spin- dependent electron-phonon scattering. On the other hand, dependent electron-phonon scattering and spin-mixing adding Co to Fe might stabilize the ferromagnetism at the electron-magnon scattering. Fe/Cr interfaces,41 thus weakening the spin mixing due to spin fluctuations. ACKNOWLEDGMENTS V. CONCLUSIONS This work was supported by the DFG SFB-166 . C. T. Yu acknowledges the Alexander von Humboldt foundation In conclusion, we have grown Fe1 xCox /Cr/Fe1 xCox for financial support. We wish to thank A. W. Oswald, J. trilayers on Al2O3(11¯02) substrates in the concentration Ciesielski, and A. Abromeit for technical assistance, and Dr. range of x 0 0.2. The structural, magnetic, and transport I. Mertig for helpful discussions. 1 M. 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