PHYSICAL REVIEW B VOLUME 59, NUMBER 18 1 MAY 1999-II Magnetic properties of Co/Re hcp 101¯0... superlattices T. Charlton, J. McChesney, and D. Lederman Physics Department, West Virginia University, Morgantown, West Virginia 26506-6315 F. Zhang, J. Zachary Hilt, and Michael J. Pechan Physics Department, Miami University, Oxford, Ohio 45056 Received 4 September 1998; revised manuscript received 14 December 1998 hcp(101¯0) Co/Re superlattices were grown via magnetron sputtering on Al2O3(112¯0) substrates. The thickness of the Co layers was approximately 1.8 nm with the Re layer thickness varying between 0.5 nm and 3.0 nm. Low angle x-ray reflectivity revealed that for our growth conditions the interfacial roughness is approximately 0.4 nm in each material at each interface. High angle x-ray diffraction, together with off- specular x-ray diffraction, showed that the growth is epitaxial with the 0001 axis in-plane and parallel to the Al2O3 0001 axis. Magnetization measurements indicate the presence of an in-plane uniaxial anisotropy in all samples and antiferromagnetic coupling when the Re layer thicknesses are less than 1.0 nm and close to 2.0 nm. The uniaxial anisotropy was measured via ferromagnetic resonance and determined to be approximately 5 times smaller than in bulk Co for thicker Re layer samples. For thin Re samples, a spin-flop transition causes a competition between the anisotropic magnetoresistance and the giant magnetoresistance when the external field is applied parallel to the easy axis. The most notable consequence is that the magnetoresistance is positive for small fields and negative for large fields when the current is perpendicular to the applied field. We also report a magnetoresistance of 4.5% at 10 K, more than twice the maximum value previously reported for hcp 0001 Co/Re multilayers. Co/Re hcp(101¯0) superlattices provide a new system whereby the role of in-plane magnetic anisotropy in the magnetoresistance of metallic superlattices can be studied. S0163-1829 99 00317-3 I. INTRODUCTION tron sputtering with the Co layer thickness fixed at 1.8 nm with varying Re layer thicknesses. The samples are epitaxial, The phenomenon of giant magnetoresistance GMR has with their c axis in the plane of the film. As a result, the been extensively studied since its discovery1 because of its superlattices have a significant in-plane twofold magnetic an- applications in magnetic sensor technology. In trilayers and isotropy which depends on the Re layer thickness. Antifer- multilayers, this phenomenon relies upon the antiferromag- romagnetic coupling is evident for Re layer thicknesses be- netic coupling between ferromagnetic layers separated by low 1.0 nm from magnetization and magnetotransport nonmagnetic metallic layers.2 Systems that have been stud- measurements. Interestingly, the magnetotransport in these ied thoroughly in both trilayer and multilayer form include samples is a combination of GMR, which depends on spin- Fe/Cr, Co/Ag, Co/Ru, Co/Cr, and Co/Cu combinations.3,4 A dependent electron interface scattering, and anisotropic mag- system that has not received as much attention is the Co/Re netoresistance AMR , which depends on the direction of the system. The largest GMR reported for Co/Re multilayers to magnetization with respect to the applied current. Depending date does not exceed 2% at 18 K.5 In all of the past studies of on the direction of the c axis and the applied current with Co/Re multilayers, the samples were hcp 0001 -oriented respect to the external magnetic field, the GMR and AMR with no indication of in-plane epitaxy.5,6 can have opposite signs and compete with each other, while There is much interest in the interplay between strong in other instances they can reinforce each other. This results uniaxial in-plane anisotropies and antiferromagnetic cou- in unusual magnetotransport properties. The maximum mag- pling between layers because the anisotropy can stabilize the netoresistance at 10 K is 4.5%, a factor of two larger than domain structure in the material, significantly alter the GMR previous work on Co/Re multilayers. We also discovered behavior, and provide knowledge about fundamental mag- that antiferromagnetic coupling occurs for other Re thick- netic interactions. The unusual magnetic and transport prop- nesses, although the GMR is very small or negligible be- erties that this combination causes have been studied in Fe/ cause of the large magnetic anisotropy with respect to the Cr 211 superlattices,7 Co/Cr multilayers,8­11 and Co/Ir antiferromagnetic coupling constant. multilayers.12 From a fundamental point of view, these sys- tems can also be used to study spin-flop transitions in anti- ferromagnets, as was previously done in Co/Cr 211 II. EXPERIMENTAL PROCEDURES superlattices.13 A. Growth In this work, we study the growth and magnetic properties The samples were grown at West Virginia University via of Co/Re superlattices grown on Al2O3(112¯0) along the magnetron sputtering in a high vacuum system with a base hcp 101¯0 direction. The samples were grown via magne- pressure of 3.0 10 7 Torr. The system consists of four 0163-1829/99/59 18 /11897 12 /$15.00 PRB 59 11 897 ©1999 The American Physical Society 11 898 T. CHARLTON et al. PRB 59 goniometer. For the low angle scans, the width of the incom- ing beam was approximately 0.02°. The slits in front of the detector were set to an angular width of 0.12° in order to admit all of the specular intensity for all the angles of inter- est. The low angle x-ray reflectivity was measured by per- forming a 2 scan at the specular condition, and then scanning again with offset by 0.10° to determine the dif- fuse background. The diffuse background was subtracted from the specular scan to obtain the true specular reflectivity.14 The true specular reflectivity was modeled us- ing an optical reflectivity model15 from which the interfacial roughness was determined. High angle x-ray diffraction was performed on the same goniometer described above, but the incoming beam was col- limated by slits to approximately 0.20° wide, while the de- tector slits were set to an angular width of 0.08°. Some 2 scans were performed with the wave vector q along the growth direction while others were performed with q having a component perpendicular to the growth direction. The lat- ter in-plane scans were used to determine the structural in- FIG. 1. Sketch of the superlattice structure used in this paper. plane coherence. scans of the in-plane peaks were also is the roughness corresponding to each interface. performed by rotating the sample about the growth direction while the detector was fixed at the Bragg condition of the sputtering guns in a cluster focused on the substrate, with in-plane peak. The appearance of discrete peaks in a scan, each gun having a shutter controlled by a crystal monitor corresponding to the crystal symmetry of the film, indicates controller. Each of the Co and Re sputtering sources has its that the sample is epitaxial. This technique has been previ- own quartz crystal monitor. The crystal monitors were cali- ously used to determine the epitaxy of Fe/Rh and Fe/V su- brated by depositing a thin film on a glass substrate and then perlattices, among others.16,17 determining its thickness from the interference pattern of the low-angle x-ray reflectivity. Up to five substrates can be mounted inside the chamber at one time. A quartz lamp C. Magnetization measurements heater can heat up the surface of the substrate to 575 °C, A commercial superconducting quantum interference de- which was calibrated with respect to the heater's thermom- vice SQUID magnetometer at West Virginia University eter by placing a thermocouple sensor on a substrate's sur- was used to measure the absolute saturation volume magne- face. tization of the samples at room temperature. The angular The Al2O3(112¯0) substrates were etched in a phosphoric dependence of the magnetization hysteresis loops were car- and sulfuric acid 3:1 mixture at 140 °C prior to mounting in ried out using a vibrating sample magnetometer VSM at the chamber. After the chamber achieved its base pressure, Miami University and at West Virginia University using a the substrate was heated to 575 °C for 15 min to further conventional dc magneto-optic Kerr effect MOKE tech- clean its surface. The substrate's temperature was then re- nique at room temperature.18 All samples were cut to very duced to 560 °C, and a nominally 5.0 nm thick buffer layer nearly the same shape ( 3 3 mm2 squares to minimize of Re was grown. This temperature was chosen because low geometry effects in the measurements. Sample volumes of angle and high angle x-ray diffraction showed that it yielded the Co layers were obtained using the deposited thickness, the smoothest, most crystalline Re buffer layers. In-plane obtained from the fit of the true specular x-ray reflectivity, x-ray diffraction revealed that this layer grew along the and the area, determined by scanning the image into a com- hcp 101¯0 direction and was epitaxial, with the 0001 di- puter and calculating the area with a drawing program. The rection of the Re coinciding with that of the Al area of the samples was also measured with a caliper. 2O3. The superlattices used to measure the magnetoresistance were grown on the buffer layer at a temperature of 158 °C see Sec. III below . A total of twenty superlattice periods were D. Ferromagnetic resonance deposited, with the Co layer being deposited first on the FMR measurements were made at room temperature with buffer layer. A sketch of the superlattice structure is found in the external magnetic field in the plane of the sample. The Fig. 1. sample was mounted in a 35 GHz cavity, film side down, at the bottom of the cavity. Angle-dependent data were ob- tained by rotating the magnet about the cavity. Multiple B. X-ray diffraction peaks in a given spectra were resolved using a spectral fitting The structure of the multilayers was analyzed using both program if necessary. The effective magnetization and an- small and high angle x-ray diffraction at West Virginia Uni- isotropy of the sample was determined by fitting the line versity. The data were acquired using a Cu rotating anode position as a function of angle to the resonance equation of a source attached to a bent graphite crystal monochromator flat disk with the external field applied in the plane of the optimized for K radiation, and a four-circle, 29 cm base sample.19 The resonance equation is given by PRB 59 MAGNETIC PROPERTIES OF Co/Re hcp 101¯0 . . . 11 899 0 2 Hcos H 4 Meff HA1 2HA2 cos2 2HA2 cos4 H cos H HA1 HA2 cos 2 HA2 cos 4 , 1 where 0 is the frequency of the source 35 Ghz , and H are the angles of the magnetization M and the applied field H, respectively, with respect to the c axis, g B / is the gyromagnetic ratio, g is the g factor for Co (g 2.19), Meff is the effective magnetization obtained from the analysis, and HA1 and HA2 first- and second-order anisotropy fields. At 35 GHz and H are essentially equal. The anisotropy fields are described by HAi 2Ki /Msat , where K1 and K2 are the first- and second-order anisotropy constants of a uniaxial an- isotropy energy of the form UK K1 sin2 K2 sin4 , and Msat is the saturation magnetization measured by SQUID magnetometry. Any possible out-of-plane uniaxial anisot- ropy is included in Meff . E. Magnetotransport measurements The magnetoresistance of the samples was measured us- ing the standard dc four-point Van der Pauw technique in a 5.5 T superconducting magnet at a temperature of 10 K. The measurements were carried out in the following configura- FIG. 2. Low angle x-ray true specular reflectivity for two Co/Re tions: 1 H c, H I; 2 H c, H I; 3 H c, H I; and 4 superlattices. The solid lines represent fits to the model described in H c, H I. Here c represents the direction of the in-plane the text and the dots represent data. For a , the model indicates c axis, and I the direction of the applied current. The data tCo 1.73 nm, tRe 0.79 nm, and for b tCo 1.87 nm, tRe were acquired by scanning the magnetic field from positive 3.03 nm. The roughness parameters for these and the other to negative values. samples can be found in Table I. Inset: Roughness parameters for nominally identical layer thicknesses (tRe 2.0 nm, tCo 1.0 nm) III. RESULTS AND DISCUSSION as a function of sample growth temperature. ( ) represents Re-Air, ( ) represents Co-Re, ( ) represents Re-Co, (*) represents A. Structure Buf-Co, and ( ) represents Buf-Sub. The solid line is a guide to the All of the samples used in the present study had similar eye. interface roughness characteristics, according to our x-ray fits. Figure 2 shows the x-ray reflectivity data and the fit for two of these samples. The solid lines in the graphs represent TABLE I. Results of fits to low angle x-ray specular reflectivity fits to the model mentioned above.15 The interface roughness measurements. Units are in nm. Uncertainties are approximately between the Co and Re layers is 0.4 nm 0.2 nm, where 0.2 nm for roughness parameters and 0.15 nm for layer 2 is approximately the full ``width'' of the interface. The thicknesses t. For the definitions of the roughness parameters, see uncertainty of these numbers was determined by changing Fig. 1. the roughness parameters by hand and then obtaining a 2 value after fitting all other parameters. 2 was then plotted as tRe tCo Buf-Sub Buf-Co Co-Re Re-Co Re-air a function of the roughness parameter in order to determine the sensitivity of the model to the parameter. Other important 0.57 1.82 0.04 0.19 0.50 0.37 0.43 parameters that were obtained include the average Co and Re 0.79 1.73 0.07 0.24 0.33 0.39 0.91 layer thicknesses, the Re buffer layer thickness, and the in- 0.82 1.87 0.11 0.28 0.37 0.47 0.84 terface roughness at the top of the sample, between the 1.01 1.91 0.09 0.23 0.42 0.35 0.45 buffer layer and the superlattice, and between the buffer 1.27 1.84 0.09 0.23 0.50 0.54 0.94 layer and the substrate. The full results are shown in Table I. 1.46 1.78 0.12 0.23 0.35 0.40 0.21 Prior to the growth of the samples presented in this study, 1.61 1.62 0.18 0.25 0.30 0.42 0.19 several superlattices with nominally identical Co and Re 1.73 1.86 0.01 0.19 0.40 0.33 0.22 thicknesses (tRe 2.0 nm, tCo 1.0 nm) were grown at dif- 1.89 1.87 0.11 0.39 0.58 0.32 0.32 ferent temperatures to optimize the growth temperature. The 2.11 1.82 0.12 0.25 0.39 0.44 0.40 inset of Fig. 2 shows the interface roughness parameters ob- 2.37 1.77 0.16 0.26 0.51 0.45 0.64 tained from the fits as a function of the growth temperature. 2.50 1.79 0.07 0.23 0.44 0.67 0.30 While the analysis of the specular reflectivity cannot differ- 3.03 1.87 0.12 0.30 0.53 0.69 0.76 entiate between interdiffusion and step disorder, it is reason- 11 900 T. CHARLTON et al. PRB 59 FIG. 3. High angle 2 scan with q along the growth direc- tion for the tRe 0.79 nm sample. The Al2O3 substrate's (112¯0) FIG. 4. a is a 2 scan of the t peak is indicated. Inset: 2 scan with misoriented by 1.07°. Re 0.79 nm superlattice with This lowers the intensities of the substrate peak and the Re buffer q along the 112¯0 direction of the buffer layer and the superlattice. layer's finite-size peak, so that the superlattice peaks are more evi- The substrate (033¯0), the Re buffer layer (112¯0), and the super- dent. The Re buffer layer (101¯0) peak, as well as the superlattice lattice equivalent (112¯0) peaks are indicated. b is a scan ob- peaks are indicated. The numbers indicate the order of the superlat- tained by rotating the sample about the superlattice 101¯0 tice peak. growth direction with q kept fixed at the superlattice (112¯0) Bragg condition. The twofold in-plane crystalline symmetry of the able to assume that at low growth temperatures the interface superlattice is evident. roughness comes about from step disorder, while at high temperatures it is dominated interdiffusion. This is possible layer fringes complicated the analysis. However, it is clear because Co and Re form an alloy for all concentrations at from these scans that the samples are crystalline and 101¯0 high temperatures.20 From this study, the optimal growth oriented. temperature of the superlattice was determined to be Figure 4 a is a 2 scan of the t 158 °C. Re 0.79 nm superlat- tice with q along the 112¯0 direction of the buffer layer and Figure 3 shows a high angle 2 scan with the wave the superlattice, that is, with q having a component perpen- vector q along the growth direction of the tRe 0.79 nm dicular to the growth direction. The substrate (033¯0), the Re sample. The Al2O3 substrate (112¯0) peak, the Re buffer buffer layer (112¯0), and the superlattice equivalent (112¯0) layer's (101¯0) peak, as well as the main superlattice peak peaks are indicated. Figure 4 b is a scan about the super- are indicated. Note the fringes around the Re buffer layer peak, which result from the long-range lateral length scale lattice 101¯0 growth direction with q kept fixed at the smoothness of the 5.3 nm thick buffer layer according to the superlattice (112¯0) Bragg condition. The twofold symmetry, low angle x-ray scattering, the rms roughness at the buffer characteristic of epitaxial growth, is evident as the equivalent layer-superlattice interface is only 0.1 nm). The inset of (112¯0) and (21¯1¯0) planes match the direction of q for Fig. 3 shows a 2 scan with misaligned by 1.07° with angles 180° apart from each other. A similar -scan symme- respect to 2 /2. In this scan the superlattice peaks are ob- try was observed for the Re buffer layer. This proves that the served more clearly because the rocking curve of the sub- sample is epitaxial, with its in-plane 0001 axis parallel to strate is much narrower ( 0.08°) than the misalignment, the 0001 axis of the substrate. Other samples with small and also because this technique effectively eliminates the tRe 2.0 nm also displayed similar in-plane peaks. In-plane fringe peaks resulting from the Re buffer layer. In contrast, peaks for samples with larger tRe were more difficult to de- typical rocking curve full widths at half maximum of the tect because of their proximity to the substrate and buffer main superlattice peak were in the 3° 5° range. In this layer peaks. way, the main superlattice peak, as well as the satellite Finally, we were also interested in determining whether peaks, are clearly visible. The high angle patterns were not the strain in the Co and Re layers depends on the Re thick- analyzed quantitatively because the presence of the buffer ness because strain could cause the effective magnetization PRB 59 MAGNETIC PROPERTIES OF Co/Re hcp 101¯0 . . . 11 901 FIG. 5. dSL(tCo tRe)/tCo plotted as a function of the ratio tRe /tCo , using the values of tCo and tRe obtained from the low angle x-ray reflectivity fits. The solid line represents a fit to a straight line FIG. 6. Magnetization hysteresis curves measured at room tem- for points with t perature for two representative samples with the external magnetic Re /tCo 1.2, which yields interplanar distances of d field H applied both parallel and perpendicular to the Al Re 2.46 nm and dCo 2.13 nm. 2O3 (112 ¯ 0) substrate's c axis. The Re layer thickness of each sample is labeled. of the Co layers to change. If the strain were the same for all samples, then the position of the main superlattice peak in-plane strain, the in-plane lattice parameter of Re decreases would be a weighted average of the Re and Co lattice pa- and that of Co increases, causing the out-of-plane (101¯0) rameters: lattice parameter of Re to increase and that of Co to decrease. For samples where t d Re /tCo 1.2 it was difficult to identify SL tCodCo tRedRe / tCo tRe , 2 the main superlattice peak because it was too close to the where d substrate and buffer layer peaks. SL is the lattice parameter determined from Bragg's law using the position of the main superlattice peak.21 We To summarize, a quantitative analysis of the low angle can rewrite this equation as x-ray reflectivity revealed approximately 0.4 nm of interface roughness. High angle x-ray diffraction showed that the dSL tCo tRe tRe samples are oriented along the 101¯0 direction with the t dCo dRe . 3 Co tCo in-plane c axis in the aligned with Al2O3 substrate's c axis. In Fig. 5 we have plotted dSL(tCo tRe)/tCo as a function of the ratio t B. Magnetic properties Re /tCo , using the values of tCo and tRe obtained from the low angle fits described above. According to Eq. Figure 6 shows magnetization hysteresis curves measured 3 , the graph should yield a straight line if dRe and dCo are at room temperature for two representative samples, those the same for all samples, with the slope being dRe and the with t intercept being d Re 0.79 nm and tRe 1.4 nm, with the external mag- Co . In Fig. 5 the straight solid line repre- netic field H applied both parallel and perpendicular to the sents a linear fit for all data points with tRe /tCo 1.2. Clearly Al the fit is excellent, and demonstrates that the lattice param- 2O3 (112 ¯ 0) substrate's c axis. For the tRe 1.46 nm, the loop is square with H c and sheared with H c. This indi- eter is on average the same for Co and Re for all samples cates that the in-plane epitaxy indeed causes the sample to with tRe /tCo 1.2. From the linear fit we obtain dCo have an in-plane magnetic anisotropy. For the t 0.213 nm and d Re 0.79 nm Re 0.246 nm, which represents an ap- sample, both of the curves are sheared, indicating that there proximately 2.5% increase with respect to the Re (101¯0) is antiferromagnetic coupling between adjacent Co layers. bulk lattice parameter of 0.239 nm, and a similar decrease of However, note that for H c, there is a break in the slope at the Co lattice parameter with respect to the bulk value of H 1130 Oe, whereas no break is observed with H c. This 0.217 nm. This is reasonable considering that the in-plane is an indication that the magnetic anisotropy causes the (12¯10) lattice parameter of bulk Re is 0.138 nm and that of antiferromagnetically-aligned Co layers to undergo a spin- bulk Co is 0.125 nm, so that in order to accommodate the flop transition, similar to the spin-flop transition in conven- 11 902 T. CHARLTON et al. PRB 59 FIG. 7. Saturation magnetization Msat ( ), measured via SQUID magnetometry, and the effective magnetization Meff ( ), measured via FMR, of the Co layers at room temperature of all of FIG. 8. a First order magnetic anisotropy constant K1 and b the samples as a function of Re layer thickness. The uncertainty in second order magnetic anisotropy constant K2 as functions of the M Re layer thickness. Values were determined from FMR angular sat ( 10%) is a result of the uncertainty of the Co layer thickness and the sample area. measurements. Inset: Position of the FMR line for the tRe 1.46 nm sample. The solid curve represents a fit to Eq. 1 . The tional antiferromagnets. In conventional antiferromagnets, error bars are due primarily to the uncertainty in Msat . this transition is first order, and causes the magnetization sublattices to ``flop'' at a critical field, so that a net magne- disorder the Co layer, thus lowering its magnetization. As the tization appears parallel to the applied field direction. The number of Re layers increases, the entropy of the boundary spin-flop transition in a similar Co/Re sample was recently layer increases, thus lowering the magnetization even more. observed directly via polarized neutron reflectivity measure- This magnetic disordering mechanism is similar to that ob- ments whose results will be published separately.22 Briefly, served in CoF2 /FeF2 antiferromagnetic superlattices, where the neutron reflectivity measured with polarization analysis the Nee´l temperature of the FeF2 (TN 78.4 K) layers is de- of the antiferromagnetic peak was used to determine the pressed by the CoF2, which has a much lower Nee´l tempera- angle of the antiferromagnetic moment as a function of mag- ture (TN 39 K).23 Increased strain is an unlikely source of netic field. These measurements showed that the spin-flop this decrease because, as was shown above, the strain is es- transition is gradual when H is applied parallel to the c axis, sentially the same for all samples with tRe 2.2 nm. When unlike the first-order spin-flop phase transition in conven- tRe 1.0 nm, there is a sudden drop in Msat . This drop could tional antiferromagnets. The effect of this behavior on the be due to interdiffusion, which is of the same order as the Re magnetoresistance measurements is discussed below. layer thickness in this range. Figure 7 shows the saturation magnetization Msat of the The magnetic anisotropy in these samples was obtained Co layers measured at room temperature of all of the samples from FMR measurements. The inset of Fig. 8 shows the as a function of Re thickness. The error bars for Msat repre- angular dependence of the position of the FMR line for the sent uncertainties in the thickness of the Co layers and the tRe 1.46 nm sample. The solid curve represents a fit to the sample area measurements ( 10%). When tRe 1.0 nm, model described above in Eq. 1 . From similar fits to spectra Msat decreases monotonically within the data uncertainty. If obtained for every sample, we obtained values for the anisot- this trend is extended to tRe 0, one obtains a value of ropy constants K1 and K2, as well as the effective magneti- Msat(tRe 0) 1400 emu/cm3, which agrees well with the zation Meff . Meff is plotted in Fig. 7 together with Msat . bulk value of Co. The decrease in Msat as tRe increases may Note that within the experimental uncertainties in these val- indicate that the Re atoms near the interfaces magnetically ues, Msat and Meff agree well in the region tRe 1.0 nm. This disorder the Co layers. One possibility is that the Re inter- means that there is very little, if any, surface or interface face atoms, which suffer from some interdiffusion with the anisotropy perpendicular to the plane. Co, may couple magnetically with a low transition tempera- The values of K1 and K2 obtained from FMR are shown ture. Just as the Co atoms would tend to order this interfacial in Figs. 8 a and 8 b . K1 is small for tRe 1.0 nm, but even- layer, the interfacial layer's large magnetic entropy would tually saturates at 0.7 106 erg/cm3 as tRe increases. K2 PRB 59 MAGNETIC PROPERTIES OF Co/Re hcp 101¯0 . . . 11 903 FIG. 9. Magnetoresistance measurements obtained at T 10 K FIG. 10. Magnetoresistance measurements obtained at T for the t 10 K for the tRe 1.46 nm sample. c is the in-plane easy axis, I is Re 0.79 nm sample. c is the in-plane easy axis, I is the applied current, and H is the applied magnetic field. the applied current, and H is the applied magnetic field. displays a similar type of behavior, with the value saturating from H 0.4 In contrast, the AMR, which is a result of s at 0.2 106 erg/cm3. For the thinnest sample K2 is nega- d scattering and spin-orbit coupling,27 depends on the di- tive. This could be the result of the interface roughness, rection of the magnetization M with respect to the current I. which for the thinnest sample would alter the magnetic prop- It is well known28 that in ferromagnetic materials , erties of the Co layers. The values of K1 and K2 are lower where is the resistivity measured with M I and is than the room temperature values of K1 4.1 106 erg/cm3 measured with M I. Note that if M or I are rotated by 180°, and K2 1.0 106 erg/cm3 reported for bulk Co.24 However, there is no change in the AMR. The maximum change in a similar reduction in the anisotropy constants has been re- AMR occurs when M is initially either parallel or perpen- ported for Co(101¯0)/Cr(211) superlattices,25 with values of dicular to I and then rotates by 90°. In Co single films the K1 1.8 106 erg/cm3 and K2 0.55 106 erg/cm3. Interest- AMR can be significant, on the order of a few percent, and is ingly, the ratio for thicker Re layers K1 /K2 3.5 in Co/Re is dependent on the film microstructure.29 In the case of the similar to that obtained in 50 nm thick, b-axis oriented Co Co/Re system, the AMR can be especially significant be- single films, although the actual values of the anisotropy cause the resistivity Re is approximately three times larger constants in the thick films are approximately 5 times greater than that of Co 18.6 cm for Re vs 5.8 cm for (K1 3.4 106 erg/cm3 and K2 1.0 106 erg/cm3).26 This Co .30 This causes a large portion of the electron transport to could be a result of the strain built into the Co layers, as occur through the Co layers, magnifying the AMR contribu- shown in the high angle x-ray diffraction, and not due to an tion. intrinsic effect that would alter this ratio. In the H c, H I configuration, the tRe 0.79 nm sample Magnetoresistance MR measurements at 10 K for two Fig. 9 a , which according to the magnetization measure- representative samples are shown in Figs. 9 and 10. The MR ments is antiferromagnetically coupled, shows an initial rise is represented by / R(H) RS.../RS , where is the in the MR as H decreases from saturation to approximately 2 resistivity, R(H) is the resistance measured at an applied kOe. However, the MR decreases again as H approaches field H, and RS is the resistance at the maximum field. The zero. This can be explained by taking into account the spin- data can be qualitatively explained assuming an in-plane flop transition inferred from the magnetization measure- uniaxial anisotropy and taking into account giant magnetore- ments, and corroborated by neutron diffraction. As the field sistance GMR and anisotropic magnetoresistance AMR decreases from saturation, the magnetizations of the Co lay- mechanisms. The GMR relies on the increased electron scat- ers change from being M c and M I to being approxi- tering when the magnetization of the Co layers are antiferro- mately M c and M I near the critical field at the spin-flop magnetically aligned and is always negative, that is, it causes transition. The degree to which M is aligned c near the the electrical resistance to decrease as the field is increased critical field depends on the relative strengths of the mag- 11 904 T. CHARLTON et al. PRB 59 FIG. 11. Sketch of the magnetizations of adjacent cobalt layers, M 1 and M 2, as functions of H with H c deduced from neutron diffraction data. Notice that the spin flop transition is gradual. netic anisotropy and the antiferromagnetic coupling. In this region the MR increases due to the GMR, because of the FIG. 12. Simulations of the MR data. c is the in-plane easy axis, I is the applied current, and H is the applied magnetic field. The change from a completely parallel to a partially antiferro- sum of the AMR and GMR is the solid line, the AMR is the dash- magnetic alignment of the magnetizations, and due to the dot line, and the GMR is a dashed line. AMR, because the magnetizations change their direction with respect to the current. The fact that the MR peaks at 2 are two surfaces for each Co layer. Equating the expressions kOe, while the magnetization of the sample with H c shows for the magnetic energy of the spin-flop state ( a change in slope at 1.1 kOe, could be a result of a nucleation 1 2) with the energy of the antiferromagnetic state ( of the spin-flop transition at the top and/or bottom surfaces. 1 0, 2 ), one obtains an expression for J After the nucleation, the rest of the layers flop gradually. AF in terms of the switching This causes a complicated magnetization arrangement as a field HSw . HSw is defined as the critical field required to function of magnetic field. This is illustrated in Fig. 11, undergo the spin-flop transition, and is determined from the which shows a possible spin configuration of the superlattice sudden change in slope in the magnetization measurements. as a function of field. The point at which the MR peaks Solving for JAF , one obtains depends on the details of the spin orientations, because the 2 AMR depends on the specific direction of the layer magne- KUtCo HSwM2 tizations with respect to the applied current. JAF 2 1 . 5 4K2 Theoretical calculations by Folkerts31 indicate that if mag- U netization reversal through magnetic domain wall motion, For the tRe 0.79 nm sample, HSw 1130 Oe from Fig. 6, GMR is observed if JAF KUtCo , otherwise there is no M 1100 G from SQUID measurements, and KU K1 K2 spin-flop transition. Here JAF is the antiferromagnetic cou- 0.60 106 erg/cm3 from FMR measurements. This yields pling strength between Co layers and KU is the effective JAF 0.11 erg/cm2, whose magnitude is smaller than, but magnetic uniaxial anisotropy constant. Following the treat- of the same order of magnitude as the coupling reported for ment by Folkerts, the total energy per bilayer per unit area Co(11¯00)/Cr(211) superlattices8 ( 0.24 erg/cm2) and Fe/ when the field is applied parallel to the easy axis can be Cr 211 superlattices13 ( 0.55 erg/cm2). We also calculated written as JAF 0.11 erg/cm2 from the saturation field, as was done for Fe/Cr 211 superlattices,7 in good agreement with the E HM cos 1 cos 2 2JAFtCocos 2 1 calculation above. Unlike the Co/Cr 211 system, however, K no separate surface and bulk-like spin-flop transitions are U sin2 1 sin2 2 , 4 clearly observed in the magnetization, although separate where 1 and 2 are the angles that the magnetizations of transitions are expected because the number of bilayers is the two bilayers make with respect to the easy axis, H is the even.13 One reason for this discrepancy could be that the external field, and M is the magnetization of each Co layer. J/KU ratio in the Co/Re system is approximately 5 times The factor of 2 in front of JAF takes into account that there smaller than in the Co/Cr 211 system, thus leading to a PRB 59 MAGNETIC PROPERTIES OF Co/Re hcp 101¯0 . . . 11 905 FIG. 13. Calculated MR dashed line and M H loop solid FIG. 14. The MR measured with respect to saturation as a func- line for the H c case. tion of tRe measured in three different configurations. H is the ap- plied magnetic field, c is the c axis, and I is the applied current. situation where the surface spin-flop nucleates a gradual tran- sition in the bulk, as discussed above. We also note that the with those of the tRe 1.46 nm sample in Fig. 10. For the large anisotropy value makes the Folkerts calculation barely H c, H I case Fig. 10 a the MR is very small. If the Co applicable, since in this case J layers are magnetically uncoupled, there is essentially no AF/2KUtCo 1.04. This could also be a result of lateral disorder, which would cause a change in the orientation of M as the field is lowered, until distribution in exchange constants, or different anisotropy both magnetizations flip at a negative field. Therefore, M is constants at the top and bottom Co layers, which would always I, and both the AMR and the GMR are zero. The smear out the surface spin-flop transition. small field dependence could be due to the normal magne- We can qualitatively analyze the magnetoresistance in the toresistance of the Re. For the H c, H I case Fig. 10 b , three other configurations in Fig. 9 by again taking into ac- the MR is also not expected to change for the same reasons. count the GMR, the AMR, and the spin-flop transition. For In practice, a small amount of negative MR ( 0.1%) is the H c, H I case Fig. 9 b , as the field is lowered from its observed, perhaps due to a slight misalignment of the sample maximum value, the angle between the Co layer magnetiza- with respect to the field. For the H c, H I case Fig. tions in spin-flop increases. This causes M to have a compo- 10 c , one would expect M to increasingly point along the nent perpendicular to I, so that the AMR decreases the resis- easy axis as H is lowered from saturation. This causes an tivity. As the field is decreased even further and adjacent Co increase in the AMR, which is reflected in the 2% nega- layers become antiferromagnetically aligned c, the resistiv- tive MR shown in the figure. For the case of H c, H I Fig. ity increases due to both the GMR and the AMR. For the 10 d , one would expect the same behavior as in the previ- H c, H I case Fig. 9 c , there is no spin-flop transition ous case, but with a positive AMR, which is exactly what is and the magnetization continuously goes from a parallel observed in the figure. alignment to an antiparallel alignment as the field is lowered The plausibility of our explanation of the unusual behav- to zero. According to Folkerts,31 the GMR is always negative ior of the tRe 0.79 nm sample can be analyzed using the in this case with little or no hysteresis. The AMR is also orientation of the magnetic moments of the layers deduced negative since M I at saturation and M I near H 0. from neutron reflectivity measurements.22 A sketch of the Therefore, a relatively large MR is observed 3.3% . The magnetic moments of two adjacent Co layers, as deduced H c, H I case Fig. 9 d is the same as the previous case, from the neutron reflectivity, is shown in Fig. 11 for the H c except that the initial drop in the MR is due to the AMR case. Note the gradual spin-flop transition. The M H loop since in this case M I at saturation and M I near H 0, can be calculated from the sum of the components of M 1 and whereas the increase in MR near H 0 is due to the GMR. M 2 along H, where M 1 and M 2 are the magnetizations in The two effects are almost of equal magnitude in this con- adjacent Co layers. To simulate the MR, expressions are figuration, so the net change in MR from saturation to H needed for the AMR and the GMR. The GMR is propor- 0 is approximately zero. tional to the magnitude of the net antiferromagnetic moment The results for the tRe 0.79 nm sample can be compared in the sample, or 11 906 T. CHARLTON et al. PRB 59 FIG. 15. MOKE magnetization loops measured with H applied parallel to the easy axis. The Re thickness is indicated in each figure. coupled antiferromagnetically. We note that the MR of the GMR M1 H M2 H A , 6 tRe 0.57 nm sample behaves like the tRe 0.79 nm sample sat M 1 0 M 2 0 in that the H c, H I MR also shows a dip near H 0 and where A is a constant, M (H) is the magnetization of adjacent that the magnitude of the MR is substantial. Co layers as a function of applied magnetic field H, and In order to obtain further insight into the magnetic cou- sat is the resistivity at saturation. The AMR depends on the pling, Fig. 14 shows the MR, max / s R(0) components of the magnetization parallel and perpendicular R(30 kOe).../R(30 kOe), where R(H) is the electrical re- to the applied current. The total AMR contribution to the sistance as a function of magnetic field. In the H c, H I resistivity can be written as configuration, the MR drops precipitously as tRe increases. Although it is tempting to conclude that the antiferromag- netic coupling is small or zero for t AMR 1 Re 1.0 nm, other types of measurements must also be performed to prove this. The 2 cos2 1 cos2 2 , 7 reason is that if JAF KUtCo , only a very small GMR and where 1 and 2 are the angles of the magnetization of two AMR would be observed because the magnetizations of ad- adjacent Co layers with respect to the applied current. Note jacent Co layers would not undergo a spin-flop transition.31 that in the AMR, for H I, sat , and for H I, sat Since KU increases with tRe , the GMR would be reduced if . JAF did not increase with tRe . An indication that this is the Figure 12 shows the calculated magnetoresistance in the case for the Co/Re samples is the MR behavior in the H c, same current and field configurations used in the experi- H I configuration. In this case, there should always be a ments. The only adjustable parameters are A for the GMR, GMR31 and the AMR should always be negative the same and for the AMR. The results of this simple phenomeno- sign as the GMR . In Fig. 14 b the value of / decreases, logical model reproduce the qualitative features of the data in but seems to oscillate slightly as tRe increases, which is remi- Fig. 9 except for the H c, H I case. The poor agreement in niscent of the GMR oscillations in the Co/Ru and Co/Cr this case may result from not accounting for the possibility systems.3 In this configuration, however, it is impossible to of misaligning the c axis with the applied field or contribu- determine whether the GMR or the AMR oscillate. Never- tions due to a more complicated domain structure not taken theless, the possible peaks in the H c, H I configuration into account by the model. Note that in this case the contri- correspond to dips in the H c, H I configuration. We there- bution to the MR is roughly an order of magnitude smaller fore conclude that the nonmonotonic variations in the MR than in the other configurations, which makes it vulnerable to for tRe 1.0 nm are a result of variations in the AMR of the other second order effects not taken into account by the samples, because the GMR should have the same sign, irre- model. spective of the direction of the applied current. The varia- For a comparison of the MR and magnetization data, the tions could be due to small differences in the structure or Co calculated MR and M H loop for the H c, H I case is layer thickness. plotted in Fig. 13. Notice that in the simulation, as in the The behavior of the magnetization hysteresis loops mea- actual data, the switching field does not correspond to the sured with H c shown in Fig. 15, however, could be an peak in the MR. From a qualitative analysis of MR measure- indication that AF coupling could also occur for tRe ments we conclude that the Co layers in the tRe 0.79 nm are 2.0 nm samples, because their hysteresis loops are sheared PRB 59 MAGNETIC PROPERTIES OF Co/Re hcp 101¯0 . . . 11 907 or have steps. A similar behavior has been observed in Fe/ layers. For thin Re samples (tRe 1.0 nm), magnetoresis- Cr 211 superlattices.7 The lack of a significant GMR for the tance measurements clearly indicate the presence of GMR, tRe 2.0 nm samples could be due to a weakening JAF , com- due to antiferromagnetic coupling between the Co layers, as bined with a larger KU as discussed above. However, the was previously observed in 0001 -oriented Co/Re steps in the magnetization loops could also be caused by the multilayers.5 In these samples the MR behavior is relatively formation of complex domain structures, so additional ex- complex due to the spin-flop transition which results in a perimental evidence, such as neutron reflectivity measure- competition between the GMR and AMR effects. Magneti- ments, is needed to prove this hypothesis. zation hysteresis loops also suggest that antiferromagnetic coupling may be present at other Re thicknesses, although IV. SUMMARY AND CONCLUSIONS further studies are necessary to unequivocally prove this. We conclude that the GMR in Co/Re superlattices for thicker Re We have grown epitaxial hcp Co/Re(101¯0) superlattices layers is not necessarily due to a lack of antiferromagnetic on Al2O3(112¯0) substrates. The interfaces of the samples coupling, but could be a result of the large magnetic anisot- were quantitatively analyzed using low angle x-ray reflectiv- ropy of the Co layers with respect to the antiferromagnetic ity. The results show that 0.4 nm of material, or two coupling between the Co layers. These results show that in monolayers of each material are mixed at each of the inter- Co-based multilayers with a strong in-plane anisotropy it is faces. High angle x-ray diffraction, including in-plane important to take into account the AMR as well as the GMR. scans, show that the films are epitaxial. The magnetization of Together, these two effects could be used to significantly the samples measured via SQUID magnetometry agree with enhance the efficiency of magnetoresistance-based devices. the FMR effective magnetization to within the uncertainty of the data, which indicates that there is no significant out-of- plane magnetic anisotropy. Because the c axis of these ACKNOWLEDGMENTS samples is in the plane, a significant in-plane magnetic an- We thank E. Mayo for performing some of the x-ray mea- isotropy is observed. The in-plane uniaxial anisotropy con- surements, M. Koepke for providing the Re sputtering target, stants K1 and K2 were also determined from FMR measure- and D. Windt and E. E. Fullerton for useful discussions. This ments. For thicker Re samples (tRe 1.0 nm), K1 0.7 research was supported by the Petroleum Research Fund 106 erg/cm3 and K2 0.2 106 erg/cm3. These values are Grant ACS-PRF No. 32814-G5 and the U.S. National Sci- approximately 5 times lower than in bulk Co, but the ratio of ence Foundation Grant No. DMR-9734051 at WVU, and these two numbers is the same as that observed in thick Co the U.S. Department of Energy Grant No. DE-FG02- films. This could be a result of the crystalline strain in the Co 86ER45281 at MU. 1 M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. 14 S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, Phys. Rev. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas, B 38, 2297 1988 . Phys. Rev. Lett. 61, 2472 1988 . 15 B. Vidal and P. Vincent, Appl. Opt. 23, 1794 1984 . 2 P. Gru¨nberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sow- 16 M. A. Tomaz, G. R. Harp, E. Mayo, D. Lederman, R. Wu, and W. ers, Phys. Rev. Lett. 57, 2442 1986 . L. O'Brien, J. Vac. Sci. Technol. A 16, 1336 1998 . 3 S. S. P. Parkin, N. More, and K. P. Roche, Phys. Rev. Lett. 64, 17 M. M. Schwickert, R. Coehoorn, M. A. Tomaz, E. Mayo, D. 2304 1990 . Lederman, W. L. O'Brien, T. Lin, and G. R. Harp, Phys. Rev. B 4 For a review, see A. Fert, P. Gru¨nberg, A. Barthe´le´my, F. Petroff, 57, 13 681 1998 . and W. Zinn, J. Magn. Magn. Mater. 140-144, 1 1995 . 18 For a review of MOKE in thin films, see S. D. Bader and J. L. 5 P. P. Freitas, L. V. Melo, I. Trindade, M. From, J. Ferreira, and P. Erskine, in Ultrathiin Magnetic Structures II, edited by B. Monteiro, Phys. Rev. B 45, 2495 1992 . Heinrich and J. A. C. Bland Springer-Verlag, Berlin, 1994 , p. 6 L. V. Melo, I. Trinidade, M. From, P. P. Freitas, N. Teixeira, M. 297. F. da Silva, and J. C. Soares, J. Appl. Phys. 70, 7370 1991 . 19 F. Schreiber, Z. Frait, Th. Zeidler, N. Metoki, W. Donner, H. 7 E. E. Fullerton, M. J. Conover, J. E. Mattson, C. H. Sowers, and Zabel, and J. Plezl, Phys. Rev. B 51, 2920 1995 . S. D. Bader, Phys. Rev. B 48, 15 755 1993 . 20 Binary Alloy Phase Diagrams ASM International, Materials 8 J. C. A. Huang, Y. Liou, Y. D. Yao, W. T. Yang, C. P. Chang, S. Park, OH, 1990 , p. 1229. Y. Liao, and Y. M. Hu, Phys. Rev. B 52, R13 110 1995 . 21 E. E. Fullerton, I. K. Schuller, H. Vanderstraeten, and Y. 9 Th. Zeidler, K. Theis-Bro¨hl, and H. Zabel, J. Magn. Magn. Mater. Bruynseraede, Phys. Rev. B 45, 9292 1992 . 187, 1 1998 . 22 T. Charlton, D. Lederman, S. M. Yusuf, and G. Felcher, J. Appl. 10 J. J. Picconatto, M. J. Pechan, and E. E. Fullerton, J. Appl. Phys. Phys. to be published . 81, 5058 1997 . 23 C. A. Ramos, D. Lederman, A. R. King, and V. Jaccarino, Phys. 11 G. R. Harp and S. S. P. Parkin, Appl. Phys. Lett. 65, 3063 1994 . Rev. Lett. 65, 2913 1990 . 12 H. Yanigihara, K. Pettit, M. B. Salamon, E. Kita, and S. S. P. 24 S. Chikazumi, Physics of Magnetism Wiley, New York, 1964 , Parkin, J. Appl. Phys. 81, 5197 1997 . p. 129. 13 R. W. Wang, D. L. Mills, E. E. Fullerton, J. E. Mattson, and S. D. 25 J. Z. Hilt, J. J. Picconatto, A. O'Brien, M. J. Pechan, and E. E. Bader, Phys. Rev. Lett. 72, 920 1994 . Fullerton, J. Magn. Magn. Mater. to be published . 11 908 T. CHARLTON et al. PRB 59 26 M. Grimsditch, E. E. Fullerton, and R. L. Stamps, Phys. Rev. B 29 P. P. Freitas, A. A. Gomes, T. R. McGuire, and T. S. Plaskett, J. 56, 2617 1997 . Magn. Magn. Mater. 83, 113 1990 . 27 J. Smit, Physica Amsterdam 16, 612 1951 . 30 C. Kittel, Introduction to Solid State Physics, 6th ed. Wiley, New 28 For a review, see I. A. Campbell and A. Fert, in Ferromagnetic York, 1986 , p. 144. Materials, edited by E. P. Wohlfarth North-Holland, Amster- 31 W. Folkerts, J. Magn. Magn. Mater. 94, 302 1991 . dam, 1982 .