PHYSICAL REVIEW B VOLUME 57, NUMBER 5 1 FEBRUARY 1998-I Infrared spectra of giant magnetoresistance Fe/Cr/Fe trilayers S. Uran, M. Grimsditch, Eric E. Fullerton,* and S. D. Bader Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 Received 3 July 1997 Magnetic-field-induced changes in infrared transmission and reflection from Fe/Cr/Fe trilayers are reported. Changes as large as 1% compared with 4­5 % changes in resistivity are observed around 2000 cm 1, and the magnitude of the effect decreases monotonically to zero at 5000 cm 1. The field dependence mimics that of the resistivity, and saturates at the same field at which the magnetization of the two Fe layers align parallel to each other. A simple model, which estimates the frequency dependence of the resistivity and includes the frequency dependence of the skin depth, produces semiquantitative agreement with experiment. S0163-1829 98 02206-1 The giant magnetoresistance GMR observed in many the 211 -oriented sample with H applied along the in-plane ferromagnetic/nonmagnetic metallic multilayer systems1,2 is easy axis. We obtain a GMR value of 3.8% for the 100 - a phenomenon which has attracted considerable attention oriented sample we obtain 5% . The shape of the MR curve both because of its potential for applications as well as its is characteristic of AF-coupled films with uniaxial intriguing origin related to the spin polarization of the non- anisotropy.7 To measure the field-induced IR response, the magnetic layers. The surface magneto-optical Kerr effect samples were placed between the poles of an electromagnet SMOKE 3 has been used with considerable success to in- and the transmission and reflectivity were measured as a vestigate these materials. The technique yields detailed infor- function of the applied field H. Shown in Fig. 1 b is the mation on the spin orientation of the constituent layers and is field-induced change measured relative to the aligned state well understood in terms of bulk magneto-optic constants. It in IR transmission measured at 2000 cm 1 for the sample appears therefore that the optical properties of GMR materi- shown in Fig. 1 a . The field-induced IR response mimics the als are well understood in the visible range. Contrary to this MR showing that the two phenomena have a common origin. situation, there is little known about the infrared IR prop- In particular, both the MR and T/T saturate above 3.5 kG erties of these materials. A priori, if the IR effects were com- when the Fe layers become aligned parallel to each other. parable in magnitude to those in the visible typically However, the IR response has the opposite sign and reduced changes of one part in 105 , they would not be observable. magnitude as compared to the resistivity measurements. This is because conventional IR techniques lack intensity, To further explore this phenomena, we have studied its stability, and polarization features which make visible frequency dependence. A typical Fourier transform IR SMOKE effects possible. We are aware of only two investi- FTIR transmission (T) spectrum, measured in the mid-IR gations of the IR response of magnetic multilayers.4,5 The region and normalized to an MgO substrate, is shown in Fig. results in Ref. 4, on the Co/Cu/permalloy system, indicate that the magnetic-field-induced changes in the IR are consid- erably larger than those in the visible. Here we present the results of an IR transmission and reflection study of antiferromagnetically AF coupled Fe/ Cr/Fe trilayers. We observe large ( 1%) changes in the transmission as fields that align the two magnetic layers are applied. We develop a model to estimate the frequency de- pendence of the magnetoresistance. The model, which con- tains no freely adjustable parameters, reproduces both the order of magnitude and the frequency response of our obser- vations. The 211 - and 100 -oriented Fe/Cr/Fe trilayer samples were made by dc magnetron sputtering onto epitaxially pol- ished single-crystal MgO 110 and 100 substrates, respec- tively, using the same growth procedure outlined for superlattices.6 The 20-Å Cr buffer layers were grown at 600 °C. The substrates were then cooled to 150 °C prior to the growth AF-coupled FE 20 Å /Cr 12 Å /Fe 20 Å trilayer which were then capped with a 20-Å Cr layer. The magnetic characterization of similarly grown Fe/Cr/Fe trilayers is de- FIG. 1. The magnetoresistance a , and field dependence of IR scribed in Ref. 7. transmission at 2000 cm 1 b , of the 112 -oriented sample for H Shown in Fig. 1 a is the magnetoresistance measured on along the easy axis. 0163-1829/98/57 5 /2705 4 /$15.00 57 2705 © 1998 The American Physical Society 2706 BRIEF REPORTS 57 FIG. 2. a Transmission spectrum dashed line of our Fe/Cr/Fe trilayer, measured in the mid-IR region and normalized to an MgO FIG. 3. Magnetic-field-dependent transmission dashed and re- substrate. b Reflectivity spectrum dashed line of the same flectivity full spectra normalized to their high-field values. The sample normalized to that of a thick Cr film. The full lines are the straight lines are the results obtained from the model. a and b are fit to the data using Eqs. 2 and 3 with only as a free param- for the 211 and 100 samples, respectively. eter. sion at around 1000 cm 1 as a field was applied. It is pos- sible that a small portion of the slope change in Figs. 3 and 4 2 a . Below 1200 cm 1 the MgO substrate is either com- could be due to the tail of this feature. The sample with the pletely opaque or shows signs of magnetically induced trans- single Fe layer behaved in a similar manner to the MgO mission changes perhaps due to magnetic impurities. We substrate, but neither showed any field-induced changes in therefore restrict our study to the 1200 to 5000 cm 1 transmission over the range 1500­ 4000 cm 1. range. The reflectivity (R), shown in Fig. 2 b , was mea- sured in the mid- and far-IR regions and was normalized to that of a thick Cr film. Below 1000 cm 1 the reststrahlen from the MgO substrate dominates the reflectivity and clearly makes the data unsuitable for analysis. Figures 3 a and 3 b show the frequency dependence of the field-induced IR response (TH 0 Tsat)/Tsat and (RH 0 Rsat)/Rsat for the 211 and 100 samples, respectively, and H along the easy axis. At any given frequency, the field dependence is analogous to that observed in Fig. 1 b but with the magni- tude of the effect varying with frequency. The IR response is a maximum at 2000 cm 1 and decays monotonically with increasing frequency to zero at 5000 cm 1. To confirm that the phenomena exhibited in Fig. 3 are indeed due to the Fe/Cr/Fe trilayer structure, we also per- formed identical measurements on pure MgO substrates and on an MgO substrate on which a single 40-Å Fe layer equal in thickness to the two Fe layers of the trilayer and with identical buffer and capping Cr layers. The MgO substrate FIG. 4. Fitted index of refraction n ( ) is plotted as the full showed a large and unexplained sharp decrease in transmis- line. The literature values Ref. 9 for bulk Cr are also shown. 57 BRIEF REPORTS 2707 Following the theory for electromagnetic waves in con- Within the framework of our simple model the origin of ducting media,8 it can be shown that for good conductors the the observed frequency dependence can only originate in the real (n) and imaginary parts of the refractive index are conductivity. Guided by this, we note that since the magne- given by toresistivity is proportional to the number of electrons that probe both Fe/Cr interfaces,1,2 it is reasonable to assume that n c/ and 2/ 1/2, 1 only those electrons that reach both interfaces within a pe- where is the skin depth, c is the velocity of light, the riod of the electromagnetic radiation (2 / ) will contribute permeability, the frequency, and the conductivity. The to the magnetoresistance. Since the travel time across the transmission and reflectivity of a metal film on a substrate Cr film cannot be less than d/vF , where vF is the Fermi are readily calculated in terms of n ( ). Following Ref. 8 velocity, this immediately leads to a cutoff frequency c . we have Using a typical Fermi velocity 1 Å/s for a ``free-electron'' metal, and d 12 Å, leads to c 30 000 cm 1. The Fermi T 1 R velocity for the electrons believed to be responsible for trans- 12 1 R23 mitting the spin information in Cr viz., at either the lens or 4 R12R23 1/2sin 12sin 23 e 2 n d/c / n0 1 ellipse in the Brillouin zone is roughly 6 times smaller10 and consequently leads to a cutoff 5000 cm 1. Since transport 2 R12R23 1/2e 2 n d/c cos 12 23 2n d/c is more likely to result from the ellipse which has s-p char- R acter, a spherical Fermi surface appears to be a reasonable 12R23e 4 n d/c 2 approximation. In this approximation only those electrons and propagating at an angle from the surface normal such that R R12 2 R12R23 1/2e 2 n d/c cos 23 12 2n d/c vFcos /d /2 6 R23e 4 n d/c / 1 2 R12R23 1/2e 2 n d/c will contribute to the magnetoresistance. As increases, the fraction of electrons that can probe both interfaces decreases cos 12 23 2n d/c R12R23e 4 n d/c , 3 and, hence, the magnitude of the effect decreases. For where n c 2 vF /d no electrons can reach both interfaces within 0 is the refractive index of MgO, R12 and R23 are the reflection coefficients at normal incidence for a plane inter- 2 / and, thus, the magnetoresistive effect disappears. For face dividing two semi-infinite media, and a spherical Fermi surface it is trivial to integrate Eq. 6 ; it 12 and 23 are the corresponding phase angles. They are given by leads to R / / 0 1 / c for c , 12 1 n 2 n2 / 1 n 2 n2 , 4 R / 0 for 23 n n0 2 n2 / n n0 2 n2 , c . 7 and Using Eqs. 1 ­ 7 and / ( 0) 3.8% from Fig. 1 a , we obtain the dashed lines shown in Fig. 3. Given the simplicity of the model we feel that there is satisfactory agreement 12 arctan 2n/ 1 2n2 , 5 between the experimental results and the model. 2 The experimental results and the model presented above 23 arctan 2nn0 / 2n2 n0 . must also be viewed in the context of the results and the Using Eqs. 1 ­ 5 we have adjusted to fit our data in model presented in Ref. 4. Experimentally there is agreement Figs. 2 a and 2 b ; the full lines are the results of such a in that large, field-induced effects are observed. There are, fitting procedure. The agreement between the fit and the data however, some puzzling differences in detail which we are is reasonable, especially given the simplicity of the model unable to reconcile. In Ref. 4 the transmission in zero field i.e., only the product of is an adjustable parameter . In increases with frequency-compared to our results Fig. 2 Fig. 4 we plot full line our fitted value of n ( ) and which are essentially flat when substrate effects are not compare it to the values for bulk Cr.9 The agreement again present. The origin of the wavelength dependence in Ref. 4 confirms that the approximations being made are realistic. is not clear, especially since at even shorter wavelengths We mention also that the same calculation using a wave- i.e., visible light their 250-Å films should become length dependent n for the MgO substrate 1.29 at opaque. The other feature which we do not understand is the 1000 cm 1 to 1.71 at 5000 cm 1 Ref. 9 does not produce reported change in sign of T/T negative to positive as the any significant differences. wavelength increases as shown in Fig. 2 of Ref. 4. Using Our first attempt to fit the data in Fig. 3 was to change the Eqs. 2 and 3 we are unable to obtain a sign change with- single free parameter discussed above. Such an approach ex- out changing the sign of which would appear to be un- plains both the sign of the IR response and the close relation physical. The sign reversal is also puzzling because at zero between the IR and MR results. However, changing the con- frequency one might expect the sign to be that determined by ductivity by 4% as suggested by the magnetoresistance the dc resistivity viz., negative , and hence, a second sign data, leads to a frequency independent change, also of about change would be required in the model of Ref. 4 at smaller 4%, in T and R. This prediction is clearly inadequate to frequencies than those measured. However, it should be kept account for the observed magnitude and frequency depen- in mind that the model developed in Ref. 4 produces agree- dence of the experimental results. ment with their experimental results. The model in Ref. 4 is 2708 BRIEF REPORTS 57 also more advanced than our present model since it contains tively accounts for the observed phenomena, including the a nonlocal description of the dielectric constant. Unfortu- magnitude of the changes, the scaling with field, and the nately, the details of the fitting procedure used in Ref. 4 frequency dependence. There are also some shortcomings of their Ref. 25 has eluded us and hence we are unable to the model, and of the experiments themselves, which require make a quantitative comparison. further investigation. For example, the use of MgO sub- Kerr measurements on similar samples7 may appear to strates complicates the analysis due to its strong absorption contradict the model presented here which predicts that all and reststrahlen, although the MgO facilitated the growth of magnetooptic effects above 5000 cm 1 should vanish. How- single crystal films which simplifies part of the data interpre- ever, the origin of the weak magnetooptic effects in the vis- tation. Experiments on Si substrates might improve the low ible region in Ref. 7 can be traced to the individual Fe layers. frequency data. From the theoretical standpoint it is neces- As mentioned in the introduction the magnitude of the sary to reformulate the simplistic arguments suggested here magneto-optic effects in pure Fe are orders of magnitude into a rigorous theoretical framework. Such an approach smaller than those presented in Figs. 1 and 3 and are not must also include the realistic band structure of the spacer detectable on the scale of the IR data. They only become layer. observable in the visible due to the existence of high perfor- mance optics, lasers and detectors. Work at ANL was supported by the U.S. DOE, Basic In conclusion, we have observed large, magnetic-field- Energy Sciences-Materials Sciences under Contract No. W- induced changes in IR transmission and reflectivity in Cr/ 31-109-ENG-38. S.U. was supported by the Turkish Minis- Fe/Cr trilayers. A model is presented which semiquantita- try of National Education. *Present address: IBM Almaden Research Center, San Jose, CA layers, and Surfaces, edited by A. Fert et al. MRS Symposia 95120-6099. Proceedings No. 384 Materials Research Society, Pittsburgh, 1 M. N. Baibich, J. M. Broto, A. Fert, F. N. VanDau, F. Petroff, P. 1995 , p. 477. Etienne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. 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