VOLUME 77, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 12 AUGUST 1996 Spin-Density-Wave Antiferromagnetism of Cr in Fe Cr(001) Superlattices Eric E. Fullerton and S. D. Bader Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439-4845 J. L. Robertson Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393 (Received 22 November 1995) The antiferromagnetic spin-density-wave (SDW) order of Cr layers in Fe Cr(001) superlattices was investigated by neutron scattering. For Cr thicknesses from 51 to 190 Å, a transverse SDW is formed for all temperatures below the Néel temperature with a single wave vector Q normal to the layers. A coherent magnetic structure forms with the nodes of the SDW near the Fe-Cr interfaces, and the magnetic coherence length greater than the Cr layer thickness. The results and modeling provide a direct confirmation of the persistence of bulklike antiferromagnetic SDW order in the Cr. [S0031-9007(96)00855-1] PACS numbers: 75.70.Cn, 75.25.+z, 75.50.Ee The magnetic structure in confined geometries of itiner- normal to the layers. The SDW period we determine is ant systems with long-period bulk ordering is a topic ripe close to the bulk value, and the magnetic coherence length for exploration. Cr interleaved in Fe Cr superlattices is jm is .tCr for all samples studied. For tCr # 44 Å the one such system. Bulk Cr is an itinerant antiferromag- neutron scattering results are consistent with commensu- net (AF) which forms an incommensurate spin-density- rate AF order. wave (SDW) below its Néel temperature TN of 311 K Epitaxial Fe Cr(001) superlattices were grown by dc [1]. The SDW is characterized by a wave vector Q deter- magnetron sputtering onto 2.5 3 2.5 cm2 single-crystal mined by the nesting of the Fermi surface along the 100 MgO(001) substrates. A 180 Å Cr(001) buffer layer was directions. The Cr spins S are transverse to Q S Q deposited at 600 ±C onto the MgO. The Fe and Cr above the spin-flip temperature TSF 123 K, and rotate superlattice layers were deposited at 100 ±C. Superlattices 90± to form a longitudinal SDW S k Q for T , TSF. grown under these conditions exhibit the expected long- Recent interest has focused on the AF order of thin Cr lay- period coupling oscillations and magnetoresistance values ers in proximity to Fe [2­9] and its interplay with the bi- as large as 150% [16]. The Fe thickness was held constant quadratic and oscillatory interlayer coupling of Fe Cr Fe at 14 Å for each sample and tCr was varied from 190 to sandwiches and superlattices [10­14]. For the thinnest 31 Å. The number of bilayers was adjusted so that the Cr films deposited on Fe(001), the expected Cr AF order total Cr thickness is $1 mm. The superlattice structure is absent due to intermixing and roughness [3,15], and was characterized by x-ray diffraction to confirm the coupling of the initial Cr layers is antiparallel to the Fe (001) epitaxial growth. Multiple superlattice peaks are [2­7]. For thicker Cr films on Fe(001), two-monolayer observed about the Fe Cr(002) reflections for all of the (ML) oscillations in the surface-terminated ferromagnetic samples. The crystalline coherence lengths are $1500 Å layer of Cr have been observed [2­4]. Reference [2] and the (002) rocking-curve widths are #0.7± for all further identifies the periodic phase slips in the Cr AF samples, except the 44 Å sample whose rocking curve ordering resulting from the incommensurability of the width is 2±. Fitting the x-ray diffraction intensity for SDW. For sputtered epitaxial Fe Cr(001), superlattices the tCr 115 Å sample yields an Fe lattice spacing of TN, identified via transport and magnetic anomalies, are 1.435 1 0.010 Å, and a Cr spacing of 1.446 6 0.003 Å suppressed for Cr thicknesses tCr , 42 Å [13]. For tCr . indicating a 0.25% out-of-plane expansion relative to 42 Å, TN initially rises rapidly and then asymptotically bulk Cr. approaches the value observed in thick Cr films. Recent Neutron diffraction measurements were performed on perturbed-angular-correlation spectroscopy (PACS) mea- the HB-2 and HB-1A triple-axis spectrometers at the HFIR surements for Fe Cr(001) superlattices grown by molec- reactor at Oak Ridge National Laboratory. The neutron ular beam epitaxy report suppression of AF order for wavelength was 2.353 Å. Initial temperature-dependent tCr , 60 Å [14]. measurements T 12 300 K were made on the HB-2 In this Letter we use neutron diffraction to directly mea- spectrometer using a focused Si(111) monochromator. sure the AF-SDW of Cr layers in Fe Cr(001) superlat- Subsequent low-temperature measurement were made on tices. TN is found to be strongly thickness dependent and the HB-1A spectrometer using a double-crystal graphite in quantitative agreement with previous transport results (002) monochromator with a pyrolytic graphite filter [13]. For tCr . 50 Å we find that a transverse SDW is to suppress harmonic contamination. A graphite (002) formed for all temperatures below TN, with a single Q analyzer crystal was used for all experiments. 1382 0031-9007 96 77(7) 1382(4)$10.00 © 1996 The American Physical Society VOLUME 77, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 12 AUGUST 1996 Magnetic scattering from the SDW results in satellites strongly on tCr. The TN values determined from Fig. 2 at the Cr 0, 0, 1 6 d positions [1,17]. The incommen- are compared in the inset with the results of Ref. [13]. surability d is given by 1 2 aQ 2p, where a 2.884 Å The TN values are in quantitative agreement and indicate is the Cr lattice constant. In bulk Cr, d varies contin- TN is reduced as the Cr thickness approaches 42 Å. The uously from 0.037 at TN to 0.049 at 10 K, correspond- magnetic scattering from the 44 and 31 Å samples is weak ing to SDW periods a d of 78 and 59 Å, respectively. and presently precludes an accurate characterization of Shown in Fig. 1 are low-temperature neutron scans about their temperature dependences. the Cr(001) position for the 115, 63, 51, and 31 Å The position of the magnetic peaks also depends on samples. Identical scans at T 280 K have been sub- the Cr thickness but in a more complex manner than the tracted to remove substrate contributions. Satellite peaks TN values. The separation of the satellite peaks for the are indeed observed near their bulk positions. The sym- 190 and 115 Å Cr samples is consistent with that of bulk metric splitting about the Cr(001) position shows that the Cr. For the 63 Å sample, the main SDW peak is shifted Cr layers (for tCr $ 51 Å) form a transverse SDW with to a higher d value and has additional scattered intensity Q normal to the layers. No evidence of a longitudinal close to the Cr(001) reflection. For the 51 Å sample the SDW is observed. For the 115 Å Cr sample, no magnetic magnetic scattering peak is broadened and split about the scattering is observed with the scattering vector in-plane expected bulk position. For the 44 and 31 Å samples two along the [100] and [010] directions, which indicates that weak magnetic peaks are observed. the Cr layers are in a single Q configuration. At first glance, the shift and splitting of the SDW Shown in Fig. 2 are the temperature dependences of peaks in the thinner Cr samples might suggest distor- the 0, 0, 1 6 d peak intensities. TN for the Cr layers is tions of the SDW as tCr becomes comparable with the reduced in temperature from its bulk value and depends bulk SDW period or scattered intensity from different re- gions of the sample. However, this will be shown not to be the case, but instead results from coherent scat- tering of adjacent Cr layers. If each Cr layer scatters incoherently, then broad peaks located at 0, 0, 1 6 d with jm tCr will be observed. However, we find that jm . tCr for all samples. jm values, estimated via Scherrer's equation, are 180, 260, 100, and 150 Å for the 115, 63, 51, and 31 samples, respectively. Since jm . tCr adjacent Cr layers scatter coherently, and inter- ference effects need to be considered. For a perfect super- lattice, instrument-resolved Bragg peaks are expected with the positions determined solely from the superlattice pe- riodicity L [located at q na L (in units 2p a)]. The SDW ordering within the Cr layers only modulates the intensities of these peaks, thus the SDW period cannot be determined directly from the peak positions. Similar observation of coherent magnetic scattering have been ob- served by neutron scattering for a number of rare-earth superlattices [18]. To fit the scattered intensities we use a Hendricks-Teller approach to model the superlattice [19,20]. We assumed the Cr layers have an AF-SDW order and the Fe layers are ferromagnetically ordered. The Fe and Cr layers are described by the magnetic scattering factors N21 X FCr q 21 npCr sin 2pndCr P 1 F n 0 3 exp iqnd (1) FIG. 1. Neutron diffraction results for Fe 14 Å Cr Cr , N super- lattices measured at 20 K. Cr thicknesses are listed to the left M21 X of the spectra. The spectra are offset and the scale factor to the FFe q pFe exp iqndFe , right indicates the relative intensities normalized to the count- n 0 ing time and total Cr thickness. The open circles are the mea- where N M is the number of Cr (Fe) atomic planes with sured intensities, and the solid lines are calculated intensities a lattice spacing of d described in the text. Parameters for the calculated intensities Cr dFe within a Cr ( Fe) layer, and F are given in Table I. The vertical dashed lines indicate the and P are the phase and period of the SDW, respectively. expected 1 1 d and 1 2 d satellite positions for bulk Cr pCr and pFe are the magnetic form factors for Cr and at 20 K. Fe [21], respectively, which are in proportion to their 1383 VOLUME 77, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 12 AUGUST 1996 TABLE I. Fitting results for the Fe 14 Å Cr tCr N superlattices shown in Fig. 1 measured at T , 30 K. The layer thicknesses were confined to 61 ML of those determined from x-ray diffraction. The bulk value for dCr, dFe and the SDW period are 1.442, 1.433, and 59 Å, respectively. The 31 Å data were fitted assuming a commensurate AF structure. Nominal tCr SDW period (Å) tCr ML tFe ML dCr Å dFe Å (Å) F 31 22 9.3 1.440 6 0.003 1.43a · · · · · · 51 36 9.4 1.445 6 0.003 1.45 6 0.03 60 6 5 2.2 6 0.4 63 43.8 9.3 1.446 6 0.003 1.42 6 0.03 61 6 5 20.1 6 0.3 115 80 9.9 1.445 6 0.003 1.44 6 0.03 58 6 4 0.0 6 0.5 190 131a 9.5a 1.446 6 0.003 1.44a 59 6 3 0.0a aParameters which could not be determined in the fitting procedure and were fixed. magnetic moments. In this simple model, all Cr layers are moment distributions determined from the fits are shown assumed to order identically and are separated by the Fe schematically in Fig. 3. Unlike TN, which is strongly layers. The fitting parameters are (i) the layer thicknesses thickness dependent, the period of the SDW is independent tCr and tFe (ii) the Fe and Cr lattice spacings, (iii) the of tCr and in agreement with that for bulk Cr. This even period and phase of the Cr SDW, and (iv) the ratio of the holds for the 51 Å Cr sample which only supports a half Fe and Cr moments. The Fe and Cr layer thicknesses were period of the SDW, and for which TN is only 37% of the confined in the fitting procedure to be within 61 ML of the bulk value. This all suggests that the changes in TN are not values determined from the x-ray diffraction results with a result of impurities or strain, which would alter the Fermi the bilayer period fixed to the value determined by x rays. surface and, therefore, the SDW period [1,22], but instead Interfacial roughness is introduced by ensemble averaging arise from a combination of finite-size effects within the 1 ML fluctuations in the Cr and Fe layer thicknesses, as Cr layers and spin-frustration effects at the Fe-Cr interface outlined in Ref. [19]. The instrumental resolution is also as was previously proposed [13]. included in the calculation. The best fit value for the SDW phase suggests that the The thick solid lines in Fig. 1 are the results of the fitting SDW orders symmetrically in the Cr layers with the nodes procedure. This simple model is able to reproduce the shift near the Fe-Cr interface (see Fig. 3) [23]. This behavior and splitting of the SDW peaks and quantitatively fits both can be qualitatively understood from theoretical calcula- the relative intensities and linewidths of the experimental tions of Cr ordering on stepped or interdiffused surfaces data. For the tCr # 63 Å samples, the spitting of the where magnetic frustration can strongly suppress the Cr peaks results from the superlattice periodicity. The Cr moments [9]. Nodes in the SDW near the Fe-Cr inter- buffer layer represents only 1% of the Cr content of the face may isolate the Cr layer from the frustrated interfaces. film and does not contribute to the observed scattering. Such a model also explains the onset of AF-ordering tran- The linewidths are determined solely from the 1 ML sition for tCr 42 Å, as observed in superlattices [13]. thickness fluctuations introduced into the calculation. The fitting parameters are given in Table I, and the magnetic FIG. 2. Temperature dependence of the 0, 0, 1 6 d mag- netic peak intensities: 190 Å (open diamonds), 115 Å (filled FIG. 3. Schematic representation of the magnetic moments circles), 63 Å (open triangles), and 51 Å (filled squares) for Fe and Cr layers determined from the fitting results of samples. The inset shows TN values determined for these Fig. 1 and Table I for the 115, 63, and 51 Å samples. The samples (filled circles) compared to the results of Ref. [12] filled circles indicate the Fe moments and the open circles the (open circles). The lines are guides to the eye. Cr moments. 1384 VOLUME 77, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 12 AUGUST 1996 If at least a half period of the SDW 30 Å is required In summary, we have investigated the AF-SDW order to sustain homogeneous AF order in the Cr layer, and the of Cr layers in Fe Cr(001) superlattices by neutron scat- nodes are located 4 ML from the interface, a minimum Cr tering. TN is strongly thickness dependent in agreement thickness 41 Å is then required to sustain AF-SDW or- with previous magnetic and transport results [13]. For der, in close agreement with experimental results. This is tCr $ 51 Å, we find a transverse SDW is formed for all consistent with results of Ref. [2] which identify periodic temperatures below TN with a single Q normal to the lay- phase slips in the Cr ordering for Cr thicknesses of 24, 44, ers. The observed SDW period is close to the bulk value. and 64 ML. This suggests that the first phase slip (or node For the tCr 31 Å, the magnetic scattering can be de- in the SDW) occurs near the interface at a Cr thickness scribed by commensurate AF order. A coherent magnetic of 4 ML. In Ref. [3], imaging of the Cr ordering near the structure is formed with the magnetic coherence length Fe-Cr interface shows irregularities for the first three ML greater than the Cr layer thickness and the nodes of the of Cr resulting from interdiffusion [15] before AF ordering SDW near the Fe-Cr interfaces. begins at the fourth ML. We thank G. Felcher for helpful discussions, Although the scattered intensity is weaker for thinner Cr C. H. Sowers for technical support, and J. Budai and layers, and previous magnetic and transport studies failed E. Specht for use of their x-ray diffractometer. Work to see any signatures of a Néel transition for tCr , 42 Å, supported by the U.S. DOE, BES-Materials Sciences, there still is magnetic scattering from the 31 Å sample under Contract No. W-31-109-ENG-38 at ANL and (see Fig. 1). The scattering persists up to at least Division of Materials Sciences, under Contract No. DE- T 175 K (above TN of the 51 Å Cr samples) and con- AC05-85OR21400 at ORNL. sists of two sharp peaks about the Cr(001) and a broad dif- fuse component centered near the Cr(001) reflection. The scattering can be quantitatively fitted assuming a commen- surate AF structure (see Fig. 1). The observe splitting of [1] E. Fawcett, Mod. Phys. 60, 209 (1988). the peaks results from the superlattice periodicity Dq [2] J. Unguris, R. J. Celotta, and D. T. Pierce, Phys. Rev. Lett. a L , and cannot be interpreted as arising from SDW 69, 1125 (1992). order. The low intensity of the 31 Å sample may be [3] D. T. Pierce, R. J. Celotta, and J. Unguris, J. Appl. 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B 51, contribution to the biquadratic coupling for T , TN [13]. 10 336 (1995). Finally, it is somewhat surprising to observe coherent [18] C. J. Majkrzak et al., Adv. Phys. 40, 99 (1991). scattering of adjacent Cr layers in all the samples. In the [19] E. E. Fullerton et al., Phys. Rev. B 45, 9292 (1992). intensity calculations, increasing the fluctuations of either [20] J. A. Borchers et al., Phys. Rev. B 51, 8276 (1995). the Cr or Fe layer thicknesses to greater than 1 ML is [21] A. J. Freeman and R. E. Watson, Acta Crystallogr. 14, 234 sufficient to suppress the coherent scattering. The high (1961). degree of order suggested by these calculations is not [22] P. Ponntag et al., Phys. Rev. B 52, 7363 (1995). expected for superlattices, and furthermore, x-ray results [23] For a Cr thickness of 51 Å it is not possible to have both suggest roughnesses .1 ML. However, x-ray scattering the Cr SDW symmetrically ordered and the nodes located measures the structural order, whereas the present neutron near the interface. In addition to the fits shown in Fig. 3, local minimum in the least-squares fitting procedure are results are probing the magnetic order. If the lateral jm is possible in which the Cr layers order asymetrically. In large compared with the structural disorder, the magnetic Fig. 3 we show the symmetric solutions. ordering may be insensitive to local imperfections of the [24] M. E. Filipkowski et al., Phys. Rev. Lett. 75, 1847 (1995). interface [25]. [25] M. J. Pechan et al., J. Appl. Phys. 75, 6178 (1994). 1385