VOLUME 75, NUMBER 2 P H Y S I C A L R E V I E W L E T T E R S 10 JULY 1995 Suppression of Biquadratic Coupling in Fe Cr(001) Superlattices below the Néel Transition of Cr Eric E. Fullerton, K. T. Riggs,* C. H. Sowers, and S. D. Bader Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 A. Berger Department of Physics and Institute of Surface and Interface Science, University of California at Irvine, Irvine, California 92717 (Received 13 February 1995) The Néel temperature (TN) of Cr in sputtered, epitaxial Fe Cr(001) superlattices is identified via transport and magnetic anomalies. The onset of the antiferromagnetism is at a thickness tCr of 42 Å. The bulk value of TN is approached asymptotically as tCr increases and is characterized by a three-dimensional shift exponent. Most strikingly, the biquadratic interlayer magnetic coupling (90± orientation of adjacent Fe layers), observed in the thick Cr regime, is suppressed below TN. These results are attributed to finite-size effects and spin frustration near rough Fe-Cr interfaces. PACS numbers: 75.70.Fr, 73.50.Jt, 75.30.Kz, 75.50.Rr Fe Cr superlattices exhibit a variety of intriguing mag- Fe(001) substrate oscillates in its magnetization ori- netic properties, including oscillatory interlayer coupling entation relative to that of the Fe with an 2 ML [1­4], giant magnetoresistance [5], non-Heisenberg bi- period, consistent with the SDW AF anticipated for quadratic coupling [6], and the first experimental realiza- Cr. Reference [13] further reported observation of the tion of the surface spin-flop transition [7]. For the case oscillations well above the bulk TN value, which sug- of Cr(100) spacers, two periods in the interlayer cou- gests that the substrate, a relatively perfect Fe whisker, pling have been observed, a short period [2 monolayers stabilizes the antiferromagnetic spin structure of the (ML)] and a long period (18 Å or 12 ML) [2­4,8]. The Cr. In a complementary study [15] it was shown that short-period oscillations result from the nested feature in the magnetism of Fe films on a Cr(001) substrate is the 100 direction of the Cr Fermi surface which also modified by the AF order of the Cr. In this Letter, is responsible for the spin-density-wave (SDW) antifer- we investigate the AF ordering of Cr spacer layers in romagnetism (AF) of Cr. The long period has also been sputtered, epitaxial Fe Cr(001) superlattices and report observed in (110)- [2] and (211)- [9] oriented films, which a number of new observations. First, we find that the suggests that it is not related to the nesting, but results in- AF order is suppressed for Cr spacers of thickness stead from a short spanning vector associated with the tCr , 42 Å. Second, for tCr . 42 Å, TN initially rises relatively isotropic "lens" feature of the Fermi surface rapidly, asymptotically approaches the bulk value for the [10]. The observed coupling depends on the roughness of thickest spacers studied (165 Å), and exhibits a transition- the spacer layers, with atomic-scale fluctuations of the Cr temperature shift exponent l 1.4 6 0.3 characteristic thickness (i.e., steps) being sufficient to suppress the short of three-dimensional (3D) Heisenberg or Ising models. period, leaving only the long-period coupling [8]. How- Third, the AF ordering of the Cr spacers results in anom- ever, Slonczewski [11] has shown that fluctuations in the alies in a variety of physical properties, including the short-period interactions can give an additional nonoscil- interlayer coupling, remanent magnetization (Mr), coer- latory, biquadriatic coupling term in which the magnetiza- civity (Hc), resistivity ( r), and magnetoresistance (MR). tion orientation between adjacent Fe layers is 90±, rather Finally, and most intriguingly, the biquadratic coupling of than 180± or 0±. the Fe layers observed for T . TN vanishes below TN. An outstanding problem in the Fe Cr system is to Epitaxial Fe Cr(001) superlattices were grown by understand the role of the magnetic ordering within the dc magnetron sputtering onto MgO(001) single-crystal Cr spacers. Bulk Cr is an itinerant antiferromagnet with substrates. The growth procedure and structural char- a Néel temperature (TN) of 311 K. The incommensurate acterizations are given in detail elsewhere [9]. The SDW is characterized by a wave vector Q determined by Fe thickness was held constant at 14 Å and tCr was the nesting. At high temperature, the Cr spin sublattices varied from 8 to 165 Å. The magnetic properties were S are transverse to Q (S Q), while below the spin-flip measured by a SQUID magnetometer from 10 to 350 K transition at 123 K S rotates 90± to form a longitudinal with the applied field H in plane along either the Fe 100 SDW with SkQ [12]. The AF order of thin-film Cr is less easy axis or 110 hard axis. Transport properties were well studied, particularly in proximity to Fe layers. Two measured using a standard four-terminal dc technique recent studies [13,14] reported observations that the with a constant current of 10 mA and H in plane along surface-terminated ferromagnetic layer of Cr on an the Fe 001 . 330 0031-9007 95 75(2) 330(4)$06.00 © 1995 The American Physical Society VOLUME 75, NUMBER 2 P H Y S I C A L R E V I E W L E T T E R S 10 JULY 1995 Transport measurements are often used as a probe of the MR increases. The reduction in the Mr value in the AF ordering in Cr and Cr alloys, where r is enhanced Fig. 2(a) is not attributable to a change in the easy-axis above its extrapolated value as the temperature T de- direction of the Fe; magnetization measurements with creases through TN [12,16]. This anomaly in r, attributed H along the 110 hard axis have an Mr 0.71Ms at to the formation of energy gaps opening on the nesting both temperatures, which is expected for a magnetization parts of the Fermi surface, is commonly used to locate TN. that rotates 45± from the field direction to the Fe 100 Shown in Fig. 1 are T-dependent transport results for an easy axis. Thus, we conclude that the reduction in Mr [Fe(14 Å) Cr(70 Å)]13 superlattice. Figure 1(a) shows r results from a change in the Fe interlayer coupling as T vs T for H 500 Oe, which is a sufficient field to align increases. The Mr value for T . TN is consistent with a the Fe magnetization. An anomaly in r below 200 K is 90± alignment of the magnetization of adjacent Fe layers, observed as an increase above its expected linear behav- indicative of biquadratic interlayer magnetic coupling ior, as shown by the dotted line. The difference between [18], while the Mr value for T , TN is consistent with the measured r and the linear extrapolation rlin is plotted a vanishing of the biquadratic coupling that leaves the in Fig. 1(b). The magnitude of the r enhancement of 7% layers relatively uncoupled. is consistent with similar measurements in bulk Cr and Shown in Fig. 3 is the T dependence of Mr, Hc, the Cr(001) films [12,17]. The reduced value of TN 195 K saturation field (Hs), and the MR of the superlattice in is determined by the point of inflection of the r vs T [see Figs. 1 and 2. All four quantities exhibit anomalous Fig. 1(c)]. behavior which is directly related to the Néel transition The AF ordering of the Cr dramatically alters the of the Cr. The Mr shows a transition at TN from a interlayer coupling of the Fe. Shown in Fig. 2 are the value of 0.53Ms for T . TN to 0.95Ms for T , TN, as magnetic and MR data measured above and below TN discussed above. The Hc values peak at TN in a manner for the same superlattice with H applied in plane along often observed in systems which undergo magnetic phase the Fe 100 easy axis. Below TN, M Ms, where Ms is transitions [19]. Hs in Fig. 3(c), the field at which the saturation value, has a nearly square hysteresis loop M reaches 90% of Ms, is roughly proportional to the and the low MR value ( 0.3%) is comparable to that interlayer coupling strength [20], and increases strongly for ferromagnetically coupled or uncoupled superlattices. with decreasing T . TN, reaches a maximum at 230 K, However, increasing T above TN to 220 K changes and then decreases sharply and approaches zero at TN. both M Ms and the MR: Mr decreases to 0.5Ms and The MR in Fig. 3(d) also shows an anomaly at TN, and is consistent with a loss of interlayer coupling below TN. Utilizing both the transport and magnetic properties to identify TN, Fig. 4(a) shows TN vs tCr for a series of (001)-oriented Fe(14 Å) Cr(tCr) superlattices. For tCr , 42 Å there is no evidence of the Cr ordering. For tCr . FIG. 1. Resistivity of an [Fe(14 Å) Cr(70 Å)]13 superlattice. (a) r vs T measured at H 500 Oe. The dashed line is a linear extrapolation rlin of the data above 280 K. (b) The FIG. 2. (a) Magnetic and (b) magnetoresistance results for the difference between the measured r and rlin normalized to [Fe(14 Å) Cr(70 Å)]13 superlattice in Fig. 1 measured above rlin. (c) Numerical derivative of r smoothed for clarity. The and below TN 195 K. H is applied along the 100 easy minimum in dr dT locates TN. axis. 331 VOLUME 75, NUMBER 2 P H Y S I C A L R E V I E W L E T T E R S 10 JULY 1995 behavior of TN vs tCr reported here can be understood as arising from a combination of finite-size effects within the Cr spacer and spin-frustration effects at the Fe-Cr interface, as will be discussed in the remainder of the paper. In thin films, magnetic properties are altered due to the surface contribution to the free energy [22]. Since this contribution is generally positive, the magnetic order is weakened at the surface and the ordering temperature is reduced. Scaling theory predicts that TN should have the form TN 2 TN tCr TN tCr b t2l Cr , (1) where l 1 n is the shift exponent, b is a constant, and n is the correlation-length exponent for the bulk system. The theoretically expected l values are 1 0.7048 1.419 and 1 0.6294 1.5884 for the 3D Heisenberg [23] and Ising [24] models, respectively. Fitting the data for tCr . 70 Å by Eq. (1) is shown by the dashed line in Fig. 4, where TN 295 K has its thick-film value. These data are well represented by l 1.4 6 0.3, which is in agreement with expectation from scaling theory. To FIG. 3. Temperature dependent magnetization results for fit the complete data set, we used the empirical expression the [Fe(14 Å) Cr(70 Å)]13 superlattice in Figs. 1 and 2. (a) Squareness ratio Mr Ms, (b) coercivity, (c) saturation field TN 2 TN tCr TN tCr b tCr 2 t0 2l0, (2) defined at 90% of Ms, and (d) the magnetoresistance. The vertical dashed line locates T where t N of the Cr layers. 0 42.3 represents the zero offset in the Cr thickness and l0 0.8 6 0.1 as shown by the solid line in Fig. 3. The sharp drop in the value of TN near tCr 50 Å and the nonuniversal value of l0 indicate the 42 Å, TN increases rapidly and reaches a value of 265 K presence of an additional effect for the thinnest Cr spacers for a 165 Å Cr thickness. For a 3000 Å thick Cr film that we identify below as being due to spin frustration. grown in similar fashion to the superlattices, a TN value We need to understand the differences between the thin of 295 K was obtained. A number of factors [12] can alter and thick Cr regimes and the relationship to isolated Cr the TN value of Cr, including impurities, pressure, defects, films. For an ideal Fe Cr(001) interface, TN tCr should grain size [21], and epitaxial strain [17]. The unusual increase with decreasing Cr thickness due to the Fe- Cr exchange coupling since the Fe Curie temperature is much higher than TN for Cr. This agrees with the experimental observations of Ref. [13]. In the present study, however, we find TN tCr decreases for thin Cr layers. We believe that this behavior arises from spin- frustration effects in the vicinity of the rough Fe-Cr interfaces [25]. Such interfaces contain atomic steps as shown in the Fig. 4 inset and discussed in Ref. [15]. The interfacial exchange energy can be minimized only locally, and frustration of the interfacial spins will occur if the Fe and Cr magnetically order long range. For a superlattice, assuming random monatomic steps at both the Fe and Cr surfaces, 25% of the Cr layer will be frustrated at both interfaces, 50% will be frustrated at one FIG. 4. T interface, and 25% will match with the Fe layers. The N for a series of [Fe(14 Å) Cr(70 Å)] 13 superlattices vs Cr thickness. The open circles are the measured values, value of TN, therefore, should be influenced by a balance and the dashed and solid curves are fitted by Eqs. (1) and (2), between the energy gained from long-range AF ordering respectively. The measured TN value for a 3000 Å Cr film (not of the Cr and the energy cost due to magnetic frustration shown) is 295 K. The inset shows a possible spin configuration of Cr on a stepped Fe surface in which the region of spin at the Fe-Cr interfaces. For thin Cr layers, the frustration frustration at the Fe-Cr interface is shown schematically by the energy is sufficiently high to suppress long-range ordering shaded ellipse to the right of the atomic step. of the Cr. As tCr increases, the system overcomes the 332 VOLUME 75, NUMBER 2 P H Y S I C A L R E V I E W L E T T E R S 10 JULY 1995 frustration energy and begins to order. The crossover of Energy, Basic Energy Sciences-Materials Sciences, un- thickness for the present samples is 42 Å of Cr. der Contract No. W-31-109-ENG-38. One of us (A. B.) Given that the Fe-Cr exchange is much stronger than gratefully acknowledges support from the Alexander von the Cr-Cr exchange interaction, a more realistic picture Humboldt-Stiftung through a Feodor Lynen Research Fel- would have the frustrated magnetic interface located near lowship. the Fe-Cr interface but within the Cr layers. Then the interfacial Cr atoms could be polarized by the Fe, and the magnetically "dead" Cr atoms (or nodes in the AF SDW) could be moved towards the interior of the Cr layer. Electronic structure calculations [26] of Fe Cr Fe *Permanent address: Stetson University, DeLand, FL trilayers determine that the energy cost in suppressing 32720. the Cr moment (at 0 K) is only 0.8 meV atom, as [1] P. Grünberg et al., Phys. Rev. Lett. 57, 2442 (1986). compared to 200 and 80 meV atom for Fe and Mn, [2] S. S. P. Parkin, N. More, and K. P. Roche, Phys. Rev. Lett. respectively. Calculations of diffuse or stepped Fe Cr 64, 2304 (1990). interfaces demonstrate that the presence of frustrated Fe- [3] J. Unguris, R. J. Celotta, and D. T. Pierce, Phys. Rev. Lett. Cr bonds can strongly suppress the Cr moment over 67, 140 (1991). extended distances [26­28]. Thus, Cr is highly sensitive [4] S. T. Purcell et al., Phys. Rev. Lett. 67, 903 (1991). to its local environment with local distortions being [5] M. N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988). [6] M. Rührig et al., Phys. Status Solidi (a) 125, 635 (1991). capable of causing strong moment reductions. [7] R. W. Wang et al., Phys. Rev. Lett. 72, 920 (1994). For the thicker Cr films (tCr . 65 Å) above TN, [8] D. T. Pierce et al., Phys. Rev. B 49, 14 564 (1994). the long-period oscillatory coupling energy decreases to [9] E. E. Fullerton et al., Phys. Rev. B 48, 15 755 (1993). a value of <0.01 erg cm2 and the observed interlayer [10] D. D. Koelling, Phys. Rev. B 50, 273 (1994). coupling becomes dominated by the nonoscillatory bi- [11] J. C. Slonczewski, Phys. Rev. Lett. 67, 3172 (1991). quadratic term. The surprising result that the biquadratic [12] E. Fawcett, Rev. Mod. Phys. 60, 209 (1988). coupling disappears below T [13] J. Unguris, R. J. Celotta, and D. T. Pierce, Phys. Rev. Lett. N gives some insight into its origin. We consider two recent theories which involve ex- 69, 1125 (1992). trinsic mechanisms for the biquadratic coupling [11,29]. [14] T. G. Walker et al., Phys. Rev. Lett. 69, 1121 (1992). The first results from fluctuations in the Cr thickness [15] A. Berger and H. Hopster, Phys. Rev. Lett. 73, 193 that average over the short-period oscillation in the cou- (1994). [16] E. Fawcett et al., Rev. Mod. Phys. 66, 25 (1994). pling; 90± (biquadratic) alignment results from an ener- [17] J. Mattson et al., J. Appl. Phys. 67, 4889 (1990). getic compromise between 0± and 180± orientations [11]. [18] Additional magnetization studies of Fe(60 Å) Below TN if the Cr spins participate in long-range AF or- Cr(70 Å) Fe(14 Å) trilayer structures are also con- dering, they must decouple from the rough interface with sistent with the interlayer coupling being biquadratic Fe and no longer respond locally to the thickness fluctua- above TN. tions. The second theory posits that paramagnetic "loose [19] S. D. Bader, D. Li, and Z. Q. Qui, J. Appl. Phys. 76, 6419 spins" in the spacer or near the interface mediate the cou- (1994). pling by being polarized by the RKKY exchange with the [20] Fitting the magnetization curves above TN for the superlat- ferromagnetic layer [29]. Below T tices and trilayers yield values for the biquadratic coupling N , these loose spins are frozen in the AF matrix and, therefore, no longer con- of 0.01­0.02 erg cm2 and the cubic anisotropy of the Fe tribute to the coupling. The relative importance of the layers K1 Ms 70 G for 70 Å Cr interlayer thicknesses. two mechanisms can, in principle, be assessed by charac- [21] M. R. Fitzsimmons et al., Phys. Rev. B 50, 5600 (1994). terizing the different functional forms they yield for the [22] K. Binder, in Phase Transitions and Critical Phenomena, temperature dependence of the biquadratic coupling. edited by C. Domb and J. L. Lebowitz (Academic Press, In summary, we have investigated the AF ordering of London, 1983), pp. 1­144. Cr layers in epitaxial Fe Cr(001) superlattices. AF order [23] K. Chen, A. M. Ferrenberg, and D. P. Landau, Phys. is suppressed for tCr , 42 Å and is attributed to finite- Rev. B 48, 3249 (1993). size and spin-frustration effects. For tCr . 42 Å, TN [24] A. M. Ferrenberg and D. P. Landau, Phys. Rev. B 44, 5081 initially rises rapidly, and then asymptotically approaches (1991). the bulk value for the thickest spacers studied (165 Å) [25] For a general description of magnetic frustration see R. Q. with a transition-temperature shift exponent characteristic Hood and L. M. Falicov, Phys. Rev. B 44, 9989 (1991). of 3D Heisenberg or Ising models. Finally, the AF [26] D. Stoeffler and F. Gautier, in Magnetism and Structure in ordering of the Cr layers dramatically alters the interlayer Systems of Reduced Dimension, edited by B. Dieny et al. (Plenum Press, New York, 1993), p. 411. coupling in the sense that the biquadratic coupling of the [27] D. Stoeffler and F. Gautier, Phys. Rev. B 44, 10 389 Fe layers observed for T . TN vanishes below TN. (1991). We thank J. Mattson and D. Stoeffler for helpful discus- [28] D. Stoeffler and F. Gautier (to be published). sions. This work was supported by the U.S. Department [29] J. C. Slonczewski, J. Appl. Phys. 73, 5957 (1993). 333