VOLUME 87, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 3 SEPTEMBER 2001 Origin of Biquadratic Coupling in Fe Cr 100 Superlattices J. Meersschaut,1,2 C. L'abbé,1 M. Rots,2 and S. D. Bader1 1Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439 2Instituut Kern-en Stralingsfysica, K. U. Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium (Received 18 April 2001; published 16 August 2001) We investigate the magnetic properties of a (100) oriented Fe 1.7 nm Cr 8.4 nm 10 superlattice by means of perturbed angular correlation spectroscopy. The magnetic ordering in the Cr layers is obtained by measuring the magnetic hyperfine interaction at implanted 111Cd nuclear probes. We identify dynamic antiferromagnetic spin fluctuations in the Cr layers and show that it gives rise to the biquadratic interlayer coupling. DOI: 10.1103/PhysRevLett.87.107201 PACS numbers: 75.75.+a, 75.20.­g, 75.50.Ee, 76.80.+y Dynamical effects play a ubiquitous role in diverse matically alters the interlayer coupling between the Fe lay- solid-state phenomena. The experimental challenge is ers of Fe Cr superlattices [10]. The biquadratic interlayer to identify suitable probes that span the time scales of coupling observed in the thick Cr regime (tCr $ 5.0 nm) interest. In the present work, we introduce perturbed is suppressed below the Néel temperature (TN) of the Cr angular correlation (PAC) spectroscopy as a novel tech- spacer. PAC measurements identified SDW ordering in nique to study dynamical phenomena in nanostructures. the Cr layers, and confirmed the SDW instability below a We complement previous neutron diffraction studies of critical thickness [11]. It is now clear that, in superlattice Fe Cr superlattices and address an open basic question systems, the long-range SDW ordering in the Cr spacer about magnetic coupling between thin metallic films -the destroys the interlayer coupling. Later, neutron diffraction microscopic origin of the non-Heisenberg, biquadratic measurements identified a gradual transition from incom- coupling. We show that biquadratic interlayer coupling, mensurate to commensurate AF order in the temperature i.e., the coupling that orients adjacent Fe layers 90± range between 175 and 310 K and to paramagnetic Cr at apart, is mediated by superparamagnetic Cr moments that TN 500 K [12]. However, the nature of the microscopic fluctuate in the GHz regime. magnetic ordering in the transitional region and its relation The discovery of interlayer coupling between ferro- to the interlayer coupling still remains unclear [13]. In this magnetic layers across nonferromagnetic spacer layers [1] Letter, we will identify dynamical effects in Cr. This in- stimulated much research. It was first recognized that the formation is essential to understand the phenomenon of coupling in Fe Cr multilayers aligns adjacent Fe layers biquadratic coupling. parallel or antiparallel, depending on the Cr thickness, The Fe 1.7 nm Cr 8.4 nm 10 superlattice was grown with a Cr thickness periodicity of 1.8 nm [2]. Then, an at 310 ±C on a MgO(100) substrate by means of mo- additional oscillation period of two monolayers was found lecular beam epitaxy (MBE) with a base pressure of [3]. Finally, a biquadratic contribution to the interlayer 5 3 10211 Torr. X-ray diffraction and Rutherford coupling was discovered that favors perpendicular align- backscattering experiments indicate high quality epitaxial ment of adjacent Fe layers [4]. The theoretical explanation growth. The temperature dependent resistivity shows an for the long- and the short-period oscillatory coupling anomaly that is smeared out between 175 and 300 K. We depends on the electronic properties of the spacer [5]. obtain a value of 200 6 5 K for TN from the minimum However, such theories lead only to parallel or antiparallel in the derivative of the resistivity. Our value agrees with alignment of the ferromagnetic layers and do not describe that for sputtered superlattices [10] and other MBE-grown the biquadratic coupling. While various mechanisms have superlattices [12]. Magnetization and magnetoresistence been proposed to explain the existence of biquadratic data were recorded with the magnetic field H applied in coupling [6], experimentally, its origin remains to be plane along the Fe [001] easy axis. We obtained simi- clarified. lar results to those reported by Fullerton et al. on an It is of fundamental importance to understand the in- Fe 1.4 nm Cr 7.0 nm 13 superlattice [10]. We recorded terplay between the intrinsic Cr spin density wave (SDW) a maximum magnetoresistance Dr r 0.62% at 200 K. magnetism [7] and the interlayer coupling in the model The temperature dependence of the saturation field, system Fe Cr. The magnetic ordering of Cr spacer layers shown in Fig. 1, indicates that the interlayer coupling is is expected to depend on the structure of the Cr [8] and of suppressed below 200 K. A study of similarly grown the Fe Cr interface [9]. One should therefore make a clear sandwiches [14] and the results of Fullerton et al. lead distinction between the results obtained on nearly ideal Fe us to conclude that our superlattice shows biquadratic whiskers and those on GaAs, Al2O3, or MgO substrates. coupling above 200 K and vanishing coupling below that The latter is studied herein. In 1995, Fullerton et al. temperature. In the following, PAC spectroscopy is used showed that antiferromagnetic (AF) ordering of Cr dra- to probe the local magnetic ordering in the Cr layers. 107201-1 0031-9007 01 87(10) 107201(4)$15.00 © 2001 The American Physical Society 107201-1 VOLUME 87, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 3 SEPTEMBER 2001 For the PAC measurements, 2 3 1013 atoms cm2 of ra- 8 dioactive 111In were implanted at 80 keV with the sample at room temperature and slightly tilted to avoid channel- ing. X-ray diffraction spectra and the magnetization were 4 measured before and after implantation with no measur- µT) able differences. Experimental PAC data were recorded in s the configuration as shown in Fig. 2(a). The three spectra H ( are consistently analyzed with 17% of the substitutional 0 nuclear probes located in the Fe layer and 83% in the Cr. Probe atoms at the interfaces and those in ill-defined envi- ronments are responsible for the rapid (,2 ns) reduction -4 of the anisotropy. The rapid oscillations in the spectra re- 50 100 150 200 250 300 flect the Fe signal. The measured hyperfine interaction temperature (K) FIG. 1. Saturation field HS vs temperature. HS is defined as the field where the remanent magnetization is 90% of the satu- a) ration magnetization. The line is a fit using the loose-spin model [23] with potential jU kBj 8 K, and using a Gaussian dis- tribution (mean 193 K, width 17 K) of blocking tempera- tures below which the biquadratic coupling is suppressed. In a PAC experiment, one measures the angular correla- tion between two photons successively emitted in the g-g cascade of 111Cd (the daughter nucleus of 111In) [15]. Dur- ing the lifetime of the intermediate nuclear level, the hyper- fine fields exert a torque on the moments of the probe. This 0.00 torque can cause a reorientation of the nuclear spin (simi- b) lar to the Larmor precession) which affects the emission -0.03 probability of the second g ray. If one looks in a particular direction, one essentially observes an exponential decay R(t) -0.06 perturbed by the hyperfine interaction. Coincidence spectra W90 and W180 are measured with detectors at 90± -0.09 and 180±, respectively. From these, the time dependent anisotropy function R t 2 W180 2 W90 W180 1 0.00 2W c) 90 is constructed. The R t spectrum (known also as the PAC time spectrum) contains the information on the hy- -0.03 perfine interactions (frequencies n v 2p and absolute fractions). For the 111Cd probes the frequency is propor- R(t) -0.06 tional to the hyperfine field by the factor 2.33 MHz T. The anisotropy function can be theoretically simulated -0.09 by calculating the time evolution of the different quan- tum states in the intermediate nuclear level under the influ- 0.00 ence of the hyperfine interaction Hamiltonian [15]. In the d) case of ferromagnetic or commensurate AF (AF0) order- -0.03 ing, the general expression reduces analytically to R t a0 1 a1 cos vt 1 a2 cos 2vt . The values a0, a1, and R(t) -0.06 a2 depend on the orientation of the hyperfine field with respect to the detectors, with a0 1 a1 1 a2 A22, a nu- -0.09 clear constant. In the case of an incommensurate SDW ordering (AF1 or AF2) one has to account for the Over- 0 50 100 150 200 hauser distribution with cutoff frequency v0 which leads time (ns) to R t a0 1 a1J0 v0t 1 a2J0 2v0t , with J0 being the Bessel function of zeroth order, and the amplitudes FIG. 2. Configuration of the sample with respect to the de- tectors (a). PAC time spectra obtained at 77 (b), 225 (c), and having the same angular dependence as in the commensu- 300 K (d). The solid lines are fits described in the text. The rate case. dashed lines represent the chromium contribution. 107201-2 107201-2 VOLUME 87, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 3 SEPTEMBER 2001 frequencies n 92.5 2 , 90.9 2 , and 89.3 2 MHz cor- R(t) respond to the bulk values at 77, 225, and 300 K, respec- 0.08 tively. The well-known behavior of in-plane magnetization for Fe is confirmed since only the single frequency of the -0.05 Fe-hyperfine field is observed. For the PAC time spectrum recorded at 77 K, Fig. 2(b), -0.18 the Cr contribution consists of a damped Bessel function 10-4 21 with frequency n 12.2 2 MHz, and therefore indicates 10-2 14 SDW ordering in the Cr layers. As explained in [16], 100 the small hyperfine field value is indicative of a transverse 7 0 * 102 * SDW (AF t 0 1). Because only the first harmonic of the Bessel function is observed, the Cr magnetization is oriented in 104 0 plane. The observation of a transverse SDW is at variance FIG. 3. Simulation of PAC spectra using the stochastic theory with our previous studies [11]. However, investigation of as described in the text. samples grown at different temperatures shows that the en- hanced value of TN and the occurrence of a longitudinal When the time scale of the fluctuation matches that of SDW (AF2) observed in earlier work was related to the re- the characteristic frequency of the hyperfine interaction, duced growth temperature (between 0 and 50 ±C). These the spectrum is that of an overdamped oscillator. For the findings not only explain the discrepancy between results limiting case of very fast fluctuations we expect the nu- of various groups [12,17], but also indicate that it is pos- cleus to see the time-averaged magnetic hyperfine field, a sible to control the type of SDW by varying the growth phenomenon known as motional narrowing in the context conditions. of line-shape studies. In our case the time-averaged field The PAC time spectra recorded at 225 K and at 300 K is zero, therefore the fast-fluctuation limit results in a are shown in Figs. 2(c) and 2(d). The Cr signal obtained paramagneticlike spectrum. here consists of an exponential-like decay. This signal is The Cr signal in the PAC spectra of Fig. 2 is well repro- obviously of magnetic origin, but cannot be analyzed in duced using the stochastic model. The three spectra are terms of a static commensurate, incommensurate, or he- analyzed consistently with only the hyperfine field value lical SDW [13], as these structures would lead to a pro- for the Fe site and the characteristic lifetimes for Cr as nounced precession pattern in the PAC time spectrum [16]. fitting parameters. We obtain for the spectra at 225 and The interface contribution consists of a steeply decaying 300 K the values of t 2.2 ns and t 0.6 ns, respec- spin polarization of Cr with a penetration depth of about tively. Relating this information to the coupling behavior 0.1 nm [18], but it cannot explain the observed spectra. In derived from Fig. 1, it becomes evident that fluctuating Cr the regime where biquadratic interlayer coupling occurs, magnetic moments coexist with the biquadratic interlayer the PAC results are incompatible with static magnetic or- coupling in the Fe Cr superlattice. dering in the Cr. The PAC data disclose superparamagnetic Cr with mo- It is known that an exponential attenuation of the ments fluctuating in the GHz regime. It is interesting to anisotropy may result from dynamical effects. We evalu- note that Fawcett et al. recently considered the phenome- ated the anisotropy function following the procedure non of superparamagnetic relaxation in Cr and recognized developed by Winkler and Gerdau [19] on the basis of the relevance to Fe Cr superlattices [21]. The fluctuat- Blume's stochastic model [20]. Using this stochastic ing magnetic behavior is not restricted to small clusters model, the anisotropy function is completely determined around diluted nucleation centers (i.e., Fe impurities), as by the various stochastic states and by their characteristic this would lead to a large paramagnetic signal in the PAC lifetime t. We consider in Fig. 3 the situation in which spectra superimposed on the signal arising from magnetic the hyperfine field can jump between two opposite direc- environments. Also, the PAC spectra rule out the possi- tions that are each 45± from a detector. This means that bility of static commensurate, incommensurate, or helical the magnetization jumps between positive and negative AF ordering along with the biquadratic interlayer coupling in-plane [001] axes, as shown in Fig. 2. Since we are in this thickness and temperature regime. On the other concerned with the Cr magnetization, we account for the hand, a local probe technique provides only limited infor- Overhauser distribution by a weighted sum taken over mation on the lateral coherence length when dynamical 1000 points in the frequency domain. For very long effects are present. Theoretical calculations predict com- characteristic times (t ¿ 1 v0), the anisotropy function mensurate AF order [13] and the formation of domains in reduces to the statistical average of the anisotropy func- the antiferromagnet [22] at elevated temperatures. We veri- tions for the individual, static hyperfine fields. Therefore, fied that a model of superparamagnetic AF0 Cr, although we obtain in the slow-fluctuation limit the Bessel function not fitting the data at 77 K, is able to fit the spectra at of zeroth order. For this orientation of the magnetic 225 and 300 K. The values for the characteristic times fields only the single frequency is present (a0 a2 0). depend slightly on the chosen stochastical model. The 107201-3 107201-3 VOLUME 87, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 3 SEPTEMBER 2001 analysis in terms of superparamagnetic Cr with polariza- tuations through the systematic measurement of the char- tion fluctuations in the plane and between two opposite acteristic times as a function of temperature and applied directions is consistent with the in-plane AF ordering ob- field. Alternatively, we expect that the spin dynamics of tained via neutron diffraction [12]. Whereas PAC mea- the spacer can be observed via inelastic neutron diffraction surements are most sensitive to spin correlation times t in the present system, or with Mössbauer spectroscopy in between 10210 and 1028 s, neutron diffraction is most the systems Fe Ag57FeAg Fe or Fe 57FeSi Fe. We also sensitive to fluctuations in the time range of 10212 to suggest that there is a need to analyze the line broaden- 10214 s. Therefore, AF ordering with fluctuations in the ing in the Mössbauer results for Fe Cr119SnCr Fe multi- time range of 1 ns will appear as static in neutron diffrac- layers [26] in terms of superparamagnetic behavior in the tion data. Moreover, neutron diffraction and nuclear tech- Cr layers. niques sample different regions of q space, and these It is a pleasure to thank A. Berger, J. Dekoster, W. regions exhibit different dynamical behavior. Evenson, M. Grimsditch, W. Sturhahn, and A. Vantomme The observed microscopic magnetic ordering in the Cr for stimulating discussions and practical help. J. M. layers is reminiscent of the loose-spin mechanism pro- wishes to thank the Belgian Science Foundation (F.W.O.- posed by Slonczewski to explain biquadratic interlayer Vlaanderen) for financial support. Work at Argonne was coupling [23]. In the loose-spin model, localized spins in supported by the U.S. Department of Energy, Office of the spacer layer contribute an exchange coupling between Science under Contract No. W-31-109-ENG-38. the ferromagnetic films. The contribution to the free en- ergy that favors biquadratic coupling is derived from con- ventional statistics. In many cases, the theory produces the correct experimental temperature dependence for the bi- [1] P. Grünberg et al., Phys. Rev. Lett. 57, 2442 (1986). quadratic interlayer coupling strength [24,25]. The model [2] S. S. P. Parkin, N. More, and K. P. Roche, Phys. Rev. Lett. reproduces also the strong temperature dependence of the 64, 2304 (1990). coupling strength above the blocking temperature of the [3] J. Unguris, R. J. Celotta, and D. T. Pierce, Phys. Rev. Lett. Cr (Fig. 1). Our PAC results provide direct evidence of 67, 140 (1991). fluctuating localized spins in the Cr layer when the Fe lay- [4] M. Rührig et al., Phys. Status Solidi (a) 125, 635 (1991). ers are biquadratically coupled. In the model chosen to fit [5] J. Kübler, Theory of Itinerant Electron Magnetism (Oxford the PAC data, the Cr spins fluctuate between two opposite University Press, Oxford, 2000). directions with a time-averaged moment of zero. In this re- [6] S. O. Demokritov, J. Phys. D 31, 925 (1998). spect, the analysis is at variance with the loose-spin model. [7] E. Fawcett, Rev. Mod. Phys. 60, 209 (1988). [8] S. Demuynck et al., Phys. Rev. Lett. 81, 2562 (1998). It is expected that more sophisticated stochastic models [9] D. T. Pierce et al., J. Magn. Magn. Mater. 200, 290 (1999). may fit the PAC spectra as well. Yet, in spite of the simpli- [10] E. E. Fullerton et al., Phys. Rev. Lett. 75, 330 (1995). fications, the present model successfully describes SDW [11] J. Meersschaut et al., Phys. Rev. Lett. 75, 1638 (1995). ordering in Cr below, and dynamical behavior in Cr above [12] A. Schreyer et al., Phys. Rev. Lett. 79, 4914 (1997). the blocking temperature. It may also be interesting to re- [13] R. S. Fishman, J. Phys. Condens. Matter 13, R235 (2001). fine the loose-spin model by incorporating fluctuations of [14] J. Dekoster et al., J. Magn. Magn. Mater. 198, 303 (1999). the loose spins between two opposite states. Probably, bi- [15] H. Frauenfelder and R. M. Steffen, in Alpha-, Beta- and linear coupling cancels out naturally when the first moment Gamma-Ray Spectroscopy (North-Holland, Amsterdam, of the magnetization of the loose spins vanishes, thereby 1965), Vol. 2, p. 997; G. Schatz and A. Weidinger, Nuclear making the assumption of spacer layer thickness fluctua- Condensed Matter Physics (John Wiley and Sons, New tions unnecessary to explain the dominance of biquadratic York, 1996), 2nd ed., p. 63. [16] J. Meersschaut et al., Phys. Rev. B 57, R5575 (1998). coupling in some systems. [17] E. E. Fullerton, S. D. Bader, and J. L. Robertson, Phys. Rev. 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Phys. 73, 5957 (1993); J. Magn. Magn. Mater. 150, 13 (1995). quadratic interlayer coupling in Fe Cr goes hand in hand [24] M. Schäfer et al., J. Appl. Phys. 77, 6432 (1995). with fluctuating magnetic moments in the Cr spacer layers. [25] G. J. Strijkers et al., Phys. Rev. Lett. 84, 1812 (2000). It becomes now possible to study the energetics of the fluc- [26] K. Mibu et al., Phys. Rev. Lett. 84, 2243 (2000). 107201-4 107201-4