VOLUME 76, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 17 JUNE 1996 Biquadratic Exchange Coupling in Sputtered (100) Fe Cr Fe A. Azevedo, C. Chesman, S. M. Rezende, and F. M. de Aguiar Departamento de Fi´sica, Universidade Federal de Pernambuco, 50670-901 Recife-PE, Brazil X. Bian and S. S. P. Parkin IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, California 95120-6099 (Received 12 January 1996) We have used Brillouin light scattering, ferromagnetic resonance, magneto-optical Kerr effect, and magnetoresistance to investigate interlayer exchange coupling in Fe 40 Å Cr t Fe 40 Å trilayers grown onto MgO(100) in UHV. Unprecedented strong room-temperature biquadratic exchange coupling (BEC) was found for values of the Cr thickness t corresponding to a region where Fe layers are weakly antiferromagnetically coupled. A common feature in both magnetic and transport measurements, which we take as a signature of the BEC, is the presence of sudden discontinuous jumps as the external magnetic field is varied. The results are in excellent agreement with model calculations that coherently take into account the same phenomenological parameters characterizing the anisotropy, Zeeman, and bilinear and biquadratic exchange energies. [S0031-9007(96)00287-6] PACS numbers: 75.70.Cn, 73.20.Dx, 75.30.Et, 78.35.+c Lately magnetic exchange interactions between ferro- peak. The results presented henceforth were obtained in magnetic films separated by nonmagnetic spacers have the sample with t 15 Å. Figure 1 shows the in-plane been widely investigated. The antiferromagnetic coupling easy-axis magnetization curve obtained with the standard [1], giant magnetoresistance [2], and oscillatory behav- magneto-optical Kerr effect (MOKE) technique. One ior of the exchange coupling [3] raised the expectations can clearly identify three distinct regions in this curve: for exciting applications and new fundamental properties. In the low-field region (0­80 Oe), the linear response The exchange coupling through nonmagnetic interlayers is a signature of the weak AF coupling between the strongly depends on the thickness and nature of the spacer two Fe films. The magnetization vectors of the two as well as on the interface roughness. This coupling is Fe films are nearly antiparallel in this region and small usually dominated by a Heisenberg type interaction bilin- deviations from the antiparallel state might be induced ear in the films magnetizations. However, there is increas- by the external field H. Above 80 Oe, two hysteresis ing evidence that near the transition from ferromagnetic loops centered at H1 100 Oe and H2 210 Oe are to antiferromagnetic (AF) coupling a non-Heisenberg bi- quadratic term plays a remarkable role. This term is re- sponsible for the peculiar effect of 90± alignment between the magnetizations of the ferromagnetic films, as recently observed in Fe/Cr/Fe (001) wedges [4,5], and trilayers of Co/Cu/Co (001) [6], Fe/Al/Fe (100) [7], and Fe/Ag/Fe [8]. Over the last few years several mechanisms have been proposed for the origin of the biquadratic exchange cou- pling (BEC) [9­12], which has recently been shown to be suppressed below the Néel temperature of Cr in the thick Cr regime in Fe/Cr superlattices [13]. In this work, we report a detailed experimental investigation of the BEC in sputtered Fe/Cr/Fe trilayers in the thin Cr regime at room temperature. We have also developed model calculations which correlate quite well the experimental results for a common set of phenomenological parameters, thus pro- viding a unified picture of this effect in the Fe/Cr system. Several samples of Fe(40 Å)/Cr(t)/Fe(40 Å) were grown by magnetron sputter deposition in a UHV cham- FIG. 1. Measured MOKE easy-axis hysteresis loop in the ber [14] onto polished, chemically cleaned single-crystal Fe(40 Å)/Cr(15 Å)/Fe(40 Å) sample. Upper inset: Measured MgO(100) substrates, with 5 , t , 35 Å, a range that saturation field in a Fe/Cr/Fe wedge as a function of the Cr corresponds to the first two "antiferromagnetic peaks," as thickness [14]. Lower inset: Open circles, measured room- temperature magnetoresistance in the same Fe(40 Å)/Cr(15 Å)/ shown in the upper inset of Fig. 1. Pronounced BEC was Fe(40 Å) of the main figure (peak MR is a 0.7% effect); the observed in samples at the right-hand side of the first AF solid line is a fit with the expression 1 2 cos f1 2 f2 . 0031-9007 96 76(25) 4837(4)$10.00 © 1996 The American Physical Society 4837 VOLUME 76, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 17 JUNE 1996 observed. Intriguingly, the four-probe magnetoresistance resentative spectra. In the low-field region, the modes are measurement (only the down-field sweep is shown in separated by approximately 2 GHz, the optical mode be- the lower inset of Fig. 1) exhibits corresponding loops ing at higher frequency [Fig. 2(a)]. For H1 , H , H2, at the same field values. In order to explore even and outside the hysteresis loops, there is an abrupt in- further this phenomenon, we also used the Brillouin light crease in this separation that reaches a value up to 7 GHz scattering (BLS) and the ferromagnetic resonance (FMR) at higher fields [Fig. 2(b)]. Within a hysteresis loop, we techniques, as discussed below. have been able to observe four peaks at each side of BLS measurements were carried out in the backscat- the laser line [Fig. 2(c)], which shows unambiguously the tering geometry, using a Sandercock tandem Fabry-Pérot bistable nature of this region. Finally, for H . H2, the (FP) interferometer in a 2 3 3 -pass configuration. The separation between the modes is again abruptly increased, light source was a single-mode-stabilized argon ion laser this time being followed by an inversion of the modes operating at 5145 Å with incident power of 100 mW. The positions with respect to the laser line. The measured up- sample was mounted between the poles of an electromag- field dispersion relation is shown by the solid (acoustic net with the field parallel to the incidence plane of the mode) and open (optical mode) circles in Fig. 3. light beam and to an easy-magnetization axis. All the The FMR measurements were performed at 9.4 GHz by BLS spectra were measured at room temperature with monitoring the derivative of the absorption line reflected an incident angle of 30±, corresponding to a scattering from a TE102 rectangular microwave cavity with Q in-plane spin-wave wave number k 1.22 3 105 cm21. 2500. A typical spectrum is shown in the inset of Fig. 4, The collimated light beam at the output of the FP inter- which in turn shows the dependence of the in-plane ferometer was focused on a solid-state photodetector with resonance field as a function of the angular position with 40% quantum efficiency at 5145 Å and a dark count less respect to H. The spectrum shown in the inset presents than 2 counts/s, connected to a multichannel board in a the FMR absorption lines for an angle f 30± with computer. Surprisingly, we have been able to observe respect to the (easy) [100] direction. As in the BLS both so-called "acoustic" and "optical" modes in the field experiments, we were able to observe both the acoustic range of 6400 Oe, within typically 10 to 15 min for each and optical modes. The linewidth of the acoustic mode, spectrum, the acoustic mode being more intense that the DH 25 Oe, is comparable to the linewidth of molecular optical one. This allowed us to verify that for each region beam epitaxy­grown samples [15], which demonstrates of the magnetization curve, there is a nicely corresponding that our sandwich is indeed single crystalline. spectrum of scattered light. In Fig. 2 we show four rep- The overall behavior can be well described in terms of the free energy per unit area, E Ea 1 Ez 1 Eex , (1) FIG. 3. BLS spin-wave dispersion relation observed in Fe(40 Å)/Cr(15 Å)/Fe(40 Å), showing the behavior of the FIG. 2. Measured BLS spectra in Fe(40 Å)/Cr(15 Å)/ acoustic (solid circles) and optical (open circles) modes as a Fe(40 Å) for four different values of the applied field, corre- function of the applied field. The corresponding dashed and sponding to different regions of the magnetization curve shown solid lines are results of numerical simulations, as described in in Fig. 1. the text. 4838 VOLUME 76, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 17 JUNE 1996 FIG. 4. Resonance fields at 9.4 GHz in Fe(40 Å)/Cr(15 Å)/ FIG. 5. Calculated magnetization curve (solid line), as de- Fe(40 Å), showing the behavior of the acoustic (solid circles) scribed in the text. The open circles are the corresponding and optical (open circles) modes as a function of the azimuth upfield MOKE measurements. Inset: Calculated equilibrium angle f between an easy axis and the applied in-plane positions f1 (solid line) and f2 (dashed line). field. The corresponding dashed and solid lines are results of numerical simulations, as described in the text. Inset: FMR spectrum for f 30±. the linearized Landau-Lifshitz equation of motion, assum- ing a small deviation of the magnetization vectors from where Ea is the anisotropy term, EZ is the Zeeman energy, their equilibrium positions [16]. The wave-vector depen- and Eex is the exchange coupling energy. The latter can dence is introduced through the effective dipolar field [17]. be written in the form A detailed account of the theoretical approach, includ- E ing magnetoresistance calculations, will be published sep- ex 2J1 M1 ? M2 1 J2 M1 ? M2 2, (2) arately. Here we present results of the simultaneous nu- where J1 and J2 are the so-called bilinear and biquadratic merical simulation of the MOKE (Fig. 5), MR (Fig. 1), coupling constants, and M1 and M2 are the unit mag- BLS (Fig. 3), and FMR (Fig. 4) data for the following netization vectors of the two ferromagnetic films. For set of realistic parameters: 4pMs 19.0 kG (Ms is sat- dominant J1, M1 and M2 are ferromagnetically or antifer- uration magnetization), 2K1 Ms 0.55 kOe (anisotropy romagnetically coupled for J1 . 0 and J1 , 0, respec- field), J1 MstFe 2150 Oe, and J2 MstFe 50 Oe (tFe tively. However, if jJ2j . jJ1j and J2 . 0, the magneti- is Fe thickness). Since the dynamic response depends on zations in the two films prefer to lie 90± to one another, in the static configuration of the magnetizations, the excita- plane, in zero magnetic field. tion frequencies change abruptly at the two phase transi- In order to fit the MOKE data, the equilibrium positions tions, as seen in the BLS results. The overall agreement of the magnetizations with respect to the in-plane field, between the numerical results and the static and dynamical namely, f1 and f2, were numerically calculated from responses is quite impressive. Notice that long-range or- the minimum of the magnetic free energy given in dering of the Cr is not expected for t , 42 Å [13]. Thus Eq. (1). The inset of Fig. 5 shows the variation of the results presented here might not change dramatically f1 and f2 as a function of the field, exhibiting three with temperature; i.e., no suppression of the BEC should phases: AF alignment occurs in the low-field region, be expected. Experiments which explore the dependence a 90± coupling prevails in the midfield range and the of the BEC on tFe will be carried out shortly. This should magnetizations are aligned with the field in the third give some insight on the microscopic nature of the cou- region (saturation). Strikingly, the two transitions are of pling in the Fe/Cr system. first order nature, in contrast to the pure AF (bilinear) In summary, we have performed magnetic and transport coupling, where the transition between the spin-flop and measurements to investigate the exchange coupling inter- saturated phases is of second order. The solid line in action between the two Fe films in Fe/Cr/Fe sandwiches. Fig. 5 is the sum cosf1 1 cosf2 2, which presumably For a Cr thickness of 15 Å, it is clearly demonstrated that reflects the MOKE measurement (open circles), since only the bilinear exchange AF coupling is relatively weak and the components along the applied field are relevant. that an unrivaled strong room-temperature BEC plays a The uniform and spin-wave modes that are measured remarkable role. To our knowledge, a coherent fit of the by FMR and BLS are the eigenmodes calculated from data from various experimental techniques with the same 4839 VOLUME 76, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 17 JUNE 1996 set of phenomenological parameters is provided for the [5] J. Unguris, R. J. Celotta, and D. T. Pierce, Phys. Rev. Lett. first time. 67, 140 (1991). We would like to thank K. P. Roche for technical sup- [6] B. Heinrich, J. F. Cochran, M. Kowalewski, J. Kirschner, port and M. Lucena for helping in some measurements. Z. Celinski, A. S. Arrot, and K. Myrtle, Phys. Rev. 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