PHYSICAL REVIEW B VOLUME 58, NUMBER 18 1 NOVEMBER 1998-II Exchange-spring behavior in epitaxial hard/soft magnetic bilayers Eric E. Fullerton,* J. S. Jiang, M. Grimsditch, C. H. Sowers, and S. D. Bader Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 Received 9 June 1997 We present results on the magnetic reversal process in epitaxial Sm-Co 11¯00 /TM TM Fe,Co bilayer films prepared via magnetron sputtering. The magnetically hard Sm-Co films have 20-T uniaxial anisotropy and coercivities 3 T at room temperature, that double on cooling, as determined by magnetometry. The TM layers are exchange coupled to the Sm-Co layer and exhibit reversible demagnetization curves expected for an exchange-spring magnet. We also present numerical solutions of a one-dimensional model that provide the spin configuration for each atomic layer. Comparison of the experimental results with the model simulations indicates that our exchange-spring behavior can be understood from the intrinsic parameters of the hard and soft layers. The simulations are extended to realistically estimate the ultimate gain in the energy product that potentially can be realized based on the exchange hardening principle. S0163-1829 98 00742-5 I. INTRODUCTION The switching of a soft-magnet film coupled ferromag- netically to a hard layer was studied by Goto et al.11 Under Exchange-spring magnets are composed of a two-phase the assumption that the hard layer is perfectly rigid and the distribution of hard- and soft-magnetic grains that have po- soft layer has no anisotropy, they solved for the magnetiza- tential applications as permanent magnets.1 The hard- tion of the soft layer with an applied field opposed to the magnetic grains provide the high anisotropy and coercive hard layer. They found that the soft layer remains parallel to fields while the soft-magnetic grains enhance the magnetic the hard layer for fields less than the exchange-bias field Hex, moment with the additional benefit of reducing the rare-earth where Hex is given by content since the soft phase can be rare-earth free. The soft grains are pinned to the hard-magnet grains at the interfaces Hex 2A/2Mst2, 1 by the exchange interaction while the center of the soft- magnet grains can rotate in a reversed magnetic field. Such A is the exchange constant that couples spins within the soft magnets are characterized by enhanced remanent magnetiza- layer, t is the soft layer thickness, and Ms is the saturation tion and reversible demagnetization curves since the soft magnetization of the soft layer. For H Hex , the spins in the grains will rotate back into alignment with the hard grains soft layer exhibit continuous rotation, as in a Bloch wall, when the applied field is removed. Although future applica- with the angle of rotation increasing with increasing distance tion of two-phase magnets will most likely be based on ran- from the hard layer. The magnetization of the soft layer is domly dispersed nanocomposite geometries,2 coupled bilayer reversible and approaches saturation as (H/Hex) 0.5. Both films provide convenient model systems for studying their predictions are consistent with experimental studies of NiFe/ properties because the relative length scales i.e., thicknesses NiCo bilayers by Goto et al., and with subsequent stud- of the hard- and soft-magnet layers can be controlled during ies of Sm-Co/NiFe,5 Sm-Co/Co-Zr,6,7 and epitaxial the deposition process. Skomski3 and Coey2 explored the CoFe2O4 / MnZn Fe2O4 exchange-coupled bilayers.8 In all theory of exchange coupled films and predicted that a giant these studies, the thickness of the soft layer was 500 Å. For energy product of 120 MGOe about three times that of com- sufficiently thin soft-magnetic layers t a domain-wall mercially available permanent magnets is possible in super- width in the hard layer , the soft layer is expected to be lattice structures consisting of aligned hard-magnet layers rigidly coupled to the hard layer, with both layers switching that are exchange coupled to soft layers with high magneti- at a nucleation field given by zation. Realization of exchange-coupled thin-film structures re- 2 thKh tsKs quires controlled growth of nanometer-scale hard-magnet HN t , 2 films. The growth of such films, their incorporation into suit- hM h tsM s able magnetic heterostructures, and understanding their mag- where th(ts), Kh(Ks), and Mh(Ms) are the thickness, anisot- netic reversal behavior are areas of current research.4­10 In ropy, and magnetization of the hard soft layers, respec- this paper we explore the reversal processes in epitaxial hard/ tively. Such behavior has been shown qualitatively for Sm- soft Sm-Co 11¯00 /TM bilayers TM Fe and Co with the Co/Fe-Co bilayers9 and Nd-Fe-B/Fe superlattices.10 transition-metal TM thicknesses in the range of 25­200 Å. The present paper is organized as follows: we present Magnetically hard Sm-Co 11¯00 has the advantage of having experimental procedures in Sec. II, the magnetization of the a uniaxial in-plane anisotropy. Thus, the rotation process of Sm-Co films and Sm-Co/TM bilayers in Sec. III, compare the exchange-coupled TM layers can be studied with the ap- the observed magnetic reversal behavior with numerical so- plied field both parallel and perpendicular to the anisotropy lutions of one-dimensional magnetic models of the system in axis of the hard layer. Sec. IV, and summarize the major conclusions in Sec. V. 0163-1829/98/58 18 /12193 8 /$15.00 PRB 58 12 193 ©1998 The American Physical Society 12 194 FULLERTON, JIANG, GRIMSDITCH, SOWERS, AND BADER PRB 58 with the expected c-axis anisotropy. For H parallel to the Sm-Co easy axis MgO 001 , a square loop is observed with a coercive field Hc of 3.4 T for this film. The coercivity increases to 7.3 T at 25 K. The Sm-Co saturation magneti- zation is 500­600 emu/cm3 as compared to 1710 and 1425 emu/cm3, for Fe and Co, respectively. For H applied in the orthogonal in-plane direction, a sheared hard-axis loop is measured. The anisotropy field, estimated from extrapolating the hard-axis loop to saturation, is 20 T. This field value is comparable to those reported for bulk Sm2Co7 20 T Ref. 14 and SmCo5 25­44 T .15 Also shown in Fig. 1 is the transverse magnetization mea- sured with H parallel to the hard axis. This measurement was FIG. 1. Room-temperature magnetic hysteresis loops for a obtained after the film was first saturated along the easy axis 200-Å Sm-Co 11¯00 film with H parallel to the hard-axis h.a. and then rotated 90° for the hard-axis measurements. For MgO 11¯0 direction circles and the easy-axis e.a. 001 direction H 0, the transverse moment equals the remanent easy-axis triangles . For the hard-axis measurements, we show both the lon- value. The moment decreases only 5% from the remanent gitudinal filled circles and transverse open circles magnetization components. value in a field of 7 T along the hard axis indicating that the moments rotate 20° from the easy axis. The shoulder ob- II. EXPERIMENTAL PROCEDURES served in the easy-axis magnetization near H 0 may result from the presence of a minority soft magnetic phase. As will The Sm-Co 11¯00 /TM bilayers are grown via dc magne- be seen later, however, such minority soft phases do not tron sputtering onto single-crystal MgO 110 substrates affect the switching of the TM layers. coated with an epitaxial 200-Å Cr 211 buffer layer. The 200-Å Sm-Co layers are deposited by cosputtering from separate Sm and Co sources with a nominally Sm B. Sm-Co/Fe bilayers 2Co7 con- centration at a substrate temperature Ts 600 °C as outlined 1. Magnetization in Ref. 4. The TM layers are then grown at Ts 300­ 400 °C with thickness values of 25­200 Å and capped with a 50-Å Shown in Fig. 2 are room-temperature hysteresis loops of Cr layer. The film structure was studied by x-ray diffraction. the Sm-Co 200 Å /Fe bilayers measured in the same geom- The magnetic properties were measured by means of i a etry as Fig. 1. For a 25-Å Fe layer Fig. 2 a , the loop Quantum Design 7-T superconducting quantum interference shapes are similar to those observed in Fig. 1. A square easy- device magnetometer, ii the longitudinal magneto-optic axis loop is measured with a Hc 1.7 T reduced 50% as Kerr effect MOKE using p-polarized, 633-nm light, and compared to the isolated Sm-Co film, indicating that the en- iii Brillouin light scattering BLS . The BLS experiments tire Fe layer is strongly coupled to the underlying Sm-Co were performed at room temperature using a 5-pass Fabry- film and that the two layers switch as a unit. The hard-axis Pe´rot interferometer and a single-mode argon laser operated transverse loop is reversible and decreases 25% in a 7-T at 514.5 nm. The magnetometer was equipped with coil sets field resulting from the increased rotation of the Fe layer to measure both the longitudinal and transverse magnetiza- from the Sm-Co easy axis. For the 100- and 200-Å Fe layers tion. Because of the nonuniform rotation process expected in the loops change shape quite significantly. For H applied an exchange-spring magnet, the longitudinal and transverse parallel to the easy axis, separate switching transitions for the data are not simply related as they would for coherent rota- Fe and Sm-Co layers are observed. This is similar to that tion of a uniformly magnetized sample and thus provide a observed in Refs. 5­8 but with much thinner soft layers in more complete description of the magnetic reversal. the present samples. The switching fields for the Sm-Co lay- ers 0.6­0.7 T are similar for the 100- and 200-Å Fe layers and are only 20% of that of the isolated Sm-Co film value. III. EXPERIMENTAL RESULTS The hard-axis data exhibit an initial low-field susceptibility A. Sm-Co films that increases with increasing Fe layer thickness. The trans- verse magnetization also shows a rapid decrease at low The structural and magnetic characterization of Sm- fields. Both effects are due to the rotation of most of the Fe Co 11¯00 films grown onto Cr 211 buffer layers are de- layer as H increases. This result is consistent with that ob- scribed in detail in Refs. 12 and 13. The epitaxial relation for served for Sm-Co/Co-Zr films.7 the Sm-Co 11¯00 films is Sm-Co 0001 Cr 011¯ MgO 001 resulting in a uniaxial in-plane structure with the magnetic easy axis parallel to the Sm-Co c axis. The nominal compo- 2. Magneto-optic Kerr effect sition of the films is Sm2Co7. However, high-resolution elec- Shown in Fig. 3 are the MOKE results for the 100- and tron microscopy identifies stacking disorder in the c-axis di- 200-Å Fe layer films. As a result of the finite penetration of rection consisting of a mixture of SmCo3, Sm2Co7, and the light, the MOKE measurements are dominated by the SmCo5 phases.13 Shown in Fig. 1 are the magnetic hysteresis switching of the top Fe layer. For the easy-axis measure- loops for a single 200-Å Sm-Co 11¯00 film measured with ment, the Fe layer starts to switch at the exchange field: 0.22 the field H applied along orthogonal in-plane directions. The and 0.09 T for the 100- and 200-Å Fe layers, respectively. films exhibit strong uniaxial in-plane anisotropy consistent Above Hex , a sharp drop in the magnetization is then fol- PRB 58 EXCHANGE-SPRING BEHAVIOR IN EPITAXIAL . . . 12 195 FIG. 2. Room-temperature magnetic hysteresis loops for Sm- FIG. 3. Room-temperature magnetic properties of Sm-Co/Fe bi- Co/Fe bilayer films with H parallel to the hard-axis circles and the layer films measured by MOKE. Hysteresis loops measured with H easy-axis triangles directions. For the hard-axis measurements, we parallel to the hard-axis open circles and the easy-axis filled show both the longitudinal filled circles and transverse open circles directions for the 100-Å Fe a and 200-Å Fe b films. c circles magnetization components. The irreversible magnetization Mirr vs reverse field measured with H parallel to the easy axis, where Mirr is the difference between lowed by an asymptotic approach to saturation until the hard the remanence acquired after saturation in one direction and the layer switches irreversibly at H remnant magnetization after subsequent application of a reverse irr, as expected for the exchange-spring state. This behavior is particularly clear for field in the opposite direction. the 200-Å Fe film. One characteristic of exchange-spring magnets is that the reorientation of the soft layer should be frequencies decrease with decreasing H, reaching a minimum fully reversible for fields below the switching field of the at H 0.25 T, and then increase for even lower fields. At hard layer. To test this behavior, we have measured the irre- H 0.55 T, the frequency changes abruptly and becomes versible magnetization change as a function of field reversal equal to the corresponding positive field value. Qualitatively for intermediate fields. Following Kneller and Hawig,1 the these results are consistent with the magnetization studies: irreversible magnetization is described by the field demagne- tization remanence Md(H), the remanence being acquired after saturation in one direction and subsequent application of an applied field in the opposite direction. The irreversible magnetization change Mirr is given by Mr Md(H) where Mr is the remanent magnetization. Shown in Fig. 3 b is Mirr/2Mr. The magnetization is fully reversible ( Mirr 0) up to fields where the Sm-Co layer switches at Hirr 0.6 and 0.7 T for the 100- and 200-Å Fe layer films, re- spectively. 3. Brillouin light scattering As a final probe of the magnetic properties we have ex- amined the magnon frequencies of the Fe layers using BLS. Shown in Fig. 4 is the field dependence of the magnon fre- FIG. 4. Room-temperature BLS results for the Sm-Co/Fe 100 quency in the 100-Å Fe sample. As with MOKE, the BLS Å bilayer film. The symbols are the magnon frequencies measured signal is dominated by contributions from magnons in the from saturation in positive fields towards negative fields. The solid top Fe layer. The field is always parallel to the easy axis. The line is a fit to Eq. 3 . 12 196 FULLERTON, JIANG, GRIMSDITCH, SOWERS, AND BADER PRB 58 the frequency minimum at 0.25 T reflects the instability as the Fe layer starts to spiral away from the easy axis of the Sm-Co layer, and the jump at 0.55 T occurs as the Sm-Co layer switches. We are not aware of any theory that quantitatively de- scribes the magnon frequencies in a magnetic layer undergo- ing such a spiral reorientation. However, in the regions be- low 0.55 T and above 0.25 T, where the magnetization of the Fe layer lies along the easy axis of the SM-Co and is also either parallel or antiparallel to the applied field, the following quantitative analysis can be made. The magnon frequency for an isolated Fe film of thickness t assuming no anisotropy is given by16 H 2 Ms 2 2 Ms 2exp 2qt 1/2, 3 where 29.4 GHz/T is the gyromagnetic ratio of Fe, and q 8.6 10 4 Å 1 is the magnon wave vector determined by our scattering geometry. In order to use Eq. 3 for our samples it must be generalized to include the constraint of FIG. 5. Room-temperature magnetic hysteresis loops for Sm- the Fe spins at the Sm-Co interface. Since the instability of Co/Co bilayer films with H parallel to the hard-axis circles and the the Fe magnetization occurs at Hex , it is reasonable to easy-axis triangles directions. For the hard-axis measurements, we invoke Hex as an effective exchange field. Replacing H by show both the longitudinal filled circles and transverse open H Hex, Eq. 3 quantitatively fits the data in Fig. 4 and circles magnetization components. yields Hex 0.22 T 0.09 T for the 200-Å sample and 4 Ms 1.8 T. The fit below H 0.55 T is obtained in the with the magnetization measured both longitudinal and trans- calculation by considering the sign change of Hex when the verse to the applied field. The Sm-Co/Fe results are similar Sm-Co layer switches. The Brillouin scattering shows that to the room-temperature data with the exception that the the spin-wave frequencies of the Fe films are consistent with switching of the Sm-Co layer has increased to 1.5 T but is isolated Fe films perturbed by an effective exchange field. still well below the 7 T value for the Sm-Co film. The This demonstrates the model behavior of our system. A more minor loop shows the switching of the Fe layer is completely rigorous description of the magnon modes that also describes reversible for field as large as 1.2 T confirming that the Fe the region in which the magnetization is in a spiral state will and Sm-Co are strongly exchange coupled. For H Hex require solving the eigenmodes of the coupled-layered sys- tem, including the anisotropy of the Sm-Co layer, and satis- fying the appropriate boundary condition at the interface, and is beyond the scope of this paper. C. Sm-Co/Co bilayers Shown in Fig. 5 are room-temperature hysteresis loops of the Sm-Co 200 Å /Co bilayers. Square easy-axis loops are observed with coercive fields of 0.73 and 0.42 T for the 100- and 200-Å Co layers, respectively. The Sm-Co/Co results contrast with those on similar Sm-Co/Fe samples in impor- tant ways: i the Co layers remain parallel with the Sm-Co to well above the expected Hex determined from Eq. 1 , ii the Sm-Co and Co layers switch at the same field, and iii the switching field of the Sm-Co layer depends strongly on the Co layer thickness. The hard-axis loops are similar to those of the Sm-Co/Fe films, and exhibit an increased low- field susceptibility with increased Co layer thickness. D. Low-temperature results To further investigate the difference in switching of the Fe and Co layers, we examined the samples at low tempera- tures in order to increase the coercivity of the Sm-Co layers. FIG. 6. Low-temperature 25 K demagnetization curves for For isolated Sm-Co films, the coercivity doubles on cooling Sm-Co/Fe and Sm-Co/Co bilayer films with H parallel to the easy from 300 to 25 K. Shown in Fig. 6 are easy-axis demagne- axis. We show both the longitudinal circles and transverse dia- tization curves for the 200-Å Co and Fe films measured at 25 monds magnetization components. The filled symbols are the de- K. Included in Fig. 6 are major loops as well as minor loops magnetization curves and the open symbols are minor loops. PRB 58 EXCHANGE-SPRING BEHAVIOR IN EPITAXIAL . . . 12 197 when the longitudinal moment decreases, the transverse mo- atomic model employed successfully in Refs. 5 and 7. We ment first increases and then more slowly decreases with divide the bilayer structure into a sum of atomic layers and increasing field. In the exchange-spring state, the rotation of the bilayer is treated as a one-dimensional chain of spins the spins away from the hard layer results in the significant normal to the layers. Each spin is characterized by a moment transverse moment observed experimentally. The fact that Mi , uniaxial anisotropy constant Ki , and is assumed to ro- such a large transverse moment is observed indicates that the tate within the plane of the film characterized by an in-plane Fe layer rotates with a preferred sense of rotation. This sug- angle i. i is measured relative to the easy-axis direction of gests that the applied field is slightly misaligned with the the hard layer, and the external field is applied at an angle H easy axis. If the field were perfectly aligned, then different with respect to the easy axis. Adjacent spins are separated by regions of the samples would rotate with opposite sense of d 2 Å and coupled by an exchange constant Ai,i 1. The rotations and the net transverse magnetization would average total energy of the system is given by to zero. At 25 K, separate switching transitions are observed for N 1 N the Sm-Co and Co layers at 1.05 and 0.5 T, respectively. The Ai,i 1 switching of the Co layer is reversible but is hysteretic about E Kicos2 i i 1 d2 cos( i i 1) i 1 the exchange field Hex 0.46 T (Hex 0.86 T for the 100-Å Co samples . This behavior arises from the intrinsic mag- N netic anisotropy of the Co layer.8 The c-axis Co anisotropy HMicos i H . 4 i 1 stabilizes the Co layer either parallel or antiparallel to the Sm-Co film and results in an abrupt and hysteretic behavior at the Co switching field. H For the bilayer system, the index i 1through Ns corre- ex for the Co layer can be roughly estimated by assuming that at H sponds to the soft layer which has magnetization, anisotropy, ex the Co layer rotates from being parallel to antiparallel with the Sm-Co layer. By equat- and exchange given by Ms , Ks , and As , respectively. The ing the Zeeman energy gain with the energy of introducing a index i Ns 1 through N represents the hard layer and is domain wall 10 ergs/cm2 in the Co layer near the in- characterized by Mh , Kh , and Ah . The hard and soft layers terface, a rough estimate for H are coupled at the interface by an exchange interaction A ex is given by / M st 0.36 T, int . in reasonable agreement with the experimental results. The equilibrium spin configuration for a given field is deter- The observed low-temperature H mined by minimizing Eq. 4 . For H parallel to the easy axis ex values for the Co lay- ers are close to the room-temperature H ( H 0), the lowest energy configuration will be i 0 for c values of the coupled bilayer. This suggests that the room-temperature H all i . We are interested in the local-minimum configuration c values for the Sm-Co/Co samples are determined primarily in which the hard layer is opposite to H i for i Ns by H 1 to N and the soft layer rotates with the applied field. To ex of the Co layer. Once the Co layer switches the Sm-Co layer follows. calculate this configuration we employ an iterative approach outlined by Camley.17,18 We start with all spins at i for all i 1to N in a small positive applied field. A spin is then IV. SIMULATION randomly chosen and rotated towards its lowest energy po- To obtain greater insight into the switching of both the sition. The new spin direction i is estimated by the follow- soft and hard layers, we use the simple one-dimensional ing expression: A tan i,i 1sin i 1 Ai,i 1sin i 1 d2HM isin H i A , 5 i,i 1cos i 1 Ai,i 1cos i 1 2d2Kicos i d2HM icos H which is determined from the criterion that dE/d i 0. This lations. Both methods give similar results. Since there is in- procedure is repeated by randomly selecting spins and rotat- evitably some misalignment between the field and the easy ing them, via Eq. 5 , until the system converges on a stable axis in an actual measurement, taking into account the mis- configuration. For a 200-spin system, this typically takes alignment angle in fact more closely simulates the real sys- 105­ 106 iterations. The total longitudinal and transverse mo- tem. ments are calculated, the field is increased and the process Shown in Fig. 7 a is the comparison of the calculated repeated in order to calculate a hysteresis loop. Since the Sm-Co/Fe 200 Å easy-axis loop to the 25-K data shown criterion dE/d i 0 is also valid for maxima as well as in Fig. 6. The parameters for the calculation are Ah minima in the energy, some care is needed to avoid such 1.2 10 6 ergs/cm, Kh 5 107 ergs/cm3, Mh 550 solutions. One such solution can be obtained for H 0 and emu/cm3, As 2.8 10 6ergs/cm, Ks 103 ergs/cm3, Ms i for all i, even if an applied field is sufficient to reverse 1700 emu/cm3, Aint 1.8 10 6 ergs/cm, and H 3°. the soft layer. To avoid this problem, we either perturb the The values of Kh and Mh were estimated from magnetization system at each field to check the stability of the solution or measurements on the Sm-Co films. The value of Aint was set we use a small but finite value of H in our easy-axis calcu- intermediate to exchange coupling of the hard and soft lay- 12 198 FULLERTON, JIANG, GRIMSDITCH, SOWERS, AND BADER PRB 58 FIG. 8. Calculated demagnetization curves for the Sm-Co/ Co 200 Å film. The model parameters are described in the text. pressed and its energy increases. The wall energy in the soft layer s , assuming no anisotropy, is expected to vary as AsMsH. The energy of a domain wall in the hard layer is h 4 AhKh. As the field increases such that s becomes greater than h , the domain wall in the soft layer moves into, and switches, the hard layer. The field at which the hard layer switches should roughly scale as AhKh /AsMs and is significantly lower than that for the isolated film. This also explains why the hard layer switches at a lower field in the FIG. 7. a Low-temperature 25 K demagnetization curves for Sm-Co/Co bilayers see Fig. 6 . Co has higher exchange and the Sm-Co/Fe 200 Å film shown in Fig. 6 compared to the model anisotropy constants than Fe, both of which increase s and calculation solid line described in the text. The longitudinal and thus reduce the Sm-Co switching field. transverse components of the magnetization are given by the circles We simulated the switching of the Sm-Co/Co 200 Å bi- and triangles, respectively. b Representative spin configuration determined from the model calculation shown in a . Open circles layer. Shown in Fig. 8 are the calculated demagnetization are Fe spins and filled circles are Sm-Co spins. The free Fe surface curve and minor loop simulated for the 200-Å Co layer for is located at zero and the Sm-Co/Fe interface is at 200 Å. parameters: Ms 1400 emu/cm3, As 4.0 10 6 ergs/cm, and Ks 3 106 ergs/cm3. All the features of the measured ers. The calculation reproduces the H data Fig. 6 are reproduced in the calculations. In particular, ex value, the field de- pendence of both the longitudinal and transverse magnetiza- the exchange field for the Co layer is large compared to that tion, as well as the switching field of the Sm-Co layer at for Fe layers of similar thickness, the switching of the Co 1.5 T. The irreversible switching of the hard layer is ex- layer is hysteretic about Hex, and the Sm-Co layer switches pected to be the least reliable parameter determined by this at a lower field than the Sm-Co/Fe films. type of modeling and the close agreement in Fig. 7 a is The reliability of the simulation can be checked by com- rather fortuitous. Shown in Fig. 7 b is the spin configuration parison to the room-temperature easy- and hard-axis data at various fields for the calculated magnetization in Fig. 7 a . both longitudinal and transverse. These comparisons are The distribution of moments is consistent with the expecta- shown in Fig. 9. The parameters in the calculation are iden- tion that the Fe located away from the interface rotates more. tical to those used in Fig. 7 with the exception that As is For the configuration at H 0.14 T the average Fe angle is decreased by 8% to reflect the weakening with increased T. 90° resulting in the maximum in the transverse moment The same set of parameters is able to quantitatively repro- with applied field. As the field increases, the turn angle of the duce the measured results, with the exception of the value of Fe spins away from the interface increases and the surface layers align with the field. At H 1.45 T just below the switching of the hard layer , the top 120 Å of the Fe layer aligns with the field. The hard layer is also significantly perturbed by the rota- tion of the Fe layers, in agreement with the calculations of Mibu et al.5 As H increases, the interfacial Sm-Co spin is also increasingly rotated and a domain wall is slowly intro- duced into the hard layer. This domain wall, nucleated by the Fe layer, reverses the Sm-Co layer at a field well below that expected for an isolated Sm-Co film. In the calculation shown in Fig. 6, the Sm-Co layer reverses at H 1.47 T. If one sets Aint 0 to decouple the Fe and Sm-Co layers, the Sm-Co layer reverses at H 15 T. The reduction of the FIG. 9. Room-temperature hysteresis loops for the Sm-Co/ switching field of the hard layer was explained in Ref. 1. As Fe 200 Å film shown in Fig. 2 filled symbols compared to the the field increases, the domain wall in the soft layer is com- model calculation open circles described in the text. PRB 58 EXCHANGE-SPRING BEHAVIOR IN EPITAXIAL . . . 12 199 FIG. 11. Calculated maximum energy produce (BH)max of Sm- Co/Fe bilayers with different layer thicknesses. The dashed curves are that of the ideal (BH)max . The square symbols are experimental (BH)max values taken from the hysteresis loops shown in Fig. 2. With increasing thickness, the Fe-layer magnetization re- verses at lower fields, and (BH)max is limited by the ex- change bias field Hex . The square symbols are the (BH)max FIG. 10. a Calculated demagnetization curves for Sm-Co/Fe values taken from the hysteresis loops shown in Fig. 2. The films with various Fe thicknesses. b Calculated irreversibility field agreement between the experimental data and model calcu- for Sm-Co/Fe films as a function of Fe thickness compared to the lation is reasonably good. The calculation shows that for measured values for the Sm-Co/Fe bilayer films measured at 25 K. bilayers with suitably thin constituent layers, (BH)max can even be greater than that of Nd-Fe-B, illustrating the impor- the room-temperature switching field of the hard layer. These tance of the exchange hardening mechanism. parameters provide a reasonable description of the sample The model does overestimate the switching fields for low and provide added confidence in the assumption that the in- Fe thickness as seen in Fig. 10 b . This results from an in- terfacial exchange is comparable with the exchange within complete description for the Sm-Co layer. The present model the layer. does not include any other region to nucleate reversal besides With these parameters we can simulate a series of hyster- the Fe layer and, thus, Hc for the isolated Sm-Co layer esis loops for different Fe layer thickness values. Shown in equals the anisotropy field for H 0 which, of course, is Fig. 10 a are easy-axis demagnetization curves for different never expected to be achieved in real films. However, as we Fe layer thicknesses from 10 to 200 Å. The switching for the have discussed previously, this does not affect the calcula- hard layer initially decreases dramatically with increasing Fe tion of (BH) thickness. Even a 10-Å Fe layer reduces the calculated coer- max . civity of the hard layer by a factor of 3. When the Fe-layer thickness become comparable to the width of a domain wall, V. CONCLUSION the switching of the hard layer becomes independent of the We have presented the experimental results on strongly Fe layer thickness. This is shown in Fig. 10 b where the exchange-coupled Sm-Co 11¯00 /TM bilayer films. Because calculated Sm-Co switching fields are compared to those of of the epitaxial growth, the magnetically hard Sm-Co layer the Sm-Co/Fe samples measured at 25 K. The general trend has an in-plane uniaxial anisotropy field as large as 20 T. in the data is well reproduced by the simulations. Such a large anisotropy field enables us to explore exchange- From the simulated hysteresis loops, we can extract the spring behavior in a new region where the soft-layer thick- maximum energy product (BH)max for the Fe/Sm-Co bilayer nesses are 20 nm. The moments in the soft layer near the structure. Shown in Fig. 11 are the calculated (BH)max interface are pinned by the hard layer and switch reversibly. curves plotted as a function of Fe layer thickness for differ- The present results can be understood from the intrinsic pa- ent Sm-Co layer thicknesses. (BH)max increases initially rameters of the hard and soft layers, indicating that the inter- with increasing Fe thickness, peaks, and then decreases. The facial coupling between the Sm-Co and the soft layer is com- peak value of (BH)max increases with decreasing Sm-Co parable to the atomic exchange whether the soft layer is Fe thickness. Also shown as dashed curves is the ideal energy- or Co. It was suggested1 that exchange coupling requires product (BH)max (2 Ms)2. At low Fe thicknesses less than crystallographically coherent interfaces and therefore the the Block wall width in the hard layer , the Fe layer couples hard and soft phases should emerge from a common matrix rigidly to the hard layer and the nucleation field HN is greater phase. The present results suggest that exchange coupling is than 2 Ms . (BH)max then increases as a result of the in- a more general and robust phenomenon since Fe and Co creased saturation magnetization, following the ideal curve. have different crystal symmetries and both are strongly 12 200 FULLERTON, JIANG, GRIMSDITCH, SOWERS, AND BADER PRB 58 coupled to the hard Co-Sm layer. development and optimization of high-performance perma- The fact that the experimental results and the simulation nent magnets. agree quantitatively permits the use of bilayers to model exchange-spring coupling in order to obtain detailed infor- ACKNOWLEDGMENT mation about the magnetization reversal process and an esti- mate of the potential enhancement in the energy product that Work at ANL was supported by the U.S. Department of can be gained due to the exchange hardening principle. 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