Journal of Magnetism and Magnetic Materials 198}199 (1999) 334}337 Invited paper Phase transitions in magnetic multilayers; statics and dynamics D.L. Mills* Department of Physics and Astronomy University of California, 4129 Frederick Reines Hall, Irvine, California 992697, USA Abstract Magnetic multilayers which incorporate ultrathin ferromagnetic "lms are physical realizations of classical, one dimensional spin systems, with spins coupled via exchange mediated by spacer layers or interactions at interfaces, and subject to anisotropy. Here by &spin', we refer to the total spin angular momentum of an ultrathin "lm in the structure. Such systems can undergo a rich range of phase transitions, in reponse to an external magnetic "eld, or change in temperature. Since inter"lm exchange is weak, modest magnetic "elds can induce spin reorientation phase transitions. We thus have a new and diverse class of magnetic materials, with phase diagrams subject to design, since both thickness, composition, or growth conditions. The paper reviews selected examples, including recent studies of the dynamic response (AC susceptibility) of an antiferromagnetically coupled Fe/Cr system which undergoes the surface spin-#op transition. 1999 Elsevier Science B.V. All rights reserved. Keywords: Magnetic multilayers; Spin reorientation transition; Phase transitions 1. Introduction intra"lm anisotropies which control them can be varied over a wide range, both in sign and magnitude by Magnetic multilayers have attracted very considerable variations in "lm thickness, composition and growth attention in recent years, as evidenced by the attendance conditions. When these materials are viewed from the at the present conference. It is fair to say that transport macroscopic perspective, we have a new class of &designer phenomena and the structural or compositional aspects magnetic materials' remarkably diverse in nature. In con- which in#uence these properties have been the primary trast, in magnetic crystals, the interion exchange coup- focus of both theorists and experimentalists, for good lings are "xed in each case, as are the anisotropy energies. reason, thanks to the exciting applications of the giant The opportunities for manipulating phase diagrams are magnetoresistance found in these materials. thus limited. Finally, in the multilayers, inter"lm ex- In this paper, we place emphasis on other aspects we change couplings are weak, so spin reorientation phase believe have yet to be studied or exploited su$ciently. transitions occur at very modest externally applied mag- These are phase transitions which involve reorientation netic "elds. This will be useful for device applications of the magnetic moments in a magnetic superlattice since, as we shall see, the dynamic response of the struc- structure, in response to either an applied magnetic "eld, tures can be tuned by driving the system through such or changes in temperature. Rich magnetic phase dia- a transition. grams can be realized, and these are subject to design and manipulation, since the inter"lm exchange couplings and 2. Examples * Corresponding author. Tel.: #1-949-8245148; fax: #1- In this section, we discuss and review selected exam- 949-8242174. ples from the literature. We begin with the Fe/Gd super- E-mail address: dlmills@uci.edu (D.L. Mills) lattice structure [1]. Both Fe and Gd are ferromagnetic, 0304-8853/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 1 1 3 0 - 5 D.L. Mills / Journal of Magnetism and Magnetic Materials 198}199 (1999) 334}337 335 and there is antiferromagnetic coupling between the two In a number of much studied superlattices, the &mag- at the interfaces between "lms. Thus, in zero magnetic netically active' constituents are ultrathin Fe "lms. The "eld, the ground state is &ferrimagnetic', with Fe and Gd Curie temperature of these "lms is typically far above "lm moments antiparallel; the material has a net fer- room temperature. The individual magnetic moments romagnetic moment, except for the special case where within a given "lm are then tightly locked together via moments in the Fe and the Gd "lms exactly compensate. e!ective exchange couplings. In response to external This is a superlattice with a magnetic structure that magnetic "elds, the total magnetic moment rotates as reminds one of YIG. a rigid entity, with all atomic moments locked parallel by Suppose the Gd "lm moments are larger that those in the very strong intra "lm exchange. Thus, each "lm may the Fe "lms. Application of a magnetic "eld then aligns be viewed as a single spin, with a very large total spin the Gd "lm moments along the "eld, with, in weak "elds, equal to the sum of that associated with each ion in the the Fe moments antiparallel to the "eld. As the temper- "lm. Since the total spin S is very large, the total spin may ature is increased, since the Curie temperature of Gd is be viewed as a fully classical object. An individual spin, as much lower than that of Fe, the Gd magnetization it rotates perhaps in response to an external magnetic decreases, so one has a compensation point where the net "eld, is subject to intra "lm anisotropy. We may describe magnetization vanishes. One may adjust the compensa- a multilayer or superlattice by an energy functional or tion temperature over a wide range, by simply varying Hamiltonian which consists of a line of such spins, each the "lm thicknesses. Above the compensation point, the subject to single site anisotropy (the intra "lm anisot- Fe magnetization is parallel to the external "eld. At ropy), and each coupled to nearest neighbors via near- higher applied "elds, a new magnetic phase intervenes est-neighbour exchange (the inter "lm exchange, possibly between the Gd-aligned, and the Fe-aligned phase. This mediated by spacer layers, of bilinear or biquadratic is the &spin twist' state, where the Fe moment, anti- character). The magnetic multilayer or superlattice is parallel to the applied "eld in low "elds, cants away from thus a physical manifestation of a purely classical, one- the anti-parallel direction, and the inter"lm exchange dimensional spin system. Viewed in the context of statist- coupling leads to a canting of the Gd magnetization. One ical mechanics, the spin con"gurations realized are those may think of this phase as similar to the spin #op-phase appropriate to the magnetic ground state, in this picture. of an antiferromagnet, rendered asymmetric by the fact Temperature enters indirectly through the temperature that the two sublattice magnetizations are unequal in variation of the inter"lm exchange, and the anisotropies. magnitude. Thus, this rather simple structure displays An example of such a structure is the Fe/Cr(2 1 1) a fascinating magnetic phase diagram. In Ref. [1], one superlattices, synthesized at Argonne Laboratory by "nds a detailed account of the phase diagram is given by Fullerton and his colleagues [4]. The Fe magnetizations rather straightforward application of mean "eld theory. lie in plane, within which there is two-fold anisotropy. We know of no studies of the dynamical response of these One may realize antiferromagnetic exchange coupling structures in the various regions of the phase diagram. between adjacent Fe "lms, via the intervening Cr layers. Ferromagnetic resonance or Brillouin light scattering The energy functional of this system is thus identical to data should prove most intersting. that of the classical antiferromagnets MnF and FeF. Magnetic superlattices with "lms of the magnetically Thus, if a magnetic "eld is applied parallel to the easy axis, ordered rare earths exhibit exotic and intersting spin these &arti"cial antiferromagnets' will undergo a spin-#op structures, and illustrated by studies of superlattices fab- transition, very similar to that in the bulk crystals. ricated from the spiral spin material Dy, and ferromag- Within these superlattices, it has proved possible to netic Gd [2]. At low temperatures, the structures have con"rm [5] a theoretical prediction made three decades a ferromagnetic moments. With increasing temperature, ago [6,7]. This is that a magnetic "eld applied anti- the magnetization is a highly non-monotonic function parallel to the surface moment of a terminated antifer- of temperature, with one or sometimes a greater number romagnet will initiate a surface spin-#op transition, at of minima reminiscent of a compensation point. Theoret- a "eld lower than that of the bulk spin-#op "eld by ical modeling reproduces this behavior nicely, and shows a factor of (2, if the anisotropy is small in strength, that as temperature is increased, the system undergoes compare to the exchange. In the next section, we discuss a sequence of transitions though rather exotic spin states. a theoretical approach we have developed recently [8], Changes in "lm thickness alter the phase diagram dra- which allows us to examine both the static spin structures matically, including the nature of the states traversed as realized in this state, along its dynamic response. temperature increases. It is possible to synthesize mag- netic superlattices from diverse combinations of rare earth metals. The Urbana group and their collaborators 3. The surface spin-6op state; statics and dynamics have carried out extensive studies of various combina- tions, to realize a remarkable range of intriguing states One may elucidate the nature of the surface spin-#op (for review see Ref. [3]). state, by "nding the con"guration which minimizes the 336 D.L. Mills / Journal of Magnetism and Magnetic Materials 198}199 (1999) 334}337 total energy of the spin array, as a function of external externally applied transverse AC "eld. The second term is magnetic "eld. Such calculations [5] provide the follow- a damping term which, it will be noted preserves the ing picture of the evolution from the low-"eld, antifer- length of each spin. romagnetic ground state, to the high-"eld ferromagnetic We start with a small external DC "eld, where we are spin arrangement. surely in the low-"eld antiferromagnetic state. We inte- When the external "eld exceeds the surface spin-#op grate the equations of motion of N spins forward in time. "eld, the surface moment, initially antiparallel to the After an initial transient stage, a steady state is reached. "eld, rotates nearly 1803, in e!fect, a twist is applied to Then we very slowly increase the DC "eld in time. When one end of the structure. A domain wall is then set up, in we reach the surface spin-#op "eld, by virtue of the an o! center position in the "nite structure. With further dissipation term, the spin system seeks and spirals down increase in "eld, the wall undergoes a series of discontinu- into the lower energy surface spin #op-state. We keep ous jumps, as it migrates to the center of the structure. In increasing the "eld slowly, and we can follow the system's this "eld regime, (dM/dH) acquires a sharp spike, with evolution to the "nal ferromagnetic state. The DC sus- each such jump. Interestingly, Trallori and co-workers ceptibility can be obtained from the total longitudinal [9] have shown that as the number of "lms NPR, this magnetization, which may be generated for each value of "eld regime acquires a chaotic character. The domain the DC "eld, as this is increased very slowly. We "nd the wall becomes centered in the structure, and then with real and imaginary part of the AC susceptibility from further increase in "eld broadens, to open up as a #ower a numerical Fourier transform of the transverse moment, to evolve into a bulk spin-#op state. The angle between which oscillates at the frequency . The surface spin-#op the spins and the external "eld is less at and near the transition is a "rst-order phase transition. We may gener- surface than in the center of the structure. This is caused ate hysteresis curves by sweeping the DC "eld "rst up- by the fact that the endmost moments are exchange wards, then downwards, through the critical "eld. We coupled to only one neighbor. There is no longer a bulk can also generates a snapshot of the con"guration for any spin-#op transition. As just described, the surface spin- H. We have now applied this technique to the study of #op state evolves continuously into the surface modi"ed hundreds of spins, though in applications to the "nite bulk spin-#op state. There is one intersting aspect of the superlattices studied in the laboratory, only 22 are re- symmetry of the spin states. The surface spin-#op quired [8]. transition occurs only in structures with an even number Here we con"ne our attention to the dependence on of ferromagnetic moments [5]. In zero "eld, the spin H of the low-frequency AC susceptibility. In Fig. 1, the structure is odd under re#ection through a point at the upper panel shows data on the "eld dependence of line of spins. At the point where the domain wall is just X taken by Fullerton, on the Fe/Cr (2 1 1) structure centered in the "nite structure, one has a spin structure which displays the surface spin-#op transition. The lower even under re#ection through the midpoint. The migra- panel is generated theoretically, as described above. We tion of the domain wall provides a mechanism for evolu- hasten to add that in the experiment, the AC "eld is tion from an odd parity to an even parity spin arrange- applied parallel to H, while we have a transverse "eld in ment (of course, the "nal ferromagnetic state is even the theory. In the #opped states, where the &active' spins under this re#ection). make a large angle with the easy axis, the principal We "nd calculations based on minimization of the features are rather insensitive to the direction of the AC energy of the spin array are tedious, and must be carried "eld. The agreement between theory and experiment is out to high accuracy. Also, only a small number of spins excellent, except the feature in the data near may be probed (15}20), in circumstances where complex H"#0.5 kG is, in the theory, the modest bump near spin states are realized. We describe now a method we !0.5 kG. This discrepancy has its origin in the large have used which can be applied to hundreds of spins, and di!erence in hysteresis loop in the theoretical model, and which yields information on the static and dynamic in the actual sample, as discussed in Ref. [8]. Here we response of the system, in one computation. We begin by focus on the three other structures. writing down the Landau}Lifschitz equation of motion The sharp, dramatic peak H"!0.6 kG is the signa- for the spin system, placed in a static magnetic "eld ture of the surface spin-#op transition, while the two H parallel to the easy axis in our case, and a time- features at H"$0.9 kG occur at the bulk spin-#op dependent transverse "eld h cos( t): "eld. While there is no true "eld-induced phase transition at the bulk spin-#op "eld in such a sample, as explained *M(i) *M(i) "M(i);H . (1) above, nonetheless there is a dramatic enhancement of *t (i)!gM(i); *t X here. The system remembers the bulk spin-#op transition, so to speak. Here H (i) is the e!ective "eld which acts on the ith spin. We see from the data and the theory, that near a This includes the external DC "eld, the single site (in- spin reorientation phase transition, there is dramatic tra"lm) anisotropy, nearest-neighbor exchange, and the enhancement in the dynamic response of the superlattice D.L. Mills / Journal of Magnetism and Magnetic Materials 198}199 (1999) 334}337 337 4. Concluding remarks We have seen that diverse magnetic superlattices may be synthesized, with a remarkable variety of exotic spin structures. Phase transitions may be induced by chang- ing the temperature, or through application of very mod- est external magnetic "elds. Near spin reorientation transitions, as we see from the X data on the Fe/Cr (2 1 1) structures, the dynamic response of the material is a!ected dramatically. It is the view of this author that in the future, far more experimental e!ort should be de- voted to the study of the dynamics of these fascinating materials, through AC suscptiblity, ferromagnetic reson- ance studies, and Brillouin light scattering. References [1] M. Sajieddine, Ph. Bauer, K. Cheri", C. Dufour, G. Mar- chal, R.E. Camley, Phys. Rev. B 49 (1994) 8815. [2] R.E. Camley, J. Kwo, M. Hong, C.L. Chien, Phys. Rev. Lett. Fig. 1. We show (a) experimental data and (b) theoretical 64 (1990) 2703. simulations of the "eld dependence of X [3] J.J. Rhyne et al., J. Magn. Magn. Mater. 129 (1994) 39.  at low frequencies, for the Fe/Cr (2 1 1) superlattice. [4] E.E. Fullerton et al., Phys. Rev. B 48 (1993) 15755. [5] R.W. Wang, D.L. Mills, E.E. Fullerton, J.E. Mattson, S.D. Bader, Phys. Rev. Lett. 72 (1994) 920. [6] D.L. Mills, Phys. Rev. Lett. 20 (1968) 18. structure. Since, as discussed above, the surface spin-#op [7] F. Ke!er, H. Chow, Phys. Rev. Lett. 31 (1973) 1061. "eld may be &tuned' over a considerable range through [8] S. Rakhmanova, D.L. Mills, E.E. Fullerton, Phys. Rev. B 57 variations in the microstructure of the superlattice, one (1998) 476. can locate this feature where desired. [9] L. Trallori et al., Phys. Rev. Lett. 72 (1994) 1925.