Optimization study of the nanostructure of hard/soft magnetic multilayers Matteo Amato Dipartimento di Fisica, Universita ` di Firenze, Largo Enrico Fermi 2, I-50125 Firenze, Italy Maria Gloria Pini Istituto di Elettronica Quantistica, Consiglio Nazionale delle Ricerche, Via Panciatichi 56/30, I-50127 Firenze, Italy Angelo Rettori Dipartimento di Fisica, Universita ` di Firenze and Istituto Nazionale di Fisica della Materia, Unita ` di Firenze, Largo Enrico Fermi 2, I-50125 Firenze, Italy Received 16 November 1998 We present numerical simulations, based on a mean-field calculation of the equilibrium configuration, for the magnetization reversal process in magnetic multilayers consisting of a hard hphase with large anisotropy, exchange coupled to a soft sphase with large magnetization. Starting from a trilayer made of 50h /100s /50h layers, and using realistic Hamiltonian parameters pertinent to epitaxial Sm-Co/Fe films, we separately inves- tigate the effect of iincreasing nanostructuration, while maintaining constant the overall hard/soft ratio, and iidecreasing the thickness of the hard phase, while keeping constant that of the soft phase. We find that the exchange-bias field and the coercive field strongly increase upon increasing nanostructuration and that the maximum energy product ( BH) max rapidly tends to the ideal value (2 M sat ) 2 . In contrast, upon reducing the thickness of the hard phase in a trilayer, the exchange-bias field and the coercive field remain nearly constant. Thus, combining both effects in an opportune way, we are able to determine the most convenient composition in order to obtain a permanent exchange-spring magnet with high performance, i.e., very high ( BH) max . S0163-18299902729-0 I. INTRODUCTION In recent years, the search for high performance perma- nent magnetic materials 1,2 has received strong impetus since the concept of the exchange-spring magnet was introduced. 3 The idea is to assemble a composite magnet consisting of two suitably dispersed and mutually exchange-coupled phases: a hard hphase, which provides a high coercive field, and a soft sphase, with a high saturation magnetiza- tion. The exchange coupling between the two phases gives origin to a typical reversible behavior of the demagnetization curve, hence the name exchange-spring magnet. In this way, one can obtain an enhancement of remanence with respect to a magnet made of the pure hard phase, so that high-energy products ( BH ) max can be reached: 4 for example, in Sm 2 Fe 17 N 3 /Fe 65 Co 35 multilayers with a volume fraction of only 9% of the hard phase, Skomski and Coey predicted a ( BH ) max as high as 137 MGOe i.e., more than twice the value obtained by a laboratory-scale Nd 2 Fe 14 B magnet 5 . The fine distribution of the two phases on a nanometric scale can be achieved by several techniques: melt spinning, 6,7 me- chanical alloying, 8,9 etc. Multilayer exchange-spring mag- nets, which can be obtained by ultrahigh vacuum vapor deposition 10 or sputtering, 11–18 are particularly appealing from the theoretical point of view because the thicknesses of the hard and soft phases are easily controllable, thus leading to a simple and well-defined structure. Moreover, they are becoming more and more interesting even for applications, owing to the possibility of being integrated in electronic devices. 19 In this paper, we present a theoretical study of the mag- netization reversal process in a two-phase multilayer. Our work was stimulated by recent experimental results and nu- merical simulations in high-quality epitaxial hard/soft Sm- Co/transition metal TMTM=Fe, Cobilayers, 16,17 grown via dc magnetron sputtering. 15 To calculate the equilibrium configuration for a multilayer, we use a mean-field method recently developed. 20,21 Starting from a trilayer made of 50h /100s /50h layers, we separately investigate the effect of the following. iIncreasing nanostructuration, while maintaining con- stant the total number of layers and the overall hard/soft ratio, in order to obtain higher exchange-bias and coercive fields. iiDecreasing the thickness of the hard phase, while keeping constant that of the soft phase, so that a higher satu- ration magnetization can be obtained. Our aim is to determine the optimal composition in order to obtain a permanent exchange-spring magnet with high per- formance. In particular, for a Sm-Co/Fe film with opportune nanostructuration and reduction of the hard phase actually, a 10h +33s +10h +34s +10h +33s +10h heptalayer, we pre- dict that a very high maximum energy product, ( BH ) max 74 MGOe, can be obtained. The paper is organized as follows. In Sec. II we present the model and the mean-field theoretical framework. In Sec. III the results of our calcula- tion are displayed and discussed. Finally, in Sec. IV we draw the conclusions. PHYSICAL REVIEW B 1 AUGUST 1999-I VOLUME 60, NUMBER 5 PRB 60 0163-1829/99/605/34147/$15.00 3414 ©1999 The American Physical Society