Available online at I-SEEC Proceeding - Science and Engineering (2013)

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1 Available online a I-SEEC 01 Proceeding - Science and Engineering (013) Proceeding Science and Engineering Science and Engineering Symposium 4 h Inernaional Science, Social Science, Engineering and Energy Conference 01 Aniferromagneic coupling in ferromagneic/ferrimagneic and ferromagneic/aniferromagneic hin films N. Chaidaungsri a,*, A. Kaewrawang a a Deparmen of Elecrical Engineering, Faculy of Engineering, Khon Kaen Universiy, Khon Kaen 4000, Thailand Absrac Nowadays, magneic coupling is wildly used in magneic hin films, e.g. he inerface in a reading sensor of magneic recording head. In his paper, we presen he aniferromagneic coupling effecs of bilayer hin films in wo cases: (i) ferromagneic/ferrimagneic and (ii) ferromagneic/aniferromagneic. In he firs case, he Objec Oriened MicroMagneic Framework (OOMMF) was used o simulae he micromagneic srucure. According o he resuls, he magneic propery of Ni/TbFeCo bilayer shows he negaive coerciviy because of srong aniferromagneic coupling. In he second case, Soner- Wohlfarh model was used in he modelling of ferromagneic/aniferromagneic layers. The resuls sugges ha he posiive exchange bias is conribued by he weak aniferromagneic coupling. In conclusion, he resuls lead o developmen of magneic hin films in fuure read head echnology. 013 The Auhors. Published by Kasem Bundi Universiy. Selecion and/or peer-review under responsibiliy of Faculy of Science and Technology, Kasem Bundi Universiy, Bangkok. Keywords: Aniferromagneic coupling; Negaive coerciviy; Posiive exchange bias 1. Inroducion Magneic coupling a inerface of magneic hin film mulilayer is used o improve magneic propery for specific applicaions. The propery is unlike in he case of a convenional magneic maerial. Magneic coupling has wo ypes - ferromagneic coupling and aniferromagneic coupling. They are widely applied for echnological applicaions, such as gian magneoresisance (GMR) using aniferromagneic coupling a inerface of he magneic hin film mulilayer in order o increase areal densiy from 1-5 Gb/in up o Gb/in [1]. Aniferromagneically coupled (AFC) media is helped o mainain hermal sabiliy even for lower values of M r δ []. A nearly single-domain sae wih improved exchange and anisoropy fields, and high hermal sabiliy have been achieved on synheic aniferromagneic coupled films (SAF) [3]. In addiion, he magneic coupling beween hard/sof magneic layers in exchange coupled composie media is used o reduce swiching field [4]. * Corresponding auhor. address: nuapon.c@kkumail.com

2 47 N. Chaidaungsri and A. Kaewrawang / Proceeding - Science and Engineering (013) Nowadays, many research groups have been focused on he magneic coupling in magneic hin films. Shan e al. [5] found he negaive exchange bias of ferromagneic/aniferromagneic bilayer because of weak ferromagneic coupling. Furhermore, Liu e al. sudied he negaive coerciviy of ferromagneic/ferrimagneic/ferromagneic rilayer because of srong aniferromagneic coupling [6]. Therefore, he magneic coupling is very imporan o develop he magneic propery of magneic hin films. For above reasons, magneic coupling is paricularly ineresing o sudy. Such properies make he bilayer an ineresing candidae for echnological magneic applicaions. The main propose of his paper focuses on he effec of aniferromagneic coupling beween inerfaces of bilayer magneic hin films. In he presen work, modeling conribuions have been made in wo areas: (i) Objec Oriened MicroMagneic Framework (OOMMF) simulaion for ferromagneic/ferrimagneic layers and (ii) analyical mehod calculaion for ferromagneic/ aniferromagneic layers. This paper is divided ino 4 secions. Secion describes abou modeling of magneic hin film srucures. Secion 3 is he resuls and discussions for ferromagneic/ferrimagneic and ferromagneic/aniferromagneic bilayer hin films. Finally, secion 4 is conclusion of his work. Nomenclaure A Ferromagneic maerial Aniferromagneic maerial M, M A The magneizaion of ferromagneic and aniferromagneic maerials, respecively H H c Applied exernal field Coerciviy H The posiive exchange bias field ex J K 1 A M s Magneic coupling consan Magneic anisoropy consan Exchange siffness consan Sauraion magneizaion The hickness of layer β The angles of he M α The angles of he M A wih respec o he easy axis wih respec o he easy axis θ E B The angles of he H wih respec o he easy axis Energy barrier heigh

3 N. Chaidaungsri and A. Kaewrawang / Proceeding - Science and Engineering (013) Modeling of Magneic Thin Film Srucures.1 Ferromagneic/Ferrimagneic srucure Fig. 1. Srucure of Ni (16 nm)/tbfeco (0 nm) hin film OOMMF [7] was used o analyze aniferromagneic coupling beween ferromagneic/ ferromagneic layers. I is widely used o analyze he hree dimensional micromagneic simulaions based on LLG equaion and calculaed by using finie differen ime domain. The magneic maerials are Ni (sof ferromagneic) and TbFeCo (hard ferrimagneic). The srucure has dimension of nm 3 as shown in Fig. 1. The magneic parameers of Ni and TbFeCo are in Table 1. Table 1. Magneic parameers of Ni and TbFeCo [6] Magneic maerial K 1 (MJ/m 3 ) A (pj/m) M s (ka/m) Ni TbFeCo Ferromagneic/Aniferromagneic srucure Fig.. (a) Schemaic of coupled ferromagneic/aniferromagneic hin film; (b) configuraion of magneizaion, M, M A and applied field, H, wih respec o easy axis [5]

4 474 N. Chaidaungsri and A. Kaewrawang / Proceeding - Science and Engineering (013) The ferromagneic/aniferromagneic layers model has been esablished based on he Soner Wohlfarh model [8] o analyze he effecs of exchange-bias coupling and he applied field. Analyical soluions indicaed he correlaion beween he magneic and srucural properies of he bilayer hin films have been derived. These soluions are useful for undersanding he srucural and magneic properies of exchange bias. 3. Resuls and Discussions 3.1 Ferromagneic/Ferrimagneic layers Fig. 3 (a) shows he hyseresis loop for bilayer of Ni/TbFeCo. The exchange siffness consan is abou -18 pj/m, where - means aniferromagnic coupling. I suggess ha increasing of aniferromagneic coupling a inerface causes he negaive coerciviy. Boh he magneizaion of Ni and TbFeCo layer will saurae wih he applied field higher han 0 koe. A reducing he applied field, he magneizaion of Ni will be roaed o he reversed direcion wih he applied field due o he aniferromagneic coupling in he inerface while he TbFeCo will be no roaed. As he magneic momen of Ni is larger han he magneic momen of TbFeCo, he ne magneizaion of he bilayer ends o be negaive. I is called negaive coerciviy for bilayer magneic hin films. Fig. 3 (b) shows he coerciviy of bilayer and rilayer. I indicaes ha bilayer need he coupling higher han rilayer o reach negaive coerciviy because bilayer has one inerface o couple less han rilayer (wo inerfaces). Therefore, bilayer and rilayer have he negaive coerciviy a exchange siffness consan abou -18 and -6 pj/m, respecively.

5 N. Chaidaungsri and A. Kaewrawang / Proceeding - Science and Engineering (013) Fig. 3. (a) The hyseresis loop for Ni/TbFeCo bilayer wih A= -18 pj/m; (b) dependence of coerciviy on exchange siffness consans for Ni(8nm)/TbFeCo(0nm)/Ni(8nm) versus Ni(16nm)/TbFeCo(0 nm) 3. Ferromagneic/Aniferromagneic layers The hin layer is assumed o be coupled wih an A underlayer by exchange-bias as shown Fig. (a) and he configuraion of momen and H-field is shown in Fig. (b). Energy of he srucure consiss of Zeeman HM cos θ β ), exchange energy ( J cos (β α) ), and anisoropy energy for ferromagneic layer energy ( ( K sin β ) and aniferromagneic ( K A A sin α ) where H, M, K, and are he applied exernal field, he magneizaion, he anisoropy consan, and he hickness of layer, respecively. β, α and θ are he angles of he M, M A,and H wih respec o he easy axis [9]. J is he aniferromagneic coupling consan beween ferromagneic and aniferromagneic layers Coerciviy In order o invesigaion of magneic properies, we will observe hyseresis loop of ferromagneic/ aniferromagneic layers by calculaed coerciviy. The coerciviy can be deermined by energy of he srucure for swiching sae condiion (H=H c ). The coerciviy depends on he magneic sae parameer β, α and θ. Subsiue he angle for iniial sae (0 o ) and reversal sae (180 o ) ino β, α, and θ, we ge Hc1, H,and c H as c3 shown in Table.

6 476 N. Chaidaungsri and A. Kaewrawang / Proceeding - Science and Engineering (013) Table. Coerciviy depen on he magneic sae parameer β, α, and θ H c1 M Analyical soluions θ β α J K A 1 A A A K J 0 o 0 o 0 o J K K A A Hc -Hc o 180 o 180 o M J A A H c3 M J K A 1 A A A K J 0 o 180 o 0 o 3.. Posiive exchange bias field The posiive exchange bias field ( H ) is he loop-shif range, i can given by Eq. (1) ex J H ex ; M A A J (1) A A Fig. 4. Schemaic of hyseresis loop respec for coerciviy a hree ypical condiions: (a) noncoupling, (b) srong aniferromagneic coupling ( J A A ) and (c) weak aniferromagneic coupling ( J A A )

7 N. Chaidaungsri and A. Kaewrawang / Proceeding - Science and Engineering (013) Fig. 4. (c) seems o sugges ha only weak aniferromagneic coupling ha could be performed posiive exchange bias. M A does no roae o he reversed direcion o negaive following H-field and M. When H- field is applied o posiive, M is hard o roae wih H-field due o weak aniferromagneic coupling Energy barrier heigh The energy barrier heigh indiscriminae he applied field is deermined as E B = E MAX - E MIN where E MAX, E MIN are he maximum and minimum energy of he srucure. I can be obained as, 1 J E B iniial K for β from 0 o (iniial) o 180 o (reversal) () K, 1 J E B reverse K for β from 180 o (reversal) o 0 o (iniial) (3) K The energy barrier of Eq. ()-(3) can plo in Fig. 5 (a)-(b), respecively. I suggess ha he energy barrier heigh increases wih increasing coupling consan. From he physical poin of view, he energy barrier is he key issue in conrolling he momen reversal properies of posiive exchange bias.

8 478 N. Chaidaungsri and A. Kaewrawang / Proceeding - Science and Engineering (013) Conclusions Fig. 5. Energy barrier of (a) iniial o reversal sae and (b) reversal o iniial sae The magneic properies of bilayer magneic hin films are invesigaed in his paper. The aniferromagneic coupling in he inerface of ferromagneic/ferrimagneic can cause he negaive coerciviy. The aniferromagneic coupling of bilayer magneic hin films is lower han rilayer. In addiional, he posiive exchange bias is in he ferromagneic/aniferromagneic layers wih weak aniferromagneic coupling. The resuls of his paper offer useful informaion for he developmen of magneic hin film wih using magneic coupling applicaion. References [1] Grünberg P, Schreiber R, Pang Y, e al. Layered Magneic Srucures: Evidence for Aniferromagneic Coupling of Fe Layers across Cr Inerlayers. Phys Rev Le 1986;57: [] Fulleron Eric E, Margulies D T, Schabes M E, e al. Aniferromagneically coupled magneic media layers for hermally sable highdensiy recording. Appl Phys Le 000;77: [3] Byeon S C, Misra A, Doyle W D. Synheic aniferromagneic sof underlayers for perpendicular recording media. IEEE Trans Magn 004;40: [4] Vicora R H, Xiao S. Exchange Coupled Composie Media. Proc IEEE 008;96: [5] Shan Z S, Jin D, Ren H B, e al. Magneic field and hermal reversal properies of exchange-bias recording films. IEEE Trans Magn 001;37: [6] Xiaoxi Liu, Kanazawa T, Songian Li, e al. Negaive Coerciviy and Spin Configuraion in Ni/TbFeCo/Ni Trilayer. IEEE Trans Magn 009;45: [7] Donahue M J, Porer D G. The objec oriened micromagneic framework (OOMMF) projec a ITL/NIST;006. [8] Soner E C, Wohlfarh E P. A mechanism of magneic hyseresis in heerogeneous alloys. IEEE Trans Magn 1991;7: [9] Nogués J, Schuller I K. Exchange bias. J Magn Magn Maer 1999;19:03-3.