0-7803-5943-7 4/00/$10.00 @2000 IEEE. AC-09

EFFECT OF THERMAL FLUCTUATION ON REVFRSAT. FIE1,I) OF MAGNETIC FINE PAKl'lCLh WlTH SURFACE ANISTROPY

Y. Nakatani, K. Hayashi, Y . Uesaka', and 11. Fukushima" Univcrsity of Elcctro-Communications, Chofu, Tokyo. 18%: Japan,

'Nihon University, Kohriyama, Fultushima, 963, Japan, -*IIonda-cho, Chiha, 286, Japan

1. Introduction 'I'he effect of thermal fluctuation on magnetic rewrding media is cousidered as an im-

port,aiit fador which determines the upper bound for recording density, and is investigated by a variety ol experiments and simulaliuns. I1 is d s o c o n s i d e d thal lhe eifect of surface

anisotropy cannot hc neglected when we are conccrned with extremely small magnetic par^

iicles [l]. [2]. The result of computer simulation has been reported on the changc duc to surface anisotropy in the magnetization reversal field of a magnetic fine particle[3]. The size of the parlirlr used in this simulation, however, w a b R S large as submicrons. Furthemiore, thc effect of thermal fluct,ua.t,ion was not, !,aIwn i n h considerat.ion. In m r study the effect of thcrmal fluctuation on the magnetization reversal in a magnetic particle of nano-meter size is investigated by computcr simulation. 2. Calculation Model

We arc concerned with a particle which has bolh surbce and cubic anisotropies, aiming to investigate the nano-meter size particle of iron. Thc shapc of thc particlc is cubic and it is represented by a combination of cubic cells of an equal size. The motion of magnetic ~~wirienl, within each calculation cell was assullied to obey the Langevin equation[.l]-[G].

I'he surface anisotropy was siniulatcd by giving the outermost cells an effective uniaxial anisdropy wilh Lhe easy axis orienting radially from the center of the particle. l h e mag- riit,ude h',, of the elfet:t.ive ariiso1,rop.y was defined from X,.S = K,v assunling the relation K, = K,v/s = Ii,d between IC, and lhe surlace anisolropy consta.nt lis, wit,h ?I; s and d dcnoting the volumc, thc arca of a facc and the length of an edge. resIxctivcly, ol tlie cal- culation cell. Here, I<, is the inagiiitude of the surface anisotropy. Thc cclls locating at the corners of t,he pa.rticle have molt,iple (two or three) numbers of outermost faces. The value of ICT, givcn by thc relation mentioned above waz iriulliplied by the niimher of tlie outermust faces in such cases. 3. Results

The nialerial para~nrlers used are: the saturation magnetization M8 of 1700 emu/cm3,

cubic anisotropy constant I{c of 4 . 2 7 ~ 1 0 ~ erg/cni3, aurLice anisot,ropy cunstant, K, 01 0-10 erg/cmz, exchange constant of 1.0 x IO-' erg/cm, gyromagnetic ratio of 1.76 x 10' rad/s.Oc and the damping constant of unity. Pirst, we investigated the relation between the sur-

Fig 1 Changr in T C Y F ~ S B I ficld by surfacc anisot,ropy. Case without thermal fluctuatiou

face anisotropy and the reversal field without introducing thermal fluctuation. We then investigated the effect of the thermal fluctuation on thc magnetizatioii reversal field.

Fig. 1 shows lhe dependence of the magnetiaat,ion reversal field a t OK on parlicle size obtained using different values 01 surhce anisotropy. The derived reversal field U,,,, can be approximated by an cxperimcntal cquation. H,.,, = ZK,

Next we investigat,ed t,liP magnrtinat.ioo reversal field affected by thermal fluctuation a t 300K and lhe surlace anisolropy of 1 erg/cm'. Rrcaiise of the effect of thermal Auct,uat,ion, the reversal ficld dccrcascs with the increase in reversal time. In the present calculation, h e reversal field vas defined as the field undcr which thc partirlc rcvcrsed its magnetization after I ,I.,?. Calciilat,ioiis which consider thermal fluctuation invplve scvcral hundrcd magne~ liaaliun reversals and hence are quite time-consuming [GI, [ 5 ] . Fig. 2 shows thc changc in the reversal field when the particle size is varied. The graph labeled with "estimate" shou~a the rcvcrsal field estimated by considering tbemial fluctuation and the energy barrier derived from thc rcvcrsal ficld calculated at OK usiiig the N&i-Arriienius equat,ion. The reversal field calculated a t 300K is smaller than the estimatcd valuc. This is considered to be due to that the surface anisotropy which tends to destroy the uniform alignmcnt of magnetization iu a

particle helps the magnetization reversal under t.he effect of the demagnetizing field within thc particlc [SI.

Fig.2 Effcet, of particle sine on reversal field ( I ia= 1 erg /cd) .

+ (2/3)Ifa/(DA4*),

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