Monte Carlo simulation study on magnetic hysteresis loop of Co nanowires

Transcription

1 Monte Carlo smulaton study on magnetc hysteress loop of Co nanowres Ryang Se-Hun, O Pong-Sk, Sn Gum-Chol, Hwang Guk-Nam, Hong Yong-Son * Km Hyong Jk Normal Unversty, Pyongyang, D.P.R of Korea Abstract; The nfluence of temperature on the magnetc hysteress and coercvty of Co magnetc nanowres was nvestgated by Monte Carlo method. Monte Carlo smulaton results of hysteress loop ndcated that both ts tendency and the coercvty were consstent wth expermental results wthn a gven error. The coercvty was calculated wth the temperature and the angle between nanowres and magnetc feld appled, varyng the temperature from 50K to 300K for Co nanowres wth a dameter of 30nm. The coercvty decreased monotoncally at all values of angle wth the ncrease of temperature T, followng the parabolc curve of T -γ. The power exponent γ, determned correspondng to angle between nanowres and magnetc feld, was 0.03~0.06 and was consstent wth the prevous expermental results. Keywords;Monte Carlo method, nanowre, coercvty, magnetc hysteress loop Correspondng author; yongsonhong77@yahoo.com 1. Introducton Because of huge potental applcaton of Co nanowres n ultrahgh densty perpendcular magnetc recordng feld, ther magnetc propertes were wdely nvestgated and the magnetc hysteress loops were determned expermentally n recent years [1-9]. MC (Monte Carlo) smulaton of magnetc hysteress loops of magnetc nanowres at room temperature was performed and the accuracy of smulaton was dentfed n comparson wth expermental results n [1-3]. Because the smulaton envronment was taken at room temperature, the nfluence of temperature on the coercvty could not be regarded. In ths work, based on the MC method, the magnetc hysteress property of Co nanowres was nvestgated. 2. Modelng and method

2 Monte Carlo smulaton was conducted for the Co nanowres wth a dameter of 30nm and a length of 600nm and nvestgated expermentally and fully so as to dentfy the accuracy of smulaton method. Assumng nanowre s a fnte cylnder of whch the aspect rato s 20, ths cylnder can be dvded by small regular global-shaped cells whch have ther spn. Consderng the exchange nteracton energy, the dpolar nteracton energy, the ansotropy energy, and Zeeman energy for ths model, the total energy of the system can be wrtten as follows. E K JS S 0 D S S 3 r 2 S M s 0H Sr S r 5 r S h The frst term s the exchange nteracton energy, where J=2Adπ/6; d s the dameter of the unt cell, A s the exchange of couplng between unt cells, and S s the spn of the th unt cell. 2 The second term s the dpolar nteracton energy, where D ( M S 0 ) / 2 (Ms s saturaton magnetzaton) denotes the strength of the dpole-dpole nteracton; 3 ( / 6) s the volume of the cell; r s the vector for the dsplacement between 0 d stes and. The thrd term represents the magnetocrystallne ansotropy energy, where K s the magnetc ansotropy constant, s the unt vector of easy axs. The last term represents Zeeman energy, where H s the magnetc feld appled and h s the unt vector of appled feld. 11 The typcal materal parameters used n ths work are A J m, A m, K J m. The temperature was vared between 50K M S 6 and 300K and the free boundary condton was used for both drectons of the length and the dameter such that the feature of nanowres appears. And the metropols algorthm was used n the smulaton of the reversal process of spn. (1) 3. Results and dscusson Fgure 1 shows the magnetc hysteress loops at 300K wth an angle H α between nanowres and magnetc feld. It s found that MC smulaton result of magnetc hysteress loops s consstent wth expermental result n both tendency

3 and coercvty H c. Consderng the effect of magnetocrystallne ansotropy, the coercvty decreases wth the ncrease of angle H α and s not zero at 90 and therefore ths s consstent wth general hysteress property. However, the coercvty s approxmately zero n the absence of the magnetocrystallne ansotropy (that s, K=0). Ths shows that the angle between the appled feld and nanowre as well as magnetc ansotropy s mportant factor on coercvty. Accordng to prevous study, f the nanowres are nfnte lengthy cylnders and the magnetocrystallne ansotropy s much less than the shape ansotropy, t was reported that the rectangular magnetc hysteress loops were obtaned n external magnetc feld appled along the axs. However, n case of Co, the magnetocrystallne ansotropy constant s K = J/m 3 and s almost equal to that of shape ansotropy. That s, the smulaton result dentfes that t s not neglgble. Fg 1. Hysteress loops of Co nanowres at varous angles (M-magnetzaton ntensty, M s -saturaton magnetzaton) Fgure 2 gves the results of the coercvty calculated wth temperature and angle H α, for Co nanowres wth a dameter of 30nm, varyng the temperature from

4 50K to 300K. Fg. 2. Varaton of the coercvty wth temperature and angle Fg. 3. Angular dependence on the varaton of the coercvty of Co nanowres at 300K wth varous dameters (30nm, 40nm, 70nm) As the fgure shows, the coercvty decreased monotoncally at all values of H α, wth the ncrease of temperature, followng the parabola of the T shape. The power exponent γ, determned correspondng to H α, was 0.03~0.06 and was consstent wth the prevous expermental results [10].

5 Fgure 3 shows the varaton of the coercvty of nanowres wth thckness and angle H α The magnetc reversal process was nvestgated to consder the mechansm of magnetc reversal of Co nanowres. Fgure 4 shows the state of the magnetc reversal of Co nanowres wth a dameter of 30nm at H 0 as the tme goes. Fg. 4. Spn reversal process wth tme at H α=0 n a magnetc feld of -318kA/m The smulaton shows the reversal nucleus s formed from both sdes and propagates n case of small angle H α for the nanowres wth small dameter. That s, the magnetc reversal propagates wth localzed nucleaton. The reversal nucleus s formed at both sdes of nanowres around the magnetc feld where t takes place (Fg 4.a) and s propagated (Fg 4.b) and the reversal

6 process s completed (Fg 4.c-d). What s mportant here s the fact that the other spns reman constant when the nucleus s formed and propagated. However, n case of angles greater than 80, that s, at H 90, the spn consdered s turned round to the drecton of magnetc feld appled wthout the nucleaton at both sdes and ths can be explaned by the coherent reversal model and s consstent wth the result obtaned from the relatonshp between coercvty and angle. In the smulaton of magnetc reversal process n Co nanowres wth a dameter of 95nm wth the ncrease of magnetc feld, t s found that all the spns are not reversed at the same tme but rotated n and they reverse wth the ncrease of dameter n the form of curlng reversal unlke nanowres wth small dameter. Conclusons In concluson, the mechansm of nanowres s farly complcated and t s assocated wth the dameter of nanowres and the drecton of external magnetc feld. But the defect of surface structure present n nanowres wll be nfluental n the magnetc reversal process of nanowres. References [1] R.Skomsk, H.Zeng, and D.J.Sellmyer, Incoherent magnetzaton reversal n nanowres, J. Magn. Magn. Mater. 249 (2002) [2] C.Verdes., et.al, J. Magn. Magn. Mater. 304 (2006), [3] W.Z.Zhang, W.Guo, L.Wang, K.H. Höglund, A.W. Sandvk, Effects of ed ge dsorder n nanoscale antferromagnetc clusters, Phys. Rev. B 82, [4] R.Skomsk, H.zeng, D.J.Sellmyer, Magnetc localzaton n transton-metal nanowres, Phys Rev. B62 (2000), [5] L.C.Sampao, E.H.C.P.Snnecker, G.R.C.Cernccharo, M.Knobel, M.Vazquez, J.Velazquez, Magnetc mcrowres as macrospns n a long-range dpole-dpole nteracton, Phys Rev. B61 (2000), [6] P.M.Paulus, F.Lus, M.Kroll, G.Schmd, Low-temperature study of the magnetzaton reversal and magnetc ansotropy of Fe, N, and Co nanowres, J.

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