SW parameter in magnetic multilayers with rough interface

Transcription

1 Journa of Phsics: Conference eries W parameter in magnetic mutiaers with rough interface To cite this artice: Z Mohammad Hosseini Naveh and H Moradi J. Phs.: Conf. er. 766 View the artice onine for updates and enhancements. Reated content - A cacuation based on Green's function method for FM/MgO /FM sandwiches with roughness at interfaces Edaati Boostan and H Moradi - Exchange-bias-ike effect in L () FePt based pseudo spin vaves C L Zha, P Mudui, J Nogues et a. - Manifestation of spin-ha effect in mutiaered M/N/M fim structures Y Pogoreov and J Åkerman This content was downoaded from IP address on //8 at :

2 Internationa Conference on Magnetism (ICM 9) Journa of Phsics: Conference eries () 766 IOP Pubishing doi:.88/ //7/766 W parameter in magnetic mutiaers with rough interface Z. Mohammad Hosseini Naveh and H. Moradi Department of Phsics, Facut of ciences, Ferdowsi Universit of Mashhad, Mashhad, Iran. E-mai: mhoseni@ahoo.com The magnetiation (M) and spin-wave (W) parameter of Fe ()/Ag () mutiaers has been cacuated in the presence of the random magnetic fied (RMF) and interaer exchange couping (IEC), using simpe W theor. We introduce roughness as RMF caused b fuctuations in the spacer thickness (T). The resuts show that the M and W parameter osciate as a function of T and the are affected b roughness strong. Kewords: pin waves; Interface structure and roughness; magnetic mutiaer PAC: 75.3.Ds; At; i 4. Introduction ince the discover of IEC, man studies have been impemented on the properties of utrathin magnetic structures which their magnetic properties have been studied theoretica []. Osciator couping has been found for a number of FM/non-magnetic meta sstems [, 3] at the origin of the discover of GMR effect. One common approach is to stud M and W parameter (B) of FM thin aers. The observed resuts show that Curie temperature and B osciate with T [5, 6], which is investigated theoretica [7, 8]. A W theor has been used to expain the T-dependence of M and B. In rea fims, we expect interfacia roughness which affects IEC [8]. B empoing the RKKY theor [9], we can reate IEC to RMF. A cacuation was performed using a mode described in Ref []. The Fe ()/Ag () mutiaer is considered as mutipane with RMFs concerned to IEC [8]. In this paper, the cases of FM and anti-fm interaer couping are soved for the T-dependence of M and B, in the presence of RMF at ow T. In section the theoretica method is described. We present resuts and discussion in section 3 and fina the major points are summaried in section Theoretica method The Heisenberg Hamitonian (H) with the nearest neighbour (NN) inter ( J ) and intra ( J ) pane exchange couping (EC) is used to describe the sstem. We approximate each thin FM aer b D square attice of spin ½ parae to the x- pane. The x,, and axes are corresponding to the [], [], and [ ] directions. uppose the RMF is appied aong the direction. This mode is on vaid for a super-attice with the FM fim thin enough to behave D. Thus W spectrum and M are derived. 5.. FM couping The Heisenberg-tpe H in the presence of a sma RMF is given b c IOP Pubishing Ltd

3 Internationa Conference on Magnetism (ICM 9) Journa of Phsics: Conference eries () 766 IOP Pubishing doi:.88/ //7/766 H J gì, ä B H (, ). ( ä, ) J ( )., [ (, ). (, ) (, ). (, )] () is spin at th site. ä and are NN vector and the component of, in x- pane respective. H is RMF acting on th site. In equation () the first and second terms are intra and inter pane EC energ and the third one is the RMF energ. Lattice parameter, in the fim pane is a and aong is b. We can app Hoestein-Primakoff transformation at ow T. H is diagona in the k space, thus W spectrum in the imit of J k BT, which on Ws with ong wave ength can be excited in the x- pane, is [9] ù( J k xa k a 4J[ cos( k b)] h J 4 J [ cos( k b)] h. () The therma average of magnetiation, ( h ), is given b [9] ( ) ð [4J (cos( )) ] 3 k b h h v k BT kbt d k d( k ) n( e 3 ( k T b B ( ) BZ e 6 ð J ð We consider Gaussian distribution of RMF with width Ä. B taking average over the RMF [7], we get h ( ) h e ð h kbt d d( ) n( e h k b 6 ð J ð ð [4J(cos( k b)) h ] kbt If, for strong interaer couping ( J k BT ), we get the Boch aw ( couping ( J k BT ), we get a quasiinear T-dependence magnetiation [9]. T 3 ). ) ), but for weak.. Anti-ferromagnetic (AF) couping At T = K and for, due to anti-ferromagnetic IEC we can divide the superattice into two subattice A and B with the propert of tending to aign a spins on subattice A in the + direction and a spins on subattice B in the direction. Thus H in the presence of a RMF is given b H J (, ). ( ä, ) J [ (, ). (, ) (, ). (, )] A gì B H, ä ( ) B gì B H ( )., The third and fourth terms are the RMF energ in the subattices A and B. In this equation,,, nb with even n compose subattice A; and,, nb B with odd n is A x compose subattice B. At ow T, we can app Hoestein-Primakoff approximation within each subattice A and B. The H transformed to the magnon variabes, a( and b (, that satisf the boson communication reations is not diagona in the k space: H [ ( k ) h 4J ][ a ( a( b ( b( ] B defining k 4J k cos( k b)[ a( b( a ( b x ( ] c. c. ù( k ) [ J [( k xa) ( k a) ] 4J h ] [4J cos( k b)], at ow T, and appropriate transformations [9] in the presence of RMF, H wi be diagona in the k space. Therefore, the configuration average of magnetiation, ( h ), can be expressed as equation (3). h () (3) (4) (5)

4 Internationa Conference on Magnetism (ICM 9) Journa of Phsics: Conference eries () 766 IOP Pubishing doi:.88/ //7/766 ( h ) h k BT 8 ð J d h h exp ðä Ä d( k b) n exp [4 ] [4 cos( )] J h J k b. kbt The resuts show that if, we get the T dependence for strong IEC and a quasi-inear T- dependence for weak IEC [9]. 6. resuts and discussions We use RKKY function for IEC strength ( J ) [8]. The average of RMF,, was reated to IEC b J R R [7]. Thus, we can find as a function of T. Using equations (3) and (6), W magnetiation is evauated in the presence of roughness, numerica (the points in the figures and show the cacuated vaues). We fixed J 7k [], and the parameter B J( 8kB for T 4 monoaer (ML)) was aowed to var with Ag spacer thickness. Thus the magnetiation is potted versus T for various Ä ( R.,.5,.5 and. ML) at T= K, figure a. As a resut of osciator behaviour of IEC versus T, W magnetiation osciates with the period of J (in the absence of roughness). When J R has minimum vaue, we observe sma dips in the presence of RMF, which occur aternative with the same period as IEC, and their depth increases b roughness. Hence, introducing RMF resut in the period of magnetiation is two times of IEC periodicit. The magnetiation wi vanish when J passes through ero ( J R has maximum vaue) aternative, figure a ( ). But in the presence of roughness the heights of the vaes wi reduce which is coser to rea mutiaers. The pot aso show that W magnetiation increases in the presence of RMF which means that the deviation of M( T ) from saturation vaue, M(T=), caused b existence of spin-waves in the sstem, decreases with RMF. The resuts aso show that W magnetiation decreases with T because of weakening IEC. The W magnetiation reduces with T due to increase of the therma excitations of Ws, figure b. It is obvious that the depth of dips increases b T We define B( T ) ( BT ) [ ( ( h ) ) ], where B ( 5 K ) is W parameter of buk Fe. Figure shows B(T) versus T in the presence of roughness for T= K. Due to IEC, B(T) osciates with the period of J. In genera, B(T) is dependent on the effective exchange seen b the Fe atoms. For thin ferromagnetic fims in a genera compare with thick ones [], the reduced coordination resuts in arger B(T) as is seen in the figure,, in compare with figure b [] for (6) Figure. M(T)/M() versus T, (a) R =,.5,.5,ML (monoaer) and T = K, (b) R.5 ML and T =, 5 and K. The points show the cacuated vaues. 3

5 Internationa Conference on Magnetism (ICM 9) Journa of Phsics: Conference eries () 766 IOP Pubishing doi:.88/ //7/766 3 T prefactor in the Boch aw. In the presence of RMF, when J R has minimum vaue, we observe sma peaks, which occur aternative with the same period as J. Hence, the period of B wi be two times of J, the same as W magnetiation. These peaks which just occur in the presence of RMF can be important in expaining experimenta resuts. Unfortunate, there isn't experimenta resut for thin Fe/Ag mutiaers. In ref. [], we have experimenta data for thick ferromagnetic Fe fims [] which behave buk ike and their W magnetiation obes the Boch aw. Our cacuations are on vaid for FM fims thin enough to behave D. Hence, their magnetic behaviour is more compicated and shows dimensiona crossover [9]. Thus, it isn't expected that our theoretica resuts is the same as experimenta one [] in detais. But, as it was mentioned, introducing RMF resut in the period of W parameter is two times of IEC periodicit, which mabe expain some parts of the experimenta resuts []. Figure. B(T)/B versus spacer thickness with T= K. The points show the cacuated vaues R =,.5,.5 and ML (monoaer) at 4. Concusion The W magnetiation and W parameter of utra-thin Fe/Ag mutiaers has been investigated in the presence of RMF for various T. The resuts show that the existence of the RMF can strong infuence the behaviour of the basic magnetic characteristics of utra-thin magnetic mutiaers incuded W magnetiation and W parameter. Our resuts show both of them osciates with T, and the period of osciations b considering RMF is two times of period of osciations when. The argest effect of the RMF on M and B is about where J is passing through ero. References [] U. Hartmann, Magnetic Mutiaers, Giant Magnetoresistance, in pringer eries in urface ciences, pringer, Berin, Heideberg, [] H.M Van Noort, F.J.A. den Broeder, H.J.G. Draaisma, J. Magn. Magn. Mater. 5 (985) 73. [3] F. Bedia, B. Martine, D. Fiorani, A. Labarta, J. Magn. Magn. Mater. 93 (99) 45. [4] R. Ekabi and et a., J.Aos Compd. 394(5) 83. [5] G. Bareuther, F. Bensch, and V. Kotter, J. App. Phs. 79 (996) 459. [6] A. Urbaniak-Kucharck, and et a., J. Magn. Magn. Mater. 7-76(4) [7] H. Moradi and G. A. Gehring, J. Magn. Magn. Mater. 5 () 8. [8] P. Bruno and C. Chappert, Phs. Rev. B 46 6 (99); Phs. Rev. Lett. 67, 6 (99). [9] Z. Q. Qiu, and et a., Phs. Rev. B. 45, 5 (99). [] C. J. Gutierre, and et a., J. App. Phs. 69 (99) 583. [] D. J. Keavne, and et a.,phs. Rev. Lett. 7, 97 (993). 4

6 Internationa Conference on Magnetism (ICM 9) Journa of Phsics: Conference eries () 766 IOP Pubishing doi:.88/ //7/766 Figure a Figure b 5

7 Internationa Conference on Magnetism (ICM 9) Journa of Phsics: Conference eries () 766 IOP Pubishing doi:.88/ //7/766 Figure 6