Recently, the current-induced spin-transfer torque has been proposed as a convenient writing process in high density magnetic random access memory. A spin-polarized current can switch the magnetization of a ferromagnetic layer more efficiently than a current induced magnetic field. Our paper discusses the switching properties of a Stoner–Wohlfarth magnetic particle for the case when spin torques and external field pulses are simultaneously present. The theoretical investigation of precessional motion is described by using Landau–Lifschitz–Gilbert equation with a spin-transfer torque term included. The main goal is to determine the parameters of field pulse for that the fast and stable switching can be achieved

Cimpoesu, Dorin

Pham, Huy

Spinu, Leonard

Stancu, Alexandru

English

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Switching behavior of a Stoner–Wohlfarth particle subjected to spin-torque effect

University of New Orleans

University of New Orleans ScholarWorks@UNO Physics Faculty Publications Department of Physics 2008 Switching behavior of a Stoner–Wohlfarth particle subjected to spin-torque effect Dorin Cimpoesu University of New Orleans Alexandru Stancu Leonard Spinu University of New Orleans Huy Pham University of New Orleans Follow this and additional works at: https://scholarworks.uno.edu/phys_facpubs  Part of the Physics Commons Recommended Citation J. Appl. Phys. 103, 07B105 (2008) This Article is brought to you for free and open access by the Department of Physics at ScholarWorks@UNO. It has been accepted for inclusion in Physics Faculty Publications by an authorized administrator of ScholarWorks@UNO. For more information, please contact scholarworks@uno.edu. Switching behavior of a Stoner–Wohlfarth particle subjected to spin-torqueeffectHuy PhamDepartment of Physics, University of New Orleans, New Orleans, Louisiana 70148, USAAdvanced Materials Research Institute (AMRI), University of New Orleans, New Orleans,Louisiana 70148, USADorin CimpoesuaAMRI, University of New Orleans, New Orleans, Louisiana 70148, USAAlexandru Stancu“Al. I. Cuza” University, Department of Physics, Iasi 700506, RomaniaLeonard SpinubDepartment of Physics, University of New Orleans, New Orleans, Louisiana 70148, USAAMRI, University of New Orleans, New Orleans, Louisiana 70148, USAPresented on 8 November 2007; received 13 September 2007; accepted 13 October 2007;published online 1 February 2008Recently, the current-induced spin-transfer torque has been proposed as a convenient writingprocess in high density magnetic random access memory. A spin-polarized current can switch themagnetization of a ferromagnetic layer more efficiently than a current induced magnetic field. Ourpaper discusses the switching properties of a Stoner–Wohlfarth magnetic particle for the case whenspin torques and external field pulses are simultaneously present. The theoretical investigation ofprecessional motion is described by using Landau–Lifschitz–Gilbert equation with a spin-transfertorque term included. The main goal is to determine the parameters of field pulse for that the fastand stable switching can be achieved. © 2008 American Institute of Physics.DOI: 10.1063/1.2830720I. INTRODUCTIONThe concept of the “spin-transfer torque” proposed bySlonczewski1 and Berger2 offers a new way of controllingthe magnetization reversal in ferromagnetic multilayer sys-tems, which replaces the conventional method utilizing mag-netic field. The transfer of the spin angular momentum be-tween two magnetic layers by the current flowingperpendicular to plane can reverse the magnetization of oneof the magnetic layers. The novel technology utilizing thespin-transfer torque is expected to reduce the switching timeof magnetization as well as to increase the recording densityof the magnetoresistive random access memories3–6MRAMs and other data storage devices. Devolder et al.7,8proposed to bias the free layer with a hard axis field, in orderto obtain a reproducible subnanosecond duration when thefree-layer easy axis is parallel to the spin polarization of thecurrent. However, the precise nature of magnetization dy-namics when spin-polarized current and external pulsed fieldare simultaneously present has not been well studied.In this paper the switching properties of a Stoner–Wohlfarth particle, subject to a continuous or short magneticfield pulse, and to a short current pulse, obtained by numeri-cal investigations, are presented. The switching is discussedas a function of the applied field strength and direction, andas a function of the length of the current pulse. Finally, thecase of asynchronously pulses is discussed.II. MODELIn typical spin-transfer investigation, the electron currentis sent along the z direction across a metallic multilayer ele-ment with layers parallel to the x ,y plane. The elementconsists of a so-called “fixed” magnetic layer with magneti-zation pinned along the x axis, a nonmagnetic spacer, and a“free” magnetic layer exposed to the torque due to x-directedspin polarization that the electrons acquire from fixed layer.The dynamic behavior of the magnetization of the free layeris governed by the modified Landau–Lifshitz–Gilbert equa-tion with spin-transfer term included.1,2 This equation can bewritten in dimensionless form asdmdt= mdmdt− m heff − m ep , 1where the free-layer magnetization m and the effective fieldheff are normalized by the saturation magnetization Ms, timeis measured in units of Ms−1, =2.211105 rad /s /A /m is the gyromagnetic ratio,  is the phenomenologicaldamping constant, the unit vector ep gives the direction ofthe spin polarization along x direction in our case, and  isproportional to the current density Je as follows: = Je / 2eMS2d , where e is the electron charge, d is the thick-ness of the free layer, and  is the Planck constant. TheaPermanent address: “Al. I. Cuza” University, Department of Physics, Iasi700506, Romania.bAuthor to whom correspondence should be addressed. Electronic mail:LSpinu@uno.edu.JOURNAL OF APPLIED PHYSICS 103, 07B105 20080021-8979/2008/1037/07B105/3/$23.00 © 2008 American Institute of Physics103, 07B105-1Downloaded 19 Jul 2011 to 137.30.164.133. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsparameter  is positive when the electrons flow from the freeinto the fixed layer. The effective field consists of appliedfield and demagnetizing field, no further anisotropy beingconsidered.As ferromagnetic material, Co with 4MS=12 kG and=0.01 was chosen. The free magnetic layer is assumed tobe ellipsoid shaped, making the demagnetizing field uniformacross the entire layer. The ellipsoid’s principal axes aretaken along x, y, and z: long-axis length of 100 nm along Oxaxis, short-axis length of 75 nm along Oy axis, and thick-ness d=2 nm, leading to demagnetizing factors Nx=0.014,Ny =0.022, and Nz=0.964.All calculations presented in the following are per-formed for a maximum value of the current pulse of 0.5 mAi.e.,   =1.2210−2. The results are obtained by numericalintegration of Eq. 1 using a standard, self-optimizing, em-bedded Runge–Kutta algorithm.III. RESULTSA. Precession of the magnetization in a dc appliedfield and a pulsed currentIn this section, the switching of the magnetization underapplication of a dc magnetic field and of a pulse of current isdiscussed. For the current pulse rise and fall sinusoidal timedependence is assumed, and the pulse is characterized by thetriplets of numbers “rise time/pulse length/fall time,” with allvalues given in units of nanoseconds, the pulse length beingdefined as interval between the time when the pulse reaches1 /2 of its amplitude, and the time when the pulse drops tothe same value.In order to characterize the precessional switching ofmagnetization subjected to a dc applied magnetic field withdifferent strengths and orientations, taking into account alsothe effect of spin-transfer torque, we have used the switchingdiagram proposed by Bauer et al.,9 in which the final valueof the projection mx of the magnetization vector is displayedas a function of the strength and direction of the appliedfield. In Fig. 1 different scenarios of the magnetizationswitching in the nonpresence/presence of the spin-transfertorque, initiated by a dc magnetic field, are shown. Prior tothe applied field, the magnetization lies along negative x di-rection and the color in grayscale from black to white on thediagram indicates the final state of mx: black areas representmx=−1 nonswitching, white areas represent mx=1, and theintermediate values of mx are represented with shades ofgray. Figure 1a represents the switching diagram in the casewhen no spin-transfer torque is included. One can observethat switching is induced only when the applied field has acomponent along the positive x direction, and the separationboundary between black and white, corresponding toswitched and nonswitched regions, is very well defined,forming an astroidlike shape. The dramatic changes are eas-ily observed in the switching diagrams in the case taking intoaccount the spin-transfer torque term with different currentpulse lengths see Figs. 1b–1d.Increasing the current pulse length, the white color re-gion enlarges gradually to the left, gnawing the astroidlikeregion, and the switching can be induced also by a field witha negative component along the x direction. One observesthat for the longest current pulse see Fig. 1d almost entireinterior region of the astroid switches.From Fig. 1 we can see that even if the supplementarycurrent-induced torque is equivalent with a variable field, theglobal effect on the switching diagram is not a translation ofthe diagram, but a deformation on the x direction, with maxi-mum deformation at Hx=0.B. Precession of the magnetization in a pulsedapplied field and a pulsed currentIn this section we describe the switching of the magne-tization in a pulsed field and a pulsed current applied syn-chronously and asynchronously, respectively. Instead of thefinal state of mx, now we map the switching time, defined asthe time required for the magnetization to approach the equi-librium position along the positive x axis, until the torqueacting on the magnetization becomes negligible there is nosignificant ringing, after the cutoff of both pulses. In Figs. 2and 3 the black areas represent no switching, and the graylevel is scaled from dark gray for 6 ns to white for 12.5 ns.We now apply a 0.25 /0.25 /0.25 pulse of field, and constructthe switching diagrams of magnetization for different casesof the pulse length of the current pulse. The result is dis-played in Fig. 2. The final state is determined by the positionof the magnetization when the field pulse and the spin-current pulse are terminated. The switching time is found inthe range of few nanoseconds. Figures 2b–2d show thatas the time length of current pulse increases, the regions ofFIG. 1. Switching diagram as a function of the applied dc field, for differentvalues of the current pulse length 0.25 /TI /0.25: a no current applied, bTI=3.25 ns, c TI=4.25 ns, and d TI=7.25 ns. The direction of the spinpolarization pinned layer is along the negative x direction and the initialdirection of magnetization is also along the negative x direction mx=−1.Black areas represent mx=−1 nonswitching, white areas represent mx=1,and the intermediate values of mx are represented with shades of gray. Themaximum value of the current pulse is 0.5 mA.07B105-2 Pham et al. J. Appl. Phys. 103, 07B105 2008Downloaded 19 Jul 2011 to 137.30.164.133. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsstable switching into the positive x direction are enlargedcompared to the case of no spin-transfer torque current ap-plied, as shown in Fig. 2a. It is clear that the longer thepulse duration of the spin-transfer current, the stronger ef-fects of spin torque on switching diagram are observed. Wecome up to a conclusion that the spin torque plays a veryimportant role in driving switching of the magnetization. Im-proved switching of a MRAM cell, therefore, could beachieved by simultaneously addressing the short pulse offield and pulse of current.If in Fig. 2 the current pulse is starting at the same timewith the pulse of field synchronously, let us now investi-gate the influence of the starting time of the current pulse,which is denoted as t1, on the magnetization reversal. In Fig.3a the current pulse starts when the field pulse reaches itsmaximum value of the sinusoidal form. The white regionthe switching region is enlarged compared with the case ofsynchronous pulses Fig. 2b. If the pulse of current startswhen the pulse of field is finished see Fig. 3b the switch-ing region decreases again. Moreover, the pulse current delayis a critical parameter in the switching behavior, as it can beobserved from the bottom panels of Fig. 3. Thus, points Aand B with the same field pulse but different t1 delays havedifferent switching outcomes, with point B remaining in theinitial state no-switching and point A switching.IV. CONCLUSIONSThe dynamic behavior of magnetization under the com-petitive torques of a spin-polarized current and an externalmagnetic field has been derived. Our calculations are usefulto develop an understanding of the current-induced magneticswitching. It is seen from diagram presentations that theswitching properties are strongly enhanced by the presenceof the spin-transfer torque. Reversal processes can becomecomplex, but switching regions are enlarged. Also, it wasshown that the switching behavior is strongly dependent ontiming of the field and current pulses, i.e., synchronous orasynchronous.ACKNOWLEDGMENTSWork at AMRI was supported by DARPA under GrantNo. HR0011-07-1-0031. Calculations were performed oncomputational facilities provided by Louisiana Optical Net-work Initiative http://www.loni.org which is supported bythe Louisiana Board of Regents. This work was partiallysupported by Romanian CNCSIS under the GrantARELSWITCH.1J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 1996.2L. Berger, Phys. Rev. B 54, 9353 1996.3J. C. Slonczewski, U.S. Patent No. 5,695,864 9 December 1997.4M. Hosomi et al., Tech. Dig. - Int. Electron Devices Meet. 2005, 459.5Y. Huai and P. P. Nguyen, U.S. Patent No. 6,920,063 B2 19 July 2005.6F. B. Mancoff, B. N. Engel, and N. D. Rizzo, U.S. Patent No. 7,149,106B2 12 December 2006.7T. Devolder, C. Chappert, J. A. Katine, M. J. Carey, and K. Ito, Phys. Rev.B 75, 064402 2007.8T. Devolder, C. Chappert, and K. Ito, Phys. Rev. B 75, 224430 2007.9M. Bauer, J. Fassbender, and B. Hillebrands, Phys. Rev. B 61, 34102000.FIG. 3. Color online Time switching as a function of the maximum valueof a pulse field with the length 0.25 /0.25 /0.25, and for a current pulse withthe length 0.25 /0.25 /0.25 starting at the moment t1: a t1=0.25 ns and bt1=0.5 ns. Black areas represent no switching, and the gray level is scaledfrom dark gray for 6 ns to white for 12.5 ns. c and d Time evolution ofmx bold line, my thin line, and mz symbols at the positions A and Bindicated in the top diagrams.FIG. 2. Time switching as a function of the maximum value of a pulse fieldwith the length 0.25 /0.25 /0.25, for different values of the current pulselength 0.25 /TI /0.25: a no current applied, b TI=0.25 ns, c TI=0.5 ns,and d TI=0.75 ns. Black areas represent no switching, and the gray level isscaled from dark gray for 6 ns to white for 12.5 ns.07B105-3 Pham et al. J. Appl. Phys. 103, 07B105 2008Downloaded 19 Jul 2011 to 137.30.164.133. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions

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Switching behavior of a Stoner–Wohlfarth particle subjected to spin-torque effect

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