In this paper, we propose a method for a synthetic antiferromagnet structure’s critical curve determination. The method is based on reversible susceptibility’s singularities detection, as the magnetic field is swept along easy axis, in both positive and negative direction, while a hard axis bias field is also applied. By performing susceptibility measurements with different values of the bias field, the critical curve can be determined. Knowing the critical curve of a synthetic antiferromagnetic structure is essential for devices such as magnetic random access memories

Cimpoesu, Dorin

Radu, Cosmin

Spinu, Leonard

Stancu, Alexandru

English

University of New Orleans

University of New Orleans ScholarWorks@UNO Physics Faculty Publications Department of Physics 2008 Measurement of the critical curve of a synthetic antiferromagnet Cosmin Radu University of New Orleans Dorin Cimpoesu University of New Orleans Alexandru Stancu Leonard Spinu University of New Orleans Follow this and additional works at: https://scholarworks.uno.edu/phys_facpubs  Part of the Physics Commons Recommended Citation Appl. Phys. Lett. 93, 022506 (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. Measurement of the critical curve of a synthetic antiferromagnetCosmin Radu,1 Dorin Cimpoesu,2,a Alexandru Stancu,3 and Leonard Spinu1,b1Advanced Materials Research Institute and Department of Physics, University of New Orleans,New Orleans, Louisiana 70148, USA2Advanced Materials Research Institute, University of New Orleans, New Orleans, Louisiana 70148, USA3Department of Physics, “Al. I. Cuza” University, Iasi 700506, RomaniaReceived 22 April 2008; accepted 11 June 2008; published online 16 July 2008In this paper, we propose a method for a synthetic antiferromagnet structure’s critical curvedetermination. The method is based on reversible susceptibility’s singularities detection, as themagnetic field is swept along easy axis, in both positive and negative direction, while a hard axisbias field is also applied. By performing susceptibility measurements with different values of thebias field, the critical curve can be determined. Knowing the critical curve of a syntheticantiferromagnetic structure is essential for devices such as magnetic random access memories.© 2008 American Institute of Physics. DOI: 10.1063/1.2953439Magnetization reversal is a paramount technological pa-rameter in designing devices using magnetic materials asnonvolatile memories, reading heads, or sensors. Due topackaging constraints, magnetic devices usually have bidi-mensional geometries as thin films and multilayers, wherethe magnetization switching occurs in the plane of the de-vice. Thus, controlling the two-dimensional 2D magneticswitching is technologically valuable in devices using designideas such as in magnetic random access memoriesMRAM. The 2D switching can be described elegantly withthe concept of critical curve CC, which is the locus ofin-plane fields at which the irreversible magnetization rever-sal occurs.1,2 Slonczewski1 introduced the idea of CC whenhe used a geometrical approach to find the equilibrium posi-tions of magnetization for a Stoner–Wohlfarth particle.3Soon, it was understood that CC is not only a theoreticalconcept to describe the magnetization reversal, but also animportant technological parameter for magnetic devices.4–7Thus, methods for CC determination were proposed and theobtained experimental CC were compared against the astroidcorresponding to a magnetic uniaxial system.7,8As the technological applications of magnetic structuresbecame more complex, multifilm structures started to replacesingle films. One example of such multifilm structures is thesynthetic antiferromagnet SAF, which is a sandwich oftwo ferromagnetic thin films antiferromagnetically coupledthrough a nonmagnetic metallic spacer, usually Ru. SAF hasmany technological applications as hard layer of exchangecoupled composite media,9 soft underlayer for perpendicularrecording,10 pinned and free layers for MRAM cells,11 harddisk reading heads, or magnetic sensors.12 The performanceof the devices using SAF structures relies heavily on theirswitching characteristics, which are governed by the indi-vidual reversal of the ferromagnetic layers, and the interlayerinteraction. Since simple theory of single films does notwork easily for coupled films, an equivalent approach had tobe developed.13–15 In the case of SAF, the CC is more com-plex, as there are two degrees of freedom, the orientations 1and 2 of both ferromagnetic layers, assuming that each layerbehaves as a single domain. The CC for SAF is obtained asthe envelope of the in-plane field trajectories giving a con-stant angle to the magnetization of one layer, leaving theorientation of the other layer as a variable. Depending of thecoupling strength between the two ferromagnetic layers, CCevolves from a simple astroid at zero coupling to a morecomplicated curve for larger coupling values see Fig. 5 inRef. 16. CCs of SAF structures have been extensivelystudied theoretically due to their importance for toggleMRAM.16–20 However, in spite of its importance, methods toexperimentally determine CC for coupled films are still lack-ing and a possible reason behind this situation is presentedbelow.The free energy F landscape for a magnetic system at agiven applied magnetic field presents a series of minima andmaxima. At equilibrium, the system is in one of its stablestates corresponding to one of the energy minima. As thefield changes, the configuration of maxima and minima isaltered and the stable states of magnetization will shift, and ifprecessional effects are neglected, the system will remain inits state of free energy minimum. However, for a criticalvalue, the minimum will evolve into a maximum or a saddlepoint and the stable state will switch to a neighboring mini-mum. The CC is in essence the locus of these critical fieldvalues but not the locus of free energy’s critical points, asthe name may suggests. In the case of a single magneticfilm, a sufficient condition for a critical state is to havesimultaneously dF /d=0, d2F /d2=0, and d3F /d30,where the angle  describes the magnetization’s orientation.For coupled films as SAF, the problem is more complicatedbecause it requires one to find the critical states of a functionfree energy of two variables 1 and 2. In this case, thecritical states can be found through the solutions of thesufficient condition: F /1=F /2=0 and 1 ,2= 2F /122F /22− 2F /122=0. Caution must bepaid to the fact that not necessarily all the solutions are criti-cal points. In general, this problem is not trivial and onlyusing numerical methods one can obtain the CC. These the-oretical intricacies are reflected also in the ability to experi-mentally determine the CC of a SAF.In this paper, we show that the method of reversiblesusceptibility can be used to successfully determine the CCof SAF structures. Recently we have used susceptibility toaOn leave from: Department of Physics, “Al. I. Cuza” University, Iasi700506, Romania.bElectronic mail: LSpinu@uno.edu.APPLIED PHYSICS LETTERS 93, 022506 20080003-6951/2008/932/022506/3/$23.00 © 2008 American Institute of Physics93, 022506-1Downloaded 08 Apr 2011 to 137.30.164.164. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsexperimentally find the CC for different magnetic filmstructures21,22 and we have shown that this method is moresensitive than the magnetic and resistance hysteresis meth-ods. In a previous paper,23 we have shown that for a SAFsystem the in-plane diagonal elements of the reversible sus-ceptibility tensor  varies inversely proportional with thefree energy discriminant the determinant of free energy’sHessian computed at the equilibrium position 10,20, i.e.,10,20. The tensor ij =Mi /Hj is obtained as the de-rivatives of components of magnetization M with respect tocomponents of applied field H, and i and j refer to the direc-tions e.g., x, y, and z in Cartesian coordinates.23 In this way,the problem of finding CC of coupled magnetic films is re-duced to the determination of the singular points of suscep-tibility. Consequently, the problem of experimentally findingCC of coupled magnetic films is naturally solved by probingthe reversible susceptibility for different in-plane appliedfields and identifying the susceptibility’s peaks located at theswitching fields. In order to prove the suitability of thismethod, we have simulated the reversible susceptibility’sfield variation with the in-plane dc field applied at differentorientations H, and we have built the CC see Fig. 1. Thesusceptibility and hysteresis curves for two different orienta-tions, for a symmetric SAF with an exchange couplinghJ=0.5, are presented in the middle and the bottom panels ofFig. 1, respectively, the magnetic field sweeping from posi-tive saturation to negative saturation continuous line andthen back to positive saturation dotted line. Depending onapplied field orientation, the magnetizations’ switching canbe more or less visible in the hysteresis loops. For a fieldapplied along the second direction denoted with II inFig. 1, the switching is very well defined, while for the firstorientation denoted with I, the switching events are notvery visible. However, one observes that the susceptibilityversus field curves present well defined peaks. For the firstorientation, the susceptibility curve has two peaks denotedwith 1 and 2 in Fig. 1 when the dc field sweeps from posi-tive saturation, when the field crosses the interior CC corre-sponding to saturation and the exterior CC correspondingto switching, and only one peak for the second orientation,because in this case the field trajectory crosses only the ex-terior CC. When the field trajectory crosses the CC for satu-ration, both reversible susceptibility’s denominator and nu-merator are zero and the reversible susceptibility has only aremovable singularity and will not determine always a “verysharp peak” in susceptibility. When the field trajectorycrosses the CC for switching, only the denominator is zeroand the reversible susceptibility has a pole or an essentialFIG. 2. Color online CCs top for a symmetric SAF with hJ=0.5, as themagnetic field is swept along easy axis, and a hard axis bias field is alsoapplied. Middle: magnetization’s projection on sweeping field’s direction.FIG. 1. Color online CCs top for a symmetric SAF with a couplinghJ=0.5, determined form susceptibility’s curves bottom peaks locations, asthe in-plane dc field is applied at different orientations. Middle: the projec-tion of the normalized magnetization on the applied field’s direction.022506-2 Radu et al. Appl. Phys. Lett. 93, 022506 2008Downloaded 08 Apr 2011 to 137.30.164.164. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionssingularity, which is very visible in susceptibility.However, the method presented in Fig. 1 does not revealthe entire interior CC because there are portions where thefield trajectory is “almost” tangent to it, and a very smallincrement of H is required in order to build the entire CC.Nevertheless, in an experiment, the H’s increment cannot bearbitrarily small, and a strategy to make these portions “vis-ible” is to use field scans that do not pass through origin,applying a bias field perpendicular to easy axis and a sweep-ing field parallel to easy axis see Fig. 2. In order to betteridentify the susceptibility peaks and to build up the satura-tion CC, both xx and yy, measured along and perpendicularto easy axis, respectively, can be used. For example in Fig. 2,the xx peaks 1 and 3 are more visible in the case I, com-pared with yy peaks 1 and 3, while in the case II the yypeaks 5 and 7 are more pronounced.For applications such as MRAM, the exchange couplingbetween the two layers should be strong enough to maketoggle writing method possible, and in Fig. 3 the simulatedcurves for hJ=2 are presented. With the increase of hJ, theCC for saturation expands and becomes the outermost curve,the inner curves being the CC for switching. When the fieldcrosses only the outermost CC, both the projection of thetotal magnetic moment on the sweeping field and suscepti-bility curves are reversible when the field decreases and thenincreases. In this case, the intersection with the saturation CCdetermines only a shoulder still more visible than in thehysteresis loops and not a very well defined peak in thesusceptibility curves. Moreover the susceptibility curve hastwo peaks denoted with i and ii in Fig. 3 which are notdetermined by intersections with CC. These “false” peakscan be eliminated by looking only for the peaks of the curveswhich are not reversible, like in case II in Fig. 3.In summary, a sensitive method for SAF CCs determi-nation, based on reversible susceptibility singularities detec-tion, is proposed. It was shown that this method can revealthe entire CC for both low and high values of the exchangecoupling. Also, the method is general and can be applied forcoupled films with nonidentical asymmetrical layers. Com-paring the hysteresis and susceptibility curves, it was shownthat susceptibility measurements are more appropriate forswitching investigations of the SAF systems.Work at AMRI was supported by DARPA under GrantNos. HR0011-05-1-0031 and HR0011-07-1-0031. This workwas partially supported by Romanian CNCSIS under GrantARELSWITCH. LS thanks J. C. Slonczewski for kindlysending Ref. 1, which is not publically available.1J. C. Slonczewski, IBM Research Center Memorandum R. M. Report No.003.111.224.2A. Thiaville, J. Magn. Magn. Mater. 182, 5 1998.3E. C. Stoner and E. P. Wohlfarth, Philos. Trans. R. Soc. London, Ser. A240, 599 1948; IEEE Trans. Magn. 27, 3475 1991.4C. C. Shir and Y. S. Lin, J. Appl. Phys. 50, 4246 1979.5J. S. Best, J. Appl. Phys. 52, 2367 1981.6B. D. Schrag, A. Anguelouch, G. Xiao, P. Trouilloud, Y. Lu, W. J.Gallagher, and S. S. P. Parkin, J. Appl. Phys. 87, 4682 2000.7A. Anguelouch, B. D. Schrag, G. Xiao, Y. Lu, P. L. Trouilloud, R. A.Wanner, W. J. Gallagher, and S. S. P. Parkin, Appl. Phys. Lett. 76, 6222000.8J. Z. Sun, J. C. Slonczewski, P. L. Trouilloud, D. Abraham, I. Bacchus, S.S. P. Parkin, and R. H. Koch, Appl. Phys. Lett. 78, 4004 2001.9S. Hernandez, M. Kapoor, and R. H. Victora, Appl. Phys. Lett. 90,132505 2007.10S. C. Byeon, A. Misra, and W. D. Doyle, IEEE Trans. Magn. 40, 23862004.11L. Savtchenko, B. N. Engel, N. D. Rizzo, M. F. Deherrera, and J. A.Janesky, U.S. Patent 6,545,906 B1 8 April 2003.12A. Veloso, P. P. Freitas, and L. V. Melo, IEEE Trans. Magn. 35, 25681999.13E. Goto, N. Hayashi, T. Miyashita, and K. Nakagawa, J. Appl. Phys. 36,2951 1965.14H. Chang, IBM J. Res. Dev. 6, 419 1962.15H. Chang, J. Appl. Phys. 35, 770 1964.16H. Fujiwara, S. Y. Wang, and M. Sun, Trans. Magn. Soc. Jpn. 4, 1212004.17H. Fujiwara, S. Y. Wang, and M. Sun, J. Appl. Phys. 97, 10P507 2005.18S. Y. Wang and H. Fujiwara, J. Magn. Magn. Mater. 286, 27 2005.19D. C. Worledge, IBM J. Res. Dev. 50, 69 2006.20D. C. Worledge, P. L. Trouilloud, and W. J. Gallagher, Appl. Phys. Lett.90, 222506 2007.21L. Spinu, H. Pham, C. Radu, J. C. Denardin, I. Dumitru, M. Knobel, L. S.Dorneles, L. F. Schelp, and A. Stancu, Appl. Phys. Lett. 86, 0125062005.22L. Spinu, A. Stancu, Y. Kubota, G. Ju, and D. Weller, Phys. Rev. B 68,220401R 2003.23D. Cimpoesu, A. Stancu, and L. Spinu, J. Appl. Phys. 101, 09D1122007.FIG. 3. Color online Same as Fig. 2, but with hJ=2.022506-3 Radu et al. Appl. Phys. Lett. 93, 022506 2008Downloaded 08 Apr 2011 to 137.30.164.164. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

Measurement of the critical curve of a synthetic antiferromagnet

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Measurement of the critical curve of a synthetic antiferromagnet

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