Mean field model for ferromagnetic nanowire arrays based on a mechanical analogy

Transcription

1 IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 25 (2013) (6pp) doi: / /25/3/ Mean field model for ferromagnetic nanowire arrays based on a mechanical analogy Costin-Ionuţ Dobrotă and Alexandru Stancu Faculty of Physics, Alexandru Ioan Cuza University of Iasi, Iasi , Romania costin.dobrota@stoner.phys.uaic.ro and alstancu@uaic.ro Received 12 September 2012, in final form 11 November 2012 Published 10 December 2012 Online at stacks.iop.org/jphyscm/25/ Abstract Nanowire arrays have typical distributions of coercive and interaction fields, as revealed in experiments by means of the first-order reversal curve (FORC) method. In an axial applied field, each nanowire is subjected to a state dependent interaction field created by all wires from the array, which strongly influences the switching fields. A mean field model based on Preisach Krasnosel skii Pokrovskii (PKP) hysterons is able to explain the interplay between interactions and critical fields in nanowire arrays and the subtle way in which switching fields are emphasized in FORC diagrams. (Some figures may appear in colour only in the online journal) 1. Introduction Systems of ordered ferromagnetic nanowires have been extensively studied in recent years due to their potential in the field of technological applications such as magnetic sensors, advanced data storage and as elements in microwave devices [1 3]. Tailoring their magnetic properties by means of geometrical characteristics, such as the nanowire dimensions and the array periodicity, represents a huge advantage for specific practical applications based on nanowire arrays. Two important issues are involved in the magnetic response of a nanowire array to the external field, especially when it is applied parallel to the nanowire s axis. On one hand, the shape anisotropy, basically due to the cylindrical form with high aspect ratio, tends to maintain the magnetization direction along the wire axis. In modern fabrication processes, especially based on anodized alumina templates, a better control of the wire diameters can be obtained and consequently intrinsic coercive fields of the magnetic wires have almost the same value, which is equivalent to a very small dispersion of the coercive field distribution. On the other hand, interwire magnetostatic interactions significantly affect magnetic properties, mainly magnetization switching of the nanowires. Considering an axial applied field, the interaction field appears as a collective effect of the fictitious magnetic charges located at the ends of the nanowires. While the length of the wires is much higher compared with their diameter, it is natural to consider long-range interaction fields that generate a mean interaction field over the whole nanowire array [4]. A powerful experimental tool used to evaluate coercive fields and interactions in any ferromagnetic system is the first-order reversal curves (FORC) diagram method, which provides a distribution of coercive and interaction fields, called FORC distribution (usually represented as a contour plot diagram). Initially developed by Mayergoyz [5, 6] as an identification procedure for the classical Preisach model (CPM) [7], the FORC protocol is now extensively used in many laboratories in magnetic characterization of ferromagnetic samples even when they are not necessarily CPM systems complying with the representation theorem [5]. In Preisach modeling, mean field interactions dependent on the magnetic state of the sample were described by Della Torre [8] as a version of the initial model, called the moving Preisach model (MPM). Pike and co-workers have extended the applicability of the FORC method to any hysteretic system [9], and the link between the mean field interactions of magnetizing/demagnetizing type and FORC diagram features was first evidenced by Stancu et al [10] /13/ $ c 2013 IOP Publishing Ltd Printed in the UK & the USA

2 J. Phys.: Condens. Matter 25 (2013) C-I Dobrotă and A Stancu 5. Conclusion Starting from a mechanical approach, we have proposed a simple model based on PKP hysterons representing negative or positive mean fields in which the reversals take place. Using a small number of PKP hysterons we have provided a FORC diagram with specific distributions, which represents the basic diagram for ferromagnetic nanowire arrays. Magnetization reversals in nanowires were correlated with the mean field evolution reflected in the FORC diagram. Generally, a negative mean field characterizes a nanowire array, but switching events of the nanowires with slightly higher intrinsic coercive fields are governed by a positive mean field, which leads to higher apparent coercive fields experimentally observed for nanowire arrays. An advantage of the proposed model is the fact that a small set of PKP hysterons can be used for better fitting of the experimental FORC diagrams in order to obtain information about switching events. A refined analysis of the evolution of the interaction fields, based on a physical approach, provides a better insight into the specific switching phenomena in nanowire arrays. Tailoring the apparent coercive fields, by means of the interaction fields, could be useful in applications requiring high coercivities. Acknowledgments This work was supported by the European Social Fund in Romania, under the responsibility of the Managing Authority for the Sectorial Operational Programme for Human Resources Development (grant POSDRU/88/1.5/S/47646) and by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE [IDEI-EXOTIC No. 185/ ]. References [1] McGary P D, Tan L, Zou J, Stadler B J H, Downey P R and Flatau A B 2006 J. Appl. Phys B310 [2] Nielsch K, Wehrspohn R B, Barthel J, Kirschner J, Gösele U, Fischer S F and Kronmüller H 2001 Appl. Phys. Lett [3] Kuanr B K, Veerakumar V, Marson R, Mishra S R, Camley R E and Celinski Z 2009 Appl. Phys. Lett [4] Dobrotă C I and Stancu A 2012 Physica B [5] Mayergoyz I D 1986 IEEE Trans. Magn [6] Mayergoyz I D 2003 Mathematical Models of Hysteresis and Their Applications (Amsterdam: Elsevier) [7] Preisach F 1935 Z. Phys [8] Della Torre E 1966 IEEE Trans. Audio Electroacoust [9] Pike C R, Roberts A P and Verosub K L 1999 J. Appl. Phys [10] Stancu A, Pike C, Stoleriu L, Postolache P and Cimpoesu D 2003 J. Appl. Phys [11] Béron F 2008 PhD Thesis Université de Montréal [12] Béron F, Clime L, Ciureanu M, Ménard D, Cochrane R W and Yelon A 2006 IEEE Trans. Magn [13] Lavin R, Denardin J C, Escrig J, Altbir D, Cortes A and Gomez H 2008 IEEE Trans. Magn [14] Peixoto T R F and Cornejo D R 2008 J. Magn. Magn. Mater. 320 e279 [15] Pirota K R, Béron F, Zanchet D, Rocha T C R, Navas D, Torrejón J, Vazquez M and Knobel M 2011 J. Appl. Phys [16] Kou X, Fan X, Dumas R K, Lu Q, Zhang Y, Zhu H, Zhang X, Liu K and Xiao J Q 2011 Adv. Mater [17] Vega V, Rosa W O, García J, Sánchez T, Santos J D, Béron F, Pirota K R, Prida V M and Hernando B 2012 J. Nanosci. Nanotechnology [18] Béron F, Carignan L P, Ménard D and Yelon A 2008 IEEE Trans. Magn [19] Rotaru A, Lim J H, Lenormand D, Diaconu A, Wiley J B, Postolache P, Stancu A and Spinu L 2011 Phys. Rev. B [20] Krasnosel skii M A and Pokrovskii A V 1989 Systems with Hysteresis (New York: Springer) [21] Visintin A 1994 Differential Models of Hysteresis (New York: Springer) [22] Iyer R V and Tan X 2009 IEEE Control Syst. Mag [23] Katzgraber H G, Pazmandi F, Pike C R, Liu K, Scalettar R T, Verosub K L and Zimanyi G 2002 Phys. Rev. Lett [24] Wernsdorfer W, Doudin B, Mailly D, Hasselbach K, Benoit A, Meier J, Ansermet J P and Barbara B 1996 Phys. Rev. Lett [25] Hertel R 2001 J. Appl. Phys [26] Bobbio S, Miano G, Serpico C and Visone C 1997 IEEE Trans. Magn [27] Matsuo T and Shimasaki M 2005 IEEE Trans. Magn [28] Pike C R, Ross C A, Scalettar R T and Zimanyi G 2005 Phys. Rev. B

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