An array of 42 mum square, 3 mum thick garnet particles has been studied. The strong crystalline uniaxial anisotropy of these particles results in the stable remanent state being single domain with magnetization parallel to the film normal. Magneto-optic measurements of individual particles provide distribution statistics for the easy-axis switching field H-sw, and the in-plane hard-axis effective anisotropy field, H-eff, which induces the formation of a metastable stripe domain structure. Both H-sw and H-eff are much smaller than the crystalline anisotropy field. Micromagnetic simulations show that the small H-sw cannot be attributed to shape anisotropy, but is consistent with smooth, localized reductions in the crystalline anisotropy caused by defects in either the particles or the substrate

Abraham C.

G. Vértesy

M. J. Donahue

M. Pardavi-Horvath

Pardavi-Horvath M.

Vértesy G.

English

Donahue, M. J.

Vértesy, Gábor

Pardavi-Horváth, M.

Repository of the Academy's Library

JOURNAL OF APPLIED PHYSICS VOLUME 93, NUMBER 10 15 MAY 2003Defect related switching field reduction in small magnetic particle arraysM. J. DonahueNational Institute of Standards and Technology, Gaithersburg, Maryland 20899G. Ve´rtesyResearch Institute for Technical Physics and Materials Science, Hungarian Academy of Sciences,H-1525 Budapest, P.O.B. 49, HungaryM. Pardavi-HorvathThe George Washington University, Department of ECE, Washington, D.C. 20052~Presented on 13 November 2002!An array of 42 mm square, 3 mm thick garnet particles has been studied. The strong crystallineuniaxial anisotropy of these particles results in the stable remanent state being single domain withmagnetization parallel to the film normal. Magneto-optic measurements of individual particlesprovide distribution statistics for the easy-axis switching field Hsw , and the in-plane hard-axiseffective anisotropy field, Heff , which induces the formation of a metastable stripe domain structure.Both Hsw and Heff are much smaller than the crystalline anisotropy field. Micromagnetic simulationsshow that the small Hsw cannot be attributed to shape anisotropy, but is consistent with smooth,localized reductions in the crystalline anisotropy caused by defects in either the particles or thesubstrate. © 2003 American Institute of Physics. @DOI: 10.1063/1.1557399#I. INTRODUCTIONThe broad statistical distribution of switching fields ofsmall, nonellipsoidal shape particles in patterned magneticmedia is an important concern for future high density mag-netic recording, MRAM and sensor arrays, and magneticMEMS.Hysteresis loop measurements on individual particles ofa model system of a 2D array of single domain, single crystalgarnet particles have shown that the measured statistical dis-tribution of switching fields, Hsw , has a large standard de-viation, Hsw522.7 kA/m66.8 kA/m (285 Oe685 Oe),with the highest measured Hsw(max)’50 kA/m ~600 Oe!.1Some of the overall reduction of the average switching field,relative to the anisotropy field of the whole 1 cm2 chip, Hu5170 kA/m ~2100 Oe!, was related to the nonuniform mag-netization due to the shape and size of the particles. How-ever, the shape effect cannot explain the broad distribution ofthe switching fields of individual particles. The originalsingle crystalline magnetic garnet film has an exceptionallyhigh crystalline quality, with a very low dislocation density,no inclusions, and no visible edge, corner, or surface defectson the individual particles. Further experimental investiga-tions have shown that there are very weak crystalline defects,revealed only by magnetic defect decoration experiments,responsible for the local reduction and the broad distributionof the switching fields.2It is expected that the reduction of Hsw is due to local-ized crystalline defects, reducing the effective anisotropyfield. In the present work statistical data were collected onthe effective anisotropy field distribution of several hundredindividual particles along the hard axis, and compared to theeasy axis switching field distribution.Numerical 3D micromagnetic modeling confirms thatthe overall reduction of the switching field, relative to the7030021-8979/2003/93(10)/7038/3/$20.00crystalline anisotropy field, cannot be explained by the par-ticle shape demagnetizing field. The switching field and ef-fective anisotropy field reduction is consistent with a modelthat includes regions of reduced anisotropy caused by de-fects, in either the particles or the substrate, with the defect’sstress induced anisotropy field extending into the particle.3–5These results have a direct consequence for the case ofsmall metallic particles, where there is a much higher prob-ability for random defects, such as grain boundaries, inclu-sions, substrate–film interface effects, and dislocation densi-ties and associated stress fields that are much higher than inthis model system.II. EXPERIMENTSThe experiments were performed on a regular 2D squarearray of particles, etched into a single crystalline magneticgarnet film ~substituted Y3Fe5O12), grown epitaxially on anonmagnetic GGG (Gd3Ga5O12) substrate. The size of theparticles is 42 mm342 mm33 mm, separated by 12 mmwide grooves. The 5 mm square sample contains about 104particles. Garnet crystals are extremely brittle, and the en-ergy of dislocation formation is very high, such that largegarnet boules are regularly grown with a dislocation densityof less than 10 cm23. SEM observations show the high qual-ity of the edges and corners of the etched particles.The mean value of the uniaxial anisotropy field, Hu ,was determined on the patterned film from differences be-tween the middle slopes of saturation hysteresis loops, mea-sured with the external field oriented in the parallel and per-pendicular directions to the easy axis. The same result wasobtained using both the vibrating sample magnetometer~VSM! and magneto-optical methods. The magnetization ofthe sample, measured using VSM and SQUID, was found tobe 12.7 kA/m (4pM s5160 G), which is very low compared8 © 2003 American Institute of Physics7039J. Appl. Phys., Vol. 93, No. 10, Parts 2 & 3, 15 May 2003 Donahue, Ve´rtesy, and Pardavi-Horvathto the uniaxial anisotropy field Hu . As a result, the particleshave strong uniaxiality, characterized by Q5Hu /4pM s.10, ensuring that the particles are single domain, havingonly two stable magnetic states, either ‘‘up’’ or ‘‘down’’along the easy axis, normal to the film plane. Each particlehas a rectangular hysteresis loop, and the switching of thewhole system proceeds by consecutive switching of indi-vidual particles. The particles were found to be only weaklyinteracting.6Hysteresis loops of individual particles were measuredmagnetooptically ~MO! in the Faraday geometry, with simul-taneous visual observation of switching events. The compo-sition of the garnet is optimized to have a very high Faradayeffect, leading to a very high contrast in MO measurements.Switching fields along the easy axis have been measuredearlier.7 Each measurement was started from the saturatedstate along the easy axis.The effective anisotropy field of many individual par-ticles was systematically measured magneto-optically, by fo-cusing the light beam on a single particle. Before each mea-surement the particles were saturated in a normal magneticfield, parallel to the easy axis. Then an in-plane magneticfield was increased from zero, and the field at which stripeswere nucleated was detected as a sudden change in the lightintensity vs magnetic field curve.The stripe domain state is the ground state of the mag-netically soft epitaxial garnet layer before it is structured intothe 2D array. Magnetization proceeds in this case by domainwall motion. In the structured state, however, the stable de-magnetized state is the ‘‘checkered’’ pattern shown in Fig.1~a!, where the magnetization of each individual particle isoriented along the easy axis. The stripe domain pattern, dis-played in Fig. 1~b!, is obtained by application of an in-planefield. This state is only metastable; application of a moderatefield of 6 kA/m60.2 kA/m (75 Oe63 Oe) normal to thefilm plane collapses the stripes and saturates the material.Reversing the normal field from this point switches the indi-vidual particles one by one, eventually reaching again thestable demagnetized state of Fig. 1~a!.III. RESULTSThe distribution of the switching fields for 370 particles,measured as the half-width of the easy-axis hysteresis loopFIG. 1. ~a! Demagnetized state of 4 garnet particles on a 2D array, havingtwo stable states of magnetization, ‘‘dark’’ and ‘‘light’’ ~checkered pattern!;~b! Metastable demagnetized state of the same four particles ~stripe domainstructure!. Particle size: 42 mm342 mm33 mm.of individual particles, and the distribution of the effectiveanisotropy field, measured as the hard axis saturating field on462 individual particles, are shown in Fig. 2. The switchingfield distribution for this set of particles has a mean valueHc520 kA/m ~250 Oe!, with a standard deviation of 10.4kA/m ~131 Oe!. The highest measured switching field is 44kA/m ~550 Oe!, in agreement with our previous data on simi-lar samples.It is expected that the reduction of Hsw is due to local-ized crystalline defects, causing a reduced effective anisot-ropy field. Our previous measurements revealed very goodquantitative correlation between the strength of the defect-domain wall interaction, and the magnitude of the switchingfield.2 Defects reduce the local nucleation field, thus decreas-ing the switching field of the particles. Figure 2 shows thatthe distribution of Heff is much broader than the switchingfield distribution, and the shape of the distribution differsfrom that of Hsw . There is a broad high field component ofHeff with the highest observed value above 120 kA/m ~1500Oe!.The highest switching field, Hsw(max), is much lowerthan Heff(max),Hu . This observation shows that the reduc-tion of the switching field is most dramatic for very strongdefects having low Heff<Hc . However, reduction of theswitching field due to weaker defects is also observed. Thisimplies that any defect can be detrimental for a small mag-netic device, reducing the characteristic field by a dispropor-tionately large amount.IV. MICROMAGNETIC MODELINGComputer simulations were performed to help interpretthe experimental results. We used the public domainOOMMF micromagnetic package8 for these simulations. Thevalues used for material parameters (M s512.7 kA/m, Ku51333 J/m3, A53310212 J/m) were representative of theexperimental samples. The simulation discretization cellswere 15.625 nm cubes, which is one-third themagnetocrystalline-exchange length AA/K547 nm, and lessthan one-tenth the magnetostatic-exchange lengthAA/(0.5m0M s2)5170 nm. The stopping criterion for identi-fication of equilibrium states was uM3Husup /M s2,0.008.To gauge the importance of shape anisotropy in theswitching mechanism, simulations were performed onFIG. 2. Distribution of the switching field along the easy axis, normal to theparticle (n5370 particles!, and of the effective anisotropy field in-plane,along the hard axis (n5462).7040 J. Appl. Phys., Vol. 93, No. 10, Parts 2 & 3, 15 May 2003 Donahue, Ve´rtesy, and Pardavi-Horvathdefect-free, 2 mm32 mm3500 nm and 4 mm34 mm3125 nm models. To break the problem symmetry, the ap-plied field was aligned 1° off the film normal. The switchingfields were found to be approximately 145 kA/m ~1820 Oe!and 140 kA/m ~1760 Oe!, respectively. These results are inclose agreement with results predicted by the Stoner–Wohlfarth uniform magnetization model for particles withthese geometries. However, the micromagnetic simulationsshow that the switching process initiates by nucleation of areversed, cylindrical domain in the middle of the particle,and proceeds by radial domain growth from the center to-wards the edges of the sample. Little variation in the mag-netization along the film normal axis was detected, presum-ably because the demagnetization field is relatively uniformin the central region of these films. Additional thin-filmsimulations were performed on smaller models, and in allcases the switching field agreed with the Stoner–Wohlfarthestimate. Although the reversal as a whole is not by uniformrotation, the central regions essentially behave as Stoner–Wohlfarth islands.Simulations were also performed where the problemsymmetry was broken by canting the crystalline easy axisaway from the film normal. Reversal was found to proceed inthe same manner as described above, with switching fieldsagreeing with Stoner–Wohlfarth calculations.Although the experimental particles are too large tosimulate directly, the apparent scale independence of theseresults suggests that they would hold for that system as well.The switching fields predicted by the above model are closeto an order of magnitude larger than the average switchingfield observed experimentally. Since the defect-free simula-tions cannot explain the experimental results, we performedsimulations on particles with isolated defects. The defectswere modeled as localized reductions in the anisotropy con-stant Ku . In the first, simple defect model, we introduced asmall region with reduced Ku5Ku ,defect into the interior ofthe sample, with a sharp transition to Ku ,bulk at the boundaryof the defect. If this region was larger than about 500 nm,then the magnetization in the defect was found to reverse atthe anisotropy field in the defect. However, the region ofreversed magnetization did not expand beyond the confinesof the defect region if the applied field was smaller than(Hu ,bulk2Hu ,defect)/4. In this case, the reversal was found tobe a two step process: ~1! nucleation of a reversed domaininside the defect, and ~2! propagation of the reversed domainthroughout the sample. This problem has been studied ana-lytically in the case of a 1D domain wall.9 While the geo-metric structure of the defect is expected to have some effect,our simulations were in good agreement with the results ofthe 1D study.In the simple defect model, the lowest attainable magne-tization reversal field for the particle as a whole occurs whenthe nucleation field and the propagation field are equal, i.e.,at one-fifth the bulk anisotropy field. Since Hu ,bulk5170 kA/m in the experimental sample, the smallest switch-ing field allowed by this model is 34 kA/m, significantlylarger than the average experimentally observed switchingfield ~20 kA/m!. However, the propagation field can be re-duced by replacing the anisotropy step with a continuoustransition region, as would be expected for a stress inducedanisotropy field decaying with distance from, for example,an inclusion in the substrate. For simplicity, we modeled thistransition as a linear ramp.10 The propagation field then de-pends upon the slope of the ramp. We found a slope of 1.23109 J/m4 sufficiently gradual to produce a propagationfield below 20 kA/m, corresponding to a transition length of1 mm in the experimental samples. It appears that this lengthmay be shortened by increasing the slope as one moves upthe ramp, but examination of this is left for future research.ACKNOWLEDGMENTSOne of the authors ~G.V.! is supported by the HungarianScientific Research Fund through Projects Nos. T-026153and T-035264.1 M. Pardavi-Horvath, G. Ve´rtesy, B. Keszei, Z. Ve´rtesy, and R. D. Mc-Michael, IEEE Trans. Magn. 35, 3871 ~1999!.2 G. Ve´rtesy and M. Pardavi-Horvath, Physica B 306, 251 ~2001!.3 M. Pardavi-Horvath, in Progress in Crystal Growth and Characterization~Pergamon, London, 1982!, Vol. 5, pp. 175–220.4 M. Pardavi-Horvath, IEEE Trans. Magn. 21, 1694 ~1985!.5 G. Ve´rtesy, M. Pardavi-Horvath, I. Tomas, and L. Pust, J. Appl. Phys. 63,1694 ~1988!.6 M. Pardavi-Horvath and G. Ve´rtesy, IEEE Trans. Magn. 30, 124 ~1994!.7 M. Pardavi-Horvath, IEEE Trans. Magn. 32, 4458 ~1996!.8 M. J. Donahue and D. G. Porter, Interagency Report NISTIR 6376, Na-tional Institute of Standards and Technology, Gaithersburg, MD, 1999.9 A. Aharoni, Phys. Rev. 119, 127 ~1960!.10 C. Abraham and A. Aharoni, Phys. Rev. 119, 127 ~1960!.

Defect related switching field reduction in small magnetic particle arrays

Crossref

Defect related switching field reduction in small magnetic particle arrays

Abstract

Similar works

Full text

Available Versions

Repository of the Academy's Library

Crossref