Circular single domains in hemispherical small size Permalloy clusters
Clodoaldo I. L. de Araujo, Jakson M. Fonseca, João P. Sinnecker, Rafael G. Delatorre, Nicolas G. Garcia, André A. Pasa
aa r X i v : . [ c ond - m a t . m e s - h a ll ] N ov Circular single domains in hemispherical Permalloy nanoclusters
Clodoaldo I. L. de Araujo, a) Jakson M. Fonseca, Jo˜ao P. Sinnecker, Rafael G. Delatorre, Nicolas Garcia, and Andr´e A. Pasa Departamento de F´ısica, Universidade Federal de Vi¸cosa, 36570-900, Vi¸cosa-MG,Brazil. Centro Brasileiro de Pesquisas F´ısicas, 22290-180, Rio de Janeiro-RJ, Brazil Departamento de F´ısica, Universidade Federal de Santa Catarina, 88040-900, Florian´opolis-SC,Brazil (Dated: August 6, 2018)
We have studied ferromagnetic Permalloy clusters obtained by electrodeposition on n-type silicon. Magneti-zation measurements reveal hysteresis loops almost independent on temperature and very similar in shape tothose obtained in nanodisks with diameter bigger than 150nm. The spin configuration for the ground state,obtained by micromagnetic simulation, shows topological vortices with random chirality and polarization.This behavior in the small diameter clusters ( ∼ . In nanostructured ferromagnetic mate-rials, the magnetization fundamental state is strongly de-pendent on the geometry and other energetic configura-tions are oftentimes more likely, e.g. nanodisks, whichinduce curvature of spin in plane with small displace-ment of spin from the border to the center, in order tokeep the exchange interaction and cancel the dipolar en-ergy. In the nanodisk center, the distance among spinsbecomes so small that the magnetization turns out of theplane and this behavior makes the nanomagnet acts asa single giant spin . When the disk thickness is muchsmaller then its diameter, the magnetization aligns as asingle domain in plane . Its behavior is also importantin nanostructured ellipsoidal monodomains, which are of-ten applied in different collective geometries, in systemsknowed as artificial spin ice, where interesting phenom-ena arise as emergent magnetic monopoles . The cir-cular monodomain nanomagnets have been investigatedin different systems, e.g. vortex in nanodisks , antidotssamples or skyrmions that just differ from vortex withthe spin in the borders turned out of the plane in di-rection opposite to the core polarization. Skyrmionsfrequently emerge in chiral materials under perpendic-ular external magnetic field with Dzyaloshinskii-Moriya( DM ) interaction , and without DM in systems withparticular geometries . The topological stability in thesestructures, point them as promising in applications suchas magnetic memory storage or logic devices , withcore and border polarization or chirality changed by ex-ternal excitation such as ( AC ) alternate current and mag- a) Departamento de F´ısica, Universidade Federal de Vi¸cosa, 36570-900, Vi¸cosa-MG, Brazil.; Electronic mail: [email protected] netic field or spin polarized currents. In general, thesestructures are fabricated by sophisticated techniques asMolecular Beam Epitaxy (MBE), e − beam nanolitogra-phy or Focused Ion Beam (FIB).In this work, we have utilized electrodeposition tech-nique, which is less expensive, faster and more suitablein production lines than the techniques cited above, tofabricate large area of Permalloy ( P y ) nanoclusters onsilicon surfaces. We propose that the curvature of thehemispherical clusters shape is responsible for the aris-ing of DM interaction which allows the emergence oftopological vortex excitations in very small structures.The P y clusters were obtained through galvanostatic de-position directly on the surface of Si substrates. Thesubstrates utilized were n-type (100) Si samples with sizeof 1 cm x 1 cm cut from wafers commercially availablewith resistivity in the range of 1-10 Ohm.cm . Electricalcontacts to each substrate for the electrodeposition weremade through
GaIn back contact. An adhesive tape wasused to mask off all the substrate except for a circulararea of 0.5 cm on which the deposition was desired.Prior to deposition the substrates were immersed in a5% HF solution for 5 to 10 s , in order to remove oxidefrom the surface. The potentials were measured against asaturated calomel electrode ( SCE ), and a
P t foil counterelectrode was placed directly opposite the working elec-trode (substrate).
P y deposits on Si were prepared froman aqueous electrolyte containing 30 mM F eSO , 700mM N iSO , 20 mM N iCl , 16 mM saccharin, and 400mM H BO , obtained from ref. , resulting in compo-sition close to the F eN i alloy (80 at.% Ni and 20 at.%Fe) for current density of 6.3 mA/cm as determinedpreviously . The electrodeposited samples were char-acterized by Scanning Electron Microscopy with FieldEmission ( SEM − F EG ) and Transmission Electron Mi-croscopy (
T EM ). The magnetization behavior as a func-tion of electrodeposition time was investigated by Super-conducting Quantum Interference Device (
SQU ID ) andthe magnetoresistive measurements (
M R ) were carriedout using dc two-point probe method, where the two ter-minals were simple copper wires placed on top of later-ally prepared
GaIn ohmic contacts (2 x 4 mm) and 2mm apart from each other, with magnetic field appliedin plane and out of plane in configuration transversal tothe measuring current. The same configurations of
GaIn ohmic contacts were utilized in the current versus voltage( I − V ) measurements.In the beginning of the electrodeposition process, F e and
N i solvated ´ıons in the electrolyte receive electrons fromthe substrate becoming adatoms. The adatoms migrateon the surface until finding a defect such as vacancies orkinks to nucleate. After the nucleation process, the clus-ters increase in size and the deposit evolves to compactthin film. Typical voltage transients were shown in Fig-ure 1(a) for current density of 6.3 mA/cm . Only sam-ples with superimposing transients were considered forfurther measurements, in order to assure the required re-producibility of the properties under investigation. Herewe are interested in samples composed by isolated clus-ters on the surface that can be found by monitoring the Figure 1. (a) Deposition transient measured against satu-rated calomel reference electrode. (b) Sample cross sectionmeasured by
T EM and (c) Images of the clusters distribu-tion obtained by
SEM − F EG . electric percolation, which can be followed by electricalconductivity measurements, realized in the set of samplesobtained in different electrodeposition times. From the( I − V ) measurements, the time where the percolationoccurs was found to be around 15 s , so we focused ourinvestigations in samples with lower deposition times.From the micrographs performed by SEM and
T EM ,presented in Figure 1(b) and 1(c), it is possible to noteisolated clusters on the surface after 12 s of electrodepo-sition. Hysteresis loops measured in the sample showedin Figure 1 for temperatures of 50K, 180K and 300Kare shown in Figure 2. The similarity of the hysteresismeasured in this work, with that observed in topologicalvortex states in nanodisks , and its very low variation inthe large temperature range investigated, are indicationsthat each cluster bear a monodomain vortex excitation.In order to investigate the spin dynamics in the clustersunder external magnetic field, micromagnetic simulation Figure 2. Magnetization measurements realized in SQUID forthe sample with 12s of electrodeposition. were performed based on Landau-Lifshitz-Gilbert equa-tion, ∂ ~M∂t = − γ ~M × ~H eff + αM s ~M × ∂ ~M∂t , (1)where γ is the gyromagnetic ratio, M s the satura-tion magnetization and H eff is the effective magneticfield, which is composed by external magnetic field,magneto-crystalline anisotropies, dipolar and exchangeinteractions. This equation is utilized to determinethe minimum energy and the transitions between spinconfigurations. For the iterations, we have utilizedthe software Object Oriented MicroMagnetic Framework( OOM M F ) , with parameters for P y as 8 . A/m for saturation magnetization, 13x10 − J/m for ex-change constant and 0 . Figure 3. Spin configuration in the ground state I and the core delocation under external magnetic field II-V, until the saturatedmonodomain following the external field orientation. possible to conclude that the ground state of magnetiza-tion in clusters array have curled vortex topology, withrandom chirality and polarizations of core vortices. Inorder to investigate the vortex formation on hemispher-ical clusters, let us considerate that magnetic materials(ferromagnetic or even antiferromagnetic) in two spatialdimensions may support topological excitations such asskyrmions and vortices. Vortices arise in classical mag-netic systems containing an easy-plane anisotropy, whichmakes the spins prefer to point along the XY -plane. Forinstance, easy-plane ferromagnets are described by theHamiltonian, H = − J X i,j [ S xi S xj + S yi S yj + λS zi S zj ] , (2)where J > ≤ λ < ~S i = ( S xi , S yi , S zi ) the classicalspin vector at site i . Considering the most realistic dis-crete lattice case, and depending on the range of λ , suchan easy-plane system supports two types of static vor-tices: the in-plane vortex (in which all spins are confinedto the XY -plane ) and the out-of-plane vortex (in whichsome spins around the vortex center can point perpendic-ularly to the XY -plane). Indeed, considering a criticalvalue of λ , denoted by λ c , then for the range λ < λ c , thestable excitation is the in-plane vortex, while for λ > λ c ,the out-of-plane vortex becomes stable . The stabilityof these solutions has only been determined via computersimulations. The critical anisotropy λ c depends on thelattice geometry: for the square lattice, λ c = 0 .
72; sim-ilarly λ c = 0 .
86 for the hexagonal lattice and λ c = 0 . . Qualitatively, similar results can be obtained for 2 D easy-plane antiferromagnetic sys-tems. Broken mirror symmetry at surfaces/interfacesof magnetic nanostructures, induces chiral DM interac-tions which may strongly affect the magnetic propertiesof the system, for example allowing the possibility ofvortex with a well defined sense of rotation (curl vor-tex with a chiral sense). When the manifold that sup- Figure 4. Hysteresis loop obtained with the micromagneticsimulation (line), compared with the experimental measure-ment at 50K (symbol). ports the spins is a curve one, or when the spin remainsin a curved manifold, the curvature results in two addi-tional effective interactions, originated from the exchangeinteractions , one is analogue to magnetic anisotropyand another to the DM interaction. The equilibriumstate of the magnetic hemispheres, can be understood asa competition between these effective curvature inducedinteractions. For example if the exchange energy den-sity is wroten in function of curvilinear coordinates, theterms are the isotropic exchange energy, anisotropy en-ergy that depends on the geometry of the manifold, andthe effective DM interaction. The last one can explainthe vortex formation on a hemispherical cluster. Whenthere is only exchange interaction (without DM inter-action), the competition between the in-plane exchangeenergy, tending to extend the vortex core, and the uni-axial anisotropy, favoring its shrinking, determines theequilibrium size of the core. It may occupy the wholenetwork being of any size, but in magnetic nanodisks, forexample, where vortices are naturally the ground state ofthese systems and they can be directly observed by ex-perimental techniques , the typical size of the vortexis down to 150 nm . The DM interaction, extends sizes ofthe vortices with favorable rotation sense and compressesthe vortices with opposite chirality . The ratio betweenthe DM constant interaction D and the exchange in-teraction J , determines the size of the vortex, being thevortex stable in a range of values where the competitionbetween the energy is favorable to the emergence of thevortex, minimizing the energy of the system. The greater Figure 5. Magnetoresistance measured with external field inplane and out of sample plane. The cartoons show the spinconfiguration in each part of the curves. the ratio D /J , smaller the size of the vortex. The DMinteraction induced by curvature, has a coupling constant D that is a function of the geometry manifold where thespins reside. To a hemispherical one, D can be dividedin two parts, which are functions of 1 /r and 1 /r , being r the radius of the hemisphere. Then to small values of r , more larger is the DM coupling and smaller are thesize of the vortex. The experimental detection of thisvortex, can be used to asses the curvature induced DMinteraction and measure the strength of the induced DMcoupling in this system. In Figure 5 are presented the magnetoresistive mea-surements performed in this work. Due to its mag-netic behavior, the clusters array presents isotropicmagnetoresistance , similar to the Giant Magne-torestance (GMR) effect in ferromagnetic-nonmagneticmultilayers . The ferromagnetic configurations ob-tained with the monodomains aligned to the externalmagnetic field, in sample plane, and in the every core po-larization aligned to the external magnetic field, appliedout of the sample plane, provide lower resistive path tothe spin polarized current which must flow throughoutthe silicon. The higher resistance close to the zero field,occurs due to the antiferromagnetic configuration of thecurling vortex states with opposite chirality and core po-larizations, in order to diminish magnetostatic energy.In summary we have investigated the behavior of magne-tization in Py clusters electrodeposited on silicon. Fromthe experimental hysteresis and spin dynamics, realizedby micromagnetic simulation, we have observed topolog-ical vortex configuration in the clusters ground state,which was attributed to the emergence of DM interac-tions in its hemispherical geometry. The vortex corealignment under out of plane external magnetic field ormonodomains formation under in plane external mag-netic field, enables the investigation of such systems inmagnetoresistive devices.The authors are grateful to Daisy de Melo Gomes (inmemoriam) for the TEM images. They also thankCAPES, CNPq, FAPESC and FAPEMIG (Brazilianagencies) for partial financial support. REFERENCES P. Weiss, J. 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