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Effects of Sr doping on the magnetic properties of Sr Ba CoO x 1−x 3 V. Pardo,1,2,∗ J. Rivas,1 and D. Baldomir1,2 1 Departamento de F´ısica Aplicada, Facultad de F´ısica, Universidad de Santiago de Compostela, E-15782 Campus Sur s/n, Santiago de Compostela, Spain 2 Instituto de Investigaciones Tecnológicas, Universidad de Santiago de Compostela, E-15782, Santiago de Compostela, Spain Magnetic properties of the Sr-doped BaCoO3 are explained on thebasis of ab initio calculations 5 andtheanalysisofexperimentalliterature. Formationofmagneticclustersbiggerthanintheparent 0 compoundandincreaseintheblockingtemperatureareobserved. Superparamagnetism remainsat 0 room temperature. The possibility of tuning the size and properties of the magnetic clusters with 2 dopingis explored. n a PACSnumbers: 71.15.Ap,71.15.Mb,71.20.Be,75.20.-g J 4 2 Ab initio electronic structure calculations are becom- ters change with Sr-doping, focusing in the half-doped ing increasingly important in materials science. The im- compound Sr Ba CoO . The description of its mag- 0.5 0.5 3 ] provement of the codes and the ever increasing capabil- neticpropertieswillbemadeusingtheexperimentaldata l e ities of modern supercomputers has produced a compa- available, interpreted via ab initio calculations. - rable improvement in the precision of the properties of r The temperature and applied field dependence of the t solids which are attainable nowadays by means of, e.g., s magnetizationmeasuredaftercoolinginzerofield(ZFC) . density functional theory calculations1. The connection t andaftercoolinginafield(FC)inRef. 22(Fig. 12)sug- a with the real physical properties of the materials is al- gest us that the Sr-half-doped compound behaves as an m ready possible and the project of designing materials assembly of non-strongly interacting particles, which we - thoretically has been under way for the last few years2. proceedtoanalyze. TwocuspsappearintheZFCmagne- d n Transition metal oxides have drawn the atten- tizationcurves,oneat50Kandanotheroneatabout140 o tion of the scientific community for the last 50 K,beingthecuspatabout50Karemainderoftheparent c years because of their interesting physical properties compoundwhichcomesoutinthe dopedcasebecauseof [ and multiple applications3. Co oxides are becom- the fabrication procedure. The physics which is genuine 1 ing increasingly important, mainly because of their ofthe doped compoundis shownby the higher tempera- v thermoelectric4,magnetoresistive5andsuperconducting6 ture one. This so-called bimodality, i.e., the appearance 6 properties. These materials also present difficulties for oftwotypesofmagneticparticlesofdifferentsizesinone 5 the abinitio calculationsbecause of havingstronglycor- sample, is usually found in granular systems11,23. Simi- 5 related electrons; the use of the LDA+U method7 or lar curves could also be understood taking into account 1 dynamical mean field theory8 is needed to predict their the effects of the surface of the clusters24,25 but we have 0 properties correctly. ruled this possibility out because of the technique used 5 0 Systems formed by magnetic nanostructures have to produce the sample, which would tend to conserve a / been studied intensively in the last few years, show- matrix with the properties of the parent compound. t a ing some interesting technological applications, in fields For describing properly what the magnetic morphol- m such as magnetic recording, sensors, MRAM and ogy of the system is we need to characterize the size of - magnetoelectronics9,10. E.g., Co nanocrystals have also these magnetic clusters and the interparticle distance. d numerous applications due to their special magnetic For doing so, we will make use of ab initio calcula- n o properties11. tionsperformedwiththeWIEN2ksoftware26,whichuses c In a recent paper12, the magnetic properties of an APW+lo full-potential method27 and the LDA+U v: BaCoO3, were analyzed considering the formation of approach28 in the “fully-localized limit”29, to deal with i nanometric magnetic clusters,ferromagneticregionsem- the strong correlations typically present in transition X bedded in a non-ferromagnetic matrix, in the mate- metal oxides. ar riniagl,thsetmartibnyg mfreoamns eoxfpearbiminenittiaol cdaalctualaatinodns.inteGrplarsesty- beTsheeenblionckRienfg. t2e2m,pFeirga.tu1r2e,oaftSar0b.o5Buta01.54C0oKO.3Wis,itahstchains behavior has also been recently found in similar value, the size of the magnetic clusters which become compounds13,14,15,16,17,18. This is usuallyrelatedto hav- blockedbelow thattemperature, butactas superparam- ing a sort of self-generated assembly of magnetic clus- agnetic particles above it (see Fig. 1), can be estimated ters in which magnetic interactions introduce glassiness withtheknowledgeoftheanisotropyconstantofthema- amongthem19,20 oracompetitionbetweenferromagnetic terial. This quantity can be calculated ab initio just by and antiferromagnetic couplings which may lead to frus- computing the total energy of the material, including trationofanylongrangemagneticorder,asitisthecase spin-orbit effects in a second variational manner30, as- in BaCoO321. sumingthemagneticmomentslieinthedifferentcrystal- Inthis paper,wewilldiscusshowthese magneticclus- lographic directions. We calculated the anisotropy con- 2 stantasK = EB (weassumecubicanisotropyduetothe 4 nearly octahedral environment where the Co ions are), where the magnetocrystalline energy E is defined as B theworkrequiredtomakethemagnetizationliealongthe hard(a)axiscomparedtoaneasy(c)direction. Wemust note here that the introduction of Sr produces severe changesinthe crystallineanisotropyenergyofthe material. It changes the easy axis from the hexagonal plane where it lies in the parent compound to the Co-chains axis (c). Also, the magnitude of the anisotropy constant has in the doped compound a value of 1.5×107erg/cm3, whichis one orderofmagnitude smallerthan in the par- entcompound,butstilllargerthanthetypicalvaluesfor systems ofCo magnetic particles,hence, stillone canas- sume that the formationofthe clusterswill havea much smallercontributiontothemagneticanistropyofthesys- temandconsiderthatthemagnetocrystallineanisotropy FIG. 1: Total magnetization vs. H/T of Sr0.5Ba0.5CoO3 for is the dominant effect. severaltemperatures(experimentaldatatakenfromYamaura et al.22). The curves superpose as expected for a system of Thesizeoftheclusterscanthenbe obtainedusingthe superparamagneticparticlesabovetheblockingtemperature. well-known expression for systems of superparamgnetic Even at room temperature, superparamagnetism is present. particles31: KV = 25k T , where K is the anisotropy B B constant, V is the typical volume of the particles, T B is the blocking temperature (which is about 140 K in generacy of both ferromagnetic and antiferromagnetic this case), k is the Boltzmann’s constant and the fac- B configurations32. Our calculations on the half-doped tor 25 appears due to the experimental technique. The compound yield a similar behavior to that found in typical volume of the clusters which comes out of our the parent compound21, ferromagnetism is marginally calculations is about 4 nm in diameter, comprising some more stable but it is orbital ordering the main energetic 500 Co atoms. The size of these clusters is much big- contribution, so-calledalternating orbitalordering along ger than those forming the parent compound, which are the Co chains21 is about 50 meV/Co more stable than about1.2nmindiameter12,butthesearestillpresentin the “ferro-orbital” solution, whereas energy differences thedopedsampleutilizedinRef. 22,accompaniedofthe due to magnetic ordering are one order of magnitude bigger ones due to the half-doped material. These de- smaller. The interplay between double exchange favor- termine the magnetic properties of the compound above ing ferromagnetism and superexchange favoring antifer- some 100 K and also at roomtemperature, where super- romagnetism might porduce frustration in this type of paramagnetismremainsforthecaseoftheSr-dopedcom- compounds and a cluster-glass behavior could turn out pound,whereasintheparentcompound,the breakingof as a result. However, this does not seem the case from the clusters occurs at about 250 K and paramagnetism the susceptibility curves we can see in Ref. 22, which do is the phase at room temperature22. Below 100 K, the not show strong interactions between the clusters. propertiesaredeterminedbytheremainingofthesmaller In Fig. 1, we plot the data of magnetization vs. H/T clusters, which become blocked below approximately 50 which appears in Ref. 22, (inset of Fig. 12) as several K. In the half-doped compound, magnetic clusters con- curves of magnetization vs. magnetic field for different taining about 500 Co atoms exist at room temperature. temperatures. The curves superpose as expected for a The possibility of controlling the size and properties of system of superparamagnetic particles above the block- the magnetic particles with doping is clear. Introducing ing temperature. As mentioned above, superposition is Sr into the undoped BaCoO produces the appearance 3 maintained for the curve at 400 K, indicating that, at of bigger clusters which can be observed already for the room temperature and above, magnetic clusters still ex- compound Sr Ba CoO (see in Ref. 22, Fig. 11 how 0.2 0.8 3 istanddeterminethemagneticpropertiesofthematerial. a second cusp starts to develop in the ZFC curve at a At high temperatures, the slope grows because the clus- higher temperature). The control of the size and mag- ters get bigger (a lower anisotropy constant when tem- neticpropertiesoftheclusterscanalsobedonebychang- ing the magnetic field19, but here we propose a different peratureincreasesimplieshighervolumeoftheclusters). way to do so, i.e., doping the sample with an isovalent These curves can be fit to a Langevin formula, which cation. Moreover,herewearedealingwithmagneticpar- approximates to a Curie law at small values of the ratio ticleswhichspontaneouslyoccurinthesystemandwhose µH , where µ is the magnetic moment of the cluster, in kBT properties can be tuned by changing the dopant concen- the following way: M ≃ N µ2H , where N is the den- tration. 3kBT sity of clusters in the material. From this fitting of the The formation of magnetic clusters in the series curves in Fig. 1, one can estimate the density of clus- SrxBa1−xCoO3 (x ≤ 0.5) is probably related to the de- ters N, which determines the way these clusters interact 3 and also the shape of the FC curve below the block- substituted by Sr, the magnetic clusters increase in size ing temperature. The result is that there is one clus- and superparamagnetism remains at room temperature ter formedby about 500 Co atoms in a sphericalvolume for the half-doped compound. The possibility of tuning withadiameterofapproximately8nm. Hence,theaver- the magnetic properties of a system of superparamag- age distance between clusters is about 2 diameters. This netic clusters by doping with an isovalent cation is ex- meansthattheclustersdonotstronglyinteractwitheach plored. It would be interesting to analyze what happens other, as it becomes clear from Ref. 22, Fig. 12, where to the system when doping it with a different divalent it can be observed that the FC curve below 140 K (the cation such as Ca. The reasoning we follow in this let- blockingtemperature)risesasexpectedfornon-strongly- termightbe extendedtoothersimilarcompoundsshow- interactingparticles33, eventhoughthis shape might de- ing phase segregation, which are of key importance for pend on the cooling speed34. Cluster-glass behavior is nanoscience and nanotechnology. We state the possibil- not observed in the sample and this is confirmed by the ityofstudyingthesevariationsinmagneticpropertiesby calculations showing that the clusters are not strongly means of electronic structure ab initio calculations. interacting (they are far enough from each other). TheauthorswishtothanktheCESGA(CentrodeSu- Inthispaperwehavepresentedanexplanationforthe percomputación de Galicia) for the computing facilities, magnetic properties of the series SrxBa1−xCoO3 charac- the Xunta de Galicia for the finantial support through terized by means of ab initio calculations. The presence a grant and the project No. PGIDIT02TMT20601PR oftheclustersisanessentialingredientinthedescription and the Ministerio de Educación y Ciencia of Spain by of the magnetic properties of the material. When Ba is Project No. MAT2004-05130. ∗ Electronic address: [email protected] 17 H. Szymczak, M. Baran, G.J. Babonas, R. Diduszko, 1 P.HohenbergandW.Kohn,Phys.Rev.136,B864(1964). J. 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