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Selective dilution and magnetic properties of La_{0.7}Sr_{0.3}Mn_{1-x}M'_xO_3 (M' = Al, Ti) PDF

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M′ M′ Selective dilution and magnetic properties of La0.7Sr0.3Mn1−x xO3 ( = Al, Ti) D. N. H. Nam,1,2 L. V. Bau,1,3,5 N. V. Khiem,4 N. V. Dai,1 L. V. Hong,1 N. X. Phuc,1 R. S. Newrock,2 and P. Nordblad5 1Institute of Materials Science, VAST, 18 Hoang-Quoc-Viet, Hanoi, Vietnam 2Department of Physics, University of Cincinnati, OH 45221-0011, USA 3Department of Science and Technology, Hongduc University, Thanhhoa, Vietnam 6 0 4Department of Natural Sciences, Hongduc University, Thanhhoa, Vietnam 0 5The ˚Angstr¨om Laboratory, Uppsala University, Box 534, SE 751-21 Uppsala, Sweden 2 (Dated: February 6, 2008) n Themagneticlatticeofmixed-valenceMnionsinLa0.7Sr0.3MnO3 isselectivelydilutedbypartial a substitution of Mn by Al or Ti. The ferromagnetic transition temperature and the saturation mo- J mentdecreaseswithsubstitutioninbothseries. Thevolumefractionofthenon-ferromagneticphases 6 evolvesnon-linearly with thesubstitution concentration and faster than theoretically expected. By 1 presenting the data in terms of selective dilutions, the reduction of Tc is found to be scaled by the relativeionicconcentrationsandisconsistentwithapredictionderivedfrommolecular-fieldtheory. ] i c PACSnumbers: 75.10.Hk,75.30.Cr,75.30.Et,75.47.Lx s - l r I. INTRODUCTION causedbytoomanyfactorsthatgovernthe propertiesof t m the materials, no universal features have been revealed to date. In this paper, we report that the reduction of . Perovskite manganites with the general composition t the ferromagnetic ordering transition temperature T of a (R,A)MnO (R: rare earth, A: alkali elements) are at- c m tractive to3scientists not only because of their poten- La0.7Sr0.3Mn1−xM′xO3(M′ =Al,Ti)scaleswiththerel- ativesubstitutionconcentrationsandisconsistentwitha - tial applications but also due to their very rich and in- d predictionfrommolecular-fieldtheory(MFT)ofthedilu- triguing physics. While most of the pristine compounds n tionofamagneticlattice. ThesubstitutionswithAland RMnO are (insulating) antiferromagnets due to anti- o 3 Ti are selective in nature because Al3+ only substitutes ferromagnetic (AF) superexchange (SE) interactions be- [c tween Mn3+ ions, the introduction of divalent alkali for Mn3+ and Ti4+ only for Mn4+. Another advantage cationssuchasSr2+,Ca2+,orBa2+ intothecomposition ofthesesubstitutionsisthatbecauseAl3+ andTi4+ ions 1 converts an adapted number of Mn3+ to Mn4+ that in do not carrya magnetic moment, they are also expected 8v turngivesriseto the Mn4+−O2−−Mn3+ ferromagnetic not to participate in the magnetic interaction. 0 (FM) double-exchange (DE)1 interaction. The presence 3 ofDEcouplingscanturnaninsulatingantiferromagnetic 1 manganite into a ferromagnet with metallic conductiv- II. EXPERIMENT 0 ity. It has been widely accepted that, along with lattice 6 distortions2,3,4 and phase segregation phenomena,5 the In this paper, La Sr Mn M′O is denoted as 0 0.7 0.3 1−x x 3 / DE mechanism plays a very important role in governing LSMAx for M′ = Al and LSMTx for M′ = Ti. All the at the properties of manganites. samples were prepared using a conventional solid state m Perovskite manganites have been intensively studied reactionmethod. Pure (≥99.99%)rawpowders with ap- in the last decade since the discovery of the Colos- propriate amounts of La O , SrCO , MnO , Al O , and - 2 3 3 2 2 3 d sal Magneto-Resistance (CMR) phenomenon.6 Chem- TiO are thoroughly ground, mixed, pressed into pellets 2 n ical substitution has been widely used as a conven- and then calcined at several processing steps with in- o tional method to uncover the underlying physics and creasing temperatures from 900 oC to 1200 oC and with c to search for compositions with novel properties. Re- intermediate grindings and pelletizations. The products : v sults for both R- and Mn-site substitution have been are then sintered at 1370 oC for 48 h in ambient atmo- i X quite well documented in the literatures. For mangan- sphere. The final samples are obtained after a very slow ites with a Mn3+/Mn4+ ratio of 7/3, substitution of cooling process from the sintering to room temperature r a different elements at the rare-earth site has shown that with an annealing step at 700 oC for few hours. Room- magnetic and transport properties of many manganites temperature X-ray diffraction patterns (measured by a depend rather systematically on the average ionic size, SIEMENS-D5000 with Cu-K radiation) show that all α hr i = y r , and the ionic size mismatch defined of the samples are crystallized in perovskite rhombohe- A i i i as σ2 =Piyiri2 −hrAi2 (where yi is the fraction and dral structures with almost no sign of secondary phases ri the ionPic radius of the ith species occupying the R- or remnants of the starting materials. The crystalstruc- site),4,7 i.e. on the degree of GdFeO -type lattice dis- tures obtained for the samples are in agreement with 3 tortion and lattice disorder. However, despite many at- earlier structural studies.8,9,10,11,12 Transport and mag- tempts at modifying the magnetic lattice of Mn ions netotransport measurements were carried out in a non- by direct substitution at the Mn-sites, the complexity commercialcryostatusingthestandard4-probemethod. 2 A. Temperature dependent characterization 10 a Temperaturedependentmagnetizationmeasurements, 8 M(T), in both zero-field-cooled (ZFC) and field-cooled (FC) protocols, are carried out for all the samples. u/g) 6 La0.7Sr0.3Mn1-xAlxO3 TdihceateFCthaMt(tThe) scuubrvsteistuptrioesnenotfedAlinorFTigi.fo1r Mclenarclayusines- m e theferromagnetic-paramagnetic(PM)transitiontemper- ( 0.00 M 4 0.02 ature Tc to drop drastically. The reduction of Tc in the 0.05 case of Ti substitution is much more substantial. The 0.10 FM-PM transition is very sharp at small x concentra- 2 0.15 tions for both doping series but becomes broader with 0.20 H = 100 G increasing x. A transition is observed for all the sam- 0 ples, even with LSMT where Mn4+ ions are supposed 0.3 10 to be completely absent. However, as is implied by the La Sr Mn Ti O 0.7 0.3 1-x x 3 b ZFC and FC M(T) curves in Fig. 1, the LSTMT0.3 sample is not a true ferromagnet, nor a pure spin glass 8 x=0.0 as has been suggested in Ref. 12 for this composition. ) This lastconclusionis alsocorroboratedby the factthat g u/ 6 our frequency-dependent ac-susceptibility measurements m x=.05 χ (T,ω) (not shown) do not indicate a dynamic phase e ac M ( 4 x=0.1 transition. The M(T) curves for this sample probably suggest the existence of an AF background state with a x=0.2 weakferromagneticcomponent—possibleindicationsof 2 a canted antiferromagnet, as was proposed in Ref. 10. The T vs. x data extracted from the M(T) curves for x=0.3 c all samples are plotted in Fig. 4 and will be discussed 0 0 50 100 150 200 250 300 350 400 later in detail. T (K) Temperature dependent transport measurements for bothseriesshowthattheresistivity,ρ,stronglyincreases with increasing x while the metal-insulator (MI) transi- FIG. 1: Field-cooled magnetization as a function of tionusuallyobservedatatemperatureT near(butlower temperature for (a) La0.7Sr0.3Mn1−xAlxO3 and (b) p than) T is shifted to lower temperatures. The MI tran- La0.7Sr0.3Mn1−xTixO3, measured in H = 100 G. The c zero-field-cooledMZFC(T)(H)ofthex=0.3sampleisadded sition is observed in all of the LSMAx samples while it for further discussions. can only be observed in LSMTx for x up to 0.1. For LSMT , the MI transition is no longer observed, but 0.2 there still exists a slope change in the ρ(T) curve at a temperaturebelow T signallinga magnetic contribution c Magnetic and magnetization measurements were per- from the FM phase to the conductivity. In agreement formed in a Quantum Design MPMS SQUID magne- with the magnetic behavior, the LSMT sample only 0.3 tometer and (sometimes) by a Vibrating Sample Mag- shows insulating characteristics. netometer (VSM). B. Magnetization characterization The theoretical zero-temperature spin-only saturation III. RESULTS AND DISCUSSION magnetization (in emu/g) of the LSMA and LSMT x x compounds follow Magnetic,transport,andmagnetotransportcharacter- (3.7−4x)103/(40.548−5.006x) if M′ =Al ization of LSMAx and LSMTx compounds has been re- Ms =(cid:26) (3.7−3x)103/(40.548−1.801x) if M′ =Ti. (1) portedpreviouslybyotherauthorsandcanbereferenced inanumberofpublications.8,9,10,11,12,13Althoughconsis- For the LSMA series, magnetization measurements at x tent tendencies as to the variation of e.g. the transition T = 5 K (the inset of Fig. 2) indicate that the sam- temperature and saturation moment with doping con- plesaresubstantiallysaturatedinanappliedfieldofjust centrationhavebeenfound,thereissignificantscatterin above 1 T. At higher fields, the LSMA and LSMA 0 0.05 the data in-between the different studies. In the current samples exhibit flat M(H) dependencies as expected for work,theessentialcharacteristicsarecarefullymeasured conventional ferromagnets at high fields and low tem- and reexamined. peratures. Closer inspection on the M(H) curves for 3 x≥0.1 shows, however,that they are quite linear in the high-field regime up to 4.5 T with a small slope which calc. increases with x. The small slope would come from the exp. suppressionof thermal fluctuations of the magnetization 80 bythemagneticfield. However,theevolutionoftheslope of the M(H) curves with x in the high field regime may signalamagneticcontributionfromcertainMnionsthat La Sr Mn Al O 0.7 0.3 1-x x 3 do not take part in the ferromagnetic phase. In addi- 60 tion,forthe wholeseries,the measuredmagnetizationin g) 100 magnetic fields up to 4.5 T does not reach the theoret- u/ ical magnetization value and even deviates further with m 80 e increasing x. Based on these features, it is presumable ( M s 40 mu/g) 60 0.00 tthhaestesseagmrepglaetsi.onThineteoxpFeMrimanendtanlovna-FluMespofhtahseessaotcucruartsioinn M (e 40 x = 00..0150 m(aangdnaetlsizoaFtiiogn. M3 sfoorfTthiesuFbMstitpuhtaiosen)parerseendteetdermininFeidg.by2 20 20 0.15 extrapolating the linear part of the M(H) curves in the T = 5K 0.20 high field regime to H = 0. The difference between ex- 0 perimental and theoretical M is then attributed to the 0 1 2 3 4 s H (T) non-FM contributions, Mnon−FM. 0 Very similar results are also obtained for the LSMT x 0 0.05 0.1 0.15 0.2 series,as can be seen in Fig. 3. Previousobservations of x thedecreaseofM inAlandTisubstitutionsinmangan- s iteshavebeenpublishedandinterpretedbyseveralother FIG. 2: La0.7Sr0.3Mn1−xAlxO3: Theoretical Ms vs. x cal- authors.10,11,12,14,15 The decrease of M was attributed culated from equation 1 (bold curve without symbols) and s to the dilution and the weakening of FM exchange cou- experimentalMs data(thincurvewith ⊙symbols) extracted plingsasingeneral. Kallelet al.10 suggestevenachange from M(H) measurements at 5 K (inset). of the spin state or the orbital ordering of the Mn ions. The deviation between the experimental M and its the- s oretical values has not been adequately considered. In a study on La Ca Mn Al O by neutron diffraction, 0.7 0.3 1−x x 3 calc. the effective magnetic momentper Mnionwasfound far exp. smaller than the saturation moment and that was ex- 80 plained by assumptions of magnetic inhomogeneity and structuraldisorder.14OurinterpretationfortheM devi- s La Sr Mn Ti O ationinterms ofmagneticphasesegregationissomehow 0.7 0.3 1-x x 3 closertothatproposedforLa Ca Mn M′O (M′= 0.7 0.3 1−x x 3 60 100 Ti, Ga) compounds by Cao et al.,15 where the authors suggest that Ti4+ and Ga3+ ions generate around them ) u/g 80 non-ferromagnetic (paramagnetic or possibly antiferro- m magnetic) regions. M (es 40 mu/g) 60 As pointed out above, there is a growing deviation e of the FM saturation magnetization from the calculated M ( 40 value with increasing substitution concentration. This 0.0 observation indicates that the substitution not only re- 20 x = 0.1 duces the total number of Mn ions but also raises the 20 0.2 T = 5K 0.3 number of non-FM Mn ions at the expense of the FM 0 phase. Since the Mn3+/Mn4+ ionic concentration ratio 0 1 2 3 4 H (T) is drivenawayfromthe optimalvalue of 7/3 by the sub- stitution, a certain amount of the Mn ions may become 0 redundant with respect to the DE couplings. I.e., the 0 0.05 0.1 0.15 0.2 0.25 0.3 x selective substitution on one Mn ionic species produces the redundancy on the other Mn species. Those redun- dant ions contribute to the non-FM phase. With small FIG. 3: La0.7Sr0.3Mn1−xTixO3: Theoretical Ms vs. x cal- culated from equation 1 (bold curve without symbols) and valuesofx,theredundantionsarethusmostlyMn4+ for experimentalMs data(thincurvewith ⊙symbols) extracted M′ = Al while they are Mn3+ for the Ti substitution. from M(H) measurements at 5 K (inset). Based on this assumption the concentration of non-FM Mn ions can approximately be derived from M . non−FM 4 is worth noting that the ionic size of Mn4+ (0.530 ˚A) is 400 smaller than that of Ti4+ (0.605 ˚A) while Mn3+ (0.645 La0.7Sr0.3Mn1-xM'xO3 ˚A)islargerthanAl3+ (0.535˚A).17 Asaresult,theeffects ofAlandTisubstitutiononthestructure,andhenceW, maynotbe the sameandevenopposite inthe twocases. 300 However,inreality,T hasbeenfoundalwaystodecrease c K) with the substitution. A detailed study on the structure T (c of LSMAx may help justify the cause. AsisseeninFig. 4,theeffectofsubstitutionwithTion 200 thereductionofT (definedby∆T =T (x)−T (0))isas Al c c c c muchasmorethantwiceofthatofAlsubstitution. How- Ti ever,as mentioned above,because the substitution is se- lective,inordertocomparetheireffects,insteadofusing 100 x as the common variable, the data should be presented 0 0.05 0.1 0.15 0.2 as functions of relative substitution concentrations, de- x fined asn =x/0.7when M′ =Al andn =x/0.3 when p p M′ = Ti. Physically, n is the average concentration of FIG. 4: La0.7Sr0.3Mn1−xM′xO3: Variation of Tc with substi- M′ per Mn site of thepselectively-substituted Mn ionic tutionconcentration x(0≤x≤0.2) for M′=Al(⊙)and Ti species (Mn3+ for M′ = Al, or Mn4+ for M′ = Ti), (⊡). or the probability that site is occupied by an M′ ion. Strikingly, as displayed in Figure 5, the T (n ) data for c p M′ = Al and Ti collapse onto one curve which follows For examples, with x = 0.2, the estimated redundant very well the linear line predicted by the molecular-field concentrationof Mn4+ is 0.187for M′ =Al and the cor- theory(seebelow). Itisalsosurprisingthatthelinearbe- responding concentration of Mn3+ is 0.064 for M′ =Ti. haviorofT (n ) ofLSMT sustainsin averywide range With sufficiently high substitution concentrations, con- c p x of n and has the tendency to reduce to zero at n =1. tributions to the the non-FM phase may also arise from p p For further understanding and analyzes of the results, the Mnions ofboth speciesthatareisolatedby the non- we use a mean-fieldapproximationto derive the relation magnetic ones. between T and n . According to the Heisenberg model, c p the potentialenergy ofexchangeinteractions ofany par- ticular magnetic ion i with the other ions j is given by C. Effects of selective dilution and the MFT U = −2S · J S where S , S are the spins of approximation i i j6=i ij j i j the ith and jPth ions respectively; and Jij the exchange integral. U can be rewritten as i Figure 4 shows the dependence of the FM-PM phase transition temperature Tc on substitution concentra- U =−2µi · J µ =−2µi·M J (2) tion, derived from the low-field M(T) data in Fig. 1. i g2 ij j Ng2 ij The T values are determined by the temperatures at Xj6=i Xj6=i c which the ∂M/∂T curves peak. The parent compound, whereM andN arethe magneticmomentandthe num- La0.7Sr0.3MnO3, has Tc = 364.4 K, in good agreement ber of magnetic ions per unit volume, respectively and with previously reported data.16 Tc decreases monotoni- µi, µj are the magnetic moment of the ith and jth ions. cally as x increases in both cases. Explanations for the For simplicity, µ is replaced with the average magnetic j decrease of Tc with Al and Ti substitution in mangan- moment per site hµi = M. Assuming that the ith ion iteshavebeensuggestedbyseveralauthors.8,10,11,13 One interacts only with its neNarest-neighbor ions, but with n explanation is simply that the decrease of T is due to c different exchange coupling constants Jiα each involves the suppression of long-range FM order of the localized z ions, then instead of summing over the ions j, the iα t2g spins by local breakdown of the exchange couplings summation is made over the interactions. We can then where the substitution occurs.8,13 Hu et al.9 assumed recast Eq. 2 as that the substituted Ti4+ ions tends to demolishthe DE Mn3+ −O2− −Mn4+ bonds and lowers the hole carrier µ ·M n i U =−2 z J . (3) concentration, thus suppressing the DE interaction and i Ng2 iα iα lowering T . Kallel et al.10 suggested that the presence Xα c of Ti in LSMTx favors SE interaction and suppresses According to the MFT, Ui = −µi·BM = −µi·λM and the DE mechanism. Significantly, Kim et al.11 recently T = λC, where B is the molecular field, and C and λ c M found that the Ti substitution in LSMTx increases the are, respectively, the Curie and Weiss constants, Eq. 3 Mn − O − Mn bond length and reduces the bond an- becomes gle. Basedonstructuraldata,theauthorscalculatedthe n 2S (S +1) variationofeg-electronbandwidthW,finding adecrease Tc = i i ziαJiα. (4) of W with x, and related it to the decrease of Tc. It 3kB Xα 5 a tendency to go to zero when n = 1. This would sim- 400 p ply mean that the zJ product of DE couplings is totally La Sr Mn M' O 0.7 0.3 1-x x 3 dominant over those of the SE ones. Considering the fact that at low dilution concentrations, since the Mn3+ 300 Al andMn4+ concentrationsarenottoodifferent,z ,z , M' = Ti DE SE1 andz arepossiblycomparable,thusitisreasonableto SE2 Al+Ti K) suppose that the SE couplings JSE1, JSE2 both are neg- ( 200 ligibly small in these systems. This could be one reason T c behind the fact that La Sr MnO is a unique man- 0.7 0.3 3 ganite in the sense that it has the highest T amongst c 100 the perovskite manganites. In a situation when the SE coupling constantsaresignificant,because either z or SE1 MFT z doesnotchangebyselectivesubstitution,according SE2 0 to Eq. 4, Tc(np) may still have a linear dependence but 0 0.25 0.5 0.75 1 should have a tendency to intercept n -axis at a certain p n value n <1. p p Apartfromchangesofthez values,thesubstitutionof FIG. 5: La0.7Sr0.3Mn1−xM′xO3: Tc is presented as a func- Al or Ti for Mn could cause some additional effects. Be- tion of relative concentration np = x/0.7 for M′ = Al cause they are nonmagnetic, the magnetic coupling will (⊙) or np = x/0.3 for M′ = Ti (⊡). The broken bebrokenatanysitetheyoccupy,leadingtoaweakening line presents a prediction from molecular-field theory. The of long-range FM ordering established by the dominant data for La0.7Sr0.3Mn0.9Al0.07Ti0.03O3 (np = 0.19) and DE interactions and a deterioration of the metallic con- La0.7Sr0.3Mn0.8Al0.14Ti0.06O3 (np = 0.36) (N) are added for ductivity. The selectivity of the substitution also drives furtherdiscussions (see text for details). the Mn3+/Mn4+ ratio away from the optimal 7/3 value contributing to developing the non-FM phase. The dif- ferences in ionic sizes between Mn and Al and Ti could For a simple system where there is only one species of modify the crystal structure, especially the angle and magneticionandhenceonekindofexchangeinteraction, lengthofthe Mn−O−Mncouplings.18 Allthese factors Eq. 4 equals the standard expression contributeto the degradationofthe ferromagnetismand metallicity of the manganite system. Nevertheless, the 2S(S+1)zJ Tc = 3k . (5) linearbehaviorofTc(np)observedinFig. 5impliesthat, B within the substitution ranges, those effects are domi- When the system is diluted by a substituting non- natedbytheeffectofdilution. Inaddition,thereisasig- magnetic element, and if the substitution is completely nificant difference between the two substitutions. While randomwithrespecttoitslatticesite,thedilutionwould theamountofAlsubstitutionreducesthenumberofhop- resultinaproportionaldependencez(n )=z(0)(1−n ) ping electrons by an equivalent amount, Ti substitution p p where0≤n ≤1andz(0)referstotheundilutedsystem. does not affect it at all. The shortage of hopping elec- p Replacingz(n )forz inEq. 5yieldsalineardependence trons would possibly explain the large number of Mn4+ p of Tc on np as illustrated in Figure 5. redundancy in the LSMAx compounds. We believe that this difference has a link to the reason why the linear Nevertheless,Eq. 5isperhapsnotrelevanttoourman- behaviorofT (n ) ofLSMA occursin a muchnarrower ganite systems at first because of the mixed-valence of c p x rangeof dilution (n ≤0.25)than that of LSMT where the Mn ions and the coexistence of different kinds of in- p x teraction including SE AF interactions Mn3+ −O2− − Tc(np)isfoundlinearuptonp =0.67. Itisworthnoting Mn3+, Mn4+ −O2− −Mn4+, and the DE FM interac- that Tc(np) would not follow the linear behavior up to tion Mn3+ −O2−−Mn4+ with corresponding exchange np = 1 as predicted by the MFT because there should exist a percolation threshold n , above which clustering constants denoted as J , J , and J , and nearest- c SE1 SE2 DE occursandthe ferromagneticnetworkcollapsesintoonly neighbor interacting ions number z , z , and z , SE1 SE2 DE short-range ordering and superparamagnetism. respectively. According to Eq. 4, a linear behavior is expected to be observed for T (n ) only if (i) the ex- In the case when both Al and Ti are substituted for c p changecouplingconstantsareunchangedand(ii)the di- Mn with according n (Al) and n (Ti), supposing that p p lution either affects z in a proportional manner such theferromagneticdoubleexchangeistotallydominantin iα that z (n ) ∝ (1−n )z (0) or does not affect it at the system, the dilution concentration of the whole sys- iα p p iα all. Supposing that J , J , J do not change with tem is determinedas n =1−(1−n (Al))(1−n (Ti)). DE SE1 SE2 p p p substitution, within the linearity regime of T (n ), it is To check the validity of the MFT analysis in this case, c p presumable that the Al (or Ti) substitution leaves z the T (n ) values of the La Sr Mn Al Ti O SE2 c p 0.7 0.3 0.9 0.07 0.03 3 (or z ) intact but possibly changes both z and z (n = 0.19) and La Sr Mn Al Ti O (n = SE1 DE SE1 p 0.7 0.3 0.8 0.14 0.06 3 p (or z ) proportionallyto 1−n . The mostremarkable 0.36) compounds are also added to Figure 5. The data SE2 p feature of the T (n ) variation in Fig. 5 is that T has fit fairly well the MFT prediction. However, when the c p c 6 superexchange interactions are taken into account, the observed in a very wide range of n in LSMT making p x physical scenario for this case will be more complicated this system an excellent candidate for studies on the ef- and may need further detailed investigations. fects ofdilution whereT couldbe almostindependently c tuned without side effects. It is also proposed that the reduction in the number of hopping e electrons is one g IV. CONCLUSION cause for the difference in the effects of dilution between theLSMT andLSMA compounds. TheMFTanalyzes x x Wehavereexaminedthemagneticandtransportprop- arefound to some extend alsovalid for the casewhen Al erties ofthe La Sr Mn M′O system, where Mn is and Ti are both substituted for Mn. 0.7 0.3 1−x x 3 selectively substituted by M′ = Al or Ti; either Mn3+ or Mn4+ is selectively substituted for, but M′ is ran- domly distributed in the Mn network. The analyzes of Acknowledgments the M(H) measurements and saturation magnetization revealedthatthesubstitutionappearstonotonlymerely This work has been performed partly under the spon- dilute the magnetic lattice of Mn ions, but also induce a sorshipofacollaborativeprojectbetweentheInstituteof redundancyofMnions. Wehaveintroducedtheselective MaterialsScience(VAST,Vietnam)andUppsalaUniver- dilution concentration n and discovered that in certain sity(Sweden). TwoofuswouldliketothanktheUniver- p ranges of n , depending on particular M′, T scales very sity of Cincinnati and the National Science Foundation p c well with n in linearity, being in good agreement with for support. Dr. L. V. Bau would like to acknowledge p theMFTapproximation. ThetendencyofT toreduceto the financial support from the Ph.D Training Program c zeroatn =1suggestsadominantroleoftheDE mech- of the Ministry of Education and Training of Vietnam, p anism in this system; the SE interaction is effectively and is in debt to the collaboration and training project negligible. Remarkably, the linear behavior of T (n ) is between the IMS and Hongduc University. c p 1 C. Zener, Phys.Rev. 82, 403 (1951). 11 M. S.Kim, J. B. Yang, Q. Cai, X. D. Zhou, W. J. James, 2 A. J. Millis, P. B. Littlewood, and B. I. Shraiman, Phys. W.B.Yelon,P.E.Parris, D.Buddhikot,andS.K.Malik, Rev.Lett. 74, 5144 (1995). Phys. Rev.B 71, 014433 (2005). 3 A. J. Millis, R. Mueller, B. I. Shraiman, Phys. Rev. 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Zhu, J. Magn. 48, 167 (1999). Magn. Mater. 263, 249 (2003). 17 R.D. Shannon,Acta Cryst. A 32, 751 (1976). 9 J. Hu, H. Qin, J. Chen, and Z. Wang, Mater. Sci. Eng. B 18 J. L. Garc´ia-Mun˜oz, J. Fontcuberta, M. Suaaidi, and X. 90, 146 (2002). Obradors, J. Phys.: Condens. Matter 8, L787 (1996). 10 N. Kallel, G. Dezanneau, J. Dhahri, M. Oumezzine, and H. Vincent,J. Magn. Magn. Mater. 261, 56 (2003).

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