Nanometer Size Effect on Magnetic Properties of Sm0.8Ca0.2MnO3

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Nanometer Size Effect on Magnetic Properties of Sm0.8Ca0.2MnO3 Nanoparticles Vladimir Markovich,*,† Ivan Fita,§,|| Andrzej Wisniewski,§ Roman Puzniak,§ Dmitrii Mogilyansky,‡ Przemyslaw Iwanowski,§ Piotr Dluzewski,§ and Gad Gorodetsky† Department of Physics and ‡The Analytical Research Services and Instrumentation Unit, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel § Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, 02-668 Warsaw, Poland Donetsk Institute for Physics & Technology, National Academy of Sciences, 83114 Donetsk, Ukraine

)

†

ABSTRACT: Magnetic properties of compacted Sm0.8Ca0.2MnO3 (SCMO) particles with average particle size of 23100 nm, prepared by the glycine-nitrate method, have been investigated. It was found that the relative volume of the ferromagnetic phase decreases with decreasing particle size. Curves of field-cooled and zero-field-cooled magnetization (MZFC) exhibit a bifurcation just below the Curie temperature, TCdc ≈ 5564 K, determined from magnetization measurements for all particles studied. The field dependence of MZFC peak shows reasonable agreement with both the de AlmeidaThouless H2/3 line and the H2 power law. Measurements of ac susceptibility in the temperature range 5300 K and the frequency range f = 10 Hz to 10 kHz show a sharp peak for both real and imaginary components in the vicinity of TCdc, apparently attributed to the Hopkinson effect. The Curie temperature determined by zeroing the imaginary part of ac susceptibility χ00 (T) shows a larger value of TC ≈ 8590 K in compliance with TC of bulk Sm0.8Ca0.2MnO3 sample. A second small peak in ac susceptibility at T ≈ 1115 K is seemingly associated with antiferromagnetic or ferrimagnetic ordering. Although for smaller particles both peaks depend on frequency, no shift to higher temperatures with increasing f, characteristic for spinglass (SG) systems, was observed. Smallest, 23 nm, SCMO particles exhibit “waiting time” dependence in time evolution of MZFC, a feature expected for SG. These particles do not show any memory effects in MZFC, which is in strong contrast with the usual behavior exhibited by ferromagnetic nanoparticles with strong enough interparticle interaction. The dissimilarity in magnetic properties and dynamic characteristics observed for SCMO and for La0.8Ca0.2MnO3 nanoparticles is discussed, taking into account a difference in the width of the band and the strength of double exchange and interparticle interactions.

1. INTRODUCTION It is well-known that the mechanism ruling ferromagnetism in manganites is double exchange (DE), mediated by a hopping of electrons between manganese ions, which facilitates both ferromagnetic (FM) order and electrical conductance, thereby resulting in FM metallic (FMM) phase. The presence of states, at which excess carriers remain localized close to an impurity or manganese ion, may energetically favor a superexchange like interactions, which may yield FM insulating (FMI) or antiferromagnetic (AFM) phases.1 DE is always ferromagnetic, unlike superexchange (SE), which involves virtual electron transfer and frequently yields antiferromagnetism. SE interactions have been analyzed in detail by Goodenough.2 Two cases need to be distinguished: antiferromagnetic interactions between half-filled orbitals and ferromagnetic interactions between half-filled and empty or full orbitals. One well-known example for manganites is the case of LaMnO3, with only Mn3+ ions present in an A-type AFM structure, where FM Mn3+OMn3+ SE operates within ferromagnetically aligned layers, whereas neighboring planes are coupled antiferromagnetically. Nanosized materials are currently a focus of intense investigations. When the size of nanoparticles (NPs) is reduced to the nanometer scale, some of the basic magnetic properties become r 2011 American Chemical Society

strongly size dependent and differ significantly from the properties of the bulk material.3,4 An ensemble of NPs with weak interparticle magnetic interactions shows a superparamagnetic (SPM) behavior, whereas the one with pronounced interparticle interactions exhibits a collective behavior. Strongly interacting and dense compacted NPs show a spin-glass (SG) behavior and may be referred, by analogy to atomic SGs in bulk materials, as superspin-glasses (SSG).5 Nevertheless, further strengthening of interparticle correlations may result in the formation of a new collective state, of long-range order, that is, superferromagnetic (SFM) state, which is different from the SSG-like one in many respects.5 We have recently carried out investigation of the magnetic and transport properties of La0.8Ca0.2MnO3 (LCMO) particles with particle size of 18 and 70 nm and Curie temperatures TC ≈ 231 and 261 K, respectively.6,7 It was found that the volume of FM phase decreases from 92% for 70 nm particles to 52% for 18 nm particles. A pronounced irreversibility of magnetization below Tirr ≈ 208 K and strong frequency-dependent ac susceptibility Received: October 6, 2011 Revised: November 30, 2011 Published: November 30, 2011 435

dx.doi.org/10.1021/jp209617u | J. Phys. Chem. C 2012, 116, 435–447

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were observed for 18 nm particles below TC. The smaller 18 nm particles have shown memory effects in zero-field-cooled and field-cooled magnetization. These features indicate the appearance of spin glass-like state in these particles, whereas ensembles of larger 70 nm particles have shown no distinctive features of SGs. It should be noted that LCMO compound presents some characteristics of large bandwidth manganites, such as a presence of a robust FMM phase.1 Nevertheless, it also has a feature that indicates strong deviations from the DE behavior, including the existence of charge/orbital-ordered phases.1 For this reason, Dagotto et al.1 labeled this compound as a representative of “intermediate bandwidth” manganites to distinguish it from the truly narrow-bandwidth compounds Pr1xCaxMnO3 or Sm1xCaxMnO3, where a FMM phase can be stabilized only by the application of high magnetic fields. The magnetic and structural studies8,9 of the RMnO3 family have shown that the electronlattice interaction is, for sufficiently small rare-earth R3+ cations, considerably stronger than that one found for LaMnO3. This is a manifestation of the more ionic character of the perovskites with smaller R3+ ionic radius. The perovskite RMnO3 family shows a gradual structural and magnetic changes as ionic radius of R3+ cation decreases; the orbital ordering remains the same as that one for LaMnO3 below cooperative orbital ordering temperature TJT.8 However, TJT increases significantly from 750 K for LaMnO3 to ∼1300 K for SmMnO3 and to ∼1500 K for TbMnO3, whereas TN of type A spin order monotonously decreases with decreasing ionic radius.8 Sm1xCaxMnO3 has a highly distorted GdFeO3-type structure that is favorable for charge localization.10 This system is characterized by low average A-site cationic radius , and correspondingly the tolerance factor of these perovskites is always lower than 1 and increases with increasing divalent ion substitution x. Consequently, no FMM state can be detected in the hole-doped region, and only FMI state is observed at x < 0.35.10 The magnetization of Sm1xCaxMnO3 at 4 K was found to increase with increasing x, reaching a maximum value of 2.4 μB/f. at x = 0.2. Nevertheless, such a magnetic moment is not sufficient to lead to delocalization of the carriers, even under magnetic field of 70 kOe.10 In this Article, we report on the study of the magnetic properties of basically low-bandwidth manganite Sm0.8Ca0.2MnO3 (SCMO) NPs, with distinct particle sizes between 23 and 100 nm, performed to get some insight into a variation of the magnetic state of this system due to finite-size effect. We show that although the relative volume of FM phase appreciably decreases with decreasing particle size, all NPs exhibit features that are almost independent of particle size. The following results were obtained in the present investigation: (i) Field-cooled and zero-field-cooled (ZFC) magnetization (MZFC) curves bifurcate below the Curie temperature, which is almost unchanged (Tdc C ≈ 5564 K) for all particles studied. (ii) The field dependence of the ZFC magnetization peak shows reasonable good agreement with both the de AlmeidaThouless (AT) line11 suggested for spin glasses and the H2 power law suggested for superparamagnets. (iii) ac susceptibility does not show features characteristic for SGs. (iv) 23 nm SCMO particles demonstrate the waiting time dependence in the time evolution of MZFC, a feature characteristic for SG. One should note that at the same time they do not show any memory effects in MZFC. Such a behavior contrasts significantly with features observed for intermediate bandwidth manganite La0.8Ca0.2MnO3 NPs,6,7 whose magnetic and dynamic properties vary remarkably with variation in size. Furthermore, an ensemble of

interacting 18 nm La0.8Ca0.2MnO3 particles exhibits SSG features developing together with SFM-like ones.

2. EXPERIMENTAL SECTION Nanocrystalline SCMO particles have been prepared by the glycine-nitrate method, similar to that developed for preparation of La0.7Ca0.3MnO3 powders.12 The NPs were characterized by X-ray powder diffraction (XRD). The XRD data were collected by means of Phillips-1050/70 powder diffractometer, with a graphite monochromator on diffracted beam providing Kα radiation (λ = 1.541 Å) and operating at V = 40 kV, I = 30 mA. The XRD pattern of the as-prepared sample presents a fully amorphous phase. After annealing at T = 700 °C, only traces of amorphous phase were detected. Subsequent heating leads to a formation of a pure orthorhombic perovskite. Transmission electron microscopy (TEM) was carried with TITAN Cubed 80300 operated at 300 kV. Before measurement, SCMO samples were dispersed in methyl alcohol and treated by ultrasound for 30 min. The droplet of the suspension was deposited onto holey carbon film. For magnetic measurements, SCMO particles were compacted, under pressure of ∼5 kbar, into cylinder-shaped samples with a diameter of 2.4 mm and height of 3.0 mm. Most of the magnetization measurements were performed in the temperature range 5290 K and in magnetic field up to 15 kOe, employing a commercial vibrating sample magnetometer (VSM) PAR 4500. The ac susceptibility was measured at the same temperature range using the magnetic option of the Physical Property Measurement System of Quantum Design. 3. RESULTS AND DISCUSSION A. Studied System. The XRD patterns of the samples, calcinated at 700, 740, 820, and 1000 °C in the flow of 40% O2 and 60% Ar, and indexed by the orthorhombic setting of the Pnma space group, are shown in Figure 1a. To refine the lattice parameters and crystallite size, we performed the Rietveld analysis of these XRD spectra using the WinMPROF computer program.13 The Rietveld plot for the sample annealed at 740 °C is shown in Figure 1b. The average crystallite size D was calculated using DebyeScherrer equation. The results obtained are listed in Table 1 jointly with the corresponding temperature of calcination, the lattice parameters, and the cell volume. Consistently with the particles size, the samples will be denoted hereinafter as SCMO23, SCMO30, SCMO50, and SCMO100. It should be noted that the cell volume and orthorhombic distortion, defined as 2(a c)/(a + c), increases with increasing crystalline size. The effect of the cell shrinkage with size reduction, presented in inset in Figure 1b, was previously observed1416 and can be explained by the increasing surface pressure in smaller NPs. An alternative cause could be attributed to a variation in oxygen and Ca stoichiometry during the calcinations at which the cell volume reduces by >0.5% with decreasing size from 100 to 23 nm. At the same time, the inverse-value of particle size 1/D, which is proportional to the surface/volume ratio, increases by a factor of 4 and is in marked contrast with the expansion of unit cell observed for nanosized La1xCaxMnO3 (x = 0.2 and 0.3 (refs 6 and 17, respectively)) and La0.8Ca0.2CoO3 samples (ref 18). According to the model of LennardJones,19 the unit cell should expand with decreasing particle size in covalent crystals and contract in the ionic systems. Although such effect has been 436

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Figure 2. (a) TEM bright-field, (b,c) high-resolution images, and (d) EDS spectrum of the sample SCMO23. Figure 1. (a) XRD spectra of samples SCMO23, SCMO30, SCMO50, and SCMO100. Indexing is done in the orthorhombic setting of the Pnma space group. (b) Rietveld plot for SCMO30 sample. The experimental data points are indicated by open circles; the calculated and difference patterns are shown by solid lines. The Bragg positions of the reflections of the orthorhombic manganite are indicated by vertical lines below the pattern. Inset shows the size dependence of the unit cell volume of Sm0.8Ca0.2MnO3 nanoparticles. Straight line shows a linear contraction of the unit cell with the inverse value of particle size due to surface effect.

an agglomeration of particles is shown in Figure 2a. The highresolution transmission electron microscopy (HRTEM) images of some isolated particles are shown in Figure 2b,c. Arrows in Figure 2b point the nearly spherical form of a particle with a diameter of ∼30 nm, and the image in Figure 2c proves their crystalline structure. The EDS analysis revealed the presence of Sm, Ca, Mn, and O elements for all samples and confirmed atomic composition of the investigated particle within experimental error. The EDS spectrum for SCMO23 is shown in Figure 2d. The approximate value of oxygen content determined by EDS analysis is equal to 3.00 ( 0.04 for all SCMO NPs studied. B. Magnetization versus Temperature and Magnetic Field. Temperature dependences of field-cooled (MFC) and zero-field-cooled magnetization (MZFC) of SCMO samples recorded at applied field of 100 Oe are shown in Figure 3. The temperature of the peak in MZFC(T) curve can be associated with the blocking temperature, TB (5060 K), which lies only slightly below the Curie temperature for all SCMO samples studied. The Mn spin sublattice undergoes magnetic transition at the Curie temperature Tdc C ≈ 5355 K for the small SCMO23, SCMO30, and SCMO50 NPs, whereas it is somewhat higher Tdc C ≈ 64 K for larger SCMO100, with Tdc C determined as the temperature at which the derivative dMFC(T)/dT has a minimum; see lower insets in Figure 3ad. The Curie temperature Tdc C for all SCMO samples (Figure 3) is significantly lower than the Curie temperature for bulk Sm0.8Ca0.2MnO3 (TC ≈ 85 K).10 Various physical reasons may account for such a difference in Curie temperatures between NPs and bulk samples. For example, a fraction of missing bonds at the surface layer destabilizes magnetic order, giving rise to magnetic frustration. Consequently, the surface layer is being more demagnetized than the core. For this reason, the surface layer is usually named magnetic dead layer (MDL).23 Small variation of chemical composition and oxygen stoichiometry in a process of preparation of NPs may also result in the decrease in TC. In general, the magnetic correlation length diverges at TC, and the correlated fluctuating magnetic moments

Table 1. Crystalline Size, Lattice Parameters, and Volume of the Unit Cell of the Sm0.8Ca0.2MnO3 Samples Annealed at Various Temperatures temperature

lattice parameters (Å)

of calcination

crystalline

(°C)

size (nm)

cell volume a

b

c

(Å3)

700

23 ( 1

5.593(2) 7.568(3) 5.371(2)

227.3(2)

740 820

30 ( 2 50 ( 2

5.596(2) 7.565(2) 5.374(2) 5.625(1) 7.553(2) 5.371(1)

227.5(2) 228.2(1)

1000

100 ( 5

5.642(1) 7.540(1) 5.370(1)

228.5(1)

addressed19 as early as in 1930, the problem is yet to be fully understood or resolved.20 Theoretical analysis of size-related changes of lattice parameters by Gamarnik21 has led to following conclusions: (i) The sign of the size effect is determined by the sign of interaction energy, νc, of a unit cell with crystal unit cells excepting the nearest ones. (ii) In the case of ionic crystals, the sign of νc can be positive or negative, depending on crystal structure. (iii) For covalent crystals νc < 0, which leads to the lattice expansion observed in experiment, as shown in the study of partially covalent oxides.22 It appears that the contraction of the unit cell with decreasing particle size (see the inset in Figure 1b and Table 1) indicates ionic character of SCMO NPs. The NPs were also characterized by TEM and scanning electron microscopy, equipped with energy-dispersive X-ray spectroscopy (EDS) facilities. The TEM bright-field image of 437



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Figure 3. (ad) Temperature dependence of MZFC (open symbols) and MFC (solid symbols) magnetization of 23100 nm SCMO samples, recorded in magnetic field H = 100 Oe. Upper insets show the difference between MFC and MZFC, whereas lower insets show the derivative dMFC/dT as a function of temperature.

in the nanosize volume are influenced by a finite size of the sample. As a result, we can anticipate a reduction in the TC with decreasing particle size.24 Nevertheless, changing NPs composition and thereby crystallographic parameters in the particle core or in surface layer may mask or even inverse the effect of variation of TC with decreasing particle size.24 Note that for FMM manganites an increase in distortion of the lattice leads to the suppression of both electron transfer and DE interaction and correspondingly to reduced value of TC. Indeed, for optimally doped La0.7Ca0.3MnO3 NPs with basically FMM ground state, two-fold decrease in distortion of oxygen octahedra around Mn3+ ions at an increase of the NPs size from 12 to 49 nm, accompanied by corresponding increase of TC from 120 to 255 K, was observed.17 In the case of SCMO with FMI ground state, DE interaction is highly suppressed, and rather spinspin SE interactions are responsible for long-range magnetic order.25 In general, SE interaction depends on the type of intervening nonmagnetic ion and on relative position of the atoms and corresponding orbitals (the overlap of wave function). Because of this, it is very difficult to predict the effect of variation of orthorhombic distortion with particle size on TC in the case of SCMO. MZFC(T) and MFC(T) curves diverge at the irreversibility temperature Tirr > Tdc C (Figure 3), and the gap between them increases strongly with decreasing temperature up to 30 K, and only below 2530 K this gap does tend to decrease; see the upper insets in Figure 3. It should be noted that the decrease in MFC with decreasing temperature below 25 K is a characteristic feature for SSG or SFM systems because MFC of SPM systems always monotonously increases as the temperature is decreased simply because the superspins are blocked (or frozen) in the direction of the field.26

Figure 4. (a) Temperature dependence of MFC of 23100 nm SCMO samples, recorded in magnetic field H = 15 kOe. Inset shows MFC(T) on an extended scale. (b) H/M versus temperature curves for Sm0.8Ca0.2MnO3 nanoparticles measured at 15 kOe. The straight lines are a CurieWeiss fit with two fitting parameters Θ and μeff.

The MFC(T) curves measured at H = 15 kOe in the temperatures range 10250 K are given in Figure 4a and on an extended scale in the inset to Figure 4a. It appears that in the paramagnetic state the MFC(T) values for SCMO30, SCMO50, and SCMO100 almost coincide, whereas for smaller SCMO23 NPs, it is significantly lower, indicating an increasing role of surface layer for smaller particles. In the plots H/M versus temperature, the 438



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Figure 5. (a,b) Magnetic field dependences of magnetization of SCMO23 and SCMO100 samples at T = 10 K measured after FC. Insets show a lowfield part of hysteresis loops on the extended scale. (c) Size dependence of spontaneous magnetization M0 and magnetization MS in H = 15 kOe at T = 10 K. (d) Coercive field of SCMO samples as a function of the particle size. Solid line is linear fit to the expression HC = a + b/D; see the text.

both ZFC or FC processes; the field for the FC process was of H = 15 kOe. All of the observed loops exhibit ferromagnetic-like behavior, and they show spontaneous magnetization, hysteresis, and coercivity below Tdc C ; see Figure 5a,b. It appears that the magnetization of SCMO samples at 10 K remains unsaturated at H = 15 kOe; see Figure 5a,b. This is likely due to a noticeable contribution of the disordered or AFM ordered surface spins, which remain unsaturated at 15 kOe. The nonlinearity in M(H) above Tdc C may be attributed to FM clusters present even at ∼70 K, significantly above Tdc C . Nonlinearity in M(H) may be related to the broad distribution in the particle size, Curie temperatures, and magnetic anisotropies in the NPs ensemble.28 The spontaneous magnetization, M0, obtained from a linear extrapolation of the high-field magnetization to H = 0 was found to be ∼16.1 emu/g (0.67 μB/f.u.) for SCMO23 at 10 K. The M0 monotonously increases with increasing particle size and reaches a value of 33.5 emu/g (1.39 μB/f.u.) for larger SCMO100 NPs. The thickness, t, of MDL can be estimated by assuming a zero magnetization of MDL and using the expression29

straight lines approximate a CurieWeiss dependence M/H = C/(T Θ) with two parameters fitted in the range of 120250 K. The slope provides the value of Mn effective magnetic moment μeff, whereas the intercept provides the value of paramagnetic CurieWeiss temperature Θ. The values of Θ and μeff were obtained as a result of the best fit in the temperature range 120250 K; see Figure 4b. It is worth noting that the Curie Weiss temperature Θ remains almost unchanged (7981 K) for 2350 nm particles, and only for SCMO100 does it approach a value of 84 K. Value of μeff varies only slightly for 30100 nm particles (μeff ≈ 5.1 μB), whereas the slope of H/MFC(T) increases significantly for SCMO23 that corresponds to a reduction in μeff to the value μeff ≈ 4.22 μB. The latter suggests that the essential magnetic changes in our NPs occur for the size below 30 nm. The net magnetic moment for calcium/strontium-doped FM manganites La1x(Ca/Sr)xMnO3 usually saturates to full ferromagnetic value ≈ (4 x)μB/f.u., where a magnetization of 4 μB (3 μB) expected for free Mn3+ (Mn4+) ions agrees fairly well with experiments, indicating the quenching of the orbital moment. In a mean field approximation, for systems of mixed valency with ions Mn3+ with concentration (1 x) and Mn4+ with concentration x, effective magnetic moment μeff may be expressed as27 μ2eff

¼

∑n

in μ2eff n

2t=D ≈ 1 ðMS =Msb Þ1=3

ð2Þ

where MS and Msb are the values of saturated magnetization for NPs and for bulk, respectively. Here we have used an available value of Msb ≈ 2.4 μB/f.u. at H = 14.5 kOe and at T = 4 K.10 The ratio t/D monotonously increases with decreasing particle size from 0.035 for SCMO100 to 0.125 for SCMO23, indicating that t varies in the range of 2 to 3.5 nm for all samples studied. The evaluated value is found to be in reasonable agreement with the data obtained for various FM manganite NPs.30,31 Comparing the values of MS for SCMO NPs and Msb, we may conclude that the relative volume of the FM phase at 5 K in SCMO particles consistently increases with increasing particle size from ∼40% for 23 nm NPs to ∼80% for SCMO100 sample. The coercive field HC observed below TB increases with decreasing temperature and particle size. At T = 10 K, HC ≈ 1.02 kOe for

ð1Þ

where μ2effn = g2Sn(Sn + 1)μ2B and in is the fraction of magnetic ion (n = 1, 2, ...) per formula unit, g is their gyromagnetic factor, and S is their spin (S1 = 2 and S2 = 3/2 for Mn3+ and Mn4+ ions, respectively). From the above expression, one may calculate that effective magnetic moment for Sm0.8Ca0.2MnO3 should be μeff = 4.71 μB. It was suggested in ref 27 that polaronic effects responsible for the formation of magnetic clusters in the paramagnetic phase may result in higher experimental value of μeff. The magnetic hysteresis loops were recorded after cooling of SCMO samples from 300 K to the measuring temperature in 439



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Figure 6. (ad) Temperature dependence of real component of ac susceptibility (χ0 ) measured during heating at different frequencies and magnetic ac field of 10 Oe for SCMO samples. Insets show the imaginary part (χ00 ) of ac susceptibility measured at different frequencies and magnetic ac field of 10 Oe.

maximum in both χ0 and χ00 appears, does not shift while changing the frequency, in distinct contrast with behavior of spin glasses. The nature of low-temperature anomaly at 1115 K (Figure 6) in the form of shoulder in χ0 for smaller SCMO23 and SCMO30 samples and of a peak for larger SCMO50 and SCMO100 and of corresponding shallow peak in χ00 remains unclear. It has to be noted, however, that pure SmMnO3 and low Sr-doped compositions Sm1xSrxMnO3 (0 e x < 0.05) show a temperatureinduced magnetization reversal at the compensation temperature Tcomp = 9.4 K and a resultant negative magnetization opposite to the magnetic field direction in a low magnetic field.36 Ivanov et al.36 suggested that this behavior originates from an antiparallel orientation of weak FM moment of Mn and of the Sm moment induced by SmMn exchange interaction. Recently, Jung et al.37 have revealed first-order-like anomalies in the magnetic and dielectric properties of SmMnO3 crystal around the compensation point, which consequently causes the large magnetocapacitive effects. These effects manifest themselves as remarkable anomalies in the temperature profiles of magnetization, dielectric constant, and dielectric relaxation time in the temperature range 715 K.37 To explain the evolution of magnetic properties of manganite NPs with sizes in the range of tens of nanometers, a coreshell structure was proposed.38 This model assumes that the inner part of the particle, the core, has the properties of bulk material, whereas the shell that is magnetically and structurally incommensurate with the bulk may exhibit other magnetic order. Therefore, we suggest that the low-temperature peak in ac susceptibility tentatively may be associated with magnetic anomalies in the surface layer or interfacial core/shell layer. It should also be noted that similarly to the behavior of the high-temperature peak, the low-temperature peak does not shift with increasing frequency. It is also worth noting that for both interacting and noninteracting NPs,39,40 as well as for SGs,41 the temperature of the peak in χ0 is known to increase with increasing frequency.

SCMO100 and 1.5 kOe for SCMO23 particles; see Figure 5d. In general, as the particles are reduced in size, the coercivity increases, reaching the maximum value at Dcr, which corresponds to transition from multidomain to monodomain state and then starts to decrease with a further decrease in size.32 The coercivity in multidomain state may be approximated by the following expression HC ¼ a þ b=D

ð3Þ

where a and b are constants. Reasonable fitting of our experimental data for HC (see solid line in Figure 5d) with the above formulas indicates that particles of this size range are in the multidomain state, in an agreement with evaluation of Dcr ≈ 20 nm (where Dcr is a critical diameter of a single domain state) obtained for various FM manganite NPs.30,33 C. AC Temperature Curves. Temperature dependence of both real and imaginary parts of ac susceptibility χ0 (Figure 6ad) and χ00 (insets in Figure 6ad) of SCMO samples was measured at several frequencies between 10 Hz and 10 kHz, with probing field of 10 Oe and temperature lessening from 300 to 5 K. Sharp peaks in χ0 , at about 5356 K for SCMO23, SCMO30, and SCMO50 samples and at ∼61.5 K for SCMO100 (Figure 5), may be associated with a transition to FM state. One might assume that this high-temperature peak in both χ0 and χ00 arises from the Hopkinson effect, that is, from the divergence of the susceptibility near TC due to the vanishing of the anisotropy, as has been observed for fine particle system34 and nanosized La0.7Ca0.3MnO3 thin films.35 In an ensemble of NPs, the Hopkinson effect is associated with the transition from blocked to SPM state, which produces an increase in the susceptibility due to the decrease in the effective anisotropy of the particles while retaining a magnetization value different from zero.33 Both χ0 and χ00 decrease with increasing frequency in the vicinity of TC; the decrease is more pronounced for smaller SCMO23 and SCMO30 samples; see Figure 6. However, the temperature Tp, at which the 32

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Figure 7. (a) Temperature dependence of remanent magnetization for SCMO nanoparticles. (b) Temperature dependence of remanent magnetization for SCMO nanoparticle normalized to value of magnetization in H = 15 kOe.

Figure 8. (a) Temperature dependence of derivative of remanent magnetization for SCMO nanoparticles. (b) Temperature dependence of derivative (d(M FC M ZFC )/dT) of the difference between M FC and M ZFC .

As previously discussed in detail,42,43 the peak in χ0 (T) corresponds to the Tdc C value extracted from dc MFC(T) dependence, whereas it is the point at which χ00 (T) approaches zero, which corresponds to TC, rather than the peak in χ00 (T), which actually occurs significantly below TC. This nuance has been discussed in detail by Nam et al.,42 who pointed out that the peaks near TC for both χ0 (T) and χ00 (T) may have a different origin. In fact, they postulate that the peak in χ00 (T) corresponds to the reversibility temperature in dc M(T), where MFC(T) and MZFC(T) bifurcate just below TC.42 It was consequently suggested42,43 to label TC as the point at which χ00 (T) approaches zero. A comparison of the experimental results observed for both χ0 (T) and χ00 (T) of SCMO samples (Figure 6) shows that both of them display high-temperature peaks, practically at the same temperature, whereas χ00 (T) approaches zero at TC ≈ 8590 K; see Figure 6. Such an evaluation of Curie temperature for SCMO NPs is found to be in a reasonable good agreement with the Curie temperature of bulk polycrystalline Sm0.8Ca0.2MnO3 sample (TC ≈ 85 K).10 D. Magnetization Curves at Remanence. To obtain additional view on the temperature evolution of magnetic phases, we have performed measurements of thermoremanent magnetization (TRM). The TRM of SCMO NPs was measured in the following way: the sample was cooled to T = 10 K in magnetic filed H = 15 kOe; then, the magnetic field was switched off, and after a waiting time of 100 s, the magnetization was recorded. It was found that TRM for SCMO 2350 nm NPs behaves in a similar way, namely, it slowly decreases with increasing temperature and tends to zero above TB; see Figure 7a. The behavior of TRM for ensemble of larger SCMO100 particles is quite different; its TRM rapidly decreases with increasing temperature in the range 10 < T < 30 K and then decreases much slower at higher temperatures. The values of the remanent magnetization obtained from hysteresis loops after FC to various temperatures

(Figure 5a,b) agree quite well with the values of TRM (Figure 7a). Figure 7b presents the temperature variation of the TRM normalized to saturated value of magnetization. (As pointed out already, we referred to the value of MS at H = 15 kOe). It is worth noting that in the presence of independent relaxation phenomena (i.e., noninteracting particles) the temperature derivative of the remanent magnetization essentially reflects the effective distribution of anisotropy energy barriers of the system.44,45 Namely, the temperature derivative of the remanent magnetization has the same trend as the temperature derivative of the difference between MFC and MZFC. O’Grady and Chantrell44 pointed out that this technique is particularly important because it avoids the need to determine particle size distributions and obtain some estimate of the anisotropy constants. In Figure 8, both the derivative of the temperature decay of TRM (Figure 8a) and the temperature derivative curve d(MFC MZFC)/dT (Figure 8b) are shown. Although in our case, both types of dependences (compare Figure 8a,b) differ significantly for SCMO23, SCMO30, and SCMO50, they show a similar distribution of the effective anisotropy energy barriers. The difference in the form of both types of dependences is possibly due to the distinction in the strength of magnetic field applied during recording of MFC and MZFC (Figure 3) and H applied during cooling at the recording of TRM (Figure 7). Moreover, the lowtemperature transition (Figure 6) may affect the form of both derivatives: d(MFC MZFC)/dT and dMTRM/dT. In the case of SCMO100, such analysis has obviously failed and the reason for this as well as of the drastic change in the form of the temperature decay of TRM, remains unclear. E. Dynamic and Spin-Glass Features. In aging experiments of a TRM, a sample is cooled in a field to a given temperature, and 441



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relax together) and at long times (a predominantly relaxation of the core moment), whereas at intermediate times, the coreshell interaction makes the relaxation more complex.48 Correspondingly, for smaller SCMO23 particles, the role of disordered surface and the coreshell interaction is greatly enhanced in a comparison with larger SCMO NPs, and dynamic behavior of remanent magnetization cannot be fitted by a single or even two logarithmic functions. A shift of the ZFC magnetization maximum to lower temperatures due to an increase in applied magnetic field is generally consistent with the changes described by the AT line11 in the (H,T) plane, introduced initially for SG systems. At low magnetic fields, the AT line is given by an expression HðTÞ ¼ H0 ð1 T=Tg Þ3=2

ð4Þ

where Tg is the spin freezing temperature and H0 is the magnetic field at which the ZFC magnetization achieves a maximum at T = 0. The temperatures at which MZFC gets its maximal value, Tmax(H) for SCMO23 (Figure 10a) and for SCMO100 (Figure 10b) samples were approximated by the AT line of the form Tmax = Tg[1 (H/H0)2/3].11 It was found that Tmax scales well with the AT line, and the best fits were obtained with Tg = 59.2 K and H0 = 3.9 kOe (Figure 10c) for SCMO23 and with Tg = 66 K and H0 = 2.25 kOe (Figure 10d) for SCMO100. The quality of the fits is shown by the coefficient of determination (R2), which is shown in the corresponding plots; see Figure 10c,d. It is relevant to note here that Wenger and Mydosh49 have demonstrated the nonuniqueness of both H2/3 (de Almeida and Thouless11) and H2 (Toulouse and Gabay50) power laws for the field-temperature transition lines in spin glasses. They have also shown49 that similar power laws can be determined from the magnetic fielddependent on SPM relaxation time that results in a better quantitative agreement with the experimental values. Let us recall that both superparamagnets and spin glasses have some similar characteristics such as: a peak in MZFC(T) (called blocking temperature for superparamagnets and freezing temperature for spin glasses) and a bifurcation of MZFC(T) and MZFC(T). In the case of superparamagnets, the blocking temperature, TB, increases with increasing particle size because the energy barrier separating the low-energy states is proportional to the volume of the particle,5,51 whereas the field dependence of TB is given by52

Figure 9. (a) Time variation of remanent magnetization of SCMO23 NPs at temperatures 10 and 45 K. (b) Time variation of remanent magnetization of SCMO100 NPs at temperatures 10 and 45 K.

it is then allowed to relax for a some waiting time tw, and then the magnetization in zero magnetic field is recorded as a function of time. The ensembles of SCMO particles exhibit a complex dynamic behavior of remanent magnetization Mr. In these measurements, samples were cooled to T < TC in magnetic field H = 100 Oe; then, magnetic field was switched off and Mr was recorded as a function of time, starting a few seconds after the removal of the magnetic field. It is well known that the classical NeelBrown model46 describes the high-temperature SPM and the low-temperature blocking behavior of magnetic single domain particles, predicting an exponential decay of the magnetization, M(t) = M0 exp(t/τ), where M0 is the magnetization at time t = 0 and τ is the characteristic relaxation time. For a finite particle-size distribution47 or for interacting NPs,3 the deviations from this simple law (e.g., logarithmic decay) are expected. Figure 9 shows magnetization relaxation as a function of time for SCMO23 (Figure 9a) and for SCMO100 (Figure 9b) samples at temperatures 10 and 45 K. Below TC, an ensemble of SCMO100 particles exhibits logarithmic decay of Mr at both temperatures. The remanent magnetization of SCMO23 demonstrates a more complex behavior at 10 K; see Figure 9a. Namely, Mr(t) of SCMO23 shows at the beginning a negative slope, indicative of intrinsic magnetization relaxation. However, after ∼1500 s the value of Mr reaches a minimum and remains almost unchanged, whereas after 3000 s it slightly increases. The results obtained using Monte Carlo simulations for magnetic NPs, assuming a coreshell model, an uniaxial anisotropy in the core, and a single-site anisotropy of the spins of the shell, are found to be in qualitative agreement with observed magnetic behavior for amorphous ferromagnetic NPs, confirming that it is strongly affected by the disordered shell spins.47 This model explains the reduced saturation magnetization with respect to the bulk value and the existence of a nonsaturated component of the magnetization at high field observed in some NPs. The above effects were also observed in our SCMO particles; see Figure 5. It was previously stated that the low-temperature magnetic relaxation cannot be fitted by a simple superposition of two logarithmic functions and this fact marks a coreshell interaction.48 The logarithmic fit is appropriate only at shorter times (core and shell

TB µ V ðHK HÞ2

ð5Þ

where V is the volume of a single particle, HK is a positive constant depending on the anisotropy field and H is the field of measurements. With increasing applied magnetic field H, the energy barrier separating the two low-energy states decreases, and as a result TB is lowered, whereas at sufficiently high field (H = HK) temperature TB zeroes.51 According to eq 5, the square root of peak temperature TB as a function of magnetic field is a straight line for SPM system. Nevertheless, results presented in Figure 3 show that TB varies only slightly with increasing size, approaching a value of 53.8 K for SCMO23 and 58.5 K for SCMO100, in distinct disagreement with eq 5, where TB is proportional to the volume of the particle. Figure 11 shows a plot of the experimentally observed TB1/2 as a function of magnetic field and a fit of eq 5. It can be seen that in the case of SCMO23 both fits have higher value of a coefficient R2 and the SPM fit is considerably better with R2 = 0.99538 (Figure 11a) for linear fit in comparison with R2 = 0.98546 for fitting of eq 4. This means 442



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Figure 10. (a,b) Temperature dependence of MZFC magnetization of SCMO23 and SCMO100, recorded in different magnetic fields; (c,d) Temperature of the peak in ZFC magnetization as function of magnetic field for SCMO23 and SCMO100. The solid lines are fitted by equation Tmax = Tg[1 (H/H0)2/3], with following parameters: Tg = 59.2 K, H0 = 3.9 kOe for SCMO23, and Tg = 66 K, H0 = 2.25 kOe for SCMO100.

similar coefficient R2, indicating that both models (SPM and SSG) provide proper description of variation of a peak in MZFC(T) with magnetic field, although both values of R2 are noticeably below 1. We have recently studied aging and memory effects in series of dc magnetization measurements for 18 nm LCMO NPs. Those experiments have shown the waiting time dependence in magnetization relaxation due to a field change after ZFC and an aging dip at the stop temperature on the reheating after ZFC procedure with single intermittent stop and wait event. These features are characteristic for SSG and are hardly expected in superparamagnets.26 For the sake of comparison of behavior of SCMO and LCMO, we have also studied aging and memory effects in SCMO NPs. When magnetic field is applied to a glassy system, which was cooled in zero field from a temperature above the glass temperature Tg to a temperature Tw < Tg, the time evolution of magnetization at Tw depends on the time spent by the system at low temperature, before application of the field. In our experimental protocol the sample was cooled to 40 K in zero magnetic field, maintained at low temperatures at H = 0 for the waiting time tw, after which the magnetic field of 10 Oe was applied. The time evolution of magnetization resulting from slow relaxation is shown in Figure 12a. The observed time dependence of magnetization can be well-approximated by a stretched exponential form53

Figure 11. Dependence of the blocking temperature TB1/2 as a function of a magnetic field for (a) SCMO23 and (b) SCMO100 samples. The solid lines show linear fit to the experimental data.

MðtÞ ¼ M0 Mg exp½ ðt=τÞβ

ð6Þ

where M0 is the magnetization of an intrinsic FM component and Mg is the initial magnetization of the glassy component, which provides the main contribution to the relaxation. The time constant τ and the dispersion parameter β are related to the relaxation rate of the SG phase. The value of the exponent β depends on the nature of energy barriers involved in the relaxation. For uniform energy barrier β = 1, whereas for the

that the ensemble of SCMO23 NPs behaves as SPM system rather than a SSG. The fits of eq 5 to experimental data (Figure 11) also appear reasonable, but for better comparison we can collate the goodness of the fits presented by a coefficient R2; see Figures 10 and 11. It appears that for larger SCMO100 particles fits of both eqs 4 (Figure 10d) and 5 (Figure 11b) have 443



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Figure 12. (a) Relaxation of ZFC magnetization of 23 nm SCMO at T = 40 K in H = 10 Oe for tw = 100, 1000, and 10 000 s. (b) Magnetic viscosity S(t) = (1/H) dM(t)/d(ln t) of 23 nm SCMO measured at 40 K for various waiting time.

Figure 13. (a) Temperature dependence of the reference magnetization MZFCref (open triangles) and of the magnetization with a stop and waiting protocol MZFCwait (open squares) at a magnetic field H = 5 Oe. First, 23 nm SCMO sample was cooled at H = 0 from 300 to 8 K with the rate of 5 K/min. Then, magnetization was measured at heating; see MZFCref. After that, the system was cooled again at H = 0 from 300 K to a stop temperature TS. The system was annealed at stop temperature TS = 40 K for the wait time 10 000 s. The cooling was resumed from TS to 8 K. Then, the magnetic field H = 5 Oe was turned on, and the magnetization MZFCwait was measured at heating. (b) ΔM = MZFCwait MZFCref versus temperature.

system with distribution of energy barriers, what is typical for SGs, 0 < β < 1. The fit of the stretched exponential eq 6 to the experimental data of Figure 12a renders the following values for the fitting parameters: β ≈ 0.468, 0.527, 0.535 and τ = 1688, 2494, 10132 s for tw at 100, 1000, and 10 000 s, respectively. The results indicate on a slow increase in time constant τ with increasing waiting time tw in some similarity with the results obtained previously for LCMO NPs.6 In classical SG systems, the time dependence of magnetization shows an inflection point at tw, which is usually detected as a peak at t ≈ tw in the magnetic viscosity S(t) = (1/H) dM(t)/d(ln t) plot versus t.46,41 The effect is predicted for SG systems by the droplet model,54 associating the maximum in magnetic viscosity S(t) with a crossover from quasi-equilibrium dynamics at t < tw to nonequilibrium dynamics at t > tw. Time dependence of the magnetic viscosity S(t) for 23 nm SCMO sample is shown in Figure 12b for various tw. In resemblance to classical SG systems,41 the peak in the S(t) shifts to longer times with increasing tw, confirming the glassy magnetic behavior. However, in contrast with the behavior of classical SG systems, and in some resemblance to the behavior of the S(t) in 18 nm LCMO NPs, the waiting time dependence of the magnetic response in 23 nm SCMO is relatively weak. Note that the maximum of S(t) moves only from 1120 to 7280 s upon three orders of magnitudes changes in waiting time, and this shift is stronger than that observed for 18 nm LCMO particles. To investigate memory effects in ZFC magnetization, we have employed a single stop point and wait for the aging protocol. The sample was first ZFC-cooled from room temperature to 8 K at

the rate of 5 K/min. The reference magnetization, MZFCref, was measured in magnetic field of H = 5 Oe during reheating back to room temperature with the rate 0.5 K/min. In the next run, the sample was cooled in zero magnetic field from 300 K to a stop point at TS = 40 K at the same cooling rate. The system was aged at TS for tw = 10 000 s. After the waiting time had elapsed, the ZFC was resumed and the sample was cooled to 8 K. At that temperature, the magnetic field of H = 5 Oe was turned on, and MZFCwait magnetization was measured again during the reheating cycle with the same heating rate 0.5 K/min as in MZFCref measurement. The temperature dependence of both MZFCref and MZFCwait is shown in Figure 13a. Usually for SG or SSG, the difference between MZFCwait and MZFCref exhibits an aging dip in the vicinity of TS, which results from spontaneous reconfigurations of magnetic moments toward the equilibrium state, through a growth of equilibrium domains at TS. Our recent study of memory effects in ZFC magnetization for 18 nm LCMO has shown not only a dip in the vicinity of TS = 100 K but also the splitting between MZFCwait and MZFCref at temperatures below and above TS.6 As it was discussed, this splitting may result only from partial rejuvenation, which is considered as a hallmark of the 444



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SSG behavior of strongly interacting NPs. This is because the number of correlated superspins in SSGs on the experimental time scale is much smaller than in canonical atomic spin glasses.6 As can be seen in Figure 13b, the difference between MZFCwait and MZFCref does not exhibit an aging dip at TS = 40 K. Instead, it displays a puzzling temperature evolution in the range 855 K and complete rejuvenation only upon approaching TC. Such enigmatic behavior does not seem to fit into the well-established pictures for both SSG and superparamagnets. Our recent study of LCMO particles has shown that 18 nm particles exhibit features characteristic of the formation of a collective state, which involves both SG-like and nonequilibrium FM components, resulting in a complex dynamic behavior.6 Contrary to what is observed for 18 nm LCMO particles, the magnetic and dynamic properties of 70 nm LCMO particles are distinctly different because they embody a 3D ferromagnets.6 It was concluded that enhanced surface SG-like shell contribution together with strong interparticle interactions in 18 nm LCMO particles are vital prerequisites for an appearance of SSG or even SFM collective state. In a distinct contrast with the different dynamic and glass characteristics of LCMO system, all SCMO samples, independently of their size and relative amount of FM phase, exhibit very similar characteristics; see Figures 36 and 10. Namely, they are characterized by almost the same TC, a significant difference between MZFC(T) and MFC(T) (Figure 3), unsaturated magnetization in H = 15 kOe at T = 10 K (Figure 5), and similar features in ac susceptibility (Figure 6), and they exhibit a similar behavior of the ZFC in magnetic field (Figure 10). In dense NPs with a random distribution of easy axis, the interparticle interaction is an additional source of magnetic frustration that may lead to a frozen collective state of the particles at low temperature. This interaction appears to be additional to surface/core exchange coupling. The main types of magnetic interactions that can be found in NP assemblies are dipoledipole interaction, which always exists, and exchange interaction through the surface of the particles being in close contact.55 It should be noted that dipolar interactions are anisotropic in nature and may favor ferromagnetic or antiferromagnetic alignments of the moments depending on the crystallographic structure. It appears that fine-particle systems have all of the ingredients necessary to give rise to a SG state, namely, random distribution of easy axes and frustration of the magnetic interactions.4 The complex interplay between both types of magnetic interactions determines the state of the system and its dynamical properties.4,5 Supplementary magnetic interparticle interaction, which may considerably contribute to the formation of collective states in LCMO NPs, arises from the scenario proposed by Rozenberg et al.56 It was suggested in ref 56 that electrons tunneling between two Mn ions located in adjacent manganite NPs may induce FM DE correlations due to local spin polarization of these electrons, similarly to electron hopping between two Mn ions in the bulk. These DE correlations across the interface between two NPs are likely to be even stronger than the bulk counterpart due to dangling of some of MnOMn bonds on the grain surfaces. The comparison between both La 1x Ca x MnO 3 and Sm1xCaxMnO3 systems have shown that the latter is characterized by a considerably smaller value of average A-site cationic radius and tolerance factor t. In particular, for x = 0.2, and t are equal to 0.1352 nm and 0.964 for LCMO, whereas for SCMO, and t are equal to 0.126 and 0.93 nm, respectively. As already mentioned, SCMO exhibits highly distorted perovskite

GdFeO3-type structure, which is favorable for the charge localization and detrimental for DE interactions.10 Consequently, no FMM state can be detected for SCMO in the hole-doped region, as shown in the magnetic phase diagram of this system.10 The FMM state with dominant DE interaction appears only for a sufficiently large size of , allowing a wide band (W) to be generated beyond a certain value of the hole concentration.10 For this reason, the SCMO system, which contains too-small A-site cations, has a too-narrow band W and does not form FMM domains in contrast with LCMO. As a result of the suppression of the DE-like correlations across the interface between two NPs, the formation of collective state with pronounced SSG/SFM features,5 observed in 18 nm LCMO particles, is hindered in the case of SCMO particles, making magnetic properties of all NPs very similar and almost size-independent. In this regard, manifestation of some SG-like features, such as waiting time dependence in ZFC magnetization and complete absence of other, such as frequency shift of peak position of ac susceptibility to higher temperature and no memory effect in MZFC, shows that exotic physics may occur in SCMO NPs. Moreover, as pointed out already, variation of TB with magnetic field for smaller SCMO23 NPs can be well-fitted with eq 5, characteristic for SPM; see Figure 11a. Nevertheless, SPM behavior is characteristic for an ensemble of noninteracting single-domain particles (superspins) as the magnetic moments of the particles act independently.35 Note, however, that the behavior of coercive field (Figure 5d) is inconsistent with SPM behavior.26 In a nutshell, we conclude that SCMO23 NPs show an anomalous magnetic behavior that cannot be described as SPM or SSG-like.

4. CONCLUSIONS The presented results show that the magnetic properties of Sm0.8Ca0.2MnO3 NPs with distinct particle sizes of 23100 nm are very similar, although the relative volume of FM phase appreciably decreases with decreasing particle size from ∼80% for larger SCMO100 to ∼40% for smaller SCMO23 NPs. The field-cooled and zero-field-cooled magnetization curves bifurcate below the Curie temperature Tdc C determined from magnetization measurements, which varies only slightly (Tdc C ≈ 5564 K) for all particles studied. The magnetization remains unsaturated at H = 15 kOe and T = 10 K. The field dependence of ZFC magnetization peak follows the AT line, indicating SG-like behavior. ac susceptibility measured in the temperature range 5300 K and the frequency range f = 10 Hz to 10 kHz shows a sharp peak for both real χ0 (T) and imaginary χ00 (T) components in the vicinity of Tdc C , attributed to the Hopkinson effect. The Curie temperature determined by zeroing of χ00 (T) gives a value of TC ≈ 8590 K for all SCMO NPs, in a compliance with Curie temperature of bulk Sm0.8Ca0.2MnO3. A second small peak of ac susceptibility at T ≈ 1115 K is seemingly associated with antiferromagnetic or ferrimagnetic ordering. Although, for smaller particles, amplitudes of both peaks depend on frequency; no shift to higher temperatures with increasing f, characteristic for SG systems, was observed. The 23 nm SCMO particles exhibit waiting time dependence in time evolution of MZFC, the feature expected for SG. Moreover, the observation of relaxation of magnetization and the associated waiting time-dependent peak in magnetic viscosity is similar to such behavior shown by other systems with strong enough interparticle interaction. No memory effect has been observed in ZFC protocol, which is in sharp contrast with the usual behavior shown by ferromagnetic 445



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NPs in the collective state. All results obtained for SMCO NPs lead to surprising conclusion that this system behaves neither as a superparamagnet nor as an SSG. Such a behavior contrasts with the magnetic and dynamic properties observed recently for 18 and 70 nm La0.8Ca0.2MnO3 particles. For a better understanding of the nature of the magnetic state and dynamic characteristics observed here for SCMO NPs, further detailed studies are cardinally needed.

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’ AUTHOR INFORMATION Corresponding Author

*Tel: + 972 8 6477127. Fax: + 972 8 6472903. E-mail: markoviv@ bgu.ac.il.

’ ACKNOWLEDGMENT This work was partially supported by the Polish Ministry of Science and Higher Education under a research project no. N 202 1037 36 and by European Fund for Regional Development (contract no. UDA-POIG.01.03.01-00-058/08-00). ’ REFERENCES (1) Dagotto, E. Nanoscale Phase Separation and Colossal Magnetoresistance; Springer Series in Solid State Physics; Springer-Verlag: Berlin, 2003. (2) Goodenough, J. B. Phys. Rev. 1955, 100, 564–573. (3) Dormann, J. L.; Fiorani, D.; Tronc, E. Adv. Chem. Phys. 1997, 98, 283–494. (4) Batlle, X.; Labarta, A. J. Phys. D: Appl. Phys. 2002, 35, R15–R42. (5) Bedanta, S.; Kleemann, W. J. Phys. D: Appl. Phys. 2009, 42, 013001/1–013001/28. (6) Markovich, V.; Fita, I.; Wisniewski, A.; Jung, G.; Mogilyansky, D.; Puzniak, R.; Titelman, L.; Gorodetsky, G. Phys. Rev. B 2010, 81, 134440/1–134440/11. (7) Markovich, V.; Jung, G.; Wisniewski, A.; Puzniak, R.; Fita, I.; Yuzhelevski, Y.; Mogilyansky, D.; Titelman, L.; Gorodetsky, G. J. Supercond. Novel Magn. 2011, 24, 861–865. (8) Zhou, J.-S.; Goodenough, J. B. Phys. Rev. Lett. 2006, 96, 247202/ 1–247202/4. (9) Alonso, J. A.; Martínez-Lope, M. J.; Casais, M. T. Inorg. Chem. 2000, 39, 917–923. (10) Martin, C.; Maignan, A.; Hervieu, M.; Raveau, B. Phys. Rev. B 1999, 60, 12191–12199. (11) de Almeida, J. R. L.; Thouless, D. J. J. Phys. A 1978, 11, 983–990. (12) Markovic, D.; Kusigerski, V.; Tadic, M.; Blanusa, J.; Antisari, M. V.; Spasojevic, V. Scr. Mater. 2008, 59, 35–38. (13) Jouanneaux, A. International Union of Crystallography Newsletter; Commission on Powder Diffraction: 1999; Vol. , 21, p 13. (14) Rozenberg, E.; Auslender, M.; Shames, A. I.; Mogilyansky, D.; Felner, I.; Sominskii, E.; Gedanken, A.; Mukovskii, Ya. M. Phys. Rev. B 2008, 78, 052405/1–052405/4. (15) Sarkar, T.; Mukhopadhyay, P. K.; Raychaudhuri, A. K.; Banerjee, S. J. Appl. Phys. 2007, 101, 124307/1–124307/7. (16) Zhang, T.; Dressel, M. Phys. Rev. B 2009, 80, 014435/ 1–014435/9. (17) (a) Kusigerski, V.; Markovic, D.; Spasojevic, V.; Tadic, M.; Zentkova, M.; Mihalik, M. J. Nanopart. Res. 2010, 12, 1299–1306. (b) Markovic, D.; Kusigerski, V; Tadic, M.; Jovan Blanusa, J.; Jaglicic, Z.; Cvjeticanin, N.; V Spasojevic., V. J. Alloys Compd. 2010, 494, 52–57. (18) Fita, I.; Markovich, V.; Wisniewski, A.; Mogilyansky, D.; Puzniak, R.; Iwanowski, P.; Meshi, L.; Titelman, L.; Varyukhin, V. N.; Gorodetsky, G. J. Appl. Phys. 2010, 108, 063907/1–063907/9. (19) Lennard-Jones, J. E. Z. Kristallogr. New Cryst. Struct. 1930, 75, 215–216. 446



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Nanometer Size Effect on Magnetic Properties of Sm0.8Ca0.2MnO3

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