Non-equilibrium magnetic properties of Sm0.43Ca0.57MnO3 nanoparticles

Non-equilibrium magnetic properties of Sm0.43Ca0.57MnO3 nanoparticles V. Markovich,1 B. Dolgin,1 R. Puzniak,2 A. Wisniewski,2 I. Fita,2,3 D. Mogilyansky,4 E. Dvir,5 G. Gorodetsky,1 and G. Jung1,2 1

Department of Physics, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel 2 Institute of Physics, Polish Academy of Sciences, PL-02-668 Warsaw, Poland 3 Donetsk Institute for Physics and Technology, National Academy of Sciences, 83114 Donetsk, Ukraine 4 The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel 5 Nuclear Research Center Negev, P.O. Box 9001, 84190 Beer-Sheva, Israel

Abstract Non-equilibrium magnetic properties of the near half-doped Sm0.43Ca0.57MnO3 nanoparticles with an average size as small as 15 have been investigated by measuring temperature dependence of zero field cooled (ZFC) magnetization, ac-susceptibility, time dependence of ZFC magnetization, relaxation of the remanent magnetization, and memory effects in ZFC magnetization. For the studied particles, charge ordering, characteristic for the bulk, is gradually suppressed with decreasing particle size and fully disappears in 15 nm particles, while the Néel temperature decreases slightly from 73 K for 60 nm to 58 K for 15 nm particles. It was found that dipolar interaction between 15 nm nanoparticles is enough to leads to the formation of a superspin glass state. Characteristic features of superspin glass state, such as ageing and memory effects have been observed in 15 nm samples. In a difference to atomic spin glasses, no strong rejuvenation of magnetization has been observed at low temperatures. PACS: 75.47.Lx; 75.50.Tt; 75.50.Lk; 75.60.Jk Keywords: nanocrystalline manganites, magnetization, particle size, spin-glass Corresponding author: Vladimir Markovich Department of Physics, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel e-mail: [email protected]

1

1. Introduction Magnetic nanoparticles (NPs) are in a focus of intensive investigations because they exhibit a plethora of properties that do not appear in their bulk counterparts.1-3 Recently, particular attention was paid to nano-sized perovskite manganites RxA1−xMnO3, where R and A are rare earth and alkaline earth, respectively.4-11 Recent theoretical studies of phenomenological models and Monte Carlo simulations of charge ordered (CO) antiferromagnetic (AFM) nanomanganites predict an enhancement of the surface charge density, accompanied by the suppression of the AFM/CO phase and an emergence of the ferromagnetic (FM) order with spin-glass (SG)-like behavior near the particle surface.11 Additional factors affect magnetic behavior of NPs in real systems. In general, the surface shells terminal ions with imperfect coordination number and various surface defects exercise elastic and electric forces capable to influence, in some distance from the surface, the regular atomic periodicity, what leads to changes in the inter-atomic exchange interactions and to different magnetic order in the outer shell with respect to that in the particle core.12 In addition, fluctuations of the chemical composition and the grain-size dispersity may also affect dynamic properties.12 In the case of manganite NPs, the cation coordination at the surface layer is reconstructed by the chemisorbed oxygen, and the oxygen surplus in the particle shell may shift the Mn3+/Mn4+ mixed valence toward Mn4+. It is well known that NPs ensembles with sufficiently weak inter-particle magnetic interactions exhibit a superparamagnetic (SPM) behavior. In general, a system with sufficient inter-particle interactions may show collective behavior, superferromagnetic (SFM), or superspin glass state (SSG).3 While some dynamic effects may be observed in both SPM and SSG, the "waiting time" dependence and memory effects in zero field cooled (ZFC) magnetization remain the unequivocal signatures of SG and of SSG.3 Existence of collective

2

SFM or SSG states have been experimentally confirmed in many systems of ferromagnetic particles,3,12-16 including FM nanomanganites.12,14-16 Spin glass features and collective states in ensembles of antiferromagnetic NPs have received relatively less attention. Monte-Carlo simulations17 and detailed experimental study18 of NiO nanoparticles have confirmed the existence of a collective state through observations of the memory effects in ZFC magnetization and the time decay of the remanent magnetization. On the other hand, recent study of non-equilibrium effects in ensembles of antiferromagnetic Co3O4 (Ref. 19) and CuO (Ref. 20) nanoparticles have shown that despite of the appearance of some dynamic effects, the real spin-glass-like state is definitely not present. We have recently reported on non equilibrium properties and on a formation of a collective state in ensembles of electron doped intermediate-bandwidth La1-xCaxMnO3 (x = 0.77, 0.8) NPs with sizes of 12 – 15 nm. These NPs demonstrate clear SSG features such as frequency shift of the freezing temperature, ZFC magnetization dependence on the waiting time, memory effects in ZFC magnetization, and decay of the remanent magnetization.21,22 A collective state in ensembles of AFM NPs with very weak dipole−dipole interaction may appear due to exchange interactions,22,23 which likely play an important role in the formation of the SSG state in basically antiferromagnetic La1-xCaxMnO3 NPs. However, the above mechanism is rather unfeasible for the narrow-bandwidth Sm1-xCaxMnO3 antiferromagnetic NPs. Sm1-xCaxMnO3 has highly distorted perovskite GdFeO3-type structure that favors charge localization and is detrimental for double exchange (DE) interactions.24-26 In the bulk Sm1-xCaxMnO3, the CO appears in the doping range 0.4 < x < 0.85 and stabilizes in different CO configurations, depending on the Mn3+/Mn4+ ratio.24-26 For example, the bulk form of Sm0.43Ca0.57MnO3 undergoes CO at TCO ≈ 285 K, the highest

3

value in Sm1-xCaxMnO3 system, and is characterized by a huge difference between TCO and the Néel temperature TN ≈ 135 K. In this paper, we discuss properties of antiferromagnetic Sm0.43Ca0.57MnO3 (SCMO) nanoparticles with an average particle size ranging from 15 to 60 nm, focusing mainly on the non-equilibrium properties, such as ac-susceptibility, aging, memory effects, and decay of the remanent magnetization in the smallest 15 nm particles.

2. Experimental The SCMO NPs were prepared by the glycine-nitrate method.27 The X-ray diffraction revealed that annealing at T ≥ 650 oC of as-prepared samples transforms the mixture of calcite and amorphous phases into a pure orthorhombic nanocrystals with the average size controlled by the annealing temperature. The average crystallite sizes and the lattice parameters were calculated using Debye-Scherrer equation. The size of NPs was additionally confirmed by transition electron microscopy (TEM) and high resolution TEM investigations. In this work, we have studied SCMO NPs with average sizes of 15, 25, 33, and 60 nm, which will be further referred to as SCMO15, SCMO25, SCMO33, and SCMO60. In order to perform magnetic measurements, SCMO NPs were compacted under the pressure of ~ 5 kbar into cylinder-shaped samples with 2.4 mm in diameter and 3 mm height. The density of such prepared samples was about 50–55 % of the bulk density, which results in high level of porosity and an absence of strains that may appear at higher compaction pressure. The ac-susceptibility, and dc magnetization measurements, as well as measurements of dynamic magnetic properties were carried out using the AC susceptibility & DC magnetization (ACMS) and vibrating sample magnetometer (VSM) options of Quantum Design Physical Property Measurement System (PPMS).

4

3. Results and discussion 3.1 ac susceptibility Temperature dependence of the real and imaginary part of ac susceptibility χ' and χ'', shown in Fig. 1, was measured at the probing field of 10 Oe of several frequencies between 10 Hz and 10 kHz in the temperature range from 10 to 315 K. At high temperatures, χ' of the larger SCMO25, SCMO33 and SCMO60 NPs exhibits a wide, not well pronounced, maximum at 250, 266, and 280 K, respectively. Since the maximum is associated with the transition to the CO state, one can conclude that TCO diminishes with decreasing particle size. Moreover, with decreasing particle size, the maximum in χ' becomes broader and disappears for SCMO15 NPs, likely indicating a complete suppression of CO. Low temperature behavior of χ' is qualitatively very similar for all samples. Below ~110 K, temperature dependence of χ' demonstrates a steep maximum that slightly decreases in height at higher frequencies. The temperature at which maximum is observed shifts toward lower temperatures with decreasing particle size. It is well known that χ' of paramagnets increases with decreasing temperature, while for antiferromagnets at temperatures below the TN, χ' decreases with decreasing temperature. Consequently, a distinct peak is expected to appear at the TN.28 The peak position may be therefore tentatively related to the TN of the AFM phase in the core of NPs. The peak in χ' may be also associated with the SG freezing temperature.29 Indeed, the frequency dependent temperature-shift resembles the spin/cluster glass-like behavior and can be characterized by the factor K = ∆Tf/Tf∆(logω), where Tf refers to the temperature of the maximum of χ' and ∆Tf is the temperature shift at a given frequency. The observed frequency shift of the peak's temperature is relatively small and the resulting K factor for all investigated SCMO NPs varies in the range 0.003 – 0.0035, values that are smaller than the lowest limit for typical spin glasses (0.0045 – 0.08).29

5

The temperature evolution of the imaginary part of ac-susceptibility χ'' is qualitatively the same for all SCMO NPs. The χ'' sharply peaks just below the onset temperature. The peak shifts towards low temperatures with decreasing particle size, similarly to the χ'(T) behavior. A step-like onset of χ''(T) is rather atypical for nanoparticle spin-glass-like ensembles which in general exhibit a smooth Lorentzian-like onset.1,3,30 In particular, a smooth onset appears in several electron- and half-doped manganite NPs.7,31,32 As discussed by De Toro et al.30 the step-like onset of the imaginary component of ac-susceptibility resembles rather the behavior of the model spin glass.

3.2 Zero Field Cooled Magnetization Figure 2 presents the ZFC magnetization of SCMO15 sample measured during a heating run in various magnetic fields. A shift of the ZFC magnetization maximum toward lower temperatures, caused by an increase in the applied magnetic field, is generally consistent with de Almeida-Thouless (AT) line in the (T, H) plane, introduced initially for anisotropic Ising SG systems.33 At low magnetic fields, the AT line is given by: p

Tmax(H) = Tg [1− (H/H0) ],

(1)

where Tg is the spin freezing temperature at H = 0, p = 2/3 for classical SG, and p < 2/3 for cluster spin glass. The value of Tmax for SCMO15 scales well with the AT line (p = 2/3). The best fit of Eq. (1) to the data was obtained for Tg = 58.0 K and H0 = 5530 Oe, see inset in Fig. 2. One can see that the magnetic field dependence of Tmax deviates from the AT line at H > 1800 Oe. Similar behavior was observed recently for nanoparticles of half-doped Pr0.5Sr0.5MnO3 manganite with sizes 16 – 19 nm.34 It was suggested that the deviation from the AT line is a manifestation of a crossover from de Almeida-Thouless to Gabay-Toulouse (Tmax(H) ∝ H2) critical lines in the field-temperature plane, that appears above the respective

6

interparticle interaction field.35 It should be noted that the Gabay-Toulouse line is generally valid for isotropic Heisenberg SG.35 Nevertheless, Wenger and Mydosh36 have underlined the non-uniqueness of both H2/3 (de Almeida and Thouless33) and H2 (Toulouse and Gabay35) power laws for the fieldtemperature transition lines in spin glasses. They have shown36 that similar power laws can be obtained from the magnetic field dependence of the superparamagnetic relaxation time. We note, however, that the very existence of the AT line in T – H phase diagram remains puzzling, since it was originally suggested for anisotropic model of SG with Ising-like interactions, while manganites represent systems with rather Heisenberg interactions.37 As discussed recently by Sirenko and Eremenko37 the role of anisotropy in processes of magnetic ordering of manganites has not been studied enough and random character of anisotropy in SGs may result in compensation of transverse components of magnetic moments at measurements of magnetization, leading to Ising-like behavior. In this case, sufficient enough magnetic field may promote a spin-reorientation phase transition in AFM component and, as a result, may induce transition from one SG state (Ising-like) to another SG state (Heisenberg-like).37 Since H2/3 variation of the Tmax cannot be solely considered as being due to SG freezing, additional experiments are needed to confirm the SG nature of the studied system.

3.3 Ageing and memory effects Recently, we have studied ageing and memory effects in dc magnetization for series of FM and AFM La1-xCaxMnO3 (LCMO) (x = 0.2,16 0.66,32 0.77,21 0.8 (Ref. 22)), NPs. Waiting time dependence of magnetization relaxation after ZFC and an ageing dip at the stop temperature during reheating after ZFC procedure were observed.16,22 The dip appeared after a single intermittent stop and a waiting time. Slow dynamics and concomitant memory (ageing) effects in nanomagnetic systems were analyzed in the framework of two separate 7

paradigms of superparamagnets and spin-glasses.38,39 It was found that SPM may exhibit various memory (ageing) effects due to polydispersity (i.e., distribution of the volume of NPs) resulting in distributions of energy barriers and blocking temperatures. It was also concluded that ageing and memory effects in ZFC magnetization are only characteristic for SGs/SSGs and are hardly expected to appear in SPMs. 38,39 In order to determine the nature of the low temperature state, and for the sake of comparison between the behavior of SCMO and LCMO NPs, we have investigated ageing and memory effects in SCMO NPs. When a magnetic field is applied to a glassy system which was ZFC from a temperature T > Tg to a temperature Tw < Tg, the time evolution of the magnetization at Tw depends on the time spent by the system at low temperature, before the field application. In our experimental protocol, the sample was cooled down to 50 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 the magnetization resulting from slow relaxation is shown in Fig. 3(a), for various waiting time intervals tw = 100, 1000, 10000 s. The time dependence of the magnetization can be well approximated by a stretched exponential form40 M(t) = MFM − Mg exp [− (t/τ)β],

(2)

where MFM is the magnetization of an intrinsic FM component and Mg is the initial magnetization of the glassy component that provides the main contribution to the relaxation. The time constant τ and the dispersion parameter β are related to the relaxation rate of the spin-glass phase. The value of the exponent β depends on the nature of energy barriers involved in the relaxation. For uniform energy barriers β = 1, while for distributed energy barriers, typical for spin-glasses, 0 < β < 1. A fit of the stretched exponential equation (2) to the experimental data presented in Fig. 3(a) renders the following fitting parameters: β ≈

8

0.298, 0.351, 0.308; τ = 1374, 2402, 36198 s, for tw of 100, 1000, and 10 000 s, respectively. It should be underlined that the stretched exponential gives a reasonable fit with χ2 < 10−8 and a very high coefficient of determination R2 ≈ 0.9999. The results show an increase of time constant τ with increasing waiting time tw, similar to the results obtained previously for LCMO NPs.16,22,32 In classical SG systems, the time dependence of the magnetization shows an inflection point at tw, which is usually detected as a peak in the magnetic viscosity S(t) = (1/H)dM(t)/d(lnt) plot versus t, at t ≈ tw .2,3,29 Time dependence of the magnetic viscosity S(t) for SCMO15 sample is shown in Fig. 3(b). Clearly, the magnetic relaxation depends on the waiting time. Notice that the time at which the maximum appears is larger than the waiting time tw, therefore, for tw = 10 000 s the maximum does not appear in the time interval 0 – 10 000 s. A key property for understanding of the dynamics of spin glasses is the occurrence of the memory effect in ZFC magnetization. This effect constitutes an unambiguous signature of SG, and of SSG in particular.3,38,39 In order to investigate the memory effect in ZFC magnetization, we have employed a single “stop-point-and-wait” ageing protocol. The sample was first cooled in zero field from room temperature down to 10 K at the rate of 3 ref K/min. The reference magnetization M ZFC was measured in the magnetic field of H = 10 Oe

during reheating back to room temperature with the rate 0.5 K/min. In the next step, the sample was cooled from 300 K, in zero magnetic field, to a stop point at TS = 50 K (TS < Tg = 58 K), at the same cooling rate. The system was aged at TS for tw = 20 000 s. After the waiting time has elapsed the ZFC was resumed and the sample was cooled down to 10 K. At this wait magnetization was temperature, the magnetic field of H = 10 Oe was turned on, and M ZFC

9

again measured during the reheating cycle, with the same heating rate 0.5 K/min. as in the ref ref wait M ZFC measurement. The temperature dependence of both M ZFC and M ZFC is shown in Fig.

ref wait and M ZFC . 4(a), while Fig. 4(b) demonstrates the difference between M ZFC

wait ref Usually, the difference between M ZFC and M ZFC in SG or SSG exhibits a rather sharp

dip in the vicinity of TS, resulting from the relaxation towards the equilibrium state through growth of the steady state domains at TS.3 It is known that the temperature decrease from TS to TS −∆T, after isothermally ageing a conventional SG phase at TS, restarts the dissipation processes.41,42 This is known as the rejuvenation effect due to which the system seems to forget its previous equilibrium stage at TS. After sufficiently large ∆T, the system rejuvenates completely and its magnetic characteristics become identical to those seen after a direct cooling from the PM phase. The width of the memory dip is also a qualitative measure of the rejuvenation effect. It can be seen that the dip width at half maximum is close to 9 K, or in relative units ∆T/Tg ≈ 0.2. Such relative width of the memory dip is larger than the one reported for atomic SG: 0.05 for Heisenberg and 0.1 for Ising SG, but narrower with respect to the ones previously reported for SSGs.42,43 Another interesting feature of the ZFC memory is the lack of rejuvenation at low ref wait temperatures. The values of M ZFC and M ZFC practically coincide at T > 70 K but differ

significantly at temperatures below Tg. Weak rejuvenation or lack of rejuvenation may be considered as an additional evidence for SSG behavior in NPs ensembles.43 Recently, we observed a somewhat similar behavior in 25 nm Sm0.1Ca0.9MnO3 NPs.44 These NPs demonstrated memory effects in ZFC magnetization with a relative dip width ∆T/Tg ≈ 0.2, the same as the one can observe for SCMO15 sample. Strong rejuvenation effects, typical for atomic SG, have not been observed in SSG.22 Note that in the framework of the droplet

10

model, a reduced rejuvenation, or absence of rejuvenation, indicates that the microscopic flip time of superspins in SSG is much longer than this in atomic SGs.22,43

3.4 Thermoremanent magnetization Supplementary information about the physical properties of magnetically disordered system, such as SG-like systems, can be obtained from the relaxation of the remanent magnetization. Thermoremanent magnetization (TRM) is the remanent magnetization obtained when a sample is cooled in an applied magnetic field, from a temperature well above Tg to a target temperature T < Tg at which the field is removed. For the TRM measurements, we have employed the following experimental procedure: the magnetic field H = 10 kOe was applied at room temperature and the sample was cooled down in the applied field to the target temperature T = 10, 30, 50 K, at the rate 1.5 K/min, and maintained at that temperature for 10 min. Next, the magnetic field was removed at the maximum rate available with our magnet (200 Oe/s) and the magnetization was immediately recorded. Figure 5 shows relaxation of TRM at T = 10, 30, and 50 K for SCMO15. The plots are limited to the low temperatures only because we detected only very small variations of magnetization at higher temperature, most likely caused by a drift of the experimental set-up. When energy barriers in the system are uniformly distributed, the decay of TRM is well approximated by the logarithmic dependence18,45 M(t) = M(0) – S log(t),

(3)

where M(0) is the magnetization at log(t) = 0 and S the magnetic viscosity.45 Note that M(0) depends on the units of the time employed, while the viscosity S is a universal, unit independent factor.17 Fitting of the equation (3) to the time evolution of TRM is illustrated in Fig. 5. To compare the goodness of the fits we compare χ2 and R2 parameters, see Table 1. Note that the current fit has the coefficient of determination R2 markedly lower than the one

11

achieved for 5.1 nm NiO NPs.18 On the other hand, we have obtained similar reduced values of R2 in fitting the data for 12 nm La0.23Ca0.77MnO3 NPs.21 This may be attributed to the intricate relaxation mechanism characterizing the complex magnetic structure and wider distribution of size and relaxation times in near half-doped and electron-doped manganites NPs in comparison with NiO NPs. It is well known,1-3 that a system with non-negligible interparticle interactions shows a collective behavior overriding individual anisotropic properties of particles. Superspin glass behavior has been observed in many FM NPs systems with intermediate strength of dipolar interactions. In our case, the superspins of NPs may collectively freeze into a SG-like phase below some critical temperature Tg. However, dipole–dipole interactions between close AFM NPs are typically rather small and the related critical temperature is well below 1 K.46 Recently, we have provided experimental evidence for a collective state in ensembles of 15 nm AFM La0.2Ca0.8MnO3 NPs, in which the FM phase at 5 K occupies only about 1% of the particle’s volume.22 Our evaluation for the mean dipolar energy in this system gave the value of 0.01 K, indicating that the dipole–dipole interactions are indeed negligible and cannot be responsible for the formation of a collective state. Therefore, it was suggested that an additional much stronger interaction, such as exchange coupling between surface atoms of neighboring particles47 or DE correlations across the interface between two neighboring NPs,48 are the most important interactions in AFM NPs and may in fact play a role similar to that of dipole–dipole interactions in FM NPs. However, as already mentioned, the narrowbandwidth Sm1-xCaxMnO3 of highly distorted perovskite GdFeO3-type structure, is favorable for charge localization but detrimental for DE interactions.24-26 Alternatively, for SCMO15 with considerable spontaneous magnetization, the dipole– dipole interactions may already be significant. The evaluation of the spontaneous magnetization M0, from field dependence of magnetization (not shown), has revealed that it

12

increases monotonously with decreasing particle size, and approaches 0.9 µB/f.u. for SCMO15 at T = 10 K. It is then possible to estimate the order of magnitude of dipolar effect in the case of SCMO15. The expression for the dipolar coupling energy between two r r r magnetic dipoles with moments m1 and m2 separated by a distance vector r is given by: 28 r r r r r r Ed–d = (µ0/4πr3)[ m1 · m2 − (3/r2)( m1 · r )( m2 · r )] .

(4)

The dipolar interaction is long-range and anisotropic in nature. One can easily estimate the order of magnitude of the dipolar potential energy from the expression:28 Ed–d = (µ0/4πr3)(m1· m2). Assuming that compacted SCMO15 NPs are in a direct contact, the evaluated dipolar potential energy Ed–d/kB is ~ 150 K. Taking into account all neighbors, the mean dipolar energy for dense ensemble of SCMO15 NPs may be around few hundreds of K. Such dipolar interactions in SCMO15 are indeed strong enough to be responsible for the formation of a collective state at low temperatures.

4. Conclusions In summary, we have studied magnetic behavior of the near half-doped Sm0.43Ca0.57MnO3 nanoparticles. In the framework of the core-shell model, one can conclude that the core of nanoparticles is AFM below the TN, while the shell is constituted by a SG-like FM surface layer. We have found that the charge ordering is progressively suppressed with decreasing particle size and disappears completely in the smallest 15 nm NPs, along with slight decrease of the TN with decreasing size. The smallest 15 nm NPs show feature characteristic of superspin glass state. Although memory and ageing effects have been observed, no strong rejuvenation occurs at low temperatures in SCMO15 NPs. Dipolar interactions in these NPs are strong enough to be responsible for the formation of a collective state at low temperatures.

13

Acknowledgments This work was supported in part by the Polish Ministry of Science and Higher Education under a research project no. N 202 1037 36, by the Polish NCN grant 2012/05/B/ST3/03157, and by the Israeli Science Foundation administered by the Israel Academy of Sciences and Humanities grant 754/09.

14

REFERENCES 1. J. L. Dormann, D. Fiorani, E. Tronc, Adv. Chem. Phys. 98 (1997) 283. 2. X. Batlle and A. Labarta, J. Phys. D: Appl. Phys. 35 (2002) R15. 3. S. Bedanta, W. Kleemann, J. Phys. D: Appl. Phys. 42 (2009) 013001. 4. T. Zhang, T. F. Zhou, T. Qian, X. G. Li, Phys. Rev. B 76 (2007) 174415. 5. E. Rozenberg, M. Auslender, A. I. Shames, D. Mogilyansky, I. Felner, E. Sominskii, A. Gedanken, Ya. M. Mukovskii, Phys. Rev. B 78 (2008) 052405. 6. V. Markovich, I. Fita, A. Wisniewski, D. Mogilyansky, R. Puzniak, L. Titelman, C. Martin, G. Gorodetsky, Phys. Rev. B 81 (2010) 094428. 7. X. H. Huang, J. F. Ding, G. Q. Zhang, Y. Hou, Y. P. Yao, X. G. Li, Phys. Rev. B 78 (2008) 224408; X. H. Huang, J. F. Ding, Z. L. Jiang, Y. W. Yin, Q. X. Yu, and X. G. Li, J. Appl. Phys. 106 (2009) 083904. 8. Y. Wang, H. J. Fan, Phys. Rev. B 83 (2011) 224409. 9. M. Perovic, V. Kusigerski, V. Spasojevic, A. Mrakovic, J. Blanusa, M. Zentkova, M. Mihalik, J. Phys. D: Appl. Phys. 46 (2013) 165001. 10. S. Zhou, Y. Guo, Z. Jiang, J. Zhao, X. Cai, Lei Shi, J. Phys. Chem. C 117 (2013) 8989. 11. S. Dong, F. Gao, Z. Q. Wang, J.-M. Liu, Z. F. Ren, Appl. Phys. Lett. 90 (2007) 082508; S. Dong, R. Yu, S. Yunoki, J. M. Liu, E. Dagotto, Phys. Rev. B 78 (2008) 064414. 12. Z. Jirák, E. Hadová, O. Kaman, K. Knížek, M. Maryško, E. Pollert, M. Dlouhá, S. Vratislav, Phys. Rev. B 81 (2010) 024403. 13. S. Bedanta, T. Eimüller, W. Kleemann, J. Rhensius, F. Stromberg, E. Amaladass, S. Cardoso, P. P. Freitas, Phys. Rev. Lett. 98 (2007) 176601. 14. V. Spasojevic, A. Mrakovic, M. Perovic, V. Kusigerski, J. Blanusa, J. Nanopart. Res. 13 (2011) 763. 15. M. Perovic, A. Mrakovic, V. Kusigerski, J. Blanusa, V. Spasojevic, Mater. Chem. Phys. 136 (2012) 196. 16. V. Markovich, I. Fita, A. Wisniewski, G. Jung, D. Mogilyansky, R. Puzniak, L. Titelman, G. Gorodetsky, Phys. Rev. B 81 (2010) 134440. 17. S. K. Mishra, V. Subrahmanyam, Phys. Rev. B 84 (2011) 024429. 18. S. D. Tiwari, K. P. Rajeev, Phys. Rev. B 72 (2005) 104433. 19. V. Bisht, K. P. Rajeev, Solid State Commun. 151 (2011) 1275. 20. V. Bisht, K. P. Rajeev, S. Banerje, Solid State Commun. 150 (2010) 884. 21. B. Dolgin, R. Puzniak, D. Mogilyansky, A. Wisniewski, V. Markovich, G. Jung, J. 15

Phys.: Condens. Matter 25 (2013) 076004. 22. V. Markovich, R. Puzniak, Y. Skourski, A. Wisniewski, D. Mogilyanski, G. Jung, G. Gorodetsky, J. Phys.: Condens. Matter 24 (2012) 266001. 23. S. Mørup, M. F. Hansen, C. Frandsen, Beilstein J. Nanotechnol. 1 (2010) 182. 24. C. Martin, A. Maignan, M. Hervieu, B. Raveau, Phys. Rev. B 60 (1999) 12191. 25. J. Hejtmánek, Z. Jirák, and M. Maryško, C. Martin, A. Maignan, M. Hervieu, B. Raveau, Phys. Rev. B 60 (1999) 14057. 26. M. Hervieu, A. Barnabé, C. Martin, A. Maignan, F. Damay, B. Raveau, Eur. Phys. J. B 8 (1999) 31. 27. D. Markovic, V. Kusigerski, M. Tadic, J. Blanusa, M. V. Antisari V. Spasojevic, Scripta Materialia 59 (2008) 35. 28. A. H. Morrish, Physical Principles of Magnetism (Wiley, New York, 1965). 29. J. A. Mydosh, Spin-Glasses: An Experimental Introduction (Taylor and Francis, London, 1993). 30. J. A. De Toro, S. S. Lee, D. Salazar, J. L. Cheong, P. S. Normile, P. Muñiz, J. M. Riveiro, M. Hillenkamp, F. Tournus, A. Tamion, P. Nordblad, Appl. Phys. Lett. 102 (2013) 183104. 31. S. N. Jammalamadaka, S. S. Rao, J. Vanacken, A. Stesmans, S. V. Bhat, V. V. Moshchalkov, AIP Advances 1 (2011) 042151. 32. V. Markovich, I. Fita, A. Wisniewski, D. Mogilyansky, R. Puzniak, L. Titelman, G. Gorodetsky, J. Appl. Phys. 108 (2010) 063918. 33. J. R. L. de Almeida, D. J. Thouless, J. Phys. A 11 (1978) 983. 34. A. K. Pramanik, A. Banerjee, Phys. Rev. B 82 (2010) 094402. 35. G. Toulouse, J. Phys. Lett. (Paris) 41 (1980) L447; M. Gabay, G. Toulouse, Phys. Rev. Lett. 47 (1981) 201. 36. L. E. Wenger, J. A. Mydosh, Phys. Rev. B 29 (1984) 4156. 37. V. A. Sirenko and V. V. Eremenko, Fiz. Nizk. Temp. 40 (2014) 230. 38. M. Bandyopadhyay, S. Dattagupta, Phys. Rev. B 74 (2006) 214410. 39. M. Sasaki, P. E. Jönsson, H. Takayama, P. Nordblad, Phys. Rev. Lett. 93 (2004) 139701; M. Sasaki, P. E. Jönsson, H. Takayama, H. Mamiya, Phys. Rev. B 71 (2005) 104405. 40. M. Ulrich, J. García-Otero, J. Rivas, A. Bunde, Phys. Rev. B 67 (2003) 24416. 41. E. Vincent, Lect. Notes Phys. 716, 7 (2007); e-print arXiv:cond-mat/0603583 42. P. E. Jönsson, R. Mathieu, and P. Nordblad, H. Yoshino, H. A. Katori, A. Ito, Phys. Rev. B 70 (2004) 174402. 16

43. P. E. Jönsson, H. Yoshino, H. Mamiya, H. Takayama, Phys. Rev. B 71 (2005) 104404. 44. V. Markovich, I. Fita, A. Wisniewski, R. Puzniak, D. Mogilyansky, A. Kohn, B. Dolgin, P. Iwanowski, G. Gorodetsky, G. Jung, J. Appl. Phys. 112 (2012) 063921. 45. C. N. Guy, J. Phys. F: Met. Phys. 8 (1968) 1309. 46. S. Mørup, D. E. Madsen, C. Frandsen, C. R. H. Bahl, M. F. Hansen, J. Phys.: Condens. Matter 19 (2007) 213202. 47. M. F. Hansen, C. B. Koch, S. Mørup, Phys. Rev. B 62 (2000) 1124. 48. E. Rozenberg, A. I. Shames, M. Auslender, G. Jung, I. Felner, J. Sinha, S. S. Banerjee, D. Mogilyansky, E. Sominski, A. Gedanken, Ya. M. Mukovskii, G. Gorodetsky, Phys. Rev. B 76 (2007) 214429.

Table 1. Values of M(0), S, χ2, and R2 parameters obtained by fitting the equation M(t) = M(0)

–

S log(t), with time in seconds, to the experimental data for SCMO15 NPs at various temperatures. The total number of fitted data points was equal to 1946. TRM T (K)

M(0) (emu/g)

S (emu/g)

χ2

R2

10

10.7359

0.1758

8.0001×10-5

0.9854

30

6.2755

0.29298

1.7019×10-4

0.9885

50

1.86785

0.11474

1.7729×10-5

0.9922

17

FIGURE CAPTIONS Fig. 1. (color online) (a,b,c,d) Temperature dependence of the real component of acsusceptibility (χ') of SCMO NPs measured during heating for ac magnetic field amplitude of 10 Oe at different frequencies. Insets show the imaginary part (χ'') of acsusceptibility. Fig. 2. (color online) Temperature dependence of ZFC magnetization for SCMO15 sample recorded in various magnetic fields. Inset shows the magnetization maximum temperature Tmax as a function of magnetic field H; solid line is the best fit of the AT line to experimental points in the range 100 − 1800 Oe, giving the freezing temperature Tg = 58.0 K. Dotted line indicates the deviation of experimental points from the AT line. Fig. 3. (color online) (a) Time evolution of the magnetization for SCMO15 sample measured in H = 10 Oe, after waiting time tw = 100, 1000, and 10 000 s. (b) Semi-logarithmic plot of the time dependence of the magnetic viscosity S(t) = (1/H)dM(t)/d(lnt), measured at 50 K, after waiting time tw = 100, 1000, and 10 000 s. ref Fig. 4. (color online) (a) Temperature dependence of the reference magnetization M ZFC and

wait of the magnetization with a stop and waiting protocol, M ZFC at magnetic field H = 10

Oe. Firstly, SCMO15 sample was cooled from 300 K to 10 K with the rate of 3 ref K/min. Then the magnetization M ZFC was measured during heating. After that, the

system was cooled again from 300 K to a stop temperature TS. The system was annealed at a stop temperature TS = 50 K for the wait time 20 000 s. Next, the cooling was resumed and the sample was cooled from TS to 10 K. At 10 K, the magnetic field wait was turned on and the magnetization M ZFC was measured at heating. (b) ∆M = wait ref M ZFC − M ZFC vs. temperature.

18

Fig. 5. (colour online) (a) Time variation of the TRM magnetization of SCMO15 NPs after FC at H = 10 kOe recorded at temperatures of 10, 30, 50 K. Solid lines are the best fits of equation (3) to the data.

19

-2

(a)

-3

SCMO15 hac= 10 Oe

8.0x10

10 Hz 100 Hz 1 kHz 10 kHz

-3

4.0x10

0.0

69 K

-3

3.0x10

(b)

SCMO25 hac= 10 Oe 10 Hz 100 Hz 1 kHz 10 kHz

-3

2.0x10

-3

1.0x10

-4

2x10

-3

2.0x10

(c)

10 Hz 100 Hz 1 kHz 10 kHz

-3

1.0x10

-5

5x10

0

(d)

-3

1.0x10

-4

5.0x10

200

300

70 K SCMO33 hac= 10 Oe

6x10

-5

3x10

0 100

200

300

72 K

SCMO60 hac= 10 Oe 10 Hz 100 Hz 1 kHz 10 kHz

100

-5

SCMO60 hac= 10 Oe

-5

χ'' (emu/g)

73 K

300

SCMO25 hac= 10 Oe

1x10

0

0.0

200

64 K

0.0 SCMO33 hac= 10 Oe

100

-4

0 72 K

SCMO15 hac= 10 Oe

4x10

0 0

χ'' (emu/g)

χ' (emu/g)

52 K -4

χ'' (emu/g)

58 K

χ'' (emu/g)

1.2x10

2x10

0 0

100

200

300

0.0 0

50

100

150

200

250

300

Temperature (K)

Fig. 1

20

15

M (emu/g)

12

9

6

50

40

1800 Oe

Tmax (K)

2600 Oe 2200 Oe 1800 Oe 1400 Oe 1000 Oe 700 Oe 400 Oe 200 Oe 100 Oe

30

3

SCMO15

0

40

80

120

2/3

2/3

160

H (Oe ) 0 0

50

100

150

200

250

300

Temperature (K)

Fig. 2

21

SCMO15

M (emu/g)

0.22

0.20

tw=100 s

0.18

tw=1000 s

(a)

tw=10000 s

T =50 K

0.16 0

2000

4000

6000

8000

10000

Time (s) -3

1x10

SCMO15

(b) -4

S (t)

8x10

-4

6x10

tw=100 s tw=1000 s

T =50 K

-4

4x10

100

Time (s)

tw=10000 s

1000

10000

Fig. 3

22

SCMO15

0.15

H =10 Oe

M (emu/g)

(a) ref

0.10

MZFC TS = 50 K tw=20000 s

0.05 wait

MZFC

0.00 0.00

(b)

∆M (emu/g)

-0.01

-0.02

H =10 Oe

-0.03

TS = 50 K tw=20000 s 0

50

100 150 Temperature (K)

200

Fig. 4

23

SCMO15 after FC at H=10 kOe

10.4

10.2

10.0

10 K

(a)

TRM (emu/g)

5.8 5.6 5.4

30 K 5.2

(b) 5.0 1.7 1.6 1.5 1.4

50 K

(c) 100

1000

10000

Time (s) Fig. 5

24