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Unusual magnetic relaxation behavior in La0.5Ca0.5MnO3 and Nd0.5Sr0.5MnO3

We have carried out a systematic magnetic relaxation study, measured after applying and switching off a 5 T magnetic field to polycrystalline samples of La0.5Ca0.5MnO3 and Nd0.5Sr0.5MnO3. The long time logarithmic relaxation rate (LTLRR), decreased from 10 K to 150 K and increased from 150 K to 195 K in La0.5Ca0.5MnO3. This change in behavior was found to be related to the complete suppression of the antiferromagnetic phase above 150 K and in the presence of a 5 T magnetic field. At 195 K, the magnetization first decreased, and after a few minutes increased slowly as a function of time. Moreover, between 200 K and 245 K, the magnetization increased throughout the measured time span. The change in the slope of the curves, from negative to positive at about 200 K was found to be related to the suppression of antiferromagnetic fluctuations in small magnetic fields. A similar temperature dependence of the LTLRR was found for the Nd0.5Sr0.5MnO3 sample. However, the temperature where the LTLRR reached the minimum in Nd0.5Sr0.5MnO3 was lower than that of La0.5Ca0.5MnO3. This result agrees with the stronger ferromagnetic interactions that exist in Nd0.5Sr0.5MnO3 in comparison to La0.5Ca0.5MnO3. The above measurements suggested that the general temperature dependence of the LTLRR and the underlying physics were mainly independent of the particular charge ordering system considered. All relaxation curves could be fitted using a logarithmic law at long times. This slow relaxation was attributed to the coexistence of ferromagnetic and antiferromagnetic interactions between Mn ions, which produced a distribution of energy barriers.

by the orientational ordering of the 3d 3 orbitals on the Mn 3+ ions 7 , called as orbital ordering (OO). Recently, X-ray resonant scattering experiments 8 suggested that CO (a long range interaction) drove the OO (a short range interaction) near T CO .
Neutron powder diffraction and magnetization studies in La 1−x Ca x MnO 3 samples, with x=0.47, 0.50 and 0.53, have shown that the Curie temperature (T C ) was approximately 265 K in all cases 9 . Huang et. al. 9 also reported the formation of a second crystallographic phase (A-II) at 230 K. Moreover, they found that the A-II phase had the same space-group symmetry (Pnma) and lattice parameters as the original F-I phase, but it differed in the weak Jahn-Teller distortions of the MnO 6 octahedrons. Furthermore, the A-II phase ordered antiferromagnetically with a CE-type magnetic structure below 160 K. Besides, both Huang et. al. 9 and Radaelli et. al. 2 observed a rapid change of the lattice parameters between 130 and 225 K in La 0.5 Ca 0.5 MnO 3 . This was associated with the development of a Jahn-Teller distortion of the Mn-O octahedra, as well as partial orbital ordering.
The physical properties in CO manganese perovskites arise from the strong competition among a ferromagnetic double exchange interaction, an antiferromagnetic superexchange interaction, and the spin-phonon coupling. These interactions are determined by intrinsic parameters such as doping level, average cationic size, cationic disorder and oxygen stoichiometry. Magnetic relaxation studies are a useful tool to study the dynamics of these competing interactions.
Fisher et. al. 14 studied the time relaxation of resistivity and magnetization in colossal magnetoresistance compounds like La 1−x A x MnO 3 (with A=Sr, Ca and x=0.3, 0.35). They found that the relaxation rate was temperature dependent and slowed down when the temperature was far from T C . The spin-spin relaxation time (τ ss ) as a function of temperature in La 0.5 Ca 0.5 MnO 3 was measured by Dho et. al. 10 using 55 Mn and 139 La nuclear magnetic resonance. They found a general decrease in τ ss with increasing temperatures. However, τ ss showed hysteretic behavior in zero field cooling and field cooling measurements, approximately in the same temperature interval where the change in lattice parameters was most pronounced.
The relaxation of electrical resistivity in Pr 0.67 Ca 0.33 MnO 3 , after a large change in applied magnetic field, which induces a transition from a ferromagnetic metallic state to a charge ordered insulator phase or conversely, was studied by Anane et. al. 11 . They found an abrupt change in the resistivity, which indicated a metal to insulator transition. Smolyaninova et. al. 12 reported the time dependence of the resistivity and magnetization in a La 0.5 Ca 0.5 MnO 3 sample at low temperatures. They fitted all the curves to a stretched exponential time dependence and explained their results using a hierarchical distribution of relaxation times.
However, to our knowledge, studies of magnetic relaxation curves (M(t)) in charge ordered compounds are not reported for a wide temperature interval. Here, we present a general magnetic characterization of two polycrystalline samples of La 0.5 Ca 0.5 MnO 3 and Nd 0.5 Sr 0.5 MnO 3 . Besides, in both cases M(t) curves were systematically measured for several temperatures. We found an unusual temperature dependence of the relaxation curves in the region approximately between the Neel (T N ) and Curie temperatures. These results could be interpreted as a consequence of the strong competition between ferromagnetic and antiferromagnetic interactions. A short version of these results were reported elsewhere 13 by some of us.

Experimental procedures
ichiometric parts of Nd 2 O 3 and MnCO 3 were dissolved in HNO 3 and mixed to an aqueous citric acid solution, to which SrCO 3 was added. The mixed metallic citrate solution presented the ratio citric acid/metal of 1/3 (in molar basis). Ethylene glycol was added to this solution, to obtain a citric acid/ethylene glycol ratio 60/40 (mass ratio). The resulting blue solution was neutralized to pH∼7 with ethylenediamine. This solution was turned into a gel, and subsequently decomposed to a solid by heating at 400 o C. The resulting powder was heat-treated in vacuum at 900 o C for 24 hours, with several intermediary grindings, in order to prevent formation of impurity phases. This powder was pressed into pellets and sintered in air at 1050 o C for 12 hours. X-ray diffraction measurements did not show any peak associated to either impurities or starting materials, indicating the high quality of the samples.
The magnetization measurements reported here were done with a Quantum Design MPMS-5S SQUID magnetometer (UFSCar-São Carlos). Besides, in order to rule out possible machine-dependent effects we repeated part of the relaxation measurements using different techniques and equipments (a Quantum Design PPMS magnetometer operating with the extraction method and another Quantum Design MPMS SQUID magnetometer) in two other laboratories (ETH-Zurich and Unicamp-Campinas, respectively). The results were consistent and reproducible in all cases.
The relaxation measuring procedure was the following: first, the sample was heated to 400 K in zero magnetic field; second, the remanent magnetic field in the solenoid of the SQUID magnetometer was set to zero; third, the sample was cooled down in zero magnetic field until the stable working temperature was reached; fourth, an applied magnetic field (H) was increased from 0 to 5 T at a rate of 0.83 T/minute and maintained for a waiting time t w =50 s; fifth, H was decreased to the end field (H end ) of zero at the same rate; finally, when H was zero (we defined this time as t=0) the M(t) curve was recorded for approximately 3 hours. In the future we will call this procedure as "the standard". However, in the case of figure 5, measurements were done after step four. We have measured also the profile of the remanent magnetic field trapped in the superconducting solenoid after increasing H to 5 T and its subsequent removal. Within the experimental region the trapped magnetic field was smaller than 1.1 mT.

Results and Discussion
A. Magnetization versus temperature measurements conditions. The large hysteresis at a magnetic field as high as 5 T is a clear evidence of the intrinsic frustration in the equilibrium configuration of the spin system, which could not be only associated to grain boundary defects. This feature makes these compounds particularly interesting to study their relaxation behavior.
We fitted the small field magnetization data for both samples, using temperatures above 300 K, to a Curie-Weiss law: M/H ∼ µ 2 ef f /(T − T Θ ), where M/H was the DC susceptibility, µ ef f was the effective paramagnetic moment and T Θ was the Curie-Weiss temperature.
In the case of the Nd 0.5 Sr 0.5 MnO 3 sample the magnetic moment of the Nd 3+ ions should also be included. The electronic levels of Nd 3+ ions at high temperatures are well described by g=8/11 and the total angular momentum J=9/2, which leads to µ T h ef f (Nd 3+ ) = g J (J + 1 )µ B = 3.62 µ B . Therefore, considering a rigid coupling of the moments of Nd 3+ ions with the moments of Mn 3+ and Mn 4+ ions, we should have µ T h ef f (Nd 0.5 Sr 0.5 Ferromagnetic and antiferromagnetic phases coexist at low temperatures for both compounds. The spins at low temperatures align in a CE-antiferromagnetic lattice 17,18 , which is also charge and orbital ordered. As we saw before, in contrast to the La 3+ ions, the Nd 3+ ions have an intrinsic total angular momentum (J=9/2). Figure   This qualitative behavior has been usually explained considering the increase in the thermal energy, which stimulates the random alignment of the spin and, as a consequence, a decrease in the magnetization.
As can be seen in figure 3b, and contrary to the previous interval, the LTLRR between 150 and 195 K increases with temperature. The fractional change in magnetization goes from 20 % at 150 K to 0.9 % at 195 K. Note from figure 2a, that above 150 K an applied magnetic field of 5 T completely destroys the antiferromagnetic phase. These results correlate with the change in the temperature dependence of the LTLRR at 150 K. Roughly speaking, between 150 and 195 K the system seems to remember its previous 5 T ferromagnetic orientation.
After removing the applied magnetic field, it starts to relax at a slower rate, even in the presence of greater thermal excitations. We will see below that, in this temperature range, the increase in thermal energy is compensated by a rapid increase in the pinning energy of  We also repeated the standard relaxation procedure at 210 K, but now with an increasing waiting time in each case: t w =50 s, t w =500 s and t w =5000 s. We would like to stress that in the last case t w was longer than one hour. The normalized increment in the magnetization was higher the longer the 5 T magnetic field remained applied. Values of M(0) also increased for longer t w . These measurements confirmed the presence of the unusual relaxation, independently of the value of the waiting time. A plausible explanation could be that the remanent trapped field in the sample after removing the H=5 T, which was higher for longer t w , was causing a self-alignment of the spins and an increase in magnetization.
Therefore, these results could be reflecting intrinsic information about the interactions in the sample.
The curve at 245 K, also shown in figure 3c, presents a smaller fractional change in mag-netization with respect to the one at 240 K. This is probably associated with the transition of the system to the paramagnetic phase. Magnetic relaxation measurements were also done between 245 K and 350 K. In this temperature interval we did not find a systematic variation of the LTLRR, probably due to the small values of the absolute magnetization. Nonetheless, above 260 K, the M(t) curves always showed the usual decreasing behavior with time.
The change in the temperature dependence of the LTLRR above 195 K could be cor- However, although antiferromagnetic fluctuations are reduced for higher temperatures, the ferromagnetic interactions also weaken. Therefore, at a given temperature, the competition of these two effects causes the system to return to the usual relaxation behavior.
It is also interesting to note the close overlap between the whole temperature interval where the unusual magnetic relaxation was found (150 K to 245 K) and the temperature interval where a rapid change in the lattice parameters (130 K to 230 K) were reported 9,2 .
This rapid change has been associated to the development of a Jahn-Teller distortion of the Mn-O octahedra, as well as to the partial orbital ordering of Mn ions 9,2 . Therefore, the close overlap between both temperature intervals suggests that the electron-phonon interaction needs to be considered to completely understand this unusual relaxation.
Recently, similarly unusual magnetic relaxation measurements were done by Sirena et.
al. 23 . They studied the relaxation of the magnetization in thin films of La 0.6 Sr 0.4 MnO 3 , after applying a 1 T magnetic field during 5 minutes and then removing it. Their measurements were done during a time window of 8 hours. This procedure was repeated for temperatures between 4 K and 200 K. They found that, above a temperature labeled as T rev , the magnetization increased with time and T rev decreased with increasing film thickness. However, no clear interpretation was reported for all the results. Once more, both temperature intervals (rapid change of lattice parameters and unusual magnetic relaxation behavior) almost completely overlap. All of these suggest that the temperature dependence of the LTLRR, and the underlying physics, are mainly independent of the particular charge-ordering material.
Moreover, in order to test the effects of a fixed applied magnetic field on the temperature dependence of the LTLRR, we repeated the standard relaxation procedure in the La 0.5 Ca 0.5 MnO 3 sample, but in this case we did not remove the 5 T field. We performed the fitting of all the relaxation curves using the logarithmic law mentioned above, where S was the only free parameter. In order to get information over the whole temperature interval we consider t n = 1000 s, removing from the fitting any transient behavior at the beginning of each relaxation measurement. Due to the fact that at long times the relaxation curves are linear in a semi-logarithmic plot, S could be considered as a normalized value of the LTLRR.

Conclusions
We performed a systematic study of magnetic relaxation curves after applying and removing