Magnetic polarons and spin-glass behavior in insulating La 1- x Sr x CoO 3 ( x = 0 . 125 and 0.15)

The evolution of magnetic polarons in Sr doped LaCoO 3 (La 1- x Sr x CoO 3 ) single crystal and polycrystalline samples are investigated by employing dc and ac magnetic measurement and small angle neutron scattering (SANS) techniques. The effect of magnetic ﬁeld and temperature on magnetic polarons is experimentally studied for La 0 . 875 Sr 0 . 125 CoO 3 and La 0 . 85 Sr 0 . 15 CoO 3 compounds that belong to the spin glass insulating regime of the broader compositional phase diagram of this system. Langevin analyses of the isothermal magnetization curves in the notional paramagnetic regime prove the existence of magnetic polarons with large moments. The dc ﬁeld superimposed ac susceptibility data and the analysis of the glassy dynamics prove that the size of polarons in 15% Sr doped crystal increase as the ﬁeld is increased while the ﬁeld effect is not visible in the 12.5% Sr doped crystal. A polycrystalline sample of La 0 . 85 Sr 0 . 15 CoO 3 is analyzed by SANS experiments, which conﬁrm nonzero correlation length at temperatures far above the macroscopic ordering temperature and hence the presence of magnetic polarons.

(Received 29 June 2020; revised 22 October 2020; accepted 2 November 2020; published 8 December 2020) The evolution of magnetic polarons in Sr doped LaCoO 3 (La 1-x Sr x CoO 3 ) single crystal and polycrystalline samples are investigated by employing dc and ac magnetic measurement and small angle neutron scattering (SANS) techniques. The effect of magnetic field and temperature on magnetic polarons is experimentally studied for La 0.875 Sr 0.125 CoO 3 and La 0.85 Sr 0. 15 CoO 3 compounds that belong to the spin glass insulating regime of the broader compositional phase diagram of this system. Langevin analyses of the isothermal magnetization curves in the notional paramagnetic regime prove the existence of magnetic polarons with large moments. The dc field superimposed ac susceptibility data and the analysis of the glassy dynamics prove that the size of polarons in 15% Sr doped crystal increase as the field is increased while the field effect is not visible in the 12.5% Sr doped crystal. A polycrystalline sample of La 0.85 Sr 0.15 CoO 3 is analyzed by SANS experiments, which confirm nonzero correlation length at temperatures far above the macroscopic ordering temperature and hence the presence of magnetic polarons. DOI: 10.1103/PhysRevResearch.2.043344

I. INTRODUCTION
LaCoO 3 is one of the rare transition metal oxides which exhibit a nonmagnetic ground state due to the presence of low spin (t 6 2g : S = 0) Co ions. This is due to the crystal field splitting energy being higher than the Hund's coupling energy for the Co ion in this system. However, the sample undergoes a spin state transition to intermediate/high spin state at a higher temperature [1,2]. Further, the hole doping of the system by means of, for example, Sr substitution at the La site also leads to the formation of finite moments on each Co site and a magnetic ground state in this system. Akin to the hole/electron doped rare-earth manganites, these rare-earth cobaltite perovskites also exhibit a rich phase diagram as a function of doping and temperature [3,4] cobaltite systems have not been as extensively studied as the manganites, and the effects of hole doping, magnetic interactions, etc., are still unclear in case of cobaltites.
An interesting aspect of these doped cobaltites is the experimental and theoretical observations pointing to presence of spin/magnetic polarons [5,6]. A combination of inelastic neutron scattering, electron spin resonance, and nuclear magnetic resonance measurements on the lightly hole doped system La 0.998 Sr 0.002 CoO 3 , predicted that the presence of spin-state polarons is the reason for high magnetic moment in hole-doped La 1-x Sr x CoO 3 as opposed to the nonmagnetic ground state of undoped LaCoO 3 [7]. Similarly, magnetic and optical spectroscopy measurements on La 1-x Sr x CoO 3 (x = 0.002, 0.005, and 0.010) indicated formation of high spin (S = 10-16) polarons centered on doped holes [2]. In systems with higher Sr doping (0.05 < x < 0.18) it has been proposed that there exists an electronically separated phase with ferromagnetic clusters embedded in a nonferromagnetic matrix [5,[8][9][10][11]. The hypothesis stems from the existence of tunnel type magnetoresistance and aging effects in the electronic transport in conjunction with the glassy magnetic state.
In the present article, we study single crystals of La 0.875 Sr 0.125 CoO 3 and La 0.85 Sr 0.15 CoO 3 by detailed ac susceptibility and dc magnetic measurement techniques. The analysis of ac susceptibility data collected with a superimposed dc field is used to determine the evolution of the size of the magnetic entities, polarons, as a function of field while the analysis of isothermal magnetization curves measured above the glass ordering temperature is used to determine the evolution of these polarons as a function of temperature. Our results suggest a growth of the magnetic polaron size with increasing magnetic field or decreasing temperature in the case of La 0.85 Sr 0.15 CoO 3 . However, the field effect is negligible on the polaron size in the sample La 0.875 Sr 0.125 CoO 3 whereas the polaron size increases with decreasing temperature. Small angle neutron scattering on polycrystalline samples has been used to estimate the size of the clusters as a function of the temperature.

II. EXPERIMENTAL DETAILS
Single crystals of La 0.875 Sr 0.125 CoO 3 and La 0.85 Sr 0.15 CoO 3 , hereafter referred to as Sr12.5 and Sr15, respectively, are prepared by the floating zone technique using a 4-mirror optical floating zone furnace from Crystal Systems Corporation. Polycrystalline samples of the intended composition are prepared using a solid state reaction method starting from La 2 O 3 , SrCO 3 and CoO in appropriate molar ratios. The final, phase pure, polycrystalline powders are pressed into cylindrical rods using a hydrostatic press followed by sintering at 1200 • C. Two such cylindrical rods are used as feed and seed rods for single crystal growth. Growth is carried out at a rate of 6 mm/h under continuous oxygen flow. The rotation rates of the upper and lower shafts are adjusted to obtain a stable molten zone during the growth. The phase purity is confirmed within the accuracy of x-ray diffraction technique by which any impurity phase with a volume above 2-3% should be visible. The composition and chemical homogeneity of the prepared crystals are confirmed by ICP-OES in a Perkin-Elmer spectrometer and energy dispersive electron spectroscopy spot analysis in a Zeiss LEO 440 scanning electron microscope. DC magnetic measurements and low frequency ac susceptibility measurements are performed in a Quantum Design MPMS superconducting quantum interference device magnetometer and high frequency ac susceptibility measurements are performed on a Quantum Design PPMS instrument. The small angle neutron scattering (SANS) data are recorded at the SANS2D instrument in the RAL-ISIS spallation source (UK) on a separately prepared polycrystalline La 0.85 Sr 0.15 CoO 3 (Sr15) sample in the q range of 0.004-0.668 Å −1 .

III. RESULTS AND DISCUSSION
Figures 1(a) and 1(b), respectively, present magnetic moment (M) versus temperature (T) plots for the crystals Sr15 and Sr12.5 in zero-field-cooled (ZFC) and field-cooled (FC) conditions. The ZFC curve of the sample Sr12.5 displays a sharp cusp at T cusp ∼ 44 K and the ZFC, FC curves fully merge above this temperature. On the other hand, the sample Sr15 exhibits a T cusp of ∼56 K along with a weak separation between ZFC and FC curves up to ∼150 K, which is far above the cusp temperature. The persistence of this separation up to a temperature far higher than T cusp may indicate the presence of minute amounts of magnetic impurities or certain inhomogeneity in the strength of magnetic interactions in the sample. Such impurities or inhomogeneities may be associated with local ordering of magnetic moments at higher temperature compared to the ordering temperature of macroscopic system. On the other hand, such a separation for the sample Sr12.5 disappears just above T cusp making a clear distinction from the higher Sr doped sample.
It is worth noting that the sample Sr15 is closer to the reported percolation limit (∼18%) and hence such an inhomogeneity in magnetic interaction strength may be expected [8,9,12]. Figure 1(a) also shows the results of a so-called dc memory experiment as an inset [13]. For the dc memory experiment, a second ZFC M (T) curve is measured after a halt at 45 K for 3000 seconds before cooling the sample further down to 10 K and application of measuring field. The data shows a dip in the M (T) curve, close to 45 K, which is otherwise identical to the reference ZFC curve measured without any stop in cooling sequence. This dip reflects the nonequilibrium character of the underlying glassy dynamics at low temperatures [13].
We investigate the nature of the magnetic anomaly observed at T cusp by using ac susceptibility measurements (Fig. 2) on these two differently doped LaCoO 3 compounds. The panels (a) and (c) show the real part, χ , and panels (b) and (d) show the imaginary part, χ , of the susceptibility measured at different frequencies, f . As shown in Figs. 2(a) and 2(c), both the compositions exhibit strong frequency dependency in ac susceptibility data indicative of a glassy magnetic system. In addition, the nature of the frequency dispersion is such that the susceptibility curves measured at different frequencies tend to gradually converge below T cusp . This behavior is characteristic of a superspin glass system [14] comprising of interacting magnetic entities that are larger than the atomic spins that constitute canonical atomic spin glasses [15].
The superspin glass state in certain manganite perovskites is of the re-entrant type and the high temperature ferromagnetic state in them does not allow for a detailed analysis of the dynamics of the re-entrant superspin glass transition [16]. However, in the present case no such difficulty exists and one can do a detailed analysis of the temperature, frequency, and magnetic field dependence of the ac susceptibility to extract information on superspin glass state [17,18].
To start with, the dynamics of the two systems are determined in zero dc field and an ac field, h, of 4 Oe is used for the measurement. A frequency dependent freezing temperature T f has been determined as the temperature at which χ reaches 1/6 th of its peak value as the measurement temperature is raised. The relaxation time, τ (=1/2π f ) is then fitted using the Vogel-Fulcher equation [19,20] k B (T f −T 0 ) ) and the power law given by critical slowing down τ = τ 0 [ T f −T g T g ] −zν . The Vogel-Fulcher equation describes a system of interacting magnetic entities with E b being the anisotropy barrier energy, T 0 is a parameter signifying the interaction strength between the magnetic entities, and τ 0 is the characteristic relaxation time [20]. On the other hand, the power law describes the dynamics of a system where a true phase transition occurs from a paramagnetic to a glassy magnetic state with a transition temperature T g , a critical exponent zν, and characteristic relaxation time τ 0 [14]. The best possible fit (not shown here) to a power law for the dynamics of sample Sr15 gives a value of zν ∼ 13, which is larger than usually observed for spin glasses. However, the dynamics for this sample conform very well to the Vogel-Fulcher equation as shown in the inset of Fig. 2(b), giving a value of 5 × 10 −12 sec for τ 0 , 285 K for E b /k B and 47 K for T 0 . In contrast, the dynamics of the sample Sr12.5 are described well by both the power law (zν = 9.4, T g = 43 K) and the Vogel-Fulcher equation as shown in the two insets of Fig. 2(d).
To study the effect of magnetic field on the dynamics, the ac susceptibility data is collected with a superimposed dc field, H (=100, 300, 500, 1000 and 3000 Oe), while keeping the ac field amplitude at 4 Oe. Figures 3(a) and 3(b) show the in-and out-of-phase results measured at 1.7 Hz for the Sr15. The ac susceptibility data for Sr12.5 sample with superimposed dc field at 1.7 Hz is presented in the Supplemental Material [21]. The data for all measured frequencies for the Sr15 sample is shown in the Supplemental Material Fig. S3  the case of 300 Oe dc bias field. Using corresponding data at all frequencies, the frequency dependent freezing temperature T f are determined as described in the zero dc field case and the Vogel-Fulcher analysis is performed by fixing the τ 0 value to be 5 × 10 −12 sec for all H values. The same τ 0 value is chosen for all H although τ 0 and E b are coupled quantities in magnetic particle (polaron) systems. The values of T 0 and E b obtained from the Vogel-Fulcher analysis for different H values are summarized in Fig. 3(c). The value of E b increases with increasing H. However, the value of T 0 is seen to be decreasing with increasing H. The increasing value of E b suggests the growth in the size of the magnetic entity with increasing H, as the anisotropy barrier energy is proportional to the volume of the magnetic entity. However, the decrease of T 0 value with increasing H is counterintuitive, as T 0 is proportional to the magnetic interaction strength between the magnetic entities. That is, in the case where there is a constant number of magnetic entities, one would expect that the interaction strength, and hence the value of T 0 , should increase with increasing size of the magnetic entity. This unexpected behavior of T 0 with H can, however, be accounted for one assumes that the separation between the magnetic entities increases with H. This assumption involves a scenario where a larger number of small magnetic polarons coalesce in the presence of a magnetic field to form a smaller number of bigger polarons. Incidentally, such a scenario has been previously reported in a different context to explain overshooting hysteresis in resistivity curves of manganites [22]. It is important to mention that the Vogel-Fulcher analysis of dynamics of the other sample, Sr12.5, with a superimposed dc field, did not affect the values of T 0 and E b as shown and described in the Supplemental Material (Fig. S3).
To determine the size of the magnetic entities that constitute the collective/glassy magnetic state of the La 1-x Sr x CoO 3 (x < ∼0.18), we have collected isothermal magnetization curves of both compounds at various temperatures above T f and fitted the data to Langevin equation given by where n is the number of magnetic entities per mol, m * is the moment of the magnetic entity in μ B , χ is a field independent Curie-type magnetic susceptibility, which prevails at high temperatures and fields. As shown in Figs. 4(a) and 4(c), the magnetization data follows the Langevin equation at each temperature above T cusp . The magnetization first increases nonlinearly at low magnetic fields, and linearly at larger fields, reflecting the contribution of m * and χ , respectively. In the present case, the value of χ at 180 K (160 K) for Sr15 (Sr12.5) is determined from linear fits of the high-field M-H data. increases as the T cusp is approached before the interpolaron interaction leads to the glassy magnetic transition at T cusp . Recent investigations on Sr15 single crystals using nonlinear ac susceptibility and neutron depolarization methods also confirmed the onset of magnetic cluster growth far above the temperature at which collective behavior sets in Ref. [25]. In this aspect, SANS is a proper tool to get an idea about the size of magnetic entities [26,27].
The SANS measurement was performed on polycrystalline sample of Sr15. Macroscopic magnetization data for this polycrystalline sample is shown in the Supplemental Material Figs. S4 and S5. The net magnetic scattering intensity, after subtracting the nuclear contribution collected at different temperatures in presence of 100 Oe magnetic field is shown in Fig. 5(a). The results clearly indicate a decrease in magnetic scattering intensity with the increase in temperature up to ∼120 K; above that temperature no significant magnetic contribution is observed. The nuclear scattering stemming from the powder nature of the sample has been estimated from SANS data collected at 285 K (well into the paramagnetic state) in the presence of a 20 kOe magnetic field.
Magnetic scattering intensity is mainly proportional to the square of volume of the magnetic entities and square of magnetic contrast ( ρ) 2 mag , between the paramagnetic matrix and magnetic entities [28,29]. In view of that, the results in Fig. 5(a) are a clear manifestation of increase in volume of magnetic entities with decrease in temperature. We have also analyzed the SANS data by using the Lorentzian function I (q) = I 0 /(q 2 + k 2 ) to calculate the correlation length (ξ ) where I 0 is constant and ξ = 1/k [30,31]. The Lorentzian fits at different temperatures for zero field SANS data are shown in the Supplemental Material Fig. S6. The extracted ξ for magnetic field of 0 Oe and 100 Oe is plotted in Fig. 5(b) as a function of temperature. Below ∼120 K the magnetic correlation length increases rapidly, which also has been shown in Fig. 4(b) from the analysis of M(H, T ) data.
In earlier reported SANS results on La 1-x Sr x CoO 3 (for x > 0.18, above the percolation limit) [32] the spin correlation length, ξ sharply increases from zero at a temperature much higher than T C and it tends to diverge as T C is approached due to onset of long-range ordering. This increase of the correlation length occurs because of preformation of magnetic clusters at temperature much higher than T C . Our SANS results for Sr15 do not suggest a divergence of ξ and thus the absence of long-range ordering. Instead, ξ increases below ∼120 K (much higher than T cusp ) due to nucleation of magnetic clusters/polarons, which eventually reach the correlation length ∼20-27 Å at low temperature. These results are consistent with the results obtained from the analyses of M(H, T ) data based on the Langevin function, the size/moment of the polaron remains finite on decreasing temperature.
In conclusion, we have found that the Sr doped LaCoO 3 crystals display magnetic properties characteristic of a magnetic polaron system. Our isothermal magnetization data 043344-5 collected above T cusp and the Langevin analysis established that the ordering magnetic entities at T cusp are not atomic moments, but correspond to magnetic polarons with several hundred μ B each. It is shown that lowering the temperature or increasing the magnetic field leads to growth of these magnetic polarons. However, the field effect on the size of magnetic polarons is not evident in case of the crystal with lower Sr doping (12.5%). The absence of the field effect in the case of the Sr12.5 can be attributed to the fact that this composition is away from the percolation threshold. The higher Sr doped compound Sr15, however, is closer to the percolation threshold (18%) and hence the polaron size shows a field dependency. Our results are consistent with the hypothesis that the SG to FM transition for systems with x > 18% Sr doping is due to the coalesce of polarons. Additionally, we also confirm the presence of magnetic polarons above T cusp by analyzing a polycrystalline sample Sr15 using the SANS technique.