Grain-size effects on the charge ordering and exchange bias in ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$: The role of spin configuration

The grain-size effects on the charge ordering and exchange bias in CE-type antiferromagnetic charge ordered manganite compound ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$ are explored by magnetometry. Reducing the size suppresses antiferromagnetism and charge ordering that does not occur any more when the size is smaller than 40 nm. At the same time ferromagnetic clusters appear and gradually become larger; their fraction increases to about 19.7% when the particle size is reduced to 20 nm. The magnetic hysteresis loops of the nanosized samples exhibit both horizontal and vertical shifts in the field-cooled process. The exchange bias field $H_{\text{eb}}$ and the coercivity $H_{\text{C}}$ do not depend monotonously on size but show a maximum at about 85 nm, which indicates that in antiferromagnetic charge-ordered manganites $H_{\text{eb}}$ can be effectively tuned by changing the grain size. These notable phenomena can be understood when the evolution of the spin configuration is considered that results from the surface-phase separation and surface effect.

Figure 1

(Color online) The x-ray diffraction patterns for the as-prepared ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$ samples at different annealing temperatures. Experiment (black cross) and Rietveld fitted (red solid line) XRD patterns for the samples with average grain size (a) 300 and (b) 20 nm. The magenta curve is the error.

Figure 2

(Color online) (a) The FE-SEM image and (c) the size distribution of the sample with average grain size 20 nm; (b) the FE-SEM image and (d) size distribution of the sample with average grain size 300 nm.

Figure 3

(Color online) Temperature dependence of the magnetization measured in ZFC (full squares) and FC (open circles) modes at $H=100\text{Oe}$ field for the ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$ samples with different grain sizes. The inset of Fig. 3a is the ac magnetization under different frequencies for the 300 nm sample. The inset of Fig. 3b shows the temperature dependence of $d{M}_{\text{ZFC}}/dT$. The inset of Fig. 3c magnifies certain ranges of the curves for the samples with grain sizes 300, 150, and 85 nm. The difference of the $T_{\text{f}}$ in dc magnetization and the $T_{\text{max}}$ in ac magnetization in Fig. 3a may be because of the different measured frequency and different dc magnetic fields.

Figure 4

(Color online) (a) ZFC relaxation magnetization and (b) corresponding relaxation rate $S\left(t\right)$ measured at $T=60\text{K}$ with different wait time as indicated for the 40-nm-sized compound ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$. The data were recorded at a field of $H=100\text{Oe}$.

Figure 5

Grain-size dependence of $T_{\text{SG}}$ and $T_{\text{CG}}$ for the compound ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$ with different grain sizes.

Figure 6

(Color online) Temperature dependence of the magnetization measured in ZFC (full squares) and FC (open circles) modes at $H=10\text{kOe}$ for the ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$ samples with different grain sizes. The inset is the $M$ vs $T$ curve for the 40 nm sample measured in $H=50\text{kOe}$.

Figure 7

(Color online) The magnetization curve $M$ vs $H$ measured at $T=10\text{K}$ after cooling the ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$ samples from room temperature in a magnetic field of $H=10\text{kOe}$. The inset is the experimental (open circles) and fitted (solid line) results of the 85 nm sample.

Figure 8

Grain-size dependencies of the charge-order transition temperature $T_{\text{CO}}$ (full squares, left axis) and ferromagnetic fraction (open circles, right axis) for compound ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$.

Figure 9

(Color online) FC (open circles) and ZFC (full squares) magnetization $M$ versus $T$ curves for 85-nm-sized ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$ sample under different magnetic fields.

Figure 10

(Color online) The magnetic field dependence of the magnetization at $T=10\text{K}$ after the ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$ samples are cooled down to $T=10\text{K}$ from room temperature in FC (open circles) under $H=10\text{kOe}$ field and ZFC (full squares) procedures for all the samples with different grain sizes.

Figure 11

(Color online) Grain-size dependencies of the $H_{\text{eb}}$, $H_{\text{C}}$, $M_{\text{eb}}$, and $M_{\text{eb}}/M_s$ of compound ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$ at $T=10\text{K}$. The inset of (a) is the grain-size dependences of FC and ZFC $H_{\text{C}}$ at $T=10\text{K}$. The inset of (b) shows $H_{\text{eb}}$ as a function of $M_{\text{eb}}/M_s$ at $T=10\text{K}$.