Competing exchange bias and field-induced ferromagnetism in La-doped $\mathrm{BaFe}{\mathrm{O}}_3$

An exchange bias (EB) effect was observed in mixed valent $\mathrm{L}{\mathrm{a}}_x\mathrm{B}{\mathrm{a}}_{1-x}\mathrm{Fe}{\mathrm{O}}_3$ ($x=0.125$, 0.25, 0.33) perovskites exhibiting the antiferromagnetic (AFM) helical order among $\mathrm{F}{\mathrm{e}}^{4+}$ ions coexisting with the ferromagnetic (FM) cluster phase in the ground state. The $\mathrm{L}{\mathrm{a}}^{3+}$ ions for $\mathrm{B}{\mathrm{a}}^{2+}$ site substitution, associated with increase in number of the AFM coupled $\mathrm{F}{\mathrm{e}}^{3+}$ - $\mathrm{F}{\mathrm{e}}^{4+}$ pairs as well as some $\mathrm{F}{\mathrm{e}}^{3+}$ - $\mathrm{F}{\mathrm{e}}^{3+}$ pairs, leads to strengthening of the AFM phase and consequently to the alteration of the EB characteristics, which depend on level of the La doping $x$. At low doping $x\le 0.25$, an abnormal dependence of the EB field, $H_{\mathrm{EB}}$, on the cooling field, $H_{\mathrm{cool}}$, was found. The $H_{\mathrm{EB}}$ increases rapidly with increasing cooling field at low $H_{\mathrm{cool}}$, but it falls suddenly at cooling fields higher than 20 kOe, reducing by an order of magnitude at 90 kOe. The suppression of EB is caused by the field-induced increased volume of the FM phase, due to the transformation of the AFM helical spin structure into the FM one. Thus, low-doped $\mathrm{L}{\mathrm{a}}_x\mathrm{B}{\mathrm{a}}_{1-x}\mathrm{Fe}{\mathrm{O}}_3$ demonstrates a competition of two alternate cooling-field-induced effects, one of which leads to the EB anisotropy and another one to the enhanced ferromagnetism. In contrast, the $x=0.33$ sample, having a strong AFM constituent, shows no field-induced FM and no drop in the EB field. Accordingly, the $H_{\mathrm{EB}}$ vs $H_{\mathrm{cool}}$ dependence was found to be well explained in the framework of a model describing phase-separated AFM-FM systems, namely, the model assuming isolated FM clusters of size ∼4 nm embedded in the AFM matrix.

Figure 1

Room temperature x-ray diffraction patterns of cubic $\mathrm{L}{\mathrm{a}}_x\mathrm{B}{\mathrm{a}}_{1-x}\mathrm{Fe}{\mathrm{O}}_3$. The diffraction peak near 29 deg (denoted by cross) results from incompletely screened copper ${\mathrm{K}}_{\beta }$ radiation of the (110) peak.

Figure 2

Temperature dependences of ZFC (open symbols) and FC (solid symbols) magnetization for $\mathrm{L}{\mathrm{a}}_x\mathrm{B}{\mathrm{a}}_{1-x}\mathrm{Fe}{\mathrm{O}}_3$ measured (a) at 100 Oe, presented in log scale, and (b) at 40 kOe. (c) Inverse susceptibility $H/M$ measured at 40 kOe. The Curie-Weiss fit is shown by a dashed line.

Figure 3

(a) Magnetization hysteresis loops of $\mathrm{L}{\mathrm{a}}_{0.125}\mathrm{B}{\mathrm{a}}_{0.875}\mathrm{Fe}{\mathrm{O}}_3$ at 10 K measured with several cooling fields $H_{\mathrm{cool}}$. The upper insets show the cooling-field-induced increase in (left) magnetization at 90 kOe and (right) remanent magnetization at $H=0$, and the lower inset presents an FC loop with $H_{\mathrm{cool}}=10\mathrm{kOe}$ over an extended scale. (b) Detailed picture of ten loop measurements performed consecutively between ±90 kOe at 10 K after cooling in a field of 10 kOe. (c) Field $H_{\mathrm{EB}}$ (see text) at 10 K versus increasing number of recurrent hysteresis loops $k$; the solid line represents the best fit with Eq. (1).

Figure 4

(a) Magnetization hysteresis loops for $\mathrm{L}{\mathrm{a}}_{0.25}\mathrm{B}{\mathrm{a}}_{0.75}\mathrm{Fe}{\mathrm{O}}_3$ at 10 K measured with ZFC mode and with $H_{\mathrm{cool}}=70\mathrm{kOe}$. Upper inset shows the cooling-field-induced increase in magnetization at 70 kOe, and the lower inset presents both symmetric ZFC and shifted FC ($H_{\mathrm{cool}}=20\mathrm{kOe}$) loops in an extended scale. (b) ZFC and FC ($H_{\mathrm{cool}}=70\mathrm{kOe}$) loops for $\mathrm{L}{\mathrm{a}}_{0.33}\mathrm{B}{\mathrm{a}}_{0.67}\mathrm{Fe}{\mathrm{O}}_3$ at 10 K. Inset shows a shift of the $H_{\mathrm{cool}}=10\mathrm{kOe}$ loop in an extended scale.

Figure 5

(a) Evolution of hysteresis loop of $\mathrm{L}{\mathrm{a}}_{0.125}\mathrm{B}{\mathrm{a}}_{0.875}\mathrm{Fe}{\mathrm{O}}_3$ at 10 K with increasing cooling field $H_{\mathrm{cool}}$. (b) Hysteresis loops of $\mathrm{L}{\mathrm{a}}_{0.125}\mathrm{B}{\mathrm{a}}_{0.875}\mathrm{Fe}{\mathrm{O}}_3$ measured with $H_{\mathrm{cool}}=10\mathrm{kOe}$ at 10 and 50 K. (c) $H_{\mathrm{EB}}$ field as a function of the maximum field of the loop $H_{\mathrm{MAX}}$ measured with constant $H_{\mathrm{cool}}=15\mathrm{kOe}$ for $\mathrm{L}{\mathrm{a}}_{0.25}\mathrm{B}{\mathrm{a}}_{0.75}\mathrm{Fe}{\mathrm{O}}_3$ at 10 K. Solid line represents exponential fit, and the dashed line indicates the asymptotic value $H_{\mathrm{EB}}$($H_{\mathrm{MAX}}\to \infty$) which is intrinsic $H_{\mathrm{EB}}$.

Figure 6

(a) Variation of the coercive fields $H_1$ and $H_2$ with cooling field $H_{\mathrm{cool}}$ in $\mathrm{L}{\mathrm{a}}_x\mathrm{B}{\mathrm{a}}_{1-x}\mathrm{Fe}{\mathrm{O}}_3$ at 10 K. (b) The average coercive field $H_{\mathrm{C}}$ versus $H_{\mathrm{cool}}$. (c) Cooling-field dependence of exchange bias field $H_{\mathrm{EB}}$ at 10 K. Bold line represents the best fit with use of Eq. (3), calculated for a system of FM clusters (size of 4.2 nm) embedded in an AFM matrix.