Training effect of the exchange bias in Co/CoO bilayers originates from the irreversible thermoremanent magnetization of the magnetically diluted antiferromagnet

The irreversible thermoremanent magnetization ($m_{\mathrm{TRM}}^{irr}$) of a sole, magnetically diluted epitaxial antiferromagnetic Co${}_{1-y}$O(100) layer is determined by the mean of its thermoremanent magnetizations ($m_{\mathrm{TRM}}$) at positive and negative remanence. During hysteresis-loop field cycling, $m_{\mathrm{TRM}}^{irr}$ exhibits successive reductions, consistent with the training effect (TE) of the exchange bias measured for the corresponding Co${}_{1-y}$O(100)/Co($11\overline{2}0$) bilayer. The TE of exchange bias is shown to have its microscopic origin in the TE of $m_{\mathrm{TRM}}^{irr}$ of the magnetically diluted antiferromagnet.

Figure 1

Exchange bias field $|B_{\mathrm{EB}}|$ of MgO(100)/Co${}_{1-y}$O(100)/Co($11\overline{2}0$)/Au vs $T$ for undiluted (circles) and diluted (squares) samples. The inset shows RHEED patterns of (a) the undiluted CoO layer and (b) the diluted Co${}_{1-y}$O layer grown on an MgO(100) substrate. The electron beam direction is parallel to $\left[010\right]$ of the MgO(100) substrate.

Figure 2

Thermoremanent magnetization of field-cooled sole-AFM MgO(100)/Co${}_{1-y}$O(100)/Au as a function of $T$ for undiluted (solid circles, II) and diluted (squares, I) samples. The zero-field-cooled (stars, III) curve of the diluted sample is shown for reference.

Figure 3

Thermoremanent magnetization at 5 K of the diluted sole-AFM MgO(100)/Co${}_{1-y}$O(100)/Au sample vs time at $B=0$ (in remanence) for both ascending (lower curves) and descending (upper curves) field branches of successive hysteresis loop cycles (indicated by 1–4). Details about the measurement procedure are described in the text.

Figure 4

Training effect of exchange bias field, $|B_{\mathrm{EB}}|$, of a diluted CoO/Co bilayer (open squares), and of the cycle dependence of $m_{\mathrm{TRM}}^{irr}$ of a diluted sole CoO layer (open circles) at 5 K. The solid lines show fits by Eq. (1) to the data for $n>1$. Solid squares are the respective calculated data points generated from Eq. (2). The inset shows $|B_{\mathrm{EB}}|$ vs $m_{\mathrm{TRM}}^{irr}$ at 5 K; the solid line is a fit to the data points marked by their respective cycle number $n$.