\section{SUPPLEMENTAL MATERIAL}



\subsection{NOTE 1. Resonance field of the free Py(8) layer as a function of temperature}

\begin{figure}[h]
\includegraphics[width=9 cm]{FigSM1.eps}\\ 
\textbf{Figure A1.} (a) Resonance field of the free Py(8) layer as a function of temperature. (a) In-plane angular profile of the resonance field ($H_\mathrm{r}$) shows the same weak uniaxial magnetic anisotropy at all temperatures. The slight increase in the magnitude of $H_\mathrm{r}$ is due to the thermal demagnetization (decrease in the effective magnetization, $M_\mathrm{eff}$) of the free Py layer, shown in panel (b). The values of $M_\mathrm{eff}$ at the given measurement temperatures were obtained from fitting the $H_\mathrm{r}$-vs-$\varphi_\mathbf{H}$ profiles [solid lines in panel (a)] using the standard FMR phenomenology [J. Smit and H. G. Beljers, Phillips Res. Rep. 10, 113 (1955)].
\label{fig_A1}
\end{figure}

\newpage
\subsection{NOTE 2. Resonance field and FMR linewidth versus temperature}

\begin{figure}[h]
\includegraphics[width=10 cm]{FigSM2.eps}\\ 
\textbf{Figure A2.} Resonance field and FMR linewidth versus temperature for the structure with a nonmagnetic seed layer (with FeMn/Ta bilayer). (a) In-plane angular profiles of the resonance field of the free Py layer show a similar behavior to that for the structure with a magnetic seed layer [with FeMn/Py bilayer; see Fig.~A1(a)]. (b) FMR linewidth ($\Delta H$) shows a much less pronounced angular dependence at all temperatures, which is in contrast to the significant temperature induced changes in $\Delta H$ for the structure with FeMn/Py [Figs.~\ref{fig_2}(c),~\ref{fig_3}(a)].
\label{fig_A2}
\end{figure}

\newpage
\subsection{NOTE 3. Rotation of the N\'eel vector of the AF}

\begin{figure}[h]
\includegraphics[width=10 cm]{FigSM3.eps}\\ 
\textbf{Figure A3.} Rotation of the N\'eel vector of the AF extracted from the angular dependences of the resonance field using the model fit detailed in Note~1. (a) In-plane angular dependences of the resonance field for the free Py layer ($H_\mathrm{r}^\mathrm{free}$) and the pinned Py layer ($H_\mathrm{r}^\mathrm{pin}$) of the Py(8)/Cu(5)/FeMn(5)/Py(5) structure, measured at 280~K. The lines are the fits performed using the model of Note~4. (b) Corresponding angular dependences of the FMR linewidth of the free Py layer ($\Delta H_\mathrm{free}$) and (c) simulated misalignment of the N\'eel vector ($\varphi_\mathbf{N}^\mathrm{sim}$) relative to the exchange-pinning direction ($\varphi_\mathbf{H} = 0\degree$) set at fabrication in the FeMn/Py bilayer. The dependence in (c) was calculated using the parameters obtained from the model fit shown in (a). The misalignment $\varphi_\mathbf{N}^\mathrm{sim}$ is linear in $\varphi_\mathbf{H}$ in the angle interval between the two maxima in $\Delta H_\mathrm{free}$-vs-$\varphi_\mathbf{H}$, shown in (b).
\label{fig_A3}
\end{figure}

\newpage
\subsection{NOTE 4. Gibbs free energy for F/AF bilayers}

To model the deviation of the N\'eel vector of the F/AF bilayer from its easy (exchange-pinning) direction, we split the energy term commonly used for describing exchange bias into two terms, corresponding to the interlayer exchange coupling at the F/AF interface and the magnetic anisotropy in AF. The Gibbs free energy per unit volume becomes


\noindent where $J_\mathrm{F}$ and $J_\mathrm{AF}$ are the constants of the uniaxial magnetic anisotropy in the pinned ferromagnetic Py and the antiferromagnetic FeMn layers, respectively; $J_\mathrm{ex}$ is the constant of exchange coupling at the Py/FeMn interface; $Z$ and $G_\mathrm{dem}$ are the Zeeman and demagnetization energies; $\mathbf{m}_\mathrm{p}$ is the unit vector along magnetization $\mathbf{M}_\mathrm{p}$ of the pinned Py.

\begin{equation}\tag{A1}
\begin{aligned}
G_\mathrm{p} = Z~+ &~G_\mathrm{F} + G_\mathrm{AF} + G_\mathrm{ex} + G_\mathrm{dem} = \\
& = -\mathbf{M}_\mathrm{p} \mathbf{H} - J_\mathrm{F}(\mathbf{x}\cdot\mathbf{m}_\mathrm{p})^2 - J_\mathrm{AF}(\mathbf{x}\cdot\mathbf{N})^2 - J_\mathrm{ex}(\mathbf{m}_\mathrm{p}\cdot\mathbf{N}) + 2\pi M_\mathrm{p}^2 (\mathbf{z}\cdot\mathbf{m}_\mathrm{p})^2.
\end{aligned}
\end{equation}

When external magnetic field $\mathbf{H}$ is oriented in the film plane, terms $G_\mathrm{F}$, $G_\mathrm{AF}$, and $G_\mathrm{ex}$ can be transformed as follows: $G_\mathrm{F} = -0.5 M_\mathrm{p}H_\mathrm{ua}\cos 2 \varphi_\mathrm{p}$, $G_\mathrm{AF} = -J_\mathrm{AF} \cos \varphi_\mathbf{N}$ and $G_\mathrm{ex} = -M_\mathrm{p}H_\mathrm{ex}\cos (\varphi_\mathrm{p}-\varphi_\mathbf{N})$, where angles $\varphi_\mathrm{p}$ and $\varphi_\mathbf{N}$ are defined in the inset to Fig.~A3(a). Minimization of (A1) gives

\begin{equation}\tag{A2}
\begin{cases}
\dfrac{J_\mathrm{AF}}{J_\mathrm{ex}} \sin( 2\varphi_\mathbf{N}) = \sin (\varphi_\mathrm{p}-\varphi_\mathbf{N}), \\[3mm]
\dfrac{Z}{J_\mathrm{ex}} \sin (\varphi_\mathrm{p}-\varphi_\mathbf{H}) = -\sin (\varphi_\mathrm{p}-\varphi_\mathbf{N}),
\end{cases}
\end{equation}

\noindent where $Z = H M_\mathrm{p}$.

Equations (A1) and (A2) can be used for fitting the angular dependence of the FMR spectra of the pinned Py layer in the general case of non-rigid $\mathbf{N}$. Curve $H_\mathrm{r}^\mathrm{pin}(\varphi_\mathbf{H})$ in Fig.~A3(a) is an example of such fitting, showing a good agreement between the fit and the experimental data.


\end{document}
