${}^{77}$Se NMR measurements of the $\pi -d$ exchange field in the organic conductor $\lambda -$(BETS)${}_2$FeCl${}_4$

${}^{77}$Se-NMR spectrum and frequency shift measurements in the paramagnetic metal (PM) and antiferromagnetic insulating (AFI) phases are reported for a small single crystal of the organic conductor $\lambda -$(BETS)${}_2$FeCl${}_4$ as a function of temperature ($T$) and field alignment for an applied magnetic field $B_0$ = 9 T. The results show that in the low $T$ limit, where the localized Fe${}^{3+}$ spins ($S_d$ = 5/2) are almost fully polarized, the conduction electrons (Se $\pi$-electrons, spin $s_{\pi }$ = 1/2) in the BETS molecules experience an exchange field ($\mathbf{B}$${}_{\pi d}$) from the Fe${}^{3+}$ spins with a value of $-$ 32.7 $\pm$ 1.5 T at 5 K and 9 T aligned opposite to $\mathbf{B}$${}_0$. This large negative value of $\mathbf{B}$${}_{\pi d}$ is consistent with that predicted by the resistivity measurements and supports the Jaccarino-Peter internal field-compensation mechanism being responsible for the origin of field-induced superconductivity.