Biquadratic exchange coupling and the magnetic properties of PrAg

Bulk magnetic and neutron diffraction studies show that the cubic (CsCl-type) compound PrAg becomes antiferromagnetic at $T_N\approx 11$°K, below which it undergoes a spin-flop transition at a critical field $H_c$ of ∼ 5 kOe. However, the temperature dependence of the initial susceptibility below $T_N$ and the field dependence of the magnetization $M$ above $H_c$ are both anomalous. The measured $M$ vs $H$ curves for PrAg above $T_N$ and those for the related pseudobinary ${\mathrm{Pr}}_{0.5}$ ${\mathrm{La}}_{0.5}$Ag (which remains paramagnetic down to 4.2°K) are tested against the isotherms of $M$ vs effective field calculated for the crysta-field states of ${\mathrm{Pr}}^{3+}$ in these compounds. This analysis reveals that the net exchange field $H_{\mathrm{exch}}$ on a Pr atom in either compound does not vary linearly with $M$ but also contains a substantial negative term in $M^3$. It is shown that this higher-order $H_{\mathrm{exch}}\mathrm{}\left(M\right)\mathrm{}$ dependence can be generated by a positive biquadratic exchange term in the spin Hamiltonian of the paramagnetic system. Moreover, When the same biquadratic exchange term is included in a two-sublattice model for the ordered magnetic state, a consistent explanation is obtained for the anomalous properties of PrAg below $T_N$. Possible mechanisms for the origin of biquadratic exchange in these materials are discussed.