A comprehensive set of muon spin spectroscopy and neutron scattering measurements supported by ab-initio and model Hamiltonian simulations have been used to investigate the magnetic ground state of Na$_2$PrO$_3$. $\mu$SR reveals N\'eel antiferromagnetic order below $T_{ \rm N}\! \sim\! 4.9$ K, with a small static magnetic moment $m_{ \rm static}\!\leq \! 0.22$~$\mu_{ \rm B}/{ \rm Pr}$ collinearly aligned along the $c-$axis. Inelastic neutron measurements reveal the full spectrum of crystal field excitations and confirm that the Pr$^{ 4+}$ ground state wave function deviates significantly from the $\Gamma_7$ limit relevant to the Kitaev model. Single and two magnon excitations are observed in the ordered state below $T_N=4.6$ K and are well described by non-linear spin wave theory from the N\'eel state using a magnetic Hamiltonian with Heisenberg exchange $J=1$ meV and symmetric anisotropic exchange $\Gamma/J=0.1$, corresponding to an XY model. Intense two magnon excitations are accounted for by $g$-factor anisotropy $g_\mathrm{ z}/g_\pm = 1.29$. A fluctuating moment $\delta m^2 = 0.57(22)$ $\mu_{ \rm B}^2/{ \rm Pr}$ extracted from the energy and momentum integrated inelastic neutron signal is reduced from expectations for a local $J=1/2$ moment with average $g$-factor $g_{ \rm avg}\approx 1.1$. Together, the results demonstrate that the small moment in Na$_2$PrO$_3$ arises from crystal field and covalency effects and that the material does not exhibit significant quantum fluctuations..
Categories: cond-mat.str-el