We present a detailed nuclear magnetic resonance (NMR) study of ${}^{239}$Pu in bulk and powdered single-crystal plutonium tetraboride (PuB$_4$), which has recently been investigated as a potential correlated topological insulator. This study constitutes the second-ever observation of the ${}^{239}$Pu NMR signal, and provides unique on-site sensitivity to the rich $f$-electron physics and insight into the bulk gap-like behavior in PuB$_4$. The ${}^{239}$Pu NMR spectra are consistent with axial symmetry of the shift tensor showing for the first time that ${}^{239}$Pu NMR can be observed in an anisotropic environment and up to room temperature. The temperature dependence of the ${}^{239}$Pu shift, combined with a relatively long spin-lattice relaxation time ($T_1$), indicate that PuB$_4$ adopts a non-magnetic state with gap-like behavior consistent with our density functional theory (DFT) calculations. The temperature dependencies of the NMR Knight shift and $T_1^{-1}$--microscopic quantities sensitive only to bulk states--imply bulk gap-like behavior confirming that PuB$_4$ is a good candidate topological insulator. The large contrast between the ${}^{239}$Pu orbital shifts in the ionic insulator PuO$_2$ ($sim$~+24.7~%) and PuB$_4$ ($sim$~-0.5~%) provides a new tool to investigate the nature of chemical bonding in plutonium materials.
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