Neutron scattering study of magnetic excitations in a 5$d$-based double-perovskite Ba${}_2$FeReO${}_6$

Motivated by exploring spin-orbit-coupled magnetism in $5d$-based transition metal oxides (TMOs) beyond the iridates, we present a powder inelastic neutron scattering study of magnetic excitations in Ba${}_2$FeReO${}_6$—a member of the double-perovskite family of materials which exhibit half-metallic behavior and high Curie temperatures $T_c$. We find clear evidence of two well-defined dispersing magnetic modes in its low-temperature ferrimagnetic state. We develop a local moment model, which incorporates the interaction of Fe spins with spin-orbital locked magnetic moments on Re and show that it captures our experimental observations. This allows us to extract moment sizes and exchange couplings, explain the magnitude of $T_c$, and infer that magnetostructural locking terms are weak. Our study further opens up Re-based compounds as model systems to explore the interplay of strong correlations and spin-orbit coupling in $5d$ TMOs.

Figure 1

Crystal structure of Ba${}_2$FeReO${}_6$. (a) Schematic of the crystallographic unit cell showing the relative orientation of Fe and Re moments. (b) Projection into the ab plane illustrating the separation between B(B${}^{\prime }$) site ions and the exchange pathway $\mathcal{J}$ between neighboring Fe and Re sites.

Figure 2

Comparison of spin wave model and measured powder-averaged magnetic scattering intensity for $T=34$ K. An empty Al-Can background signal has been subtracted from the data. [(a) and (b)] Neutron scattering data for incident energies of 27 and 120 meV, respectively. [(c) and (d)] Powder-averaged dynamic structure factor calculated from the spin wave model with $6{\mathcal{J}}_{\mathrm{eff}}\mathcal{F}=39$ meV and $6{\mathcal{J}}_{\mathrm{eff}}\mathcal{R}=25$ meV.

Figure 3

Representative cuts through $S(Q,E)$. (a) Temperature dependence of magnetic Bragg peaks at $\{\pi ,\pi ,\pi \}$ and $\{2\pi ,0,0\}$ determined by integrating the $E_i=120$ meV data over the elastic line resolution [$-4<E<4$ meV]. (b) Temperature dependence of Bose factor corrected inelastic scattering near the magnetic zone center. (c) Constant energy cuts from the $E_i=27$ meV data at 34 K; each energy cut was integrated over $\pm 1$ meV, and the 7-meV cut is offset for clarity. (d) Bose factor–corrected inelastic scattering at 34 K integrated over a magnetic Brillouin zone representing the magnetic density of states; the solid line is an equivalent cut from the spin-wave-model calculation. An empty-can background has been subtracted from the data in (c) and (d).

Figure 4

(a) Spectrum of $H_{\mathrm{Re}}$ (in units of $\lambda$) versus $J_H/\lambda$, with degeneracies indicated in brackets. For $J_H=0$, the eigenstates at three distinct energies correspond to different ways of filling two electrons into SO-coupled single-particle states with angular momentum $j=3/2$ and $j=1/2$. When $\lambda =0$, we find two-particle angular-momentum eigenstates ${}^{3}P$, ${}^{1}D$, and ${}^{1}S$ in increasing order of energy. A weak SO coupling, with $J_H/\lambda \gg 1$, splits the lowest ${}^{3}P$ manifold into ${}^3{P}_2$, ${}^3{P}_1$, and ${}^3{P}_0$. (b) Interaction dependence of total orbital and spin angular momentum and magnitude of SO energy. For $J_H\gtrsim 2\lambda$, the ground state is composed of $L=1,S=1$ moments, which lock to yield a total angular momentum $\vec{\mathcal{R}}=\vec{L}+\vec{S}$, with $\mathcal{R}=2$.

Figure 5

(a) Neutron scattering intensity at 34 K for and incident energy of 120 meV. An empty Al-can background has been subtracted from the data. [(b)–(d)] Constant energy cuts across bands of inelastic scattering at 70, 40, and 25 meV, respectively. Solid black lines are a fit to $I\left(Q\right)=A\left(E\right)+B{Q}^2$ delimiting the $Q$-dependent contribution of phonon scattering at each energy.