Spin-orbit coupling controlled ground state in ${\mathrm{Sr}}_2{\mathrm{ScOsO}}_6$

We report neutron scattering experiments which reveal a large spin gap in the magnetic excitation spectrum of weakly-monoclinic double perovskite ${\mathrm{Sr}}_2{\mathrm{ScOsO}}_6$. The spin gap is demonstrative of appreciable spin-orbit-induced anisotropy, despite nominally orbitally-quenched $5d^3{\mathrm{Os}}^{5+}$ ions. The system is successfully modeled including nearest neighbor interactions in a Heisenberg Hamiltonian with exchange anisotropy. We find that the presence of the spin-orbit-induced anisotropy is essential for the realization of the type I antiferromagnetic ground state. This demonstrates that physics beyond the LS or JJ coupling limits plays an active role in determining the collective properties of $4d^3$ and $5d^3$ systems and that theoretical treatments must include spin-orbit coupling.

Figure 1

(a) Schematic of the energy levels for ${\mathrm{Os}}^{5+}$ in an octahedral environment. $t_{2\mathrm{g}}\text{–}{e}_{\mathrm{g}}$ splitting of $3.6\mathrm{eV}$ determined by x-ray absorption spectroscopy [30]. In the strong SOC limit the $t_{2\mathrm{g}}$ level can be further split into $J_{\mathrm{eff}}=\frac{1}{2}$ and $\frac{3}{2}$ levels. Nominally the ${\mathrm{Os}}^{5+}$ ion is in the $LS$ coupling limit and an $L=0$ state results. (b) ${\mathrm{Sr}}_2{\mathrm{ScOsO}}_6$ magnetic structure, with moments depicted along $a$. One $P{2}_1/n$ unit cell is shown, with O and Sr ions omitted for clarity. Dashed lines show examples of the NN $\left(\times 12\right) {\mathcal{J}}_1$ and NNN $\left(\times 6\right) {\mathcal{J}}_2$ exchanges. (c) Schematic of the relevant orbitals for NN and NNN exchange pathways, assuming formal valence states.

Figure 2

$E_{\mathrm{i}}=60\mathrm{meV}$ neutron scattering intensity maps for $95\mathrm{K}⪆T_{\mathrm{N}}$, and $T<T_{\mathrm{N}}$ of 80, 50 and 6 K.

Figure 3

(a) Constant-$Q$ cuts from $E_{\mathrm{i}}=120\mathrm{meV}$ data. Solid line is the result of fitting Gaussians to the elastic line and to the inelastic magnetic signal at 6 K. A. U. stands for arbitrary units. (b) ${\chi }^{\prime \prime }\left(T\right)$ at fixed $Q$ and $E$, with an exponential, ${\chi }^{\prime \prime }\left(T\right)\propto exp(-\mathrm{\Delta }/k_{\mathrm{B}}\mathrm{T})$, fit to the $T<T_{\mathrm{N}}$ data. N.I. stands for normalized intensity. (c) Constant-$Q$ cuts from $E_{\mathrm{i}}=60\mathrm{meV}$ data, which have been corrected for the Bose factor. Solid line is a guide to the eye. (d) Constant-$E$ cuts from $E_{\mathrm{i}}=60\mathrm{meV}$ data. In all panels, error bars are sometimes smaller than the symbols.

Figure 4

(a) Simulated spin-wave spectra. Modeled using linear spin-wave theory [38], with powder averaging performed by sampling ${10}^4$ random points in reciprocal space. Gaussian energy broadening of $4\mathrm{meV}$ is applied as an approximation to instrument resolution at $E_i=60\mathrm{meV}$, estimated from the full width at half maximum of the incoherent part of the elastic line in the data. (b) The equivalent data collected at $T=6\mathrm{K}$. The intensity at high $Q$ in the data is due to phonon scattering, which is not included in the model. The shaded region in the calculations indicates the region of $(Q,E)$ space which is inaccessible in the experiment. (c) Constant-energy cuts through the calculation and data. A global scale factor has been used for the calculation, and a flat background applied for each cut.