Low-moment magnetism in the double perovskites Ba${}_2$$M$OsO${}_6$ ($M=\text{Li},\text{Na}$)

The magnetic ground states of the isostructural double perovskites Ba${}_{\text{2}}$NaOsO${}_{\text{6}}$ and Ba${}_{\text{2}}$LiOsO${}_{\text{6}}$ are investigated with muon-spin relaxation. In Ba${}_{\text{2}}$NaOsO${}_{\text{6}}$ long-range magnetic order is detected via the onset of a spontaneous muon-spin precession signal below $T_{\mathrm{c}}=7.2\pm 0.2\mathrm{K}$, while in Ba${}_{\text{2}}$LiOsO${}_{\text{6}}$ a static but spatially disordered internal field is found below 8 K. A probabilistic argument is used to show from the observed precession frequencies that the magnetic ground state in Ba${}_{\text{2}}$NaOsO${}_{\text{6}}$ is most likely to be low-moment ($\approx 0.2$${\mu }_{\mathrm{B}}$) ferromagnetism and not canted antiferromagnetism. Ba${}_2$LiOsO${}_6$ is antiferromagnetic and we find a spin-flop transition at $5.5\text{T}$. A reduced osmium moment is common to both compounds, probably arising from a combination of spin-orbit coupling and frustration.

Figure 1

(a) Double-perovskite crystal structure. Alternation of OsO${}_6$ octahedra (top left and bottom right) and NaO${}_6$ octahedra, with barium ions occupying the remaining space. (b) Magnetization measured at 2 K in a SQUID magnetometer for Ba${}_2$$M$OsO${}_{\text{6}}$. (c) Magnetization measured at 4 K in pulsed field for Ba${}_2$LiOsO${}_6$, calibrated against the SQUID magnetization data. Data from a 45 T shot (dashed line) are noisier than those from a 25 T shot (solid line) but show no evidence for additional magnetic transitions.

Figure 2

Muon data above and below the magnetic transition for (a) Ba${}_{\text{2}}$LiOsO${}_{\text{6}}$ and (b) Ba${}_{\text{2}}$NaOsO${}_{\text{6}}$. The inset to (a) shows the temperature dependence of the Gaussian relaxation rate in Ba${}_{\text{2}}$LiOsO${}_{\text{6}}$ (the solid line is a best fit to a phenomenological ${[1-{(T/T_{\mathrm{N}})}^{\alpha }]}^{\beta }$ form; see text). The 1.5 K data in (a) can be fitted to either an exponentially damped Kubo-Toyabe function (green dashed line) or an exponentially damped oscillation plus a fast-relaxing component (black solid line). Fits in (b) are described in the text.

Figure 3

The frequency $\nu \left(T\right)$ extracted from fits to $A\left(t\right)$ spectra as a function of sample temperature $T$, along with fits to various models (see text). Data are only shown for the larger frequency ${\nu }_1$ because ${\nu }_2$ was held in fixed proportion during fitting (see text).

Figure 4

(a) Probability density functions (PDFs) of the moment ($\mu$) on the Os site in Ba${}_2$NaOsO${}_6$ inferred by Bayes’ theorem from dipole-field simulations using representative trial magnetic structures (FM, ferromagnetic; AFM, antiferromagnetic) and the experimentally observed frequencies. (b) PDFs evaluated using the constraint of a fixed ferromagnetic component $\mu \sin \alpha =0.2$${\mu }_{\mathrm{B}}$. Inset shows the assumed structure: antiferromagnetic moments along $\widehat{\mathit{m}}$ rotated as shown by an angle $\alpha$ about $\widehat{\mathit{n}}$.