Magnetostriction-Driven Muon Localization in an Antiferromagnetic Oxide

Magnetostriction results from the coupling between magnetic and elastic degrees of freedom. Though it is associated with a relatively small energy, we show that it plays an important role in determining the site of an implanted muon, so that the energetically favorable site can switch on crossing a magnetic phase transition. This surprising effect is demonstrated in the cubic rocksalt antiferromagnet MnO which undergoes a magnetostriction-driven rhombohedral distortion at the Néel temperature $T_{\mathrm{N}}=118\mathrm{K}$. Above $T_{\mathrm{N}}$, the muon becomes delocalized around a network of equivalent sites, but below $T_{\mathrm{N}}$ the distortion lifts the degeneracy between these equivalent sites. Our first-principles simulations based on Hubbard-corrected density-functional theory and molecular dynamics are consistent with the experimental data and help to resolve a long-standing puzzle regarding muon data on MnO, as well as having wider applicability to other magnetic oxides.

Figure 1

(a) Muon asymmetry $A(t)$ of single crystal MnO at selected temperatures. The black line is a fit to the function $A(t)=A_b+A_o\cos ({\gamma }_{\mu }{B}_{\mu }t)\exp (-\lambda t)$, where $B_{\mu }$ is the local field at the muon site, ${\gamma }_{\mu }$ is the muon gyromagnetic ratio, and the baseline ($A_b$) and oscillating ($A_o$) amplitudes depend on the setup of the experiment. (b) Fourier transform of $A(t)$ at various temperatures. The red and black arrows are the prediction of the local field at the muon site obtained from DFT considering ab initio or experimental contact field, respectively, while the dipolar part is computed assuming $4.9{\mu }_{\mathrm{B}}$ per Mn atom. Data for various temperatures are displaced vertically on both panels for clarity.

Figure 2

Muon sites in MnO. The arrows on Mn (purple) spheres show the magnetic order; oxygen is shown as red spheres. The muon sites are shown by orange and green spheres (to distinguish symmetrically inequivalent sites $2c$ and $6h$ in the rhombohedral cell) and labeled 1, 2, and 3 to identify muon sites with the same $|{\mathbf{B}}_{\mu }|$ in the AFM phase.

Figure 3

Results from MD simulations. (a) Angular autocorrelation function, Eq. (1), for a muon bound to an oxygen, with solid fit curves (see text). Shaded areas display the uncertainty. (b) The MSD of the muon. Solid lines are linear fit to the data highlighted by opaque points. (c) Muon diffusion coefficient (brown squares) and decay rate of the angular autocorrelation function (turquoise circles) as a function of the inverse temperature, together with fits to Arrhenius equations (see main text). Finally, the inset shows the values obtained for the exponent of the stretched exponential fits shown in (a).