Quest for Frustration Driven Distortion in ${\mathrm{Y}}_2\mathrm{M}{\mathrm{o}}_2{\mathrm{O}}_7$

We investigated the nature of the freezing in the geometrically frustrated Heisenberg spin glass ${\mathrm{Y}}_2\mathrm{M}{\mathrm{o}}_2{\mathrm{O}}_7$ by measuring the temperature dependence of the static internal magnetic field distribution above the spin-glass temperature, $T_g$, using the muon spin relaxation technique. The evolution of the field distribution cannot be explained by changes in the spin susceptibility alone and suggests a lattice deformation. This possibility is addressed by numerical simulations of the Heisenberg Hamiltonian with magnetoelastic coupling at $T>0$.

Figure 1

(a) Longitudinal field asymmetries for $T=23.2\mathrm{K}$ and $T=45.2\mathrm{K}$; (b) and (c) real and imaginary transverse field asymmetries for $T=45.2\mathrm{K}$ and $T=23.2\mathrm{K}$, respectively. The solid lines are fits to Eqs. (1, 2).

Figure 2

A plot of the static ($\Delta$), longitudinal ($R_{\mathrm{LF}}$), and transverse ($R_{\mathrm{TF}}$) relaxation rates, on a log scale, versus susceptibility and temperature. In the inset we present $\Delta$ versus magnetic field at a constant temperature of 22.5 K.

Figure 3

The minimum energy per spin obtained by the simulation program as described in the text. In the inset we depict a tetrahedral unit of the pyrochlore lattice with its spins connected by springs to enable visualization of the magnetoelastic term.

Figure 4

Nuclear and magnetic computer-simulated neutron scattering in the 111 direction. Inset: (a) Nuclear scattering from a perfect pyrochlore lattice. (b) Magnetic scattering from one of the ground states of the Heisenberg Hamiltonian (without magnetoelastic term) on this lattice. (c)–(f) Nuclear and magnetic scattering from the states obtained by a computer simulation of the Heisenberg Hamiltonian with the magnetoelastic term with $k=10$ and $J^{\prime }=0.1$ [Eq. (5)] at different temperatures (note the scale difference). In (c) and (d) $T={10}^{-6}J$ and in (e) and (f) $T={10}^{-4}J$. Main figure: magnetic scattering amplitude as a function of temperature.