  Electronic and magnetic properties of molybdenum pyrochlores A2Mo2O7 are
studied by the fully relativistic density-functional theory plus on-site
repulsion (U) method, with focusing on the spin-glass insulating material
Y2Mo2O7. We find that the system exhibits peculiar competition in energy
between different magnetic states in the large-U insulating region. The
magnetic competition cannot be explained by the conventional picture based on
the geometrical frustration of isotropic Heisenberg antiferromagnetic exchange
interactions. Through an analysis by using a generalized spin model, we find
that the effective spin interactions are distinct from the simple Heisenberg
form and strongly anisotropic in spin space. We also reveal that they give rise
to keen competition between antiferromagnetic and ferromagnetic states. The
complex form of the magnetic interactions indicates a crucial role of the
orbital degree of freedom. Analyzing a three-orbital Hubbard model, we clarify
that the magnetic competition is tightly connected with orbital frustration in
the 4d2 electronic configuration through the spin-orbital interplay. The
results challenge the conventional picture of the spin-glass behavior that
attributes the origin to the geometrical frustration of purely
antiferromagnetic exchange interactions.
