  We report the magneto-dielectric response of single crystals of the spin-ice
compound Dy2Ti2O7 down to 0.26 K. The dielectric constant under zero magnetic
field exhibits a clear decrease reflecting the development of the local
two-spins-in, two-spins-out structure below about 1.2 K. Both the real and
imaginary parts of the dielectric constant under magnetic fields sensitively
respond to various changes in the spin structures. We found that the real part
can be described in terms of local spin correlations among the moments of
tetrahedra, rather than among individual Dy3+ moments. Using the peaks in the
imaginary part, we have constructed a precise field-temperature phase diagram
in the [111] field direction. We thus demonstrate that the magneto-dielectric
response can be a high-sensitivity local probe of the spin state of
geometrically frustrated systems.
