Ferropericlase [(Mg,Fe)O] is one of the most abundant minerals of the earth's lower mantle. The high-spin (HS) to low-spin (LS) transition in the Fe 2+ ions may dramatically alter the physical and chemical properties of (Mg,Fe)O in the deep mantle. To understand the effects of compression on the ground electronic state of iron, electronic and magnetic states of Fe 2+ in (Mg 0.75 Fe 0.25 )O have been investigated using transmission and synchrotron Mössbauer spectroscopy at high pressures and low temperatures (down to 5 K). Our results show that the ground electronic state of Fe 2+ at the critical pressure P c of the spin transition close to T = 0 is governed by a quantum critical point (T = 0, P = P c ) at which the energy required for the fluctuation between HS and LS states is zero. Analysis of the data gives P c = 55 GPa. Thermal excitation within the HS or LS states (T > 0 K) is expected to strongly influence the magnetic as well as physical properties of ferropericlase. Multielectron theoretical calculations show that the existence of the quantum critical point at temperatures approaching zero affects not only physical properties of ferropericlase at low temperatures but also its properties at P-T of the earth's lower mantle. , which has a 79% abundance (1-6). Great interest recently has been focused on the pressure-induced electronic transition in (Mg,Fe)O, in which the Fe 2+ ions transform from the high-spin (HS) state [total spin momentum (S) = 2] to the low-spin (LS) state (S = 0) (7-14). A series of observed physical and chemical properties of (Mg,Fe)O have been altered dramatically by the spin transition in the relevant range of pressure-temperature (P-T) conditions of the deep earth's mantle, including thermal (15, 16) and electrical (17) conductivity, density (18,19), incompressibility (18), and sound velocity (20). Most previous investigations on the spin transition of iron in ferropericlase were performed at either room temperature or high temperatures. At pressures near the spin cross-over, the Fe ions may exist in a mixed condition, with HS and LS states coexisting as the result of thermal fluctuations. This mixed state results in a wide cross-over with a smooth, continuous transition from the HS to the LS state with a pressure interval (ΔP) of ∼20 GPa (9, 14). Studies on the electronic and magnetic states at low temperatures may provide crucial information on the ground state of the Fe ions in ferropericlase at high pressures (21).We have investigated electronic and magnetic properties of Fe 2+ in two representative compositions of ferropericlase (Mg 1-x Fe x )O (x = 0.25 and 0.2) at high pressures and low temperatures using transmission Mössbauer spectroscopy (TMS) and synchrotron Mössbauer spectroscopy (also called nuclear forward scattering, NFS) in diamond anvil cells (DACs) up to 90 GPa. Hyperfine parameters of iron ions derived from the Mössbauer spectra are used to construct the magnetic phase diagram. We find quantum critical point in the phase diagram at 55 GPa and low temperatures wher...