The magnetic properties of CeRu 2 Si 2 at microkelvin temperatures ͑down to 170 K) and ultrasmall magnetic fields (0.02ϳ6.21 mT) are investigated experimentally. The simultaneously measured ac susceptibility and static magnetization show neither evidence of the magnetic ordering, superconductivity down to the lowest temperatures nor conventional Landau Fermi-Liquid behavior. The results imply the magnetic transition temperature in undoped CeRu 2 Si 2 is very close to absolute 0 K. The possibility for proximity of CeRu 2 Si 2 to the quantum critical point without any doping is discussed. DOI: 10.1103/PhysRevB.67.180407 PACS number͑s͒: 75.30.Cr, 71.10.Hf, 71.27.ϩa The unusual properties of heavy fermion ͑HF͒ systems are determined by the competition between intersite spin couplings, Ruderman-Kittel-Kasuya-Yosida interaction, and intrasite Kondo interaction. 1 In a system dominated by the Kondo effect, the Pauli paramagnetic ͑PP͒ state with massive quasiparticles is achieved through screening of the f electron's magnetic moments by conduction electrons below the characteristic temperature T K . The physical properties of the HF compounds below T K are well understood within the framework of the Landau Fermi-liquid ͑LFL͒ theory.Recently, however, non-Fermi-liquid ͑NFL͒ behavior was observed in a large class of HF compounds near the quantum critical point ͑QCP͒. 2,3 NFL systems exhibit anomalous temperature dependence of the physical quantities in contrast to the LFL theory, such as specific heat ⌬C/TϰϪln T, resistivity ⌬ ϰT ⑀ (1р⑀Ͻ2), and magnetic susceptibility ⌬ ϰ either 1ϪͱT or Ϫln T. In general, the quantum ͑zero-temperature͒ phase transition is driven by a control parameter other than temperature, for example, composition, pressure, or magnetic field, and is accompanied by a qualitative change in the correlations in the ground state. The second order quantum phase transitions and QCPs in HF systems can be classified into two types. ͑i͒ The longwavelength fluctuations of the order parameter are the only critical degrees of freedom and the quantum criticality is developed as spin-density wave instability, 4,5 here the zerotemperature spin fluctuations are given by the Gaussian fluctuations of the order parameter. ͑ii͒ Local critical modes coexist with long-wavelength fluctuations of the order parameter and there is non-Gaussian distribution of the fluctuations. 6 These are the so-called locally critical phase transitions where the quantum criticality of CeCu (6Ϫx) Au x ͑Ref. 7͒ and YbRh 2 Si 2 ͑Ref. 8͒ are regarded as type-͑ii͒ QCP. 6 CeRu 2 Si 2 with a ThCr 2 Si 2 -type crystal structure is well known to be a typical HF compound with an electronic specific-heat coefficient ␥ϭ350 mJ/K 2 mol below T K ϭ20 K. 9,10 This compound exhibits the pseudometamagnetic transition into the ferromagnetically ordered state induced by the magnetic field at H M ϭ7.8 T below 10 K. 11-15 The neutron-scattering measurements note short-range antiferromagnetic ͑AFM͒ correlations in CeRu 2 Si 2 even below T K . These time-fluctuati...