Mean-field type Ising spin glass in a diluted rare-earth intermetallic compound

We have investigated a phase transition of a long-range RKKY Ising spin glass DyxY1−xRu2Si2 by means of the dc and the ac magnetization measurements. The static nonlinear susceptibility χ2 exhibits a divergent behavior toward Tg = 1.925 K with the exponent of γ = 1.08. The characteristic relaxation time τ obtained from the ac magnetization measurements also diverges to the same Tg with the exponent of zν = 1.9 in zero static field . These results indicate the spin glass phase transition belonging to the mean-field universality class, in which the exponents of γMF and (zν)MF are 1 and 2 respectively. Moreover, we observed the divergence of τ in a finite field of 500 Oe toward Tg = 1.412 K with the exponent of zν = 2.1, being quite similar to that in zero field. It strongly suggests an existence of the spin glass phase transition in a finite field and the replica symmetry breaking (RSB) in the long-range Ising spin glass DyxY1−xRu2Si2. In spite of the long-period investigation on the spin glass for more than 30 years, there are still several unsolved problems [1, 2]. One of them is whether the replica symmetry breaking (RSB) predicted by the mean-field theory of the spin glass [3] occurs or not in real spin glass materials. In the mean field picture, the spin glass state has a complicated multi-valley structure of the free-energy and survives in a finite magnetic field [4]. Alternative theory of the spin glass, so called the droplet theory based on the renormalization group arguments, predicts no RSB and that only two thermodynamic states related each other by a global spin flip exist in the spin glass state [5]. In the droplet picture, no spin glass phase transition exists in the presence of a magnetic field. Many numerical studies have been employed extensively on a stability of the spin glass phase in the presence of magnetic field [6, 7, 8, 9, 10] , however it is still controversial. Recent experimental study of the short-range Ising spin glass FexMn1−xTiO3 gave an evidence against an equilibrium phase transition in a finite magnetic field and indicated that the droplet picture is appropriate [11, 12]. On the other hand, the magnetic torque measurements of several Heisenberg spin glasses exhibit the existence of true phase transitions in fields [13]. In this article, we reported recent ac and dc magnetization measurements for the Ising spin glass DyxY1−xRu2Si2 . DyRu2Si2 is a rare-earth intermetallic compound with the tetragonal ThCr2Si2-type crystal structure, exhibiting two successive antiferromagnetic transitions with TN1 = 29 K and TN2 = 3.5 K [14]. The compound has a strong uniaxial magnetic anisotropy and recognized as an Ising antiferromagnet. In the diluted system DyxY1−xRu2Si2, where the magnetic Dy-ion is substituted by the non-magntic Y-ion, a spin glass transition is undergone with x = 0.103. In this compound, the Ising Dy-moments interact via the longrange RKKY interaction, and hence, its spin glass phase transition could belong to a different universality class from the short-range Ising spin glass such as FexMn1−xTiO3. Our analyses of the static and the dynamic critical phenomena present that DyxY1−xRu2Si2 exhibits the mean field type phase transition in zero and finite fields where the replica symmetry should be broken. The single crystalline sample of DyxY1−xRu2Si2 with x = 0.103 was grown by the Czhochralski method with a tetra-arc furnace. The concentration of Dy was determined by comparing the saturated magnetization of the diluted compound along the magnetic easy c-axis with that of the pure compund DyRu2Si2. The ac and the dc magnetizations were measured with use of a SQUID magnetometer MPMS (Quantum Design). The ac measurements were performed with an ac-field of 3 Oe and frequency of 0.5 Hz ≤ ω ≤ 1000 Hz.