Dynamics of an Ising Spin-Glass in the Vicinity of the Spin-Glass Temperature

Abstract

The dynamics of the short-range Ising spin-glass Feo.sMno.sTiCh has been investigated with a SQUID magnetometer. The dynamic spin-correlation function, q(t), as reflected in low-field ac susceptibility and time-dependent magnetization measurements, was studied in the time interval 10~6-10 4 sec. The functional form of q{t) shows a remarkable agreement with the results obtained from Monte Carlo simulations on a three-dimensional Ising spin-glass. The temperature dependence of the relaxation times above the spin-glass temperature is well described by conventional power-law scaling.PACS numbers: 75.40.GbThe slow, nonexponential relaxation of spin-glasses has been extensively investigated both experimentally and theoretically. Despite the simplicity of the theoretical formulation, analytical solutions are very complicated. Monte Carlo (MC) simulations are therefore important in order to learn more about the physics of the spin-glass dynamics. Most MC simulations have been performed on Ising spin-glasses with either long-range or short-range exchange interactions. The predictions of these simulations should be compared with experiments on real Ising spin-glass materials. Some model compounds of this type have been studied earlier: FezTiOs, 1 " 3 YEr (2 at.%), 4 and Feo.sMno.sTiOs. 5 ' 6 It has been argued that any small anisotropy present in more isotropic spin-glass systems induces Ising critical behavior. 7 There exist a number of papers on dynamic scaling performed on such systems. 8 In this paper we report extensive SQUID measurements on the time-dependent susceptibility of a shortrange Ising spin-glass Feo.sMno.sTiCh. Combining ac susceptibility and time-dependent magnetization measurements, the time interval 10 _6 -10 4 sec of the spinglass relaxation is covered. The experimentally detected time dependence of the zero-field susceptibility shows a remarkable agreement with the time decay of the dynamic spin-correlation function obtained in MC simulations on a three-dimensional, short-range Ising spin-glass by Ogielski. 9 A single crystal of the hexagonal Feo.sMno.sTiCh (Ref. 5) was cut into the shape of a rectangular parallelepiped, 2x2x5 mm 3 , with its long axis parallel to the c axis. Feo.5Mno.sTi03 behaves as an Ising spin-glass with the spins aligned along the hexagonal c axis. 5 The origin of the spin-glass behavior is a random mixture of ferromagnetic and antiferromagnetic exchange interactions within the hexagonal layers, which implies real bond disorder. In MC simulations, bond disorder is often used to model the disorder in spin-glasses.The ac susceptibility along the c axis was measured in the frequency interval 5 x 10 " 4 < coIln < 5 x 10 4 Hz and in the temperature range 0.9 < 777^ < 1.4 (7^=20.9 K). The measurements were performed by step cooling the sample in a small ac field («0.1 G). At constant temperature the ac susceptibility, x(co) = s^' (cy) + /z"(ft)), was measured. The experimental precision was of the order of « 10 ~4. The real, X\ and imaginary, X", parts were simultaneously measured wit...

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