VOLUME 66, NUMBER 22 PHYSICAL REVIEW LETTERS 3 JUNE 1991 Irreversibility Crossover in a Cu:Mn Spin Glass in High Magnetic Fields: Evidence for the Gabay-Toulouse Transition G. G. Kenning, D. Chu, and R. Orbach Department of Physics, University of CaliforniaL, os Angeles4, 05 Hilgard Avenue, Los Angeles, California 90024 (Received 17 December 1990) The longitudinal components of the zero-field-cooled (MzFc) and field-cooled (MFc) magnetization of dilute Cu:Mn have been measured in magnetic fields between 2 6 and 30 kG. The difference, AM;„„ =M&& — Mzz&, is taken to be the irreversible magnetization. Above = 500 6, a weak irreversibility and a strong irreversibility are observed. The onset temperature of the former, or weak irreversibility, follows the Gabay-Toulouse H-T relation with a coefficient close to the mean-field value for a Heisen- berg system. The onset temperature of the latter is found to agree quantitatively with the mean-field d'Almeida-Thouless-like H-T crossover relation for longitudinal freezing in a Heisenberg system. PACS numbers: 75.30. Kz, 75.40. Gb, 75.60. Lr The issue of whether there is a phase transition for a three-dimensional Heisenberg spin glass in zero magnet- ic field or an Ising spin glass in a magnetic field has been the subject of controversy. ' The infinite-range Sher- rington and Kirkpatrick model is predicted to have a finite-temperature phase transition in zero and finite magnetic fields for both Ising and Heisenberg spin-glass systems. However, this model is formulated in an infinite-dimensional space, so its relationship to physical three-dimensional systems is unclear. Within this mean-field model, the onset of the phase transition is mathematically associated with replica-symmetry break- ing, leading to a highly degenerate set of solutions in phase space, with an ultrametric relationship between states. The very large (infinite in the thermodynamic limit) energy barriers between "pure states" leads to slow equilibration and irreversible behavior. The pur- pose of this investigation is to use sensitive SQUID mag- netization measurements, over a large magnetic field range, to determine the onset of irreversibility for a Heisenberg spin glass with weak unidirectional anisotro- py. The irreversible magnetization will be defined in our experiments as the diff'erence hM;„= M qg — M zing, where Mqp is the field-cooled magnetization and Mzqp is the zero-field-cooled magnetization. We investigate dilute Cu:Mn alloys for magnetic fields between 2 G and 30 kG. We find the onset of a single strong irreversible transition at low magnetic fields (H & 100 6) which we identify with longitudinal freezing appropriate to an Is- ing spin glass. This follows from the observation of Kotliar and Sompolinsky that in small magnetic fields the presence of a unidirectional anisotropy in an other- wise Heisenberg spin-glass system generates Ising-like behavior. This has been well established by a number of investigators. However, the numerical relation between H and T diAers from the predictions of d'Almeida and Thouless by an order of magnitude. At higher magnetic fields (H & 500 G) two onsets of irreversibility are ob- served for the first time: one "weak" and the other "strong" with a common extrapolated zero-field transi- tion temperature considerably below that found for low magnetic fields. We associate the weak irreversibility with a Gabay-Toulouse transition. A similar transition line was noted by de Courtenay, Fert, and Campbell by a direct measurement of the transverse magnetic irrever- sibility but for a considerably smaller field range. How- ever, in addition we also observe a strong irreversibility at lower temperatures which we associate with a cross- over to longitudinal freezing. This important observation is new and will have important physical consequences (see below). Remarkably, when we compare with the mean-field calculations we find quantitative agreement for H ~ 15 kG. At higher field values we observe devia- tions from the mean-field predictions suggesting that higher-order field corrections to the mean-field theory are necessary. The interpretation of our results in low magnetic fields follows from the observation of Kotliar and Sompolin- sky that an otherwise Heisenberg spin glass (e. g. , Cu:Mn with S= — , 'on the Mn site) in the presence of Dzyaloshinskii-Moriya anisotropy (strength d) exhibits Ising-like spin-glass behavior near a transition tempera- ture Ts at low magnetic fields (d » h t, where h =— gpttH). This behavior would, of course, exhibit solely longitudinal freezing along a transition line in the H-T plane, T~(H). Fischer has extended their result to take into account the spin size 5 and obtains the follow- ing critical line in the H-T plane: 3 S h = lkBT (0)]'r' n+2 3 where r =1 — Tg(H)/T~(0), and n is the number of spin degrees of freedom. Fischer uses n=1 for an Ising sys- tem, and n=3 for a classical Heisenberg system. Equa- tion (1) has the same form as that calculated by d'Almeida and Thouless and agrees in magnitude with their result for n=1 and S =3. We shall refer to the line in the H-T plane where longitudinal freezing follows the power laws of Eq. (1) as the AT line. As the mag- netic field increases to a value h »d, a new regime is entered which exhibits both a transverse freezing of the spins and a longitudinal freezing. According to Gabay and Toulouse, upon lowering the temperature at constant magnetic field one first encounters transverse freezing, 1991 The American Physical Society 2923