Spin-glass freezing in Kondo-lattice compounds

Abstract

A theory is presented that describes a spin-glass phase at finite temperatures in Kondo-lattice systems with an additional Ruderman-Kittel-Kasuya-Yosida interaction represented by long range, random couplings among localized spins as in the Sherrington-Kirkpatrick ͑SK͒ spin-glass model. The problem is studied within the functional integral formalism where the spin operators are represented by bilinear combinations of fermionic ͑anticommuting͒ Grassmann variables. The Kondo and spin-glass transitions are both described with the mean-field-like static ansatz that reproduces good results in the two well-known limits. At high temperatures and low values of the Kondo coupling there is a paramagnetic ͑disordered͒ phase with vanishing Kondo and spin-glass order parameters. By lowering the temperature, a second order transition line is found at T SG to a spin-glass phase. For larger values of the Kondo coupling there is a second order transition line at roughly T k to a Kondo ordered state. For TϽT SG the transition between the Kondo and spin-glass phases becomes first order.

The Ising spin glass in a transverse field revisited. Results of two fermionic models

“…The advantage of the fermionic formulation is that it has a natural application to problems in condensed matter theory, where the fermion operators represent electrons that also participate in other physical processes, like superconductivity [11,12] and the Kondo effect [13]. In the present paper we use two fermionic models within a grassmannian field 2 , but they are labeled instead by the fermionic occupation numbers n σ = 0 or 1 , giving two more states with S z = 0.…”

“…We consider two models: the unrestrained, four states model that has been used previously [9,11,12,13], and also the two states model of Wiethege and Sherrington where the number operators satisfy the restraint n i↑ + n i↓ = 1, what gives S z i = ± 1 2 , at every site [15] The partition function in the 4S-model is given by…”

Theory of the Kondo Lattice: Competition Between Kondo Effect and Magnetic Order

“…The SGKondo transition was firstly studied theoretically [53], then in the presence of ferromagnetic ordering [54] or antiferromagnetic ordering [55] and finally the model has been improved in order to obtain a good description of the QCP [56], by introducing a transverse magnetic field.…”

“…The average value J 0 has been taken equal to zero to describe the SG-Kondo transition [53], while the case J 0 < 0 produces a complex phase diagram with spin glass, ferromagnetic, mixed (a spin glass with spontaneous magnetization) and Kondo phases [54]. Finally, the case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 …”

“…[53]. However, the experimental situation appears to be really complicate, as shown for example by recent experiments on CeN i 1−x Cu x alloys [51,52].…”