Isotropic Spin Glass Research Articles

Collective spin dynamics under dissipative spin Hall torque

Current-induced spin torques in layered magnetic heterostructures have many commonalities across broad classes of magnetic materials. These include not only collinear ferromagnets, ferrimagnets, and antiferromagnets but also more complex noncollinear spin systems. We develop a general Lagrangian–Rayleigh approach for studying the role of dissipative torques, which can pump energy into long-wavelength magnetic dynamics, causing dynamic instabilities. While the Rayleigh structure of such torques is similar for different magnetic materials, their consequences depend sensitively on the nature of the order and, in particular, on whether there is a net magnetic moment. The latter endows the system with a unipolar switching capability, while magnetically compensated materials tend to evolve toward limit cycles, at large torques, with chirality dependent on the torque sign. Apart from the ferromagnetic and antiferromagnetic cases, we discuss ferrimagnets, which display an intricate competition between switching and limit cycles. As a simple case for compensated noncollinear order, we consider isotropic spin glasses and a scenario of their coexistence with a collinear magnetic order.

Theory of isotropic itinerant-electron spin glasses in the vicinity of amorphous Fe

Finite-temperature magnetism in the vicinity of amorphous Fe has been investigated by developing the theory of amorphous metallic magnetism which takes into account transverse spin fluctuations. The calculated magnetic phase diagram as a function of temperature and d electron number shows up the existence of isotropic spin glass around amorphous Fe and non-collinear ferromagnetism near the ferromagnetic boundary.

Finite-temperature theory of amorphous metallic magnetism with vector spins

A finite temperature theory of amorphous metallic magnetism which takes into account vector spins is developed to study noncollinear magnetism in amorphous Fe. This theory is based on the functional integral method for thermal spin fluctuations and the distribution function method for local magnetic moments with structural disorder. The numerical results at 35 K show up the existence of an isotropic spin-glass in amorphous Fe. When the d electron number n d is increased, the spin-glass changes toa noncollinear ferromagnet at n d = 7.40 and finally to a collinear ferromagnet beyond n d = 7.47.

Finite temperature theory of noncollinear magnetism in amorphous Fe

Noncollinear magnetism in the vicinity of amorphous Fe has been investigated by developing the finite temperature theory of amorphous metallic magnetism which takes into account the transverse spin fluctuations. The theory is based on the functional integral technique to the degenerate-band Hubbard Hamiltonian with Hund’s rule coupling and the distribution function method for local magnetic moments with structural disorder. It is shown that an isotropic spin-glass is realized in amorphous Fe, by taking into account the transverse components of local magnetic moments. The origin of the spin-glass around amorphous Fe is explained by the nonlinear magnetic couplings between Fe local moments and the local environment effects on the amplitude of Fe local moments. When the d electron number N is increased, the isotropic spin-glass changes to a noncollinear ferromagnet at N=7.40 and finally changes to a collinear ferromagnet beyond N=7.47 at 35 K.

Mean-field renormalization group for the q-state clock spin-glass model

The mean-field renormalization group is used to study the phase diagrams of a d-dimensional q-state clock spin-glass model. We found, for q = 3 clock, the transition from paramagnet to spin glass is an isotropic spin-glass phase, but for q = 4 clock, the transition from paramagnet to spin glass is an anisotropic spin-glass phase. However, for q ⩾ 5 clock, the result of anisotropic spin-glass phase depends on the temperature and the distribution of random coupling. While the coordinate number approaches infinity, the critical temperature evaluated by the mean-field renormalization group method is equal to that by the replica method.

Itenerant spin glass states and asperomagnetism of amorphous Fe and iron-rich Fe/Zr alloys

A realistic tight-binding approach for the self-consistent calculation of the itinerant spin configurations of disordered metallic systems has been developed and is used to study numerically the problem of the magnetic states at T = 0 K of iron-rich amorphous alloys of the type Fe 1− x Zr x H y , and of fictitious amorphous Fe of different densities. In our approach, the local spin polarization is not restricted to the z-direction, i.e. the polarization magnitude as well as its direction can vary from site to site. The calculations show that the spin configurations depend strongly on the preparation, and that changes of the relative spin orientations can lead to drastic changes of the itinerant atomic moments. Metastable spin configurations with essentially isotropic distribution can be prepared by relaxing the system in gradually vanishing external fields with isotropically distributed randomness and zero spatial average, whereas with a non-vanishing average the so-called asperomagnetic configurations are obtained, i.e. ferromagnetic states with randomly frozen transverse components. For iron-rich Fe 1− x Zr x alloys with x = 0.07, according to our calculation, the isotropic spin glass configuration would have slightly lower energy than the asperomagnetic state, by amounts corresponding to ≈ 0.003 eV per electron, while for the hydrogenated system Fe 1- x Zr x H y with y ≈ 2 x, the asperomagnetic state would be favoured by ≈ 0.004 eV. For two computer models of (fictitious) amorphous Fe with densities of 7.39 and 9.19 g cm −3, the spin-glass and the asperomagnetic states have roughly the same energy, although for the low-density sample the magnitudes of the moments are quite different in both states.

Dynamics of vector spin glasses with random anisotropy

The dynamics of vector spin glasses with additional random anisotropy is investigated in the mean field approximation. We find a cross-over of the upper critical line from a behaviour of Heisenberg spins with a field-temperature dependence\(\tilde T_f - T \propto H^2\), for large fieldsH, to Ising like behaviourTf−T∝T2/3, for small fields and fixed anisotropy, in agreement with results of Kotliar and Sompolinsky. Here,\(\tilde T_f\) andTf are characteristic spin glass temperatures. In addition, one has a second line with reversed behaviour which presumably represents a cross-over line from weak to strong non-ergodicity. The local transverse susceptibility χT(ω) varies for large fields and ω→0 along the upper critical line as ωvT, with a critical exponentVT = 1/2 − 11D/60 πJ, whereD andJ are the anisotropy and exchange coupling constants, respectively. On the Ising-like part of the upper critical line one has isotropic spin glass parameters,qL=qT, and susceptibilities, and a critical exponent,\(v = 1/2 - {{\sqrt 3 ({{5h^2 } \mathord{\left/ {\vphantom {{5h^2 } 4}} \right. \kern-\nulldelimiterspace} 4})^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} } \mathord{\left/ {\vphantom {{\sqrt 3 ({{5h^2 } \mathord{\left/ {\vphantom {{5h^2 } 4}} \right. \kern-\nulldelimiterspace} 4})^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} } \pi }} \right. \kern-\nulldelimiterspace} \pi }\) which is similar to that of Ising spins along the de Almeida-Thouless line.

On the equivalence of the Sompolinsky and Parisi solutions for the SK spin glass

Using simple properties of the Parisi overlap function P(q) the author demonstrates that the Parisi and Sompolinsky solutions are entirely equivalent both for Ising and isotropic spin glasses. Studying the notorious Potts model, he shows that existence of P(q) leads to important new criteria for the physical solutions of a replica approach, which supplement those based on the familiar stability analyses.