Finite-temperature phase diagram of nonmagnetic impurities in high-temperature superconductors using ad=3 tJmodel with quenched disorder

Abstract

We study a quenched disordered d =3 tJ Hamiltonian with static vacancies as a model of nonmagnetic impurities in high-T c materials. Using a renormalization-group approach, we calculate the evolution of the finite-temperature phase diagram with impurity concentration p and find several features with close experimental parallels: Away from half filling, we see the rapid destruction of a spin-singlet phase ͑analogous to the superconducting phase in cuprates͒ which is eliminated for p տ 0.05; in the same region for these dilute impurity concentrations, we observe an enhancement of antiferromagnetism. The antiferromagnetic phase near half filling is robust against impurity addition and disappears only for p տ 0.40.The electronic properties and phase diagram of high-T c materials are particularly sensitive to impurities--substitution of 3d transition elements ͑Zn, Ni, Co, and Fe͒ or other metals ͑Al and Ga͒, for the Cu atoms of the CuO 2 planes. 1 The interplay between disorder, strong antiferromagnetic correlations in the parent compound and doped charge carriers offers a window onto the nature of both the superconducting phase and the normal state above T c . Doping by nonmagnetic ͑S =0͒ Zn ions provides one representative example: the most pronounced effect is the rapid destruction of the superconducting phase. 1,2 In yttrium barium copper oxide ͑YBCO͒, the transition temperature is reduced at a rate of ϳ15 K / at % of impurities so that it takes Zn concentrations of only about 6% to entirely eliminate superconductivity. 2 This is in contrast to the antiferromagnetic phase at half filling, which requires a far larger Zn concentration ͓about 40% in lanthanum strontium copper oxide ͑LSCO͒ ͑Ref. 3͔͒ to completely suppress. The effects in the metallic region above T c are equally surprising: nuclear-magnetic-resonance experiments have found that Zn atoms induce local magnetic moments at nearest-neighbor Cu sites 4 and enhance antiferromagnetic correlations for several lattice spacings around the impurity. 5,6 In lightly hole-doped LSCO, there have been observations of an initial increase in the Néel temperature with Zn addition and even impurity-induced reappearance of long-range antiferromagnetic order. 7,8 In this work we model the effects of nonmagnetic impurities in high-T c materials through a d =3 tJ Hamiltonian with quenched disorder in the form of static vacancies. Through a renormalization-group ͑RG͒ approach, we obtain the evolution of the global temperature vs chemical-potential phase diagram with disorder. Our results capture, in a single microscopic model, some of the major qualitative features of impurity doping in real materials: the rapid suppression of a spin-singlet phase, analogous to the superconducting phase in cuprates, the gradual reduction of the antiferromagnetic phase near half filling, and the enhancement of antiferromagnetism away from half filling for small impurity concentrations.We consider the quenched disordered tJ model on aThe static impurities at each site i occur with probability ...

Frustrated further-neighbor antiferromagnetic and electron-hopping interactions in thed=3t−Jmodel: Finite-temperature global phase diagrams from renormalization group theory

“…In the limit of very strong on-site Coulomb repulsion, secondorder perturbation theory on the Hubbard model yields the tJ model [2,3], in which sites doubly occupied by electrons do not exist. Studies of the Hubbard model [4] and of the tJ model [5], including spatial anisotropy [6] and quenched non-magnetic impurities [7] in good agreement with experiments, have shown the effectiveness of renormalization-group theory, especially in calculating phase diagrams at finite temperatures for the entire range of electron densities in d = 3. These calculations have revealed new phases, dubbed the τ phases, which occur only in these electronic conduction models under doping conditions.…”

Devil's staircase continuum in the chiral clock spin glass with competing ferromagnetic-antiferromagnetic and left-right chiral interactions

“…On the other hand, this approximation for the cubic lattice is an uncontrolled approximation, as in fact are all renormalization-group theory calculations in d = 3 and all mean-field theory calculations. However, as noted before [40], the local summation in position-space technique used here has been qualitatively, near quantitatively, and predictively successful in a large variety of problems, such as arbitrary spin-s Ising models [41], global Blume-Emery-Griffiths model [42], first-and second-order Potts transitions [43,44], antiferromagnetic Potts critical phases [9,10], ordering [45] and superfluidity [46] on surfaces, multiply re-entrant liquid crystal phases [47,48], chaotic spin glasses [49], randomfield [50,51] and random-temperature [52,53] magnets including the remarkably small d = 3 magnetization critical exponent β of the random-field Ising model, and hightemperature superconductors [54].…”

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