Antiferromagnetism in two-dimensionalt−Jmodel: A pseudospin representation

Abstract

We discuss a pseudospin representation of the two-dimensional t-J model. We introduce pseudospins associated with empty sites, deriving a new representation of the t-J model that consists of local spins and spinless fermions. We show, within a mean-field approximation, that our representation of t-J model corresponds to the isotropic antiferromagnetic Heisenberg model in an effective magnetic field. The strength and the direction of the effective field are determined by the hole doping δ and the orientation of pseudospins associated with empty sites, respectively. We find that the staggered magnetization in the standard representation corresponds to the component of magnetization perpendicular to the effective field in our pseudospin representation. Using a many-body Green's function method, we show that the staggered magnetization decreases with increasing hole doping δ and disappears at δ ≈ 0.06 − 0.15 for t/J = 2 − 5. Our results are in good agreement with experiments and numerical calculations in contradistinction to usual mean-field methods.

Magnetism and superconductivity in thet−t′−Jmodel

“…In this case, we obtain a rather large magnetic phase, with a critical doping that slightly depends on the superexchange coupling J, in contrast with previous mean-field calculations that predicted ␦ c ϳ J. 45,46 The superconducting correlations show a domelike behavior and vanish when the Mott insulator at halffilling is approached. Interestingly, compared to the RMFT that predicts a quadratic behavior of the pair-pair correlations as a function of the doping ␦, here we found that a linear behavior is more plausible.…”

Green’s function theory for spin-12ferromagnets with an easy-plane exchange anisotropy

“…7,13,19,20,21,22,23,24,25,26,27,28,29,30,31 In order to calculate the magnetic properties, many previous authors 7,21,22,23,24,25 have employed the Green's function theory with the set of Green's functions {G…”

“…14,15,16,17,18 The spin reorientation transition induced by a transverse magnetic field has also attracted considerable interest for both ferromagnetic and antiferromagnetic cases. 7,13,19,20,21,22,23,24,25,26,27,28,29,30,31 Some of them were studied by using Green's function formalism with the RPA decoupling. However, in this paper, we point out that one should pay careful attention in applying the RPA decoupling scheme to such a complicated system, which has an anisotropy in the plane perpendicular to the direction of the magnetization.…”

Magnon–magnon interactions in O(3) ferromagnets and equations of motion for spin operators

“…As noted in the Introduction, RPA is widely used tool for studying magnetic systems [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][31][32][33][34][35][36][37][38][39][40][41][42]. Thus, to be able to correctly interpret results obtained from RPA, it is of interest to fully grasp the approximation in itself.…”

“…[13][14][15][16][17] and references therein). Equally important is the flexibility of the method making it easily adjustable to systems with complex [18][19][20][21][22] or low-dimensional lattices [23][24][25][26][27][28][29][30], second and thirdneighbor interaction or anisotropies [13,15,[31][32][33][34][35], which is of great importance when studying real compounds. Also, the TGF method is recognized as useful in theories of diluted magnetic systems [36,37], nuclear spin order in quantum wires [38], multiferroics models [39,40] and even in theories of itinerant electron systems where Heisenberg Hamiltonian appears as an intermediate effective model [22,41,42].…”