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

Abstract

The many-body Green's function theory with the random-phase approximation is applied to the study of easy-plane spin-1/2 ferromagnets in an in-plane magnetic field. We demonstrate that the usual procedure, in which only the three Green's functions S µ i ; S − j (µ = +, −, z) are used, yields unreasonable results in this case. Then the problem is discussed in more detail by considering all combinations of Green's functions. We can derive one more equation, which cannot be obtained by using only the set of the above three Green's functions, and point out that the two equations contradict each other if one demands that the identities of the spin operators are exactly satisfied. We discuss the cause of the contradiction and attempt to improve the method in a self consistent way. In our procedure, the effect of the anisotropy can be appropriately taken into account, and the results are in good agreement with the quantum Monte Carlo calculations.

Correlated cluster mean-field theory for spin systems

“…Although we have considered here only the two simple cases, this method is expected to be useful also for studies of more complicated and interesting systems. For example, the CCMF method should work well for the XXZ model (Heisenberg-Ising model) with easy-plane anisotropy 30,34 and, of course, with Ising-type anisotropy, which lies between the two models we considered here. Also, the extensions to systems with four-spin (ring) exchange interactions, 35 higher spins, and random systems 36,37 should be considered in future studies.…”

“…The temperature dependence of the magnetization m obtained by the CCMF approach is compared with those from the MFT, BPW, the so-called randomphase approximation (RPA), 27,28 Kikuchi's square approximation, 23 and quantum Monte Carlo (QMC) calculations 29,30,31,32 in Fig. 5.…”

“…Besides, a special attention is required in applying the RPA scheme to a relatively complicated system as is pointed out in our recent study. 30 In the "Weiss-type" approaches, the effective fields are defined in terms of some kind of mean fields (e.g., h eff = zJm in the simple MFT), and those values are determined by the corresponding self-consistency conditions. Oguchi's method, the SCCF, and CCMF approaches are categorized into this group.…”

“…The difference is only that the Ising interaction between neighboring spins in a cluster is replaced by the Heisenberg one, S i · S j , in this case. The temperature dependence of the magnetization m obtained by the CCMF approach is compared with those from the MFT, BPW, the so-called randomphase approximation (RPA), 27,28 Kikuchi's square approximation, 23 and quantum Monte Carlo (QMC) calculations 29,30,31,32 in Fig. 5.…”

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

“…[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].…”