The Néel temperature of a D -dimensional bcc Heisenberg antiferromagnet

• Published in: Solid state communications Vol. 151; no. 23; pp. 1753 - 1757
• Main Authors: Radošević, Slobodan M., Rutonjski, Milica S., Pantić, Milan R., Pavkov-Hrvojević, Milica V., Kapor, Darko V., Škrinjar, Mario G.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.12.2011; Elsevier
• Subjects: A. Heisenberg antiferromagnet; Condensed matter: electronic structure, electrical, magnetic, and optical properties; D. Generalized hypergeometric function; D. Green’s functions; D. Néel temperature; Exact sciences and technology; General theory and models of magnetic ordering; Magnetic properties and materials; Physics; Studies of specific magnetic materials; D. Generalized hypergeometric function; A. Heisenberg antiferromagnet; D. Green’s functions; D. Néel temperature; Hypergeometric functions; Temperature dependence; FCC lattices; Critical points; Antiferromagnetic materials; Self consistency; Heisenberg model; Random phase approximation; Green function; XXZ model; Time dependence; BCC lattices; D. Green's functions; Anisotropy; Temperature effects; Neel temperature; Critical temperature; Green's function methods; A Heisenberg antiferromagnet
• ISSN: 0038-1098; 1879-2766
• DOI: 10.1016/j.ssc.2011.08.034

The double-time temperature-dependent Green’s function method is used to determine the Néel temperature of a Heisenberg antiferromagnet with easy axis X X Z anisotropy on a D -dimensional bcc lattice. Exact equations within the random phase approximation (RPA) and Callen approximation (CA) in terms of generalized hypergeometric functions valid for arbitrary D , S , and η ≥ 1 are given. Analytical and numerical results presented here strongly suggest that, for D ≥ 2 , the CA gives a higher critical temperature. It is also shown that the RPA set of self-consistent equations yields a Néel temperature closer to the experimental value for compound (CH 3NH 3) 2MnCl 4. ► Tyablikov’s and Callen’s methods are compared. ► The Néel temperature is determined by using D -dimensional Watson-like integrals. ► Exact solutions in terms of generalized hypergeometric function are given. ► Callen’s approach yields higher critical temperature for D ≥ 2 . ► Tyablikov’s method gives Néel temperature closer to the experimental value for compoung (CH 3NH 3) 2MnCl 4.