Calculation of generalized spin stiffness constant of strongly correlated doped quantum antiferromagnet on two-dimensional lattice and it’s application to effective exchange constant for semi-itinerant systems

Abstract

The generalized spin stiffness constant for a doped quantum antiferromagnet has been investigated both analytically and numerically as a function of doping concentration at zero temperature, based on the strongly correlated t-J model on two-dimensional square lattice. The nature of the theoretical dependence of the stiffness constant on doping shows a striking similarity with that of the effective exchange constant, obtained from the combination of other theoretical and experimental techniques in the low doping region. This correspondence once again establishes that spin stiffness can very well play the role of an effective exchange constant even in the strongly correlated semi-itinerant systems. Our theoretical plot of the stiffness constant against doping concentration in the whole doping region exhibits the various characteristic features like a possible crossover in the higher doping regions and persistence of short range ordering even for very high doping with the complete vanishing of spin stiffness occurring only close to 100% doping. Our results receive very good support from various other theoretical approaches and also brings out a few limitations of some of them. Our detailed analysis highlights the crucial importance of the study of spin stiffness for the proper understanding of magnetic correlations in a semi-itinerant magnetic system described by the strongly correlated t-J model. Moreover, our basic formalism can also be utilized for determination of the effective exchange constant and magnetic correlations for itinerant magnetic systems, in general in a novel way.

Effective Interaction in a Non-Fermi Liquid Conductor and Spin Correlations in Under-Doped Cuprates

“…Thus there is a genuine need for an alternative approach to be attempted. This provides us with a very strong motivation to employ our scheme based onD s [12]. This would further give us a solid ground for detailed comparison of our calculational results obtained for the 1D and 2D t-J models.…”

“…Moreover, we could predict a point of possible quantum phase transition in the over-doped regime, with our strongly correlated model extended to that region [12]. Our calculational results for the generalized spin stiffness constant corresponding to a single pair of mobile holes (D s ) were compared with the experimental observations on layers of La 2−x Sr x CuO 4 [12,13]. The comparison established the role of D s as an effective intra-layer exchange constant between a pair of holes in the quasi-2D doped antiferromagnetic materials, at least in the regime of low doping concentration (δ) [12].…”

“…In a previous paper of ours, we have determined the effective magnetic couplings and predicted the various possible magnetic phases of the doped quantum antiferromagnets on a two-dimensional (2D) lattice. In our calculation we had imposed the strict 'no double occupancy condition'(NDOC) on each site in the ground state wave function, characterizing a non-Fermi liquid (NFL) state [12]. We had studied the interactions between the itinerant spin degrees of freedom in details, in the under-doped phase, in particular with our calculation of generalized spin stiffness constant (D s ) for this model [12].…”

“…In our calculation we had imposed the strict 'no double occupancy condition'(NDOC) on each site in the ground state wave function, characterizing a non-Fermi liquid (NFL) state [12]. We had studied the interactions between the itinerant spin degrees of freedom in details, in the under-doped phase, in particular with our calculation of generalized spin stiffness constant (D s ) for this model [12]. Moreover, we could predict a point of possible quantum phase transition in the over-doped regime, with our strongly correlated model extended to that region [12].…”

“…We had studied the interactions between the itinerant spin degrees of freedom in details, in the under-doped phase, in particular with our calculation of generalized spin stiffness constant (D s ) for this model [12]. Moreover, we could predict a point of possible quantum phase transition in the over-doped regime, with our strongly correlated model extended to that region [12]. Our calculational results for the generalized spin stiffness constant corresponding to a single pair of mobile holes (D s ) were compared with the experimental observations on layers of La 2−x Sr x CuO 4 [12,13].…”