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

TL;DR

This paper investigates the generalized spin stiffness constant in doped quantum antiferromagnets using the t-J model, revealing its similarity to the effective exchange constant and its significance in understanding magnetic correlations in semi-itinerant systems.

Contribution

It introduces a combined analytical and numerical approach to compute the spin stiffness constant and demonstrates its role as an effective exchange constant in strongly correlated doped systems.

Findings

Spin stiffness decreases with doping, vanishing near 100% doping.

Theoretical results align with experimental and other theoretical data.

Persistence of short-range magnetic order at high doping levels.

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.