Nature of the spin liquid in underdoped cuprate superconductors

Abstract

In the present paper, we address a long-standing problem of the magnetic ground state and magnetic excitations in underdoped cuprates. Modeling cuprates by the extended t−J model, we show that there is a dimensionless parameter λ which drives quantum magnetic criticality at low doping x. Hence we derive the zero temperature λ−x phase diagram of the model. It is argued that all underdoped cuprates are close to the quantum tricritical point x=0,λ=1. The three phases “meet” at the tricritical point: (i) Néel antiferromagnet, (ii) spin spiral with antinodal direction of the spiral wave vector, (iii) algebraic spin liquid. We argue that underdoped cuprates belong either to the spin-liquid phase or they are on the borderline between the spin liquid and the spin spiral. We calculate the energy position Ecross of the inelastic neutron scattering response maximum at q=(π,π) and compare our results with experiments. We also explain softening of magnons in the intermediate regime observed in inelastic neutron scattering.

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