Doping and temperature dependence of incommensurate antiferromagnetism in underdoped lanthanum cuprates

The doping, temperature and energy dependence of the dynamical spin structure factors of the underdoped lanthanum cuprates in the normal state is studied within the t-J model using the fermion-spin transformation technique. Incommensurate peaks are found at [(1±δ)π, π], [π, (1±δ)π] at relatively low temperatures with δ linearly increasing with doping at the beginning and then saturating at higher dopings. These peaks broaden and weaken in amplitude with temperature and energy, in good agreement with experiments. The theory also predicts a rotation of these peaks by π/4 at even higher temperatures, being shifted to [(1± δ/ √ 2)π, (1 ± δ/ √ 2)π]. 74.25.Ha, 74.72.-h, 74.20.Mn Typeset using REVTEX 1 In spite of the tremendous efforts dedicated to the studies of anomalous properties of high Tc superconductors, many important problems still remain open. Among others, the destruction of antiferromagnetic long range order (AFLRO) and appearance of incommensurate antiferromagnetism (IAF) in doped cuprates is one of the challenging issues for the theory of strongly correlated electron systems. Moreover, the interplay of AF and superconductivity in these compounds is of fundamental importance for the high Tc theory. Experimentally, by virtue of systematic studies using NMR and μSR techniques, particularly the inelastic neutron scattering, rather detailed information on dynamical magnetic properties has become available now, awaiting an adequate theoretical interpretation. It has been established that beyond certain critical doping (∼ 3%) the commensurate AFLRO disappears, being replaced by IAF, characterized by incommensurability parameters δ, i.e., the AF Bragg peaks are shifted from [π,π] to four points [π(1 ± δ), π], [π, (1 ± δ)π] [1]. For very low dopings δ varies almost linearly with concentration x, but saturates at higher dopings. These peaks broaden and weaken in amplitude as the temperature and energy increase. These features are fully confirmed by the data on lanthanum cuprates [1–4], and have also been found recently on yttrium cuprates [5]. Theoretically there is a general consensus that IAF emerges due to doped charge carriers. Several attempts have been made to make this argument more precise, including the hole induced frustration [6], stripe formation [7], spiral phase [8] and Fermi surface nesting [9]. Based on the phenomenological ansatz of marginal Fermi liquid behavior [10] and tight binding calculation, a detailed fitting of the experimental data was attempted [11]. Recently experiments show stronger singularities of AF fluctuations [12] than what is anticipated from the phenomenological models. The proximity to a quantum critical point [13] was proposed as an alternative explanation [12]. However, to the best of our knowledge, no systematic calculations have been performed within the standard strong correlation models for the dynamical spin structure factors (DSSF) to confront the experimental data. Exact diagonalization is limited by system sizes, while the quantum Monte Carlo technique faces the negative sign problem for lower temperatures [14]. Thus it is rather difficult to obtain conclusive results. 2 In this paper, using the fermion-spin theory [15] which implements properly the local single occupancy constraint, we calculate explicitly DSSF for cuprates within the t-J model and reproduce all main features found in experiments [2–4,12], including peak position as well as temperature and energy dependence. Apart from the ratio t/J (taken to be 2.5), there are no other adjustable parameters in the calculations. Moreover, the theory predicts the magnetic peaks will be rotated by π/4 at even higher temperatures, i.e., being shifted to [(1± δ/ √ 2)π, (1± δ/ √ 2)π]. To avoid complications due to bilayers we will focus on the normal state IAF in lanthanum cuprates. We start from the t-J model on a square lattice,