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, 74.20.Mn Typeset using REVT E X 1In spite of the tremendous efforts dedicated to the studies of anomalous properties of high T c 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 T c 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 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 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,with the local constraint σ C † iσ C iσ ≤ 1, whereη = ±x, ±ŷ, and S i = C † i σC i /2 are spin operators with σ = (σ x , σ y , σ z ) as Pauli matrices. The single occupancy local constraint can be treated properly in analytical form within the fermion-spin theory [15] based on the slave particle approach [16]where the spinless fermion operator h i describes the charge (holon) degrees of freedom, while the pseudospin operator S i describes the spin (spinon) degrees of freedom. In this representation, the low-energy Hamiltonian of the t-J model (1) can be rewritten as [15],with, where x is the hole doping concentration, the holon hopping parameter φ = h † i h i+η , and S + i and S − i as the pseudospin raising and lowering operators, respectively. It has been shown [15] that the constrained electron operator can be mapped exactly using the fermion-spin transformation defined with an additional projection operator.However, this projection operator is cumbersome to handle in the actual calculations, and we have not presented it ex...