PHYSICAL REVIE%' B VOLUME 51, NUMBER 9 1 MARCH 1995-I Magnetic structure and spin dynamics of the Pr and Cu in PrzCuo4 I. W. Sumarlin and J. W. Lynn Center for Superconductivity Research, Department of Physics, University of Maryland, College Park, Maryland 20742 and Reactor Radiation Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 T. Chattopadhyay Institut Laue-Langeuin BoAe Postale 156X, 38042 Grenoble Cedex, France S. N. Barilo and D. I. Zhigunov Institute of Physics of Solids and Semiconductors, Belarus Academy of Sciences, 220726 Minsk, Belarus J. L. Peng Center for Superconductivity Research, Department of Physics, University of Maryland, College Park, Maryland 20742 (Received 5 October 1994) Neutron-scattering techniques have been used to study the magnetic structure and spin dynamics of the Pr and Cu spins in PrzCu04. In the ordered state the Cu spin-wave velocity c has been determined to 0 be 0. 85+0.08 eVA, which corresponds to an in-plane nearest-neighbor exchange constant J =130+13 meV. A spin-wave gap of -5 meV has been observed, corresponding to a reduced anisotropy constant aI~=(J — J"")/J of -2X10 . In the paramagnetic regime the evolution of the Cu spin-correlation length with temperature is adequately described by the renormalized classical theory for the quantum nonlinear sigma model. For the Pr ions, significant dispersion is observed for the first excited-state crystal-field level, directly demonstrating that there are Pr-Pr exchange interactions both within the a-b plane as well as along the c axis. These interactions along the c axis must be mediated through the CuO planes which are also involved in superconductivity in these cuprate materials. A singlet-doublet mag- netic exciton mode1, with Pr-Pr Heisenberg exchange terms as large as -0.8 meV, provides a good quantitative description of the measured dispersion relations. The temperature dependence of the mag- netic excitons also can be qualitatively understood with this theory if the exchange terms are modified by a temperature-dependent renormalization factor. The zero-field ordered moment at low temperatures for the Cu is determined to be 0. 40+0. 02'&, in good agreement with results reported by other groups. However, field-dependent diffraction measurements suggest that the correct Cu spin structure is the non- collinear one, where spins in adjacent layers along the c axis are orthogonal, rather than the collinear structure assumed by other groups. This noncollinearity is also reAected in the configuration of the small induced moments (0.08+0.005p&) that develop at low temperatures on the Pr ions. The magnetic-field — temperature phase diagram for the case of an applied field along the [110]direction re- veals that the spin-rotation energy increases rapidly with decreasing temperature from -200 K down to 4.5 K. I. INTRODUCTIQN Magnetism studies of the insulating R2Cu04 materials and their electron-doped sup erconducting compounds R2 „Ce„CuO~ (R =Pr, Nd, Sm, and Eu) have shown that these materials exhibit a variety of interesting mag- netic behavior involving both the rare-earth and the copper spins. ' ' The very strong Cu-0 bonding in the a-b plane gives rise to a magnetic energy scale much larger than the typical phonon energy scale, and pro- duces two-dimensional- (2D) like magnetic behavior;"' the weak exchange coupling along the c axis then induces long-range antiferromagnetic order at a relatively modest T& in the range 250 — 300 K. ' Hence the Cu spins provide one of the best physical realizations of a 2D quantum Heisenberg antiferromagnet — a system of cen- tral importance itself in the study of quantum mag- nets. ' ' No long-range order is observed in the super- conducting phase, but the large magnetic energy scale within the Cu-0 planes persists, and has supported speculation that magnetism may be directly involved in the formation of the superconducting state. The rare- earth ions, on the other hand, typically order at much lower temperatures ( ( 6 K.) in both the insulating and the superconducting phases. ' The coexistence of long- range rare-earth magnetic order with superconductivity in these systems has provided an interesting situation where the interplay between the two cooperative phe- nornena can be studied. In this paper, we report our neutron-scattering studies of the magnetic structure and spin dynamics of the Pr and Cu spins in Pr2Cu04, which address three aspects concerning the magnetism of this class of materials. The first aspect concerns the dynamics of the Cu spins, which are dominated by the huge isotropic in-plane exchange interactions. The spin-wave branches propagating in the a-b plane are thus highly dispersive, but we have been 0163-1829/95/51(9)/5824(16)/$06. 00 51 5824 1995 The American Physical Society