Low-dimensional magnetic ordering and Ising- and XY-like anisotropy of Er3+ in the system ErBa2Cu3Ox with 6

Abstract

Magnetic ordering of ${\mathrm{Er}}^{3+}$ ions in ${\mathrm{ErBa}}_{2}$${\mathrm{Cu}}_{8}$${\mathrm{O}}_{\mathrm{x}}$ with 6.12\ensuremath{\le}x\ensuremath{\le}6.91 has been studied for both orthorhombic and tetragonal phases by means of magnetic-susceptibility and heat-capacity measurements. Superconductivity in the orthorhombic phase samples was confirmed by the onset of a diamagnetic susceptibility. The superconducting transition temperature ${T}_{c}$ was observed to decrease from 92 to 55 K as x was reduced from 6.91 to 6.31. The tetragonal samples with x=6.23 and 6.12 remained paramagnetic down to 1.2 K and showed no overt trace of diamagnetism. The states of ${\mathrm{Er}}^{3+}$ ions in ${\mathrm{ErBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6}$ and ${\mathrm{ErBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ were calculated by means of crystalline electric field (CEF) theory using both a point-charge model and scaled inelastic neutron scattering results for ${\mathrm{HoBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$.The calculated susceptibility is in excellent agreement with data on the tetragonal specimens for 1.2 K \ensuremath{\le}T\ensuremath{\le}160 K. For the orthorhombic samples, sharp heat-capacity peaks which resemble those for a two-dimensional Ising system and evidently correspond to the magnetic ordering of ${\mathrm{Er}}^{3+}$ moments are found. The transition temperature ${T}_{m}$ decreases smoothly from 0.604 to 0.545 K as x is varied from 6.91 to 6.31. In contrast, tetragonal samples show only a broad rounded heat-capacity anomaly having its maximum at 0.5 K and closely resembling that for a one-dimensional XY model. The change of ${\mathrm{Er}}^{3+}$ ion anisotropy from Ising-like to XY-like is explained by the CEF calculation which shows the ground state to be planar for the tetragonal phase but with the b axis slightly favored in the orthorhombic structure. Randomness in the coupling of ${\mathrm{Er}}^{3+}$ moments caused by structural disorder may effectively reduce the dimensionality of magnetic ordering as has been found in the case of random dilution. These results imply that the dominant magnetic interactions of ${\mathrm{Er}}^{3+}$ ions in these materials are of short range.