Ultrasonic study of CuO and a landau model for monoclinic multiferroics

Abstract

Encouraged by recent experiments on multiferroic systems using high-resolution ultrasonic measurements, we measured the temperature and field dependence of the velocity of acoustic modes in order to determine the magnetic phase diagram of the monoclinic multiferroic cupric oxide (CuO). A new transition at TN₃ = 230 K corresponding to an intermediate state between the antiforromagnetic incommensurate non-collinear spiral phase (AF2) observed below TN₂ = 229.3 K and a paramagnetic phase (PM), is revealed. Anomalies associated with a first order transition to a commensurate collinear phase (AF1) are also observed at TN₁ = 213 K. Our dielectric constant measurements confirm that only the spiral phase supports a spontaneous electric polarization. As well, we report on a spin-flop transition between 11 T - 13 T in the low temperature AF1 collinear phase with B ∥ b. Most of the experiments were carried out in Memorial University of Newfoundland with the exception of the high magnetic field (B > 7 T) measurements which are part of Professor Guy Quirion's short visit to l'Uuiversité de Sherbrooke. In addition, a non-local Landau-type free energy is developed for CuO and similar monoclinic multiferroics. In contrast with previous results of other groups, but in support of a recent proposal, our analysis clearly reveals the necessity for an incommensurate of collinear phase (AF3) between the PM and the spiral AF2 states. Such a phase has been shown, both theoretically and experimentally, to occur in other geometrically frustrated antiferromagnets where symmetry allows for uniaxial anisotropy at second order and in multiferroic compounds similar to CuO. We compare the model predictions to the B-T phase diagram of CuO obtained using ultrasonic velocity data. The same sequence of magnetic phase transitions is observed as in other multiferroic systems with spiral spin-driven ferroelectric order such as MnWO₄, AMSi₂O₆, some of the orthorhombic systems RMnO₃, the Kagomé-related compound Ni₃V₂O₈ and LiCuVO₄.