Ultrasonic study of the critical behavior of the antiferromagnet CsNiCl₃

Abstract

To study the critical behavior of the quasi-one-dimensional antiferromagnet CsNiCl₃ near the phase transitions, its elastic constants are investigated using high-resolution ultrasonic velocity measurements as function of temperature and magnetic field applied along the c-direction. The experimental data we present with respect to the longitudinal mode, -- [special characters omitted], -- and the transverse modes, -- [special characters omitted], -- generate a phase diagram in good agreement with published results by showing two zero-field transitions at TN₁ ≈ 4.75 K, TN₂ ≈ 4.35 K, and multicritical point at (Tm ≈ 4.50 K, Hm ≈ 2.29 T). Moreover, the critical exponent 3 extrapolated from the temperature dependence of -- [special characters omitted] -- shows XY criticality with a constant value 0.35 ± 0.02 for H < Hm . However, field dependent behavior is observed for H > Hm . This is the first experimental evidence that the high-field phase transition associated with the 120° spin configuration is weakly first-order and experimentally resolves the controversy about the true criticality of the high-field phase boundary. This result is also strengthened by the step-like variation demonstrated by temperature dependence of -- [special characters omitted] -- at fields higher than the multicritical field (Hm ≈ 2.29 T) and hysteresis phenomena observed in field dependence of -- [special characters omitted] -- at T = 5.00 K. Numerical predictions are made based on the Landau model. The elastic constants of CsNiCl₃ in different phases are calculated using the total free energy, which is derived according to the Landau free-energy, the elastic energy, and the magnetoelastic coupling terms invariant under the symmetry operation of the hexagonal group P6₃/mmc. Meanwhile, the non-mean-field order parameter and quadratic-quadratic (q-q) couplings are considered to optimize the numerical prediction and achieve a good reproduction of the experimental data. Furthermore, by studying the numerical predicted elastic constants and strains, a decrease of the spin structure symmetry, from hexagonal to orthorhombic, is proved in the elliptical phase.