Critical Exponents of Erbium

The exponent P that describes the sinusoidally modulate d * paramagnetic phase transition crosses over from a value of 0.39 near TN to a mean field value away from TN. Electrical resistivity measurements near TN are given for the c axis and the critical behaviour is discussed. Erbium orders below its NBel temperature TN= 85 K with its spins directed along the c axis of the hcp crystal and with the amplitude of spins in successive basal plane layers sinusoidally modulated [I]. Unlike the theoretically well studied spiral magnets Dy, Ho and Tb, which are characterized by a n = 4 component order parameter [2], theoretical predictions about the nature of the phase transition in erbium, which is characterized by a n = 2 order parameter, are largely lacking [3]. Our recent neutron scattering and ultrasonic measurements indicate that the sinusoidal H paramagnetic phase transition in erbium is of a continuous nature and occurs without any evidence of hysteresis in TN as observed in heating and cooling runs [4]. Simultaneous measurement on an as received erbium crystal of the magnetic order parameter, using neutron scattering, and of the ultrasonic attenuation and velocity anomalies, indicate that the N&l temperature as observed with neutrons is 0.25 K lower than that indicated by ultrasonics. This difference, however, disappeared after annealing the crystal in vacuum at 950 OC [4]. The critical exponent P that characterizes the sublattice magnetization was studied through neutron scattering on single crystal erbium. A study of the critical behaviour of the electrical resistivity was also conducted. Single crystals were obtained from Goodfellow (Cambridge, England) and have a purity of 99.99 % . Temperatures were controlled, using an Air Products refrigerator, to within f 0.03 K for the neutron measurements and f 0.01 K for the resistivity measurements. A temperature stabilization time of 15 min was allowed between successive temperature points in order to ensure thermal equilibrium conditions during measurements. The neutron measurements were performed in transmission mode on a thin disc shaped crystal. A n+-diffractometer, employing 1.4 A neutrons selected with a Ge (3 1 1) monochromator crystal, was used. The resistivity was determined by a standard four-point measurement on a c axis bar shaped crystal using a 7 decade potentiometer. It is known that the magnetic older of Er is characterized by the occurrence of higher harmonics at lower temperatures [I]. Our measurements indicate that the third harmonic (e.g. (1 0 1 36)) vanishes above 75 K and consequently the order parameter was studied by measurement of the intensity of the first order harmonic above this temperature. Integrated w 20 intensity' scans through the (1 0 6) magnetic satellite were performed as a fdnction of temperature. The results, after subtraction of the background contribution, are depicted in figure 1. The observed intensity I is given by The reduced temperature is denoted by t = J(T TN) /TN 1. The first term describes the spontaneous sublattice magnetization M cc tP, while the following two terms, with amplitudes Cand C+, refer to the critical scattering below and above TN respectively. From an analysis of the paramagnetic data it follows that 7 = 1.45 f 0.2 and C+ = 0.35 f 0.05 (broken line in Fig. 1). A correction for the critical scattering below TN was made using Schofield's parametric representation of the equation of state [5] The exponent 7 is taken the same above and below TN, according to the scaling hypothesis. A least-squares fit of all measured data points (73 K to TN) yields ,B = 0.48 and TN = 80.5 K. Using these parameters, the first term in equation (1) is plotted by a broken line in figure 1 (fit B). A satisfactory fit to the experimental points is achieved. The effect of systematically deleting the lower temperature points from the @-analysis was investigated. It was found that the calculated value of