SPIN-FLOP TRANSITION IN CuCl2.2H2O : ANOMALIES OF MAGNETIC PROPERTIES AND MACROSCOPIC STRUCTURE

Magnetic properties have been studied using simultaneously induction and modulation techniques. The difference between results obtained is assigned to the formation of domain walls. The experiment described is the first attempt to measure susceptibilities separately that are related to reversible and irreversible processes at phase transitions in a magnetic field. Hydrated copper chloride has orthorhombic symmetry Pbmn ( D Z ~ ) and below TN = 4.3 K, in the absence of a magnetic field, is a compensated antiferromagnet with its antiferromagnetism direction along the crystal a-axis. At Ht = 6.5 kOe which is parallel to this axis, the orientational transition occurs in the crystal. During this transition the antiferromagnetism vector changes its direction and as a result is oriented along the baxis. Of great interest is the state which is realized in a sample within a narrow magnetic field range near Ht. In particular, if the transition takes place via the first order phase transition, the domain structure can be expected to appear [I]. It should disappear as a field deviates from the a-axis by the angle cp which is larger than the critical one cpc. To date literature data on domain structure in CuC12.2H20 is somewhat controversial and the cp, angle is undefined. In the present work magnetic properties of this antiferromagnet were studied. To obtain evidence about the appearance of magnetic inhomogeneities we used an experimental method sensitive to them. Measurements were performed in two ways simultaneously at T = 1.5 K. The first experiment was carried out using the induction method in a pulsed 3 x s magnetic field, its amplitude slightly exceeding Ht. Digital recording and computer processing of the results make it possible to obtain the dependence of differential magnetic susceptibility X d (H) and magnetization md (H) on the field strength. Differential susceptibility exhibits a sharp decrease as an external field deviates from Ht either towards low or high fields. The transition width is regarded as a magnetic field range AH where susceptibility diminishes to half of its maximum value X ~ O . The measurements indicated that the tilted field in the hard (ac) -plane slighly influences the parameters of curves obtained. The following results are achieved at zero tilting in this plane and given in figure 1 versus the angle cp of tilting in the easy (ab) plane. Magnetic susceptibility Xd0 (curve 1) increases as the rp angle decreases, achieving the sharp maximum at rp = 0. Simultaneously the transition width AH decreases (curve 2). At cp < 5 minutes it reaches practically the constant value of about 60 Oe. Let us consider possible formation mechanisms for the limiting transition width. The field nonuniformity on the sample is evaluated to be 4 Oe. If the transition is the first-order one the theory of an intermediate state gives 47r NAM for the transition width where N is the demagnetization factor, in our case, of a spherical sample, being equal to 1/3pand AM the variation of magnetization at the transition which can be estimated as 3 Gs [2]. Thus, the lower limit of AHis about 12 Oe for the domain structure formation. The experimental result is approximately five times as large as the calculated value. Some different mechanisms seem to be responsible for the observed transition width. Among them crystal inhomogeneities or mosaic cannot be neglected though their manifestations in other properties were not observed. Let us concern ourselves with the second way of measurement of magnetic properties used in the present work. The above induction method is complemented with the longitudinal modulation of a pulsed magnetic field with a small amplitude (about 1 Oe) and frequency of about 2 MHz. The induced sigo ~ m t n . 1 0 40 -20 0 20 40 Fig. 1. The transition width AH (2) and susceptibilities X ~ O (1) and Xmo (3) versus the angle of the external field tilting within the (ab) plane of easy magnetization. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888369 C8 822 JOURNAL DE PHYSIQUE nal on the modulation frequency is separated from a low-frequency one using high-frequency filters and is recorded digitally after detection. Experimental curves Xd (H) and X , (H) measured by the former and the latter methods proved to be similar in a wide range of cp angles, not too close to cp = 0 . They can coincide within the experimental errors in the entire field region by fitting a common scale factor for various cp angles. However, for small angles of tilting the results for CuC12.2HzO obtained from two methods are explicitly different. In this case there is a magnetic field region near Ht where X m (H) is less. As the cp angle decreases, X, is suddenly reduced and achieves the minimum X,O at cp GO (curve 3 in Fig. 1). Herewith, X,o appears half as much as X d o . By performing numerical integration one can obtain the curve of the field dependence-of the sample magnetization from the dependence of magnetic susceptibility on the magnetic field strength, the curve processing makes it possible to calculate approximately the total variation of magnetization AM at the spin-flop transition. As was to be expected, the first method measured AMd value proved to be independent of the cp angle (Fig. 2). At the same time, AM, obtained from modulation measureGents diminishes with a decrease of the p angle and is nearly halved at cp = 0. Fig. 2. Variations of magnetization at the transition measured by induction (1) and modulation (2) versus the angle of the external field tilting within the (ab) plane of easy magnetization. Modulation measurements of the angle dependence of magnetic susceptibility and the total magnetization variation were repeated for a stationary magnetic field. This experiment made it possible to reduce the modulation frequency from 2 MHz to 200 Hz. In this case we did not detect qualitative changes of the curves X,O (cp) and AM, (cp) : as before, their drop was observed at cp =O. The decrease of the modulation amplitude does not result in variations of the curve forms. Anomalies of magnetic properties observed at the spin-flop transition give evidence about the appearance of an additional magnetization mechanism for small angles of tilting of an external field to the crystal axis. These anomalies can be explained using concepts about reversible and irreversible magnetization of ferromagnets 131. In this interpretation the appearance of an additional mechanism at a strict orientation of a magnetic field is assigned to magnetic inhomogeneities in the antiferromagnetism vector orientation due to the spin-flop transition. The inhomogeneities, absent for large cp angles, are stable a t cyclic variations of a small amplitude field, therefore, their shift contributes little to magnetic susceptibility measured by modulation. At the same time, magnetic susceptibility measured by induction involves irreversible magnetization which occurs by jump changes of magnetized region positions for a sufficiently large deviation of an external field from equilibrium. Thus, the above experiment permits us to detect the appearance of magnetic inhomogeneities, as well as to separate reversible and irreversible magnetizations. It should be noted that reversible magnetization observed in this experiment can be excessive due to the influence of sample crystalline nonuniformities and, hence, should be considered as the estimate of its upper limit. [I] Baryachtar, V. G., Borovik, A. E., Popov, V. A., Sow. J. JETP Lett. 9 (1969) 634. [2] Galkin, A. A., Vetchinov, A. V., Dan'shin, N. K., Popov, V. A., Sov. J. Low Temp. Phys. 3 (1977) 185. [3] Vonsovskii, S. V., Shur, Ya. S., Ferromagnetism, Moscow (1948).