Phase Transitions of a Geometrically Frustrated Spin System CdCr2O4in Very High Magnetic Fields

Abstract

In the spinel type compound CdCr2O4, Cr 3þ ions form a pyrochlore lattice composed of corner-shared tetrahedra. The magnetic interaction between the Cr-ions is antiferromagnetic, as evident from a large negative Weiss temperature W of 70:5K in high-temperature Curie–Weiss behavior of the magnetic susceptibility. The effective magnetic moment of the Cr-ion estimated from the Curie– Weiss law is 3:75 B, which is consistent with the free ion value of Cr3þ (3d, S 1⁄4 3=2, peff 1⁄4 3:87 B). Due to the strong geometrical frustration of the pyrochlore lattice, CdCr2O4 exhibits an antiferromagnetic long-range order at a relatively low Neel temperature TN 1⁄4 7:8K (TN=j Wj 0:1), accompanied by a tetragonal lattice distortion. The ground state spin configuration was revealed by the neutron scattering experiment to be a helical spin structure. Recently, field dependence of the magnetization MðBÞ of this compound along the [100], [110], and [111] directions has been examined by using a nondestructive long-pulse magnet (NLPM) up to 46 T at 1.6K. The magnetization curves are almost isotropic, implying the magnetic anisotropy is weak. This fact is consistent with the ground state of Cr3þ in which the magnetic moments, because of the orbital singlet (t 2ge 0 g) state, behave as Heisenberg spins. Behavior of MðBÞ is, however, rather unusual. For all directions, MðBÞ shows a linear increase up to 28 T where a first-order transition with a discontinuous jump in MðBÞ occurs. Above 28 T, MðBÞ exhibits a plateau with 1/2 of the full moment (1:5 B/Cr) up to 46 T. It is proposed that a collinear 3-up and 1-down (#) spin configuration is realized for each tetrahedron in this state. It is well known that MðBÞ of ideal antiferromagnetic Heisenberg spins on a pyrochlore lattice linearly increases with B until a full saturation occurs, without showing the ‘‘1/2’’ plateau. Recently, Penc et al. explained the robust half-magnetization plateau of CdCr2O4 by introducing a biquadratic interaction term. They showed that coupling to the lattice effectively yields a biquadratic term in the exchange interaction, leading to a half-magnetization plateau. They also derived an overall magnetization process of the model. In particular, a second-order transition from the plateau state into an intermediate one was predicted with further increasing field, before a full saturation of the moment is reached by a firstor a second-order transition. Such a magnetization curve has indeed been observed in a similar chromium spinel HgCr2O4 having weaker exchange interactions. In order to explore the phase transitions anticipated in high fields, we have performed magnetization measurements on single crystals of CdCr2O4 in very high magnetic fields up to 80 T produced by a destructive single-turn pulse magnet. Magnetization along the [111] direction was measured by an induction technique; a pair of pick-up coils (‘‘upper’’ and ‘‘lower’’ coils) were wound in series opposite, whereby the strong induction voltage coming from the rapidly changing field could be compensated. A few pieces of thin single crystals of CdCr2O4, molded by epoxy, was mounted into one of the pickup coils. An example of the raw data is given in Fig. 1, where the time variation of the magnetic field B (a), and the induced voltage of the pick-up coils (b) are shown. The latter reflects the time variation of the magnetization dM=dt. Two curves for dM=dt represent the results of two independent shots with the sample in the ‘‘upper’’ or ‘‘lower’’ pick-up coils. Six anomalies indicated by white allows are the signals from the sample, because these appear in both ‘‘upper’’ and ‘‘lower’’ data. Note that the polarity of these anomalies reverses between these two curves, because the winding senses of the two pick-up coils are opposite to each other. Moreover, the first, second, and third anomalies in the increasing field sweep correspond with the sixth, fifth and fourth ones in the decreasing field sweep, respectively. Differential susceptibility dM=dB is given by ðdM=dtÞ= ðdB=dtÞ. Here, we made a subtraction between the ‘‘upper’’ and ‘‘lower’’ data to obtain dM=dt. We further subtracted a smooth background from the dM=dt curve. Thus obtained dM=dB vs B plot is shown in Fig. 2. In this plot, only the falling field process is shown for simplicity. The magnetization curve obtained by NLPM is also shown for comparison.