Magnetic phases of CsCuCl 3 : Anomalous critical behavior H. B. Weber, T. Werner, J. Wosnitza, and H. v. Lo ¨ hneysen Physikalisches Institut, Universita¨t Karlsruhe, D-76128 Karlsruhe, Germany U. Schotte Hahn-Meitner-Institut, D-14109 Berlin, Germany ~Received 26 June 1996; revised manuscript received 3 September 1996! We report high-resolution measurements of the specific heat of the hexagonal antiferromagnet CsCuCl 3 with ferromagnetically coupled Cu 21 chains in magnetic fields parallel to the hexagonal axis. The zero-field data can be described assuming a second-order phase transition with a chiral XY critical exponent a near 0.35, except very close to the Ne´el temperature where the transition seems to be of weakly first order. This might be an indication for the failure of XY chiral universality. The previously observed first-order transition from an ‘‘umbrella’’ to a coplanar spin structure at high fields merges the transition line to the paramagnet in a multicritical point ( T c 510.59 K, B m 55.5 T!. The transition to the new coplanar structure from the saturated paramagnetic phase above B m seems, rather unexpectedly, also to be describable as a second-order transition with a ’0.23. @S0163-1829~96!04246-4# In hexagonal antiferromagnets of the ABX 3 type ~like CsNiCl 3 , CsMnBr 3 , and CsCuCl 3 ) the magnetic B 2 1 ions form a triangular lattice within the ab planes. The antiferro- magnetic interaction between three neighboring spins leads to a 120° spin structure with a twofold chiral degeneracy as the lowest-energy configuration. Based on symmetry argu- ments as well as 4-« renormalization-group studies and re- sults from Monte Carlo analysis, two chiral universality classes were proposed: the chiral XY universality class Z 2 3S 1 5O (2) and the chiral Heisenberg universality class SO (3). 1 However, this proposal is still the subject of controversial debate. The question is whether the transition is really of second order and universal, or whether it is of weakly first order or tricritical and fakes universal behavior near the criti- cal temperature T c in the sense of an ‘‘almost second-order transition.’’ 2 For the chiral XY case histogram Monte Carlo studies 3 and a three-loop renormalization-group analysis 4 point to weakly first-order or tricritical behavior. For the chi- ral Heisenberg case, on the other hand, a histogram Monte Carlo study supports the notion of universality for the chiral Heisenberg case. 5 Recently, the second-order scenario has obtained new support by a self-consistent screening theory. 6 For a review on the theoretical dispute, see Ref. 7. Experiments on triangular ABX 3 antiferromagnets with easy-plane anisotropy yielded critical exponents which are compatible with the universality assumption for the XY chirality. The exponents b , g , and n have been extracted from neutron-scattering data. 8 More decisive is the exponent a of the specific heat, because the prediction for a differs significantly from those of the conventional universality classes ( a <0.112) for both the chiral XY ( a 50.3460.06) and the tricritical case ( a 50.5). For CsMnBr 3 , the expo- nents a 50.3960.09 ~Ref. 9! and a 50.4060.05 ~Ref. 10! have been measured. These results do not change in mag- netic fields B uu c . Furthermore, chiral XY symmetry can be induced in the spin-flop phase of an easy-axis hexagonal antiferromagnet in sufficiently high magnetic fields B uu c , as evidenced by the critical exponents a 50.3760.08 in B 56T for CsNiCl 3 ~Ref. 11! and a 50.3460.08 in B 57 T for CsMnI 3 . 12 All these materials exhibit antiferro- magnetic ( J 0 .0) spin order along the c axis. Within the notion of chiral XY universality, the exchange term J 0 is irrelevant, that means, a change in the sign of J 0 should not influence the critical behavior. CsCuCl 3 has a unique magnetic structure below T N 510.7 K in that it is an antiferromagnet with a dominant ferromagnetic coupling along c which is masked by the slow spiraling of the spin chains in the c direction ~pitch about 5°) caused by Dzyaloshinskii-Moriya ~DM! interaction. The latter acts also as an easy-plane anisotropy, hence to a good approximation the spins lie in the ab plane. 13 In addition, the Cu 2 1 spin is 1/2, thus quantum effects can be expected. The most exciting result about CsCuCl 3 is the recent discovery 14,15 of a first-order magnetic phase transition in an external field B uu c from a ~chiral! ‘‘umbrella’’ low-field structure to a coplanar ‘‘up-up-down’’ structure in high field. This transition is believed to occur because it is favored by quantum and thermal fluctuations. 15 In this paper we deter- mine the critical behavior of the various phase transitions and establish the phase diagram in the region where the three phase lines meet. The single-crystalline samples were grown from aqueous solution. The specific heat was determined by a standard semiadiabatic heat-pulse technique in a 4 He calorimeter. The temperature resolution of D T / T ,5 310 26 allows small heat pulses of about 2 mK at the transition. The crystal orientation with respect to the field has been done visually using the freshly cleaved planes which indicate the c axis of the crys- tal. The crystal mass was 42 mg, which yields a heat capacity which is at least four times larger than the heat capacity of the sample holder. At high temperatures, CsCuCl 3 has the same crystal structure as CsNiCl 3 , but it undergoes a structural phase transition at 423 K leading to a helical arrangement of dis- torted CuCl 3 octahedra along the c axis due to the coopera- PHYSICAL REVIEW B 1 DECEMBER 1996-II VOLUME 54, NUMBER 22 54 0163-1829/96/54~22!/15924~4!/$10.00 15 924 © 1996 The American Physical Society