Bose-Einstein Condensation of Magnons inCs2CuCl4

Abstract

We report on results of specific heat measurements on single crystals of the frustrated quasi-2D spin-1/2 antiferromagnet Cs2CuCl4 (TN = 0.595 K) in external magnetic fields B < 12 T and for temperatures T > 30 mK. Decreasing B from high fields leads to the closure of the field-induced gap in the magnon spectrum at a critical field Bc ≃ 8.51 T and a magnetic phase transition is clearly seen below Bc. In the vicinity to Bc, the phase transition boundary is well described by the power-law Tc(B) ∝ (Bc − B)1/φ with the measured critical exponent φ ≃ 1.5. These findings are interpreted as a Bose-Einstein condensation of magnons.PACS numbers: 75.30.Kz,75.45.+j,03.75.Nt In a quantum antiferromagnet (AFM) a fully spinpolarized state can be reached at high magnetic field B exceeding a saturation field B c . In this state, spin excitations are gapped ferromagnetic magnons. With decreasing B and passing through B c , an antiferromagnetic long-range order of the transverse spin component develops. Provided the symmetry of the spin Hamiltonian is such that the rotational invariance around the applied field is preserved, the transverse spin component ordering can be regarded as a Bose-Einstein condensation (BEC) in a dilute gas of magnons. This concept was formulated theoretically many years ago [1, 2]. For most of the known AFMs, B c can be well above 100 T. An exceptionally low and easily accessible saturation field of B c ≈ 8.5 T, however, is needed in the quantum spin-1/2 AFM Cs 2 CuCl 4 . In this system the dominant exchange spin coupling J is rather weak, J = 4.34(6) K [3]. The other isotropic spin coupling constants and the anisotropic Dzyaloshinsky-Moriya (DM) interaction are smaller and were determined with high accuracy by neutron experiments [4]. Thus, the spin Hamiltonian involves the isotropic exchange H 0 , the DM anisotropic term H DM and the Zeeman energy H B and is given byCs 2 CuCl 4 falls into the class of easy-plane AFMs with U (1)-rotational invariance around the crystallographic aaxis. Thus, for B applied along the a-axis, the U (1) symmetry can be broken spontaneously due to the transverse spin component ordering at T c . This is accompanied by the appearance of a Goldstone mode with linear dispersion, which is interpreted as signature of a magnon BEC [4]. However, an unambiguous evidence for a BEC description of the field-induced phase transition would be the determination of the critical exponent φ in the field dependence of the critical temperatureTheory for a 3D Bose gas predicts a universal value φ BEC = 3/2 [5], which coincides with the result of a mean-field treatment [6].A magnon BEC in TlCuCl 3 was recently reported [6,7]. In this quantum AFM with a dimerized spinliquid ground state, the saturation field is rather high, B c,2 ≈ 60 T, and the BEC transition was studied near the first critical field, B c,1 ≃ 5.6 T. At B = B c,1 , the singlet-triplet excitation gap is expected to close and a BEC occurs for B > B c,1 [6]. However, a few experimental findings show deviations from a pure magnon BE...

Universal properties of highly frustrated quantum magnets in strong magnetic fields

“…Although the effects of the localized magnons have not been observed experimentally so far, recent studies on the spin-1/2 diamond-chain compound azurite Cu 3 (CO 3 ) 2 (OH) 2 [26,27] and the frustrated quasi-two-dimensional spin-1 2 / antiferromagnet Cs 2 CuCl 4 [28] represent closely related physics.…”

Evidence of a field-induced Berezinskii–Kosterlitz–Thouless scenario in a two-dimensional spin–dimer system

“…Signatures in w(H,T ¼ constant) at H c1 and H c2 , with H c1 denoting the critical field where the lower triplon branch crosses zero energy, and H c2 the field above which all dimers are fully polarized, are also expected and found in 3D-coupled systems 36 . Unlike these 3D systems, however, where sharp, l-like peaks in thermodynamic quantities indicate thermodynamic transitions at the on-and off-set of conventional long-range order 37,38 no indications of such l-like peaks are revealed in w(H, T ¼ constant) for TK91.…”

Nematic phase and phase separation near saturation field in frustrated ferromagnets

“…This approach has succeeded to explain various experimental results. [26][27][28][29] Applying this approach, we found the appearance of a spin nematic phase or a phase separation under high-magnetic field in the J 1 -J 2 model on the bcc lattice. Section VII is devoted to the conclusion.…”