A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet. An important unsolved question is whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin-density-wave (SDW) type, or suddenly, as expected if the heavy electrons are abruptly localized by magnetism. Here we report measurements of the low-temperature Hall coefficient (R(H))--a measure of the Fermi surface volume--in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. R(H) undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP.

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Unconventional superconductivity and other previously unknown phases of matter exist in the vicinity of a quantum critical point (QCP): a continuous phase change of matter at absolute zero. Intensive theoretical and experimental investigations on itinerant systems have shown that metallic ferromagnets tend to develop via either a first-order phase transition or through the formation of intermediate superconducting or inhomogeneous magnetic phases. Here, through precision low-temperature measurements, we show that the Grüneisen ratio of the heavy fermion metallic ferromagnet YbNi(4)(P(0.92)As(0.08))(2) diverges upon cooling to T = 0, indicating a ferromagnetic QCP. Our observation that this kind of instability, which is forbidden in d-electron metals, occurs in a heavy fermion system will have a large impact on the studies of quantum critical materials.

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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...

Dilatometric and magnetic experiments on high-quality single crystals of the superconducting compounds UPd2Al3 and CeRu2, which have enhanced spin susceptibilities, demonstrate a first-order transition between weak and strong pinning at T < 0.9T(c) (H > 10 kOe). This is compatible with a staggered order parameter due to the formation of a ''Fulde-Ferrell-Larkin-Ovchinnikov'' state