Bose-Einstein condensation denotes the formation of a collective quantum ground state of identical particles with integer spin or intrinsic angular momentum. In magnetic insulators, the magnetic properties are due to the unpaired shell electrons that have half-integer spin. However, in some such compounds (KCuCl3 and TlCuCl3), two Cu2+ ions are antiferromagnetically coupled to form a dimer in a crystalline network: the dimer ground state is a spin singlet (total spin zero), separated by an energy gap from the excited triplet state (total spin one). In these dimer compounds, Bose-Einstein condensation becomes theoretically possible. At a critical external magnetic field, the energy of one of the Zeeman split triplet components (a type of boson) intersects the ground-state singlet, resulting in long-range magnetic order; this transition represents a quantum critical point at which Bose-Einstein condensation occurs. Here we report an experimental investigation of the excitation spectrum in such a field-induced magnetically ordered state, using inelastic neutron scattering measurements of TlCuCl3 single crystals. We verify unambiguously the theoretically predicted gapless Goldstone mode characteristic of the Bose-Einstein condensation of the triplet states.
KCuCl3 is a three-dimensional coupled spin-dimer system and has a singlet ground state with an excitation gap ∆/kB = 31 K. High-field magnetization measurements for KCuCl3 have been performed in static magnetic fields of up to 30 T and in pulsed magnetic fields of up to 60 T. The entire magnetization curve including the saturation region was obtained at T = 1.3 K. From the analysis of the mag-netization curve, it was found that the exchange parameters determined from the dispersion relations of the magnetic ex-citations should be reduced, which suggests the importance of the renormalization effect in the magnetic excitations. The field-induced magnetic ordering accompanied by the cusplike minimum of the magnetization was observed as in the iso-morphous compound TlCuCl3. The phase boundary was almost independent of the field direction, and is represented by the power law. These results are consistent with the magnon Bose-Einstein condensation picture for field-induced magnetic ordering. PACS number 75.10.Jm
We report on the observation of high-frequency collective magnetic excitations, ប Ϸ 1.1 meV, in hematite ͑␣-Fe 2 O 3 ͒ nanoparticles. The neutron scattering experiments include measurements at temperatures in the range 6-300 K and applied fields up to 7.5 T as well as polarization analysis. We give an explanation for the field-and temperature dependence of the excitations, which are found to have strongly elliptical out-of-plane precession. The frequency of the excitations gives information on the magnetic anisotropy constants in the system. We have in this way determined the temperature dependence of the magnetic anisotropy, which is strongly related to the suppression of the Morin transition in nanoparticles of hematite. Further, the localization of the signal in both energy and momentum transfer brings evidence for finite-size quantization of spin waves in the system.
KCuCl3 is an S = 1/2 magnetic insulator with a singlet ground state and a finite spin excitation gap. Above the gap, dispersive triplet excitation modes propagate in the whole reciprocal space. From single-crystal inelastic neutron investigations the three-dimensional coupling scheme is rationalized in the framework of a dimer Heisenberg model, and related to the structural features of KCuCl3. The experimental and theoretical characterization presented completes earlier works on the compound under investigation, providing also higher-order expressions for the singlet-triplet dispersion relation. The latter may also be of relevance for the parent quantum systems TlCuCl3 and NH4CuCl3, albeit at different coupling ratios with respect to KCuCl3.
Elementary excitations in valence bond magnets have a finite spin gap ⌬ϭg B H c to well-defined triplet states. The degeneracy of the triplet states is lifted in the presence of an external field, according to the Zeeman interaction term. The energy and intensity of the excitation spectra in Sϭ1/2 valence bond KCuCl 3 and TlCuCl 3 are investigated by inelastic neutron scattering at finite external fields. Experimental observations along representative directions of reciprocal space are addressed up to H/H c ϳ0.6 and H/H c ϳ0.9, respectively. A comprehensive analysis of the split Zeeman modes is reported, which shows excellent agreement with first principles. The obtained results extend former characterizations at Hϭ0 and are of importance in the context of the field-driven quantum criticality realized in the sister compounds KCuCl 3 and TlCuCl 3 .
We discuss the transition strength between the disordered ground state and the basic low-lying triplet excitation for interacting dimer materials by presenting theoretical calculations and series expansions as well as inelastic neutron scattering results for the material KCuCl 3 . We describe in detail the features resulting from the presence of two differently oriented dimers per unit cell and show how energies and spectral weights of the resulting two modes are related to each other. We present results from the perturbation expansion in the interdimer interaction strength and thus demonstrate that the wave vector dependence of the simple dimer approximation is modified in higher orders. Explicit results are given in 10 th order for dimers coupled in 1D, and in 2 nd order for dimers coupled in 3D with application to KCuCl 3 and TlCuCl 3 .
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