Neutron scattering from copper benzoate, Cu(C 6 D 5 COO) 2 ·3D 2 O, provides the first direct experimental evidence for field-dependent incommensurate low energy modes in a one-dimensional spin S = 1/2 antiferromagnet. Soft modes occur for wavevectorsq = π ± δq(H) where δq(H) ≈ 2πM (H)/gµ B as predicted by Bethe ansatz and spinon descriptions of the S = 1/2 chain. Unexpected was a field-induced energy gap ∆(H) ∝ H α , where α = 0.65(3) as determined from specific heat measurements. At H = 7 T (gµ B H/J = 0.52), the magnitude of the gap varies from 0.06−0.3J depending on the orientation of the applied field. To search for incommensurate spin correlations, we used inelastic neutron scattering to probe the wavevector-dependent spin susceptibility of the model one-dimensional S = 1/2 antiferromagnet (AFM) copper benzoate, Cu(C 6 D 5 COO) 2 · 3D 2 O. In contrast to other systems that have been studied in this context [7,8], in copper benzoate the exchange constant J is small enough to permit the large values of the reduced field, h = gµ B H/J ≈ 1 needed to observe this effect, while still being large enough to allow the interesting low energy part of the spectrum to be explored with a cold neutron triple-axis spectrometer [9]. Our most important result is that a magnetic field induces new low-energy modes in the excitation spectrum of copper benzoate at incommensurate wavevectorsq = π ± δq, where δq(H) ≈ 2πM(H)/gµ B , with M(H) being the magnetization per spin, as predicted by theory [1][2][3]. The modes are not completely soft, however, because the field also induces a gap in the excitation spectrum both at the incommensurate wave vector and atq = π. A, c = 6.30Å, and β = 89.5• [11]. Copper ions within a spin chain are separated by c/2 and coordinated by edge sharing, tetragonally distorted oxygen octahedra. The near-neighbor intrachain exchange interaction is J = 1.57 meV [9]. For this work, deuterated single crystals were prepared as described previously [9]. Specific heat measurements in magnetic fields up to H = 8.8 T were made on individual single crystals of typical mass 0.01 g using the relaxation method. For the neutron scattering measurements, approximately 500 crystals with total mass 3.82 g were mutually aligned to within 5• in the horizontal (h0l) scattering plane. Neutron scattering measurements in fields up to H = 7 T b were performed on the SPINS cold neutron triple-axis spectrometer at NIST. FWHM beam divergences were′ , and the fixed final energy was 2.5 meV, yielding energy and wavevector resolution ∆E = 69 µeV and ∆q/π = 0.02, respectively. We refer to wave vector transfer along the chain asq = Q · c/2 = lπ. The normalized magnetic scattering intensitỹ I(q, ω) [9], was derived from the detector count rate by subtracting T = 25 K data as a background, dividing by the squared magnetic form factor for copper, and normalizing to
High-field magnetization, field-dependent specific heat measurements, and zero-field inelastic magnetic neutron scattering have been used to explore the magnetic properties of copper pyrazine dinitrate ͓Cu(C 4 H 4 N 2 )(NO 3 ) 2 ͔. The material is an ideal one-dimensional spin-1/2 Heisenberg antiferromagnet with nearest-neighbor exchange constant Jϭ0.90(1) meV and chains extending along the orthorhombic a direction. As opposed to previously studied molecular-based spin-1/2 magnetic systems, copper pyrazine dinitrate remains gapless and paramagnetic for g B H/J at least up to 1.4 and for k B T/J at least down to 0.03. This makes the material an excellent model system for exploring the Tϭ0 critical line that is expected in the H-T phase diagram of the one-dimensional spin-1/2 Heisenberg antiferromagnet. We present accurate measurements of the Sommerfeld constant of the spinon gas versus g B H/JϽ1.4 that reveal a decrease of the average spinon velocity by 32% in that field range. The results are in excellent agreement with numerical calculations based on the Bethe ansatz with no adjustable parameters. ͓S0163-1829͑99͒11201-3͔
Cu 2 ͑1,4-diazacycloheptane͒ 2 Cl 4 contains double chains of spin-1 2 Cu 2ϩ ions. We report ac susceptibility, specific heat, and inelastic neutron-scattering measurements on this material. The magnetic susceptibility (T) shows a rounded maximum at Tϭ8 K indicative of a low-dimensional antiferromagnet with no zero-field magnetic phase transition. We compare the (T) data with exact diagonalization results for various onedimensional spin Hamiltonians and find excellent agreement for a spin ladder with intrarung coupling J 1 ϭ1.143(3) meV and two mutually frustrating interrung interactions J 2 ϭ0.21(3) meV and J 3 ϭ0.09(5) meV. The specific heat in zero field is exponentially activated with an activation energy ⌬ϭ0.87(1) meV. A spin gap is also found through inelastic neutron scattering on powder samples that identify a band of magnetic excitations for 0.8ϽបϽ1.5 meV. Using sum rules we derive an expression for the dynamic spin-correlation function associated with noninteracting propagating triplets in a spin ladder. The Van Hove singularities of such a model are not observed in our scattering data, indicating that magnetic excitations in Cu 2 ͑1,4-diazacycloheptane͒ 2 Cl 4 are more complicated. For magnetic fields above H c1 Ӎ7.2 T specific-heat data versus temperature show anomalies indicating a phase transition to an ordered state below Tϭ1 K. ͓S0163-1829͑98͒05810-X͔ SPIN GAP IN A QUASI-ONE-DIMENSIONAL Sϭ 1 2 . . .
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