O17NMR Study ofq=0Spin Excitations in a

Abstract

We used17 O NMR to probe the uniform (wavevector q = 0) electron spin excitations up to 800 K in Sr2CuO3 and separate the q = 0 from the q = ± π a staggered components. Our results support the logarithmic decrease of the uniform spin susceptibility below T ∼ 0.015J, where J = 2200 K. From measurement of the dynamical spin susceptibility for q = 0 by the spin-lattice relaxation rate 1/T1, we demonstrate that the q = 0 mode of spin transport is ballistic at the T = 0 limit, but has a diffusion-like contribution at finite temperatures even for T ≪ J. 75.40.Gb, 76.60.EsThe one-dimensional Heisenberg spin chain has one of the simplest Hamiltonians, H = J i S i · S i+1 , yet our understanding of its fascinating quantum mechanical properties is still developing with recent theoretical [1][2][3][4][5][6][7][8] and experimental [9][10][11][12] studies. A recent breakthrough in experimental studies of spin chains is the identification of a nearly ideal 1D S = 1 2 Heisenberg antiferromagnet, Sr 2 CuO 3 , by Motoyama et al. [9] In this system, S = 1 2 spins reside at Cu sites, and the superexchange interaction J is mediated by hybridization with the 2p σ orbital of the in-chain O(1) site, see Fig.1(a). Based on the fit of the uniform spin susceptibility χSr 2 CuO 3 has proven to be an ideal material for the experimental studies of S = Heisenberg spin chain can be probed at unprecedently low scales of temperature and energy. The second major advantage of Sr 2 CuO 3 is that 63 Cu NMR is observable at the magnetic cation site, because the large J suppresses the nuclear relaxation rates. In a series of publications, Takigawa et al. reported detailed 63 Cu NMR investigations of the low energy spin excitations [10][11][12]. They successfully tested the theoretical predictions for the q = ± π a staggered mode in the scaling limit [2], including the low temperature logarithmic corrections to the staggered dynamical susceptibility [4]. The third major advantage of Sr 2 CuO 3 , although it has never been exploited in the earlier NMR works, is the high local symmetry of the crystal structure. The Cu-O-Cu chain is strictly straight and the in-chain O(1) site is located in the middle of adjacent Cu sites as shown in Fig.1(a). Therefore the staggered components of the magnetic hyperfine fields from Cu electron spins are canceled out at the in-chain O(1) sites. Accordingly, one can probe the low energy spin excitations for the q = 0 long wavelength mode (see Fig.1(c) 17 O NMR studies have been reported despite the rich information expected for the unexplored q = 0 mode.In this Letter, we report the first successful 17 O NMR investigation of Sr 2 CuO 3 single crystals. We accurately measured the temperature dependence of the uniform spin susceptibility χ ′ (q = 0) by NMR Knight shift at the in-chain O(1) site without suffering from the contribution by free-spins that limits the accuracy of bulk susceptibility measurements and 63 Cu NMR at low temperatures. We found that χ ′ (q = 0) decreases steeply below T ∼ 0.015J without the signature ...

Conservation laws, integrability, and transport in one-dimensional quantum systems

“…This type of behavior has been observed for gapped S = 1 spin chains 56 and gapless spin chains with large half-integer S. 52 More surprisingly, spin diffusion has also been observed in S = 1/2 chain compounds by NMR 54,55 and by muon spin resonance. 57 It is important to note that in the NMR experiment of Ref.…”

“…19 The analytical results were supported by DMRG calculations for the time-dependent current-current correlation function as well as by a comparison with the NMR experiment on Sr 2 CuO 3 . 54 We also argued that ballistic transport can be reconciled with diffusion in the autocorrelation function because ballistic channels of propagation can coexist with diffusive ones. This can be made precise with the help of the memory matrix approach, 10 which allows one to incorporate known conservation laws in the low energy effective theory.…”

“…57 It is important to note that in the NMR experiment of Ref. [54], the q-dependence of the form factor suppresses the contribution from q ∼ π modes in the autocorrelation function, so that the 1/T 1 signal is completely dominated by q ∼ 0 modes.…”

“…Since the experimental diffusion constant was found to be fairly large, 54 it becomes important to determine whether the diffusion constant is mainly determined by integrability-breaking interactions present in the real system or by umklapp processes already contained in the integrable Heisenberg model.…”

“…[52][53][54][55] Strictly speaking, linear response theory expresses 1/T 1 in terms of the Fourier transform of the transverse spin-spin correlation function S + j (t)S − j (t) . The small magnetic field applied in NMR experiments breaks the rotational spin invariance of Heisenberg chains from SU(2) down to U(1) and the total S ± are not conserved.…”