Reduction of ordered moment and Néel temperature of quasi one-dimensional antiferromagnets Sr2CuO3 and Ca2CuO3

We report elastic neutron diffraction and muon spin relaxation (μSR) measurements of the quasi one-dimensional antiferromagnets Sr2CuO3 and Ca2CuO3, which have extraordinarily reduced TN/J ratios. We observe almost resolution-limited antiferromagnetic Bragg reflections in Sr2CuO3 and obtain a reduced ordered moment size of ∼0.06μB. We find that the ratio of ordered moment size μ(Ca2CuO3)/μ(Sr2CuO3) = 1.5(1) roughly scales with their Néel temperatures, which suggests that the ordered moment size of quasi one-dimensional antiferromagnets decreases continuously in the limit of vanishing inter-chain interactions. PACS numbers: 76.75.+i, 75.25.+z, 75.10.Jm Typeset using REVTEX 1 One-dimensional spin systems with antiferromagnetic interactions have received considerable attention because of their pronounced quantum mechanical effects. In the absence of inter-chain interactions, both integer and half-odd integer spin-chain systems have spinsinglet ground states, rather than an antiferromagnetically ordered Néel state [1–3]. Yet, for half odd-integer spin-chains, the spin-excitations are gap-less at momentum k = 0 and π [4]; this indicates that the ground state of a half-odd integer spin-chain is closer to the Néel ordered state than the integer spin systems, which have a so-called Haldane gap [3]. Because of the gap-less feature of half-odd integer spin-chains, one interesting question is whether the ground state is ordered or disordered when inter-chain interactions are introduced. Previously, it was proposed that there is a non-zero critical coupling ratio (J /J = Rc), below which the system retains a singlet ground-state [5]. Recent renormalization group calculations however suggest that the ground state may depend on microscopic details of the model which describes the spin-spin interactions [6,7]. Numerical studies of the Heisenberg model suggested a vanishing critical coupling ratio (Rc ∼ 0); namely, for infinitesimally small inter-chain couplings, half odd-integer spin-chains should exhibit Néel order [7]. Experimentally, KCuF3 is the most investigated quasi-one-dimensional S=1/2 antiferromagnet. Unfortunately, this material has relatively large coupling ratio R = J /J ∼ 2K/203K = 1.0×10, as shown from neutron inelastic scattering measurements [8]. Probably reflecting the large coupling ratio R, the TN/J ratio (∼ 39K/203K = 0.2) and the ordered moment size (= 0.49(7)μB [9]) were also found to be relatively large. To investigate the regime of the critical coupling ratio, model materials with smaller interchain couplings are needed; the quasi one-dimensional S=1/2 antiferromagnets Sr2CuO3 and Ca2CuO3 are suitable candidates. The intra-chain interaction (2J ∼ 2600 K) of these materials have been estimated from susceptibility [10,11] and infrared light absorption [12]. Néel ordering of these compounds was first observed in μSR measurements [13], with a significantly reduced TN/J ratio of ∼ 5K/1300K = 4 × 10 −3 for Sr2CuO3 and TN/J ∼ 11K/1300K = 8 × 10 for Ca2CuO3. Since TN/J is a measure of the coupling ratio R 2 [7,15], the reduced TN of these two compounds demonstrates their good one-dimensionality. A previous elastic neutron scattering measurement of Ca2CuO3 [16] has found an extremely reduced size of ordered moments (=0.05(3)μB), although this result contains a systematic uncertainty due to extinction. In the case of Sr2CuO3, powder neutron measurements were unable to observe antiferromagnetic Bragg reflections, placing an upper limit of any ordered moment of < 0.1μB [10]. In this Letter we report μSR and neutron scattering measurements of single crystalline Sr2CuO3 and Ca2CuO3 specimens, aiming to clarify the relationship between TN/J and the size of ordered moments. The crystal structure of Sr2CuO3 and Ca2CuO3 (Fig.1) is similar to that of La2CuO4, but lacks oxygen ions between the Cu ions in one direction (c-axis). As a result, chains of corner shared CuO4 tetragons extend in the b-axis direction, with a strong antiferromagnetic interaction due to the 180 Cu-O-Cu coupling. The lattice parameters of Ca2CuO3 are smaller than those of Sr2CuO3 by 7.0% (c-axis) and 3.6% (aand b-axis) [10,17]. The reduced c-axis parameter of Ca2CuO3 probably enhances the inter-chain coupling (J ), as its higher TN suggests. A single crystal of Sr2CuO3 (∼ φ3mm×2cm) was grown employing the traveling-solventfloating-zone (TSFZ) method, as described in Ref. [11]. In order to search for antiferromagnetic Bragg reflections, we performed elastic neutron scattering measurements at the High Flux Beam Reactor (HFBR) at Brookhaven National Laboratory, using the H4M and H7 triple-axis spectrometers. For the measurements, two pyrolytic graphite (PG) filters were employed to eliminate contamination of higher order reflections from the monochromator. In Fig.2a, we show diffracted neutron counts around the point (0, 1/2, 1/2), where an antiferromagnetic Bragg reflection was observed below TN = 5.41(1)K. We confirmed with tighter collimation (10’-40’-S-10’-80’) that the width of this Bragg reflection is as narrow as that of a nuclear reflection (011). This is direct evidence of antiferromagnetic long range order in Sr2CuO3. We observed other antiferromagnetic Bragg reflections at (h, k/2, l/2), where h is an integer and k and l are odd-integers. We fit the (0, 1/2, 1/2) reflection with a Gaussian form, and plot the peak intensity (I0) and width (σ) in Fig.2b as a function of 3 temperature. In order to determine the ordered spin-direction and the moment size, we measured the integrated intensities of magnetic Bragg reflections in both the 0kl− and hkk−zones. The intensity distribution was best explained using the assumption that ordered moments are aligned along the b-axis direction, parallel to the chain. By normalizing the magnetic Bragg intensities with those of several relatively weak nuclear Bragg reflections, such as (200) and (400), we find the ordered moment size to be 0.06(3) μB. Because of extinction of nuclear reflections, the ordered moment size obtained here should be considered as an upper limit. Since extinction of nuclear reflections depends on the quality of individual crystals, the size of ordered moments obtained by the above method contains a relatively large systematic error. With muon spin relaxation (μSR) on the other hand, we can compare the relative size of moments between iso-structural materials quite accurately. Muons in Sr2CuO3 and Ca2CuO3 are expected to occupy the same crystallographic position and experience dipolar fields from the ordered moments below TN. The relative size of ordered moments can be deduced from the muon spin precession frequencies. The μSR measurements were performed at the M15 surface-muon channel at TRIUMF (Vancouver, Canada), using a conventional μSR spectrometer [18] combined with a dilution refrigerator and a ‘low-background’ apparatus [19] with a He gas-flow cryostat. We evaluated the time evolution of muon spins, using the conventional ZF/LF-μSR technique [18,20]. In Fig.3a, we show the spectrum for Sr2CuO3. Below TN, we observe spontaneous muon spin precession in zero external magnetic-field; this is a signature of a well-defined static local field from ordered moments. We analyzed the spectra assuming two muon sites: Pμ(t) = A1Pμ1(t) +A2Pμ2(t) (1) where A1,2 is the fractional site population of the muons (A1 + A2 = 1). We assumed the following conventional form for the signal from each site: Pμi(t) = Aosci exp(−∆it) cos(γμHμit+ φi) 4 +Arlxi exp(−t/T1i) (i = 1, 2) (2) where, the first (second) term presents the muon spin precession (T1 relaxation), due to the local field component perpendicular (parallel) to the initial muon spin direction. In Fig.3c, we show the local fields (Hμ1,2) as a function of temperature. In Sr2CuO3, the ratio of the two local fields was independent of temperature; this suggests that both of the muon sites are stable and that muons do not hop on the time scale of the muon lifetime. In Fig.3b, we show μSR spectra of Ca2CuO3. Because of the shape of our Ca2CuO3 specimen, we performed the μSR measurements with a crystal orientation (Pμ(0) ⊥ a-axis) which was different from that of the Sr2CuO3 case (Pμ(0) ‖ a-axis ⊥ chain). Consequently, we observed only one signal in the ordered phase. We confirmed, from independent measurements of polycrystalline Ca2CuO3 pellets, that the higher frequency signal also exists and that the signal observed in the single crystalline sample corresponds to the lower frequency signal. The muon local fields are plotted in Fig.3c. The ratio of the local fields of the two systems, which is equal to the relative size of ordered moments, was μ(Ca2CuO3)/μ(Sr2CuO3) = 35(3)G/23.2(1)G = 1.5(1) in the T → 0 limit. In high-Tc related oxides, muons generally form an O-μ + bond with a bond length of ∼ 1.0 Å [21]. Assuming such O-μ bond formation, we performed an electrostatic potential calculation, and determined the stable muon positions in (Sr,Ca)2CuO3. Fig.1 shows the off-chain O-μ bond site, which is responsible for the lower-field signal. We calculated the magnetic dipolar-field for this site, and found that the local field from a given size of ordered moment agrees within 10% in Sr2CuO3 and Ca2CuO3. Therefore, the local field ratio in these two compounds reflects the relative size of their moments. We estimated the ordered moment sizes from the dipolar-fields, as summarized in Table I. The moment sizes obtained by μSR and neutron techniques agreed within the errors, suggesting that uncertainties due to extinction or muon site ambiguity are, in fact, rather small. In Fig.4, we plot the ordered moment size of several quasi 1d antiferromagnets as a function of TN/J . As expected, the ordered moments shrink as the TN/J ratio decreases.