Nature of ege_g Electron Order in La1−x_{1-x}Sr1+x_{1+x}MnO4_4

Synchrotron x-ray scattering measurements of the low-temperature structure of the single-layer manganese oxide La$_{1-x}$Sr$_{1+x}$MnO$_4$, over the doping range $0.33 \le x \le 0.67$, indicate the existence of three distinct regions: a disordered phase ($x < 0.4$), a charge-ordered phase ($x \ge 0.5$), and a mixed phase ($0.4 \le x 0.5$, the modulation vector associated with the charge order is incommensurate with the lattice and depends linearly on the concentration of $e_g$ electrons. The primary superlattice reflections are strongly suppressed along the modulation direction and the higher harmonics are weak, implying the existence of a largely transverse and nearly sinusoidal structural distortion, consistent with a charge density wave of the $e_g$ electrons.Comment: 4 pages, 4 figure

Thermodynamics of Spin S = 1/2 Antiferromagnetic Uniform and Alternating-Exchange Heisenberg Chains

The magnetic susceptibility chi and specific heat C versus temperature T of the spin-1/2 antiferromagnetic alternating-exchange (J1 and J2) Heisenberg chain are studied for the entire range 0 \leq alpha \leq 1 of the alternation parameter alpha = J2/J1. For the uniform chain (alpha = 1), detailed comparisons of the high-accuracy chi(T) and C(T) Bethe ansatz data of Kluemper and Johnston are made with the asymptotically exact low-T field theory predictions of Lukyanov. QMC simulations and TMRG calculations of chi(alpha,T) are presented. From the low-T TMRG data, the spin gap Delta(alpha)/J1 is extracted for 0.8 \leq alpha \leq 0.995. High accuracy fits to all of the above numerical data are obtained. We examine in detail the theoretical predictions of Bulaevskii for chi(alpha,T) and compare them with our results. Our experimental chi(T) and C(T) data for NaV2O5 single crystals are modeled in detail. The chi(T) data above the spin dimerization temperature Tc = 34 K are not in agreement with the prediction for the uniform Heisenberg chain, but can be explained if there is a moderate ferromagnetic interchain coupling and/or if J changes with T. By fitting the chi(T) data, we obtain Delta(T = 0) = 103(2) K, alternation parameter delta(0) = (1 - alpha)/(1 + alpha) = 0.034(6) and average exchange constant J(0) = 640(80) K. The delta(T) and Delta(T) are derived from the data. A spin pseudogap with a large magnitude \approx 0.4 Delta(0) is consistently found just above Tc, which decreases with increasing T. Analysis of our C(T) data indicates that at Tc, at least 77% of the entropy change due to the transition at Tc and associated order parameter fluctuations arise from the lattice and/or charge degrees of freedom and less than 23% from the spin degrees of freedom.Comment: 53 two-column REVTeX pages, 50 embedded figures, 7 tables. Revisions required due to incorrect Eq. (39) in Ref. 51 which gives the low-T approximation for the specific heat of a S = 1/2 1D system with a spin gap; no conclusions were changed. Additional minor revisions made. Phys. Rev. B (in press

Thermodynamics of spin S=1/2 antiferromagnetic uniform and alternating-exchange Heisenberg chains

The magnetic susceptibility chi*(t) and specific heal C(t) versus temperature t of the spin S=1/2 antiferromagnetic (AF) alternating-exchange (J(1) and J(2)) Heisenberg chain are studied for the entire range 0 less than or equal to alpha less than or equal to 1 of the alternation parameter alpha=J(2)/J(1), (J(1), J(2)greater than or equal to 0, J(2)less than or equal to J(1) t=k(B)T/J(1), chi*=chi J(1)/Ng(2)mu(B)(2)). For the uniform chain (alpha=1), the high-accuracy chi*(t) and C(t) Bethe ansatz data of Klumper and Johnston (unpublished) are shown to agree very well at low t with the respective exact theoretical low-t logarithmic correction predictions of Lukyanov [Nucl. Phys. B 522, 533 (1998)]. Accurate (similar to 10(-7)) independent empirical fits to the respective data are obtained over t ranges spanning 25 orders of magnitude, 5X10(-25)less than or equal to t less than or equal to 5, which contain extrapolations to the respective exact t=0 limits. The infinite temperature entropy calculated using our C(t) fit function is within 8 parts in 10(8) of the exact value In 2. Quantum Monte Carlo (QMC) simulations and transfer-matrix density-matrix renormalization group (TMRG) calculations of chi*(alpha,t) are presented for 0.002 less than or equal to t less than or equal to 10 and 0.05 less than or equal to alpha less than or equal to 1, and an accurate (2X10(-4)) two-dimensional (alpha,t) fit to the combined data is obtained for 0.01 less than or equal to t less than or equal to 10 and 0 less than or equal to alpha less than or equal to 1. From the low-t TMRG data, the spin gap a(rr) is extracted for 0.8 less than or equal to alpha less than or equal to 0.995 and compared with previous results, and a fit function is Formulated for 0 less than or equal to alpha less than or equal to 1 by combining these data with literature data. We infer from our data that the asymptotic critical regime near the uniform chain limit is only entered for alpha greater than or similar to 0.99. We examine in detail the theoretical predictions of Bulaevskii [Sov. Phys. Solid State 11, 921 (1969)], for chi*(alpha,t) and compare them with our results. To illustrate the application and utility of our theoretical results, we model our experimental chi(T) and specific heat C-p(T) data for NaV2O5 single crystals in detail. The chi(T) data above the spin dimerization temperature T(c)approximate to 34 K are not, in quantitative agreement with the prediction for the S=1/2 uniform Heisenberg chain, but can be explained if there is a moderate ferromagnetic interchain coupling and/or if J changes with T. Fitting the chi(T) data using our chi*(alpha,t) fit function, we obtain the sample-dependent spin gap and range Delta(T=0)/k(B)=103(2) K, alternation parameter delta(0)=(1-alpha)/(1+alpha)=0.034(6) and average exchange constant J(0)/k(B)=640(80) K. The delta(T) and Delta(T) are derived from the data. A spin pseudogap with magnitude approximate to 0.4 Delta(0) is consistently Found just above T-c, which decreases with increasing temperature. From our CP(T) measurements on two crystals, we infer that the magnetic specific heat at low temperatures T less than or similar to 15 K is too small to be resolved experimentally, and that the spin entropy at T-c is too small to account for the entropy of the transition. A quantitative analysis indicates that at T-c, at least 77% of the entropy change due to the transition at T-c and associated order parameter fluctuations arise from the lattice and/or charge degrees of freedom and less than 23% from the spin degrees of freedom.This article is published as Johnston, D. C., R. K. Kremer, Matthias Troyer, X. Wang, A. Klümper, S. L. Bud’ko, A. F. Panchula, and P. C. Canfield. "Thermodynamics of spin S= 1/2 antiferromagnetic uniform and alternating-exchange Heisenberg chains." Physical Review B 61, no. 14 (2000): 9558. DOI: 10.1103/PhysRevB.61.9558. Copyright 2000 American Physical Society. Posted with permission