Effects of Two Energy Scales in Weakly Dimerized Antiferromagnetic Quantum Spin Chains

Abstract

By means of thermal expansion and specific heat measurements on the high-pressure phase of (VO)2P2O7, the effects of two energy scales of the weakly dimerized antiferromagnetic S = 1/2 Heisenberg chain are explored. The low energy scale, given by the spin gap ∆, is found to manifest itself in a pronounced thermal expansion anomaly. A quantitative analysis, employing T-DMRG calculations, shows that this feature originates from changes in the magnetic entropy with respect to ∆, ∂S m /∂∆. This term, inaccessible by specific heat, is visible only in the weak-dimerization limit where it reflects peculiarities of the excitation spectrum and its sensitivity to variations in ∆.PACS numbers: 75.50. Ee, 75.40.Cx, 75.30Et, 75.80.+q, 71.15.Mb, 05.10.Cc In recent years, many interesting and unexpected effects have been discovered in low-dimensional antiferromagnetic (afm) quantum-spin systems. Prime examples include the Haldane gap for spin S = 1 chains, magnetization plateaux in coupled-dimer systems, and the different ground states for even-and odd-leg ladder systems, see, e.g. [1,2,3,4]. These phenomena reflect the intricate many-body quantum character of the systems which renders advanced mathematical methods necessary to gain a quantitative understanding of the experimental observations. In this communication, we want to address another non-trivial collective phenomenon, overlooked in the past, of the effects of two different energy scales caused by a weak alternation in the spin-spin interaction of an S = 1/2 afm Heisenberg chain. These scales determine the physical properties of the interacting system at different temperatures. If J 1 and J 2 (< J 1 ) denote the alternating afm coupling constants between nearest neighboring spins along the chain, we define J 1 as the large scale and the spin gap ∆, induced by any amount of alternation [5]α < 1 withα ≡ J 2 /J 1 , as the small one. The dominant feature, governing the magnetic and thermodynamic properties at elevated temperatures, is connected with J 1 . In the magnetic susceptibility χ, for example, the maximum due to short-range order is located at k B T max χ = 0.64J 1 , practically independent of α [6]. However as will be shown below, the small energy scale introduces a second distinct anomaly [7], which can be extraordinarily large in the coefficient of thermal expansion. The feature observed here is no longer proportional to that in the specific heat, viz., the so-called Grüneisen-scaling [8] does not apply.For the study of the effects of two energy scales in the interesting weak-dimerization regime, the high-pressure variant of (VO) 2 P 2 O 7 (HP-VOPO) appears particularly well suited. HP-VOPO, first synthesized by Azuma et al. [9], comprises one kind of S = 1/2 (V 4+ ) chains with alternating afm Heisenberg interactions [9,10], as opposed to the ambient-pressure (AP) variant, where two slightly different chain types were identified [10,11]. No magnetic ordering has been found in HP-VOPO down to 1.5 K ∼ 0.01J 1 /k B , the lowest temperature studied so far, indi...

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