Luttinger liquid behavior in the alternating spin-chain system copper nitrate

Abstract

We determine the phase diagram of copper nitrate Cu(NO3)2·2.5D2O in the context of quantum phase transitions and novel states of matter. We establish this compound as an ideal candidate to study quasi-1D Luttinger liquids, 3D Bose-Einstein-Condensation of triplons, and the crossover between 1D and 3D physics. Magnetocaloric effect, magnetization, and neutron scattering data provide clear evidence for transitions into a Luttinger liquid regime and a 3D long-range ordered phase as function of field and temperature. Theoretical simulations of this model material allow us to fully establish the phase diagram and to discuss it in the context of dimerized spin systems.PACS numbers: 75.10. Jm, 75.30.Sg, 75.40.Cx There has been a flourish of interest in quantum antiferromagnets of late, due to a fascinating range of novel ground states as well as a multitude of exotic fieldinduced phases. A current focus of these studies involves materials with a reduced dimensionality. In particular, one-dimensional (1D) systems [1] have been shown to exhibit remarkable properties such as Luttinger liquid (LL) behavior, a concept relevant to a wide range of systems including quantum wires or nanotubes [2,3]. In this context, magnetic insulators such as the gapless uniform spin chain KCuF 3 [4] have been used as model systems allowing extensive studies of LLs.Presently, of particular interest are spin S = 1 2 alternating antiferromagnetic chain systems. Here, an antiferromagnetic coupling J 1 leads to a formation of spin pairs (dimers) while a weaker antiferromagnetic interdimer exchange J 2 couples the dimers along one dimension. Thus, the system is described in an external field h by the HamiltonianBecause of the dimer formation, such materials exhibit a singlet ground state separated from a low lying triplet of finite width by an energy gap, ∆. The gap is closed by the application of a magnetic field which Zeemansplits the triplet into its three constituents. At the critical field H c1 , the lower S z = 1 mode starts to collapse into the ground state, while at a second critical field H c2 the S z = 1 triplet state has fully shifted below the singlet and a gap reopens. Between the two critical fields a LL of interacting triplets develops.At very low temperatures, and with a weak interchain interaction J ′ present in real materials, the triplet states (triplons) condense into a long-range ordered (LRO) ground state between the two critical fields, a phase that is described as Bose-Einstein-condensation (BEC) of triplons [5][6][7]. The concept of a BEC of triplons was first introduced for the 3D interacting dimer system TlCuCl 3 [8], and later extended to other 2D or 3D coupled dimer systems [9,10]. Quasi-1D materials involving alternating spin chains or ladders, in addition, may show evidence of both LL and BEC phases [11]. Therefore they would allow the unique opportunity to study crossover effects between 1D and 3D physics. Only the ladder series (Hpip) 2 Cu(Br,Cl) 4 is discussed in terms of such a dimensional crossover from a LL ...

Rb-NMR study of the quasi-one-dimensional competing spin-chain compound Rb2Cu2Mo3Matsui1, Yagi2, Hoshino3 et al. 2017Phys. Rev. B164150View full textAdd to dashboardCite

“…5, where we plot against the field the Néel temperature N determined from the temperature dependence of NMR line width, the cross-over temperature TL , and also the spin excitation gap, taken from our previous report by Yagi et al [18]. One notes that N takes the maximum of 1 K, at the midst of gapless field region between C and S , that is, at around 8 T. This behavior, that is, the bell-shaped dependence of N against the applied magnetic field is quite alike as the field-induced magnetic order observed in other quantum spin systems [20][21][22][38][39].…”

“…However, recent many experimental reports on various low dimensional quantum spin systems found rather a clear line between the TLL and the paramagnetic phase [20][21][22]. This line is conspicuous only in the vicinity of the quantum critical point (QCP), where the system changes from gapped to gapless state or vici versa [20][21][22]. We will try to find whether or not the line can be seen by NMR in the present system.…”

“…Usually, the change between the paramagnetic and TLL state is considered to be a crossover, where the system is expected to show only a gradual change rather than a specific temperature point. However, recent many experimental reports on various low dimensional quantum spin systems found rather a clear line between the TLL and the paramagnetic phase [20][21][22]. This line is conspicuous only in the vicinity of the quantum critical point (QCP), where the system changes from gapped to gapless state or vici versa [20][21][22].…”

Temperature dependence of the NMR spin-lattice relaxation rate for spin-12chains

“…This model can describe very well some interesting compounds, like, for example, the copper nitrate [Cu(NO 3 ) 2 · 2.5D 2 O], discussed in Refs. [51] and [52]. For this compound the coupling parameters are determined as J /k B ≈ 3.377 K and δJ /k B ≈ 1.903 K, and we will focus on these strongly dimerized parameters in the following.…”

Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

“…Nowadays, quasi one-dimensional (1D) frustrated systems, despite their simple structure, are at the center of attention as a playground for novel ground states that can emerge from frustration and strong quantum fluctuations due to low dimensionality. So far, various unconventional magnetic states such as quantum spin liquids [2,3], spin-Peierls states [4], and Tomonaga-Luttinger (TL) liquid phases [5] have been investigated. Currently, among the hottest topics are magnetic multipolar and in particular spin-nematic states [6][7][8][9][10][11] in which magnon bound states are formed from a subtle competition between geometrical balance of ferromagnetic (FM) and antiferromagnetic (AFM) correlations among spins.…”