From order to randomness: Onset and evolution of the random-singlet state in bond-disordered BaCu$_2$(Si$_{1-x}$Ge$_x$)$_2$O$_7$ spin-chain compounds

TL;DR

This study explores how introducing bond disorder in spin-chain compounds transitions the system from ordered to a random singlet state, revealing disorder's significant impact on magnetic properties and confirming theoretical predictions.

Contribution

It provides experimental evidence of the evolution from ordered to random singlet states in disordered spin chains, using magnetometry and NMR techniques.

Findings

Weak disorder reduces magnetic ordering temperature.

Maximum disorder induces a random singlet state.

Disorder influences NMR relaxation features.

Abstract

Heisenberg-type spin-chain materials have been extensively studied over the years, yet not much is known about their behavior in the presence of disorder. Starting from BaCu$_2$Si$_2$O$_7$, a typical spin-1/2 chain system, we investigate a series of compounds with different degrees of bond disorder, where the systematic replacement of Si with Ge results in a re-modulation of the Cu$^{2+}$ exchange interactions. By combining magnetometry measurements with nuclear magnetic resonance studies we follow the evolution of the disorder-related properties from the well-ordered BaCu$_2$Si$_2$O$_7$ to the maximally disordered BaCu$_2$SiGeO$_7$. Our data indicate that already a weak degree of disorder of only 5% Ge, apart from reducing the 3D magnetic ordering temperature $T_\mathrm{N}$ quite effectively, induces a qualitatively different state in the paramagnetic regime. At maximum disorder our data indicate that this state may be identified with the theoretically predicted random singlet (RS) state. With decreasing disorder the extension of the RS regime at temperatures above $T_\mathrm{N}$ is reduced, yet its influence is clearly manifest, particularly in the features of NMR relaxation data.

Equations

$$\chi (T)={\chi }_0+{\chi }_{\mathrm{CW}}(T)+{\chi }_{\mathrm{spin}}(T).$$

$$\chi (T)\sim T^{-1}{\ln }^{-2}(\Omega /T),$$

$$\frac{1}{T_{1z}}\propto {\hslash }^2{k}_{\mathrm{B}}T{\gamma }_n^2\sum _{\begin{array}{c}\alpha =x,y,z\\ \mathbf{q}\end{array}}\left[{\tilde{A}}_{x\alpha }^2(\mathbf{q})+{\tilde{A}}_{y\alpha }^2(\mathbf{q})\right]\frac{{\chi }_{\alpha \alpha }^{\prime \prime c}(\mathbf{q},{\omega }_n)}{{\omega }_n}$$

Full text

One-dimensional systems, disordered spin chains, antiferromagnetism, nuclear magnetic resonance

I Introduction

The study of electronic properties of physical systems in the presence of disorder spans many decades,Abrahams (2010) starting with the strong (Anderson) localization studies in the 1950sAnderson (1958) up to the present-day investigations of quantum confinement in nanostructures.Oka et al. (2014) The breadth of phenomena taking place in disordered systems, such as quantum percolation,Schubert and Fehske (2009) ballistic transport,Stevens (1987) quantum glassiness,Chamon (2005) or many-body localizationAlet and Laflorencie (2018) have been studied primarily theoretically, e.g., as a function of dimensionality, nature of disorder, degree of interaction, etc. Of particular interest is the physics occurring in low-dimensional quantum magnets under a varying degree of disorder. At very low temperatures and high magnetic fields, close to a quantum phase transition, disorder suppresses the global phase coherence and induces novel quantum critical behavior.Zheludev and Roscilde (2013); Zapf et al. (2014) But even under less extreme conditions, the disorder-induced breaking of translational invariance promotes random couplings between individual spins and leads to a so-called random-singlet (RS) state,Dasgupta and Ma (1980); Fisher (1994); Motrunich et al. (2000) a regime where spins couple across arbitrary distances to form weakly-bound singlets, which dominate the magnetic features and the related dynamics. What exactly happens when a regular spin-chain is exposed to an increasing degree of disorder is not well known. Until recently, progress has been slow as far as numerical simulationsShu et al. (2018) and, especially, experimental investigationsHammerath et al. (2011); Hlubek et al. (2010); Utz et al. (2017) of disordered low-dimensional systems are concerned. The main reasons include computational difficulties due to the large size of realistic disordered systems and, regarding experiments, the scarcity of suitable systems in which disorder can be easily tuned over a broad range without changing the structural character of the material.

It is known for some time that the series of BaCu2(Si1-xGex)2O7 compounds represents one of the best physical realizations of an $S=1/2$ Heisenberg-type spin-chain system (see, e.g., Table 1 in Ref. et al., 2002), where bond disorder can be introduced in a controlled way. For $x=0$, the compound crystallizes in the orthorhombic space group Pnma ($D^{16}_{2h}$) with lattice constants $a=6.862$ Å, $b=13.178$ Å, and $c=6.897$ Å.Yamada et al. (2001) Replacing Si by Ge results in isostructural compounds across the entire series, but introduces a variation in the O-Cu-O bond angle from 124*∘* in the Si case ($x=0$) to 135*∘* in the Ge case ($x=1$).Yamada et al. (2001) As a consequence, the exchange-coupling constant almost doubles, from $J=24.1$ meV to 46.5 meV, when $x$ changes from 0 to 1.Tsukada et al. (1999); Kenzelmann et al. (2001) In this way the randomization, in the form of varying couplings, enters the magnetically relevant Cu-O chains. The parent compound BaCu2Si2O7 orders antiferromagnetically at $T_{\mathrm{N}}=9.2$ K, i.e., at a much lower temperature than 280 K, the equivalent of the exchange energy $J=24.1$ meV. Since also the $x>0$ members have similar (or lower) $T_{\mathrm{N}}$ values, this qualifies the BaCu2(Si1-xGex)2O7 series as one of the best 1D systems for studying bond-disorder effects.