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arXiv:1812.09045 · Physical review. B./Physical review. B

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

T. Shiroka, Federico Eggenschwiler, H. R. Ott, J. Mesot

Published Jan 8, 2019• 10 citations
arXivHTMLPDF

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 ${\mathrm{BaCu}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}$, a typical spin-$\frac{1}{2}$ chain system, we investigate a series of compounds with different extents of bond disorder, where the systematic replacement of Si with Ge results in a remodulation of the ${\mathrm{Cu}}^{2+}$ exchange interactions. By combining magnetometry measurements with nuclear magnetic resonance studies, we follow the evolution of the disorder-related properties from the well-ordered ${\mathrm{BaCu}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}$ to the maximally disordered ${\mathrm{BaCu}}_{2}{\mathrm{SiGeO}}_{7}$. Our data indicate that already a weak degree of disorder of only 5% Ge, apart from reducing the three-dimensional 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 nuclear magnetic resonance relaxation data.

DOI
10.1103/physrevb.99.035116

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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 BaCu2Si2O7{\mathrm{BaCu}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}BaCu2​Si2​O7​, a typical spin-12\frac{1}{2}21​ chain system, we investigate a series of compounds with different extents of bond disorder, where the systematic replacement of Si with Ge results in a remodulation of the Cu2+{\mathrm{Cu}}^{2+}Cu2+ exchange interactions. By combining magnetometry measurements with nuclear magnetic resonance studies, we follow the evolution of the disorder-related properties from the well-ordered BaCu2Si2O7{\mathrm{BaCu}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}BaCu2​Si2​O7​ to the maximally disordered BaCu2SiGeO7{\mathrm{BaCu}}_{2}{\mathrm{SiGeO}}_{7}BaCu2​SiGeO7​. Our data indicate that already a weak degree of disorder of only 5% Ge, apart from reducing the three-dimensional magnetic ordering temperature TN{T}_{\mathrm{N}}TN​ 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 TN{T}_{\mathrm{N}}TN​ is reduced, yet its influence is clearly manifest, particularly in the features of nuclear magnetic resonance relaxation data.
NMR measurements of the (29)Si spin-lattice relaxation time T(1) were used to probe the spin-1/2 random Heisenberg chain compound BaCu(2)(Si(1-x)Ge(x))(2)O(7). Remarkable differences between the pure (x=0) and the fully random (x=0.5) cases are observed, indicating that randomness generates a distribution of local magnetic relaxations. This distribution, which is reflected in a stretched exponential NMR relaxation, exhibits a progressive broadening with decreasing temperature, caused by a growing inequivalence of magnetic sites. Compelling independent evidence for the influence of randomness is also obtained from magnetization data and Monte Carlo calculations. These results suggest the formation of random-singlet states in this class of materials, as previously predicted by theory.
Low-dimensional spin systems, consisting of arrays of spins arranged in chains or ladders, have been investigated intensively in recent years using both exactly solvable theoretical models as well as a variety of experimental techniques. In case of random variations of the exchange couplings the renormalization group theory predicts the existence of a random-singlet (RS) state, corresponding to spins coupled at all possible distances and energy scales. The scarce availability of suitable random systems, however, has so far prevented the experimental identification of this peculiar magnetic ground state. In a combined effort using nuclear magnetic resonance (NMR), dc magnetometry and numerical simulations, we now find compelling evidence for the formation of a random-singlet state in this class of materials. Randomness seems to generate a broad distribution of local magnetic fields, in turn reflected in stretched exponential NMR relaxations. This distribution exhibits a progressive broadening with decreasing temperature, caused by the growing inequivalence of magnetic sites, as expected from the RS theory. Our findings suggest that NMR is the tool of choice for probing the low-energy physics also in other disordered magnets, where extended-scale excitations are dominant.
Combining quantum Monte Carlo simulations with the maximum entropy method, we study the dynamical structure factor S(k,ω)S(k,ω)S(k,ω) of spin-1/2 antiferromagnetic Heisenberg chains with various random bond distributions. We emphasize the crossover behavior in the dynamical properties from pure chain to disorder-dominated random singlet phase due to bond randomness. For the distribution corresponding to the infinite randomness fixed point, S(k,ω)S(k,ω)S(k,ω) develops broad non-spinon excitations as well as the random-singlet peak near (k,ω)=(π,0)(k, ω) = (π, 0)(k,ω)=(π,0), consistent with the known results obtained by the real-space renormalization group method. For weak disorder, however, we find clear signature of spinon excitations, reminiscent of pure spin chains, blurred by disorder. We discuss the implication for experiments on random-bond antiferromagnetic spin chains, realizable, e.g., in BaCu2_22​(Six_xx​Ge1−x_{1-x}1−x​)2_22​O7_77​.
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Finite-temperature local dynamical spin correlations S(nn)(ω) are studied numerically within the random spin-1/2 antiferromagnetic Heisenberg chain. The aim is to explain measured NMR spin-lattice relaxation times in BaCu(2)(Si(0.5)Ge(0.5))(2)O(7), which is the realization of a random spin chain. In agreement with experiments we find that the distribution of relaxation times within the model shows a very large span similar to the stretched-exponential form. The distribution is strongly reduced with increasing T, but stays finite also in the high-T limit. Anomalous dynamical correlations can be associated with the random singlet concept but not directly with static quantities. Our results also reveal the crucial role of the spin anisotropy (interaction), since the behavior is in contrast with the ones for the XX model, where we do not find any significant T dependence of the distribution.
In frustrated magnets, the experimental realization of a quantum disordered ground state (QDGS), especially quantum spin liquid (QSL) ground state, is a central topic in condensed matter physics.Several promising candidates were reported, and a number of QSL-like behavior, such as excitation continuum, Tlinear specific heat, and so on, were observed.However, whether the QSL-like behavior is owing to the synergy between spin frustration and quantum fluctuation or bond randomness effects has not been clarified yet.Several theoretical studies have demonstrated that the synergy effect between the magnetic frustration and the bond randomness suppresses magnetic ordering and induces a QSL-like state.This QSL-like state was proposed to be a random-singlet (RS) state, where not only nearest-neighbor spins but also distant spins form singlet pairs with random coupling energy.Since thermodynamic properties of RS and QSL are predicted to be similar to each other, it is important to elucidate the microscopic nature of randomness-induced QDGSs.However, its experimental verifications are still insufficient due to a lack of model materials.In this work, I synthesized polycrystalline samples of SrLaCuSbO 6 (SLCSO) and SrLaCuNbO 6 (SLCNO) by a solid-state reaction.Magnetic Cu 2+ ions with S = 1/2 Heisenberg spins form a square lattice with nearest-neighbor (J 1 ) and next-nearest-neighbor (J 2 ) exchange interaction.Thus, SLCSO and SLCNO were magnetically described as quasi-two-dimensional S = 1/2 J 1 -J 2 square lattice Heisenberg antiferromagnet (SLHAF).The temperature dependence of the magnetic susceptibilities of both compounds shows a broad maximum characteristic of an S = 1/2 SLHAF.However, both compounds undergo magnetic phase transitions at T N = 13.6 and 15.7 K for SLCSO and SLCNO, respectively, due to weak inter-layer interactions.Neutron powder diffraction measurements reveal contrasting spin structures in both compounds.The spin structures of SLCSO and SLCNO below T N are Néel antiferromagnetic and collinear antiferromagnetic, respectively.This result demonstrates that the nearest-neighbor interaction is dominant in SLCSO, whereas the next-nearest-neighbor interaction is dominant in SLCNO.The magnitude of the ordered moment was evaluated at 3.5 K to be m = 0.39(3) µ B for SLCSO and 0.37(1) µ B for SLCNO, which are significantly reduced from 1µ B expected in the classical spin case.The shrink of the ordered magnetic moment was caused by not only magnetic frustration effects but also bond randomness effects arising from the site disorder of Sr 2+ and La 3+ ions.Next, I synthesized the mixed system SrLaCuSb 1-x Nb x O 6 with 0.1 ≤ x ≤