Low-energy excitations of the semimetallic one-dimensional S=1/2 antiferromagnet Yb4As3

doi:10.1016/S0921-4526(01)00576-2

Physica B: Condensed Matter

Volume 300, Issues 1–4, 1 July 2001, Pages 121-138

https://doi.org/10.1016/S0921-4526(01)00576-2 Get rights and content

Abstract

We investigate a new route to quasi-one-dimensional spin-chain systems which originates from the charge-ordering transition out of a homogeneous mixed-valence state. We present evidence that Yb₄As₃ and P, Sb doped mixed crystals are well described by this mechanism. Many thermodynamic and low-temperature transport heavy-fermion-like properties can be explained by the existence of low-lying quasi-one-dimensional spin excitations in the Yb³⁺-chains. The observation of soliton excitations in a transverse external field gives further support to the existence of spin chains in Yb₄As₃. We also present recent results on spin-glass behavior at very low temperature caused by the interchain coupling and disorder. In addition, the yet unexplained magnetotransport effects are discussed.

Introduction

The study of one-dimensional spin systems is of great interest for the understanding of generic quantum many-body effects which have no classical counterparts. An example is the connection between long-range behavior of spin correlation functions and the low-lying spin excitations in one-dimensional Heisenberg antiferromagnetic chains. While for S=1 a “Haldane gap” in the excitation spectrum exists, leading to an exponential decay of the spin correlations, spin chains with $S= 12$ show the gapless two-spinon continuum excitations as described by des Cloizeaux and Pearson [1] which is connected with the quasi-long-range order characterized by an algebraic decay of the spin correlations at long distance. Perturbations like exchange anisotropies, interchain coupling, staggered fields caused by Dzyaloshinskii–Moriya interactions and alternating g-tensors as well as lattice dimerization can lead to a gap formation also for $S= 12$ chains. In some cases the low-lying excitations in the continuum limit can be well described by a quantum sine-Gordon model which leads to localized soliton-like excitations in addition to the extended spinon excitations. Most observations of these fundamental properties of spin chains have so far been studied in insulating Cu oxides or halides ( $S= 12$ ) or $Ni (S=1)$ compounds where the spin chains are dictated by the crystal structure of the insulator at all temperatures.

Recently, an exciting new route to one-dimensional spin physics has been found in compounds that exhibit a charge-ordering transition. In such compounds no localized spins on fixed atomic positions exist at high temperatures. They rather are homogeneous mixed-valence (semi-)metals or valence-fluctuating insulators at high temperatures. Their 3d or 4f electrons are strongly correlated and close to localization, i.e., having a low effective kinetic energy. If the intersite Coulomb repulsion is large enough it may dominate the kinetic energy and, once the charge-disorder entropy due to hopping is low enough, lead to a charge-ordering transition at a critical temperature T_co below which the valence fluctuations are suppressed. The resulting inhomogeneous mixed-valence state consists of two species of ions with valence Z and (Z+1). This transition may be compared to a Wigner crystallization on a lattice [2], and its earliest example is the Verwey transition in magnetite [3], although this picture turned out to be too simplified for this compound.

If one of the valence species, say Z, has no magnetic moment, a fascinating possibility arises. The charge ordering transition may lead to a structure where the species (Z+1) with spin S occupies only sites which lie on well-isolated chains (not necessarily linear) with only weak exchange interactions between the chains, thus creating a one-dimensional system of localized atomic spins at low temperature out of the high-temperature state.

This new scenario has recently been found to be realized in the 3d-layer compound sodium vanadate [4] where in addition an exchange dimerization in the chains leads to a spin-gap formation. The best studied and well confirmed system for the charge-ordering route to one-dimensional spin physics is the 4f-pnictide compound Yb₄As₃. It is the aim of this article to review the existing experimental and theoretical research to support this picture in detail.

Yb₄As₃ is a semimetallic pnictide compound which belongs to a whole family of $R_{4} X_{3} (R = rare earth, X = As, Bi, P, Sb$ ) compounds which have anti-Th₃P₄ structure, see Table 1. They have first been systematically investigated by Ochiai et al. [5]. These mixed-valence compounds may both be insulating or (semi-)metallic depending on the number of holes present in the pnictide p-valence bands. The more metallic compounds stay in a homogeneous mixed-valence state for all temperatures investigated. If only a few hole carriers are present, the intersite Coulomb interactions between the R-ions will be badly screened and a charge ordering of the two ionic species R²⁺ and R³⁺ at a temperature T_co is observed. If one species has no magnetic moment, the other species of ions with nonzero moment will form a single family of parallel antiferromagnetic spin chains. This is the case for all compounds in Table 1 which have finite T_co, except for Eu₄As₃, where the Eu²⁺-ions carry the nonzero magnetic moment. If the magnetic interchain coupling is large enough, magnetic order will appear at low temperatures as, e.g., is the case in Sm₄Bi₃ with $T_{C} ≃2.7 K$ . On the other hand, for very weak interchain coupling one has a quasi-one-dimensional Heisenberg antiferromagnet down to very low temperatures. This unique case is realized in Yb₄As₃ and also presumably in Yb₄P₃ and the mixed systems. In contrast to this scenario, Eu₄As₃ forms a three-dimensional magnetic system, with the magnetic ordering temperature being substantially larger than in Sm₄Bi₃.

This article is organized as follows. In Section 2, we discuss the charge-ordering transition and its description within a mean-field model. Section 3 investigates the crucial concept how one-dimensional spin physics, which dominates the low-temperature thermodynamics of Yb₄As₃, emerges from the charge-ordering transition. In Section 4, we discuss the evidence for localized soliton-like spin excitations as obtained from the field dependence of the specific heat, thermal expansion and transport coefficients. This lends further support to the one-dimensional spin-chain picture of Yb₄As₃. In Section 5, we present recent results for the collective magnetic behavior, i.e., spin-glass freezing found at very low temperatures where the interchain coupling becomes important. In Section 6, we discuss recent results on transport properties, notably their field dependences, which are not understood so far, but are likely to be connected with the existence of light and heavy carriers found in the lsda+u band-structure calculations. Section 7 finally gives our conclusion and outlook.

Section snippets

Charge-ordering transition

The high-temperature phase of Yb₄As₃ is cubic (lattice constant $a=8.788 A ̊$ ) and has the anti-Th₃P₄ crystal structure with space group $I 4 ̄ 3 d$ . The Yb-ions occupy the phosphorus sites on the three-fold symmetry axes, the As-ions are located on the Thorium sites. The arrangement of the Yb-sites can be viewed as being aligned on four families of interpenetrating chains oriented parallel to the space diagonals of a cube, known as body-centered cubic rod packing [18] which is illustrated in Fig. 1.

Low-temperature thermodynamic and transport properties at B=0: magnons

For B=0 and at temperatures below about $10 K$ , the thermodynamic properties of Yb₄As₃ resemble that of a typical heavy-fermion metal. Above $T≈0.5 K$ , the specific heat is dominated by a term linear in temperature, C=γT, with $γ≈200 mJ /(K^{2} mol)$ [29], cf. Fig. 5. Upon lowering the temperature, C(T)/T shows a steep increase with a low-temperature asymptotic T⁻³ dependence and a shoulder-like anomaly near $T=0.2 K$ . We shall return to these low-T results in Section 5. The static magnetic susceptibility is

Field-induced spin gap and solitons

In the following we discuss the response of the $S= 12$ spin chains to external magnetic fields. Concerning the dependence of the specific-heat coefficient γ for an antiferromagnetic $S= 12$ Heisenberg chain on an applied magnetic field B, one would expect deviations from γ(B=0) of the order (B/J)², i.e. about 1% at $4 T$ uniformly for all temperatures with k_BT/J⪡1. As is demonstrated in Fig. 5, the behavior of the specific heat is quite different.

Above $2 K$ changes in γ are indeed comparatively small. At

Ferromagnetic interchain coupling and spin-glass freezing

The anisotropy of the magnetic susceptibility of a single-domain Yb₄As₃ crystal was first measured by Aoki et al. from room temperature down to $2 K$ in a commercial SQUID magnetometer by applying uniaxial pressure along one of the $〈1 1 1〉$ directions in an acrylic resin pressure cell [8], [51], see Fig. 14. In this measurement, the single-domain formation was almost perfect since (1) with increasing uniaxial pressure a saturation of the pressure-induced anisotropy $χ_{||} (15 K)/χ_{⊥} (15 K)$ was observed (χ_||,

Resistivity and magnetoresitivity

The electrical resistivity of Yb₄As₃,ρ(T), was reported to follow a T² law between 2 and $100 K$ with a large coefficient $A≈0.75 μΩ cm / K^{2}$ that fulfills (within a factor of 2) the Kadowaki–Woods scaling [5] found for typical heavy-fermion metals. However, the low carrier concentration of only about 0.001 per formula unit [5] excludes the usual Kondo effect underlying the formation of heavy quasiparticles in metallic strongly correlated electron systems. Light [m=(0.6…0.8)m₀ [57], m₀: free-electron

Conclusion and outlook

We have presented an interpretation of the exceptional thermodynamic, magnetic and transport properties of Yb₄As₃ and its Sb and P substituted crystals. These mixed-valent pnictides exhibit a charge ordering of Yb²⁺ and Yb³⁺ driven by intersite Coulomb interactions and a deformation potential coupling to the lattice. This transition is of central importance for its low-temperature physical properties. The observation of spin excitations which can be described by the des Cloizeaux–Pearson

Uncited Reference

[65]

Acknowledgements

We would like to thank Prof. P. Fulde for long-standing fruitful cooperations in the field of strongly correlated electron systems. We also want to thank Prof. K. Ueda for various valuable discussions.

References (65)

E.J.W. Verwey et al.
Physica
(1941)
A. Ochiai et al.
Physica B
(1997)
A. Ochiai et al.
J. Magn. Magn. Matter
(1995)
H. Aoki et al.
Physica B
(1997)
R.J. Gambino
J. Less-Common Met.
(1967)
G. Wortmann et al.
J. Magn. Magn. Mater.
(1986)
A. Ochiai et al.
J. Magn. Magn. Mater.
(1985)
K. Neumaier et al.
Physica B & C
(1981)
K. Iwasa et al.
J. Magn. Magn. Mater.
(1998)
M. Kohgi et al.
Physica B
(1997)

K. Iwasa et al.

Physica B

(2000)

O. Nakamura et al.

Physica B

(1991)

R. Helfrich et al.

J. Magn. Magn. Mater.

(1998)

M. Kohgi et al.

Physica B

(1999)

H. Aoki et al.

Physica B

(2000)

H. Matsui et al.

Physica B

(1998)

J. des Cloizeaux et al.

Phys. Rev.

(1962)

P. Fulde

Ann. Phys.

(1997)

A. Yaresko et al.

Phys. Rev. B

(2000)

A. Ochiai et al.

J. Phys. Soc. Japan

(1990)

A. Ochiai et al.

JJAP Series

(1998)

H. Aoki, Ph.D. Thesis, Tohoku University, 2000,...

P. Bonville et al.

J. Phys. I (France)

(1994)

S. Suga et al.

J. Phys. Soc. Japan

(1989)

A. Ochiai, Ph.D. Thesis, Tohoku University, 1988,...

M. O'Keeffe et al.

Acta Crystallogr. A

(1977)

P. Fulde et al.

Europhys. Lett.

(1995)

K. Takegahara et al.

J. Phys. Soc. Japan

(1991)

T. Goto et al.

Phys. Rev. B

(1999)

J. Labbé et al.

J. Phys. France

(1966)

M. Rams et al.

Hyperfine Interactions

(1996)

S. Suga et al.

J. Phys. Soc. Japan

(1998)

Cited by (27)

Field-dependent specific-heat of the pure and diluted 4f electron system Yb<inf>4</inf>As<inf>3</inf>
2007, Inorganica Chimica Acta
The experimental field-dependent specific heat of the polydomain pure Yb₄As₃ and diluted (Yb_1−xLu_x)₄As₃ (x = 0.01, 0.03) systems is presented and compared with that calculated by the numerical quantum transfer-matrix method. The simulations have been performed using the S = 1/2 antiferromagnetic Heisenberg model with the transverse staggered field (appearing as a result of the antisymmetric Dzyaloshinskii–Moriya interaction) and a uniform magnetic field perpendicular to the staggered field. In the model calculations the fixed microscopic parameters have been taken and the impurity distribution has been considered. A significant improvement with respect to the previous results is shown.
Transfer matrix simulation technique: Effectiveness and applicability to the low-dimensional magnetic spin systems
2006, Journal of Computational and Applied Mathematics
The deterministic quantum transfer-matrix (QTM) technique, its mathematical background, effectiveness and applicability to the real physical low-dimensional magnetic systems are presented. Modelling is based on the Heisenberg Hamiltonian which describes the macroscopic Haldane-gap and molecular-based spin $S = 1$ chains, small size magnetic clusters embedded in some supramolecules and other interesting compounds. Using QTM, the spin degrees of freedom are accurately taken into account, yielding the thermodynamical functions at finite temperatures. The finite-temperature results for some isotropic and anisotropic systems as well as for systems with uniform and non-uniform interactions are reviewed. For Yb₄As₃ with antisymmetric interactions new results are presented—the field-dependent specific heat for finite chains and the field dependence of the energy gap. In order to demonstrate the effectiveness and applicability of the method to modelling of non-magnetic impurity effects, variation of the QTM approximants is shown for finite segments.
As the computational complexity of our problems is exponential, the efficiency of parallelization using the Message Passing Interface (MPI) system library was analysed and estimated as close to $100 %$ for our platform SGI Origin 3800 with 64 processor units. For the quantum chain simulations, both the memory and CPU bound for $k_{B} T / J ⩽ 0.1$ was established. For the finite ring simulations, the CPU time resources imposed the limits.
Strongly correlated electrons
2006, Solid State Physics - Advances in Research and Applications
Field-dependent specific heat and magnetization for the S=1/2 antiferromagnetic chain Yb<inf>4</inf>As<inf>3</inf>: Simulation and experiments
2005, Journal of Magnetism and Magnetic Materials
The $S = \frac{1}{2}$ antiferromagnetic Heisenberg model with the transverse staggered field and uniform magnetic field perpendicular to the staggered field is applied to the semimetallic compound Yb₄As₃. The field-dependent specific heat for infinite and finite chains as well as the magnetization for infinite chains are calculated by the numerical quantum transfer-matrix method. Specific heat data for polydomain samples of Yb₄As₃ and $({Yb}_{0.99} {Lu}_{0.01})_{4} {As}_{3}$ at $B = 12 T$ are presented and compared with numerical results obtained for microscopic parameters taken from theoretical predictions. Magnetization data for single domain and polydomain samples of Yb₄As₃ are also compared with simulation results.
Thermal conductivity of the one-dimensional S=1/2 antiferromagnet Yb <inf>4</inf>(As<inf>1-x</inf>P<inf>x</inf>)<inf>3</inf> (x = 0 and 0.3)
2004, Journal of Magnetism and Magnetic Materials
The thermal conductivity κ of Yb₄(As_1−xP_x)₃ (x=0 and 0.3) was measured in the temperature range between 0.1 and 7 K in applied magnetic fields up to 8 T. The fact that κ(T) follows, between 0.4 and 3 K, the relation aT+bT² confirms our earlier interpretation of the dominating role of magnons both as heat carriers and as scatterers for the phonons. Above 1 K, κ decreases with increasing magnetic field, the opening of a gap in the magnon-excitation spectrum being a possible explanation of this behavior.
Antiferromagnetic interactions in the semimetallic Yb<inf>4</inf>As <inf>3</inf>: Field-dependent specific heat and magnetization data
2004, Journal of Magnetism and Magnetic Materials
The $S= 12$ antiferromagnetic Heisenberg model with the Dzyaloshinsky–Moriya interaction is applied to a semimetallic compound Yb₄As₃. The field dependent specific heat and the magnetization of this model are calculated by the numerical quantum transfer-matrix method and compared with experiment. New specific heat experimental results for the polydomain sample in the field applied are presented and compared with the theoretical predictions obtained without adjustable microscopic parameters.

View all citing articles on Scopus

^☆: Dedicated to Professor Dr. Erwin Müller-Hartmann on the occasion of his 60th birthday.

View full text

Low-energy excitations of the semimetallic one-dimensional S=1/2 antiferromagnet Yb4As3☆

Abstract

Introduction

Section snippets

Charge-ordering transition

Low-temperature thermodynamic and transport properties at B=0: magnons

Field-induced spin gap and solitons

Ferromagnetic interchain coupling and spin-glass freezing

Resistivity and magnetoresitivity

Conclusion and outlook

Uncited Reference

Acknowledgements

Physica

Physica B

J. Magn. Magn. Matter

Physica B

J. Less-Common Met.

J. Magn. Magn. Mater.

J. Magn. Magn. Mater.

Physica B & C

J. Magn. Magn. Mater.

Physica B

Physica B

Physica B

J. Magn. Magn. Mater.

Physica B

Physica B

Physica B

Phys. Rev.

Ann. Phys.

Phys. Rev. B

J. Phys. Soc. Japan

JJAP Series

J. Phys. I (France)

J. Phys. Soc. Japan

Acta Crystallogr. A

Europhys. Lett.

J. Phys. Soc. Japan

Phys. Rev. B

J. Phys. France

Hyperfine Interactions

J. Phys. Soc. Japan

Low-energy excitations of the semimetallic one-dimensional S=1/2 antiferromagnet Yb₄As₃☆