Low-temperature heat transport of spin-gapped quantum magnets

This article reviews low-temperature heat transport studies of spin-gapped quantum magnets in the last few decades. Quantum magnets with small spins and low dimensionality exhibit a variety of novel phenomena. Among them, some systems are characteristic of having quantum-mechanism spin gap in their magnetic excitation spectra, including spin-Peierls systems, S=1 Haldane chains, S= 1/2 spin ladders, and spin dimmers. In some particular spin-gapped systems, the XY-type antiferromagnetic state induced by magnetic field that closes the spin gap can be described as a magnon Bose-Einstein condensation (BEC). Heat transport is effective in probing the magnetic excitations and magnetic phase transitions, and has been extensively studied for the spin-gapped systems. A large and ballistic spin thermal conductivity was observed in the two-leg Heisenberg S=1/2 ladder compounds. The characteristic of magnetic thermal transport of the Haldane chain systems is quite controversial on both the theoretical and experimental results. For the spin-Peierls system, the spin excitations can also act as heat carriers. In spin-dimer compounds, the magnetic excitations mainly play a role of scattering phonons. The magnetic excitations in the magnon BEC systems displayed dual roles, carrying heat or scattering phonons, in different materials.     

Translation-rotation coupling and heat transfer in orientationally-disordered phase of CCl4

The isochoric thermal conductivity of an orientationally-disordered phase of CCl₄ is analysed within a model in which heat is transferred by phonons and above the phonon mobility edge by ”diffusive” modes migrating randomly from site to site. The mobility edge ω₀ is found from the condition that the phonon mean-free path cannot become smaller than half the phonon wavelength. The contributions of phonon-phonon, one-, and two-phonon scattering to the total thermal resistance of solid CCl₄ are calcualted under the assumption that the different scattering mechanisms contribute additively. An increase in the isochoric thermal conductivity with temperature is explained by suppression of phonon scattering at rotational excitations due to a decrease in correlation in the rotation of neighbouring molecules.     

Quasi-one-dimensional magnons in an intermetallic marcasite

We present inelastic neutron scattering measurements and first principles calculations examining the intermetallic marcasite CrSb(2). The observed spin-wave dispersion implies that the magnetic interactions are strongly one-dimensional with antiferromagnetic chains parallel to the crystalline c axis. Such low-dimensional excitations are unexpected in a semiconducting intermetallic system. Moreover, we observe a clear anisotropic thermal conductivity indicating that the magnetic anisotropy enhances thermoelectric properties along particular crystallographic directions.     

Thermal properties of carbon nanotubes and nanotube-based materials

The thermal properties of carbon nanotubes are directly related to their unique structure and small size. Because of these properties, nanotubes may prove to be an ideal material for the study of low-dimensional phonon physics, and for thermal management, both on the macro- and the micro-scale. We have begun to explore the thermal properties of nanotubes by measuring the specific heat and thermal conductivity of bulk SWNT samples. In addition, we have synthesized nanotube-based composite materials and measured their thermal conductivity. The measured specific heat of single-walled nanotubes differs from that of both 2D graphene and 3D graphite, especially at low temperatures, where 1D quantization of the phonon bandstructure is observed. The measured specific heat shows only weak effects of intertube coupling in nanotube bundling, suggesting that this coupling is weaker than expected. The thermal conductivity of nanotubes is large, even in bulk samples: aligned bundles of SWNTs show a thermal conductivity of >200 W/m K at room temperature. A linear K(T) up to approximately 40 K may be due to 1D quantization; measurement of K(T) of samples with different average nanotube diameters supports this interpretation. Nanotube–epoxy blends show significantly enhanced thermal conductivity, showing that nanotube-based composites may be useful not only for their potentially high strength, but also for their potentially high thermal conductivity. Received: 17 October 2001 / Accepted: 3 December 2001 / Published online: 4 March 2002     

Thermal transport associated with ballistic phonons in asymmetric quantum structures

Using the scattering matrix method, we investigate the thermal conductance associated with ballistic phonons at low temperatures in asymmetric quantum structures. The results show that when the structure is an ideal quantum wire, the universal value π ² κ _B²(3h) can be observed at very low temperatures. However, for asymmetric quantum structure, the thermal conductance is less than the universal value π ² κ _B²(3h), even at T → 0. The results also show that the thermal conductance is strongly dependent on the transport direction. The rectification effect can be observed in the asymmetric structure and can be adjusted by changing the structural parameters. A brief analysis of these results is given.      

Magnons coherent transmission and heat transport at ultrathin insulating ferromagnetic nanojunctions

A model calculation is presented for the magnons coherent transmission and corresponding heat transport at insulating magnetic nanojunctions. The system consists of a ferromagnetically ordered ultrathin insulating junction between two semi-infinite ferromagnetically ordered leads with ideally flat crystal interfaces. The ground state of the system is depicted by an exchange Hamiltonian neglecting smaller dipolar and anisotropy terms. The spin dynamics are analyzed using the equations of motion for the spin precession displacements, valid in the limit of low temperatures compared to an order-disorder transition temperature characteristic of the system. The coherent transmission and reflection spectra at the nanojunction boundary are calculated in the Landauer-Buttiker formalism using the matching theory, for all the magnons in the lead bulk, at arbitrary angles of incidence on the boundary, and for variable temperatures. The model calculations yield the thermal conductivity κ _m due to the magnons coherent transmission between the two leads maintained at slightly different temperatures. The model is general, and is applied in particular to the Fe/Gd/Fe system to calculate the coherent transmission of magnons and their thermal conductivity at the junction boundary, for different thicknesses of the Gd junction and its corresponding magnetic order. The calculated results elucidate the comparison between the heat transport from magnons with that in parallel channels from electrons and phonons, at the nanojunction boundary.     

Spin thermal conductivity of the haldane chain compound Y(2)BaNiO(5)

We have measured the thermal conductivity of the spin S=1 chain compound Y(2)BaNiO(5). Analyzing the anisotropy of the thermal transport allows us to identify a definite spin-mediated thermal conductivity kappa(s) along the chain direction. The calculated spin-related energy diffusion constant D(E)(T) shows a broad peak around 120 K. Close to room temperature, D(E)(T) approaches the theoretically predicted high-temperature value, while scattering of spin excitations by magnetic impurities seems to be the major limiting factor of kappa(s) at low temperature.     

Magnetothermal transport in the spin-1/2 chains of copper pyrazine dinitrate

We present experiments on the thermal transport in the spin-1/2 chain compound copper pyrazine dinitrate Cu(C4H4N2)(NO3)2. The heat conductivity shows a surprisingly strong dependence on the applied magnetic field B, characterized at low temperatures by two main features. The first one appearing at low B is a characteristic dip located at muBB approximately kBT, that may arise from umklapp scattering. The second one is a plateaulike feature in the quantum critical regime, muB|B - Bc| < kBT, where Bc is the saturation field at T=0. The latter feature clearly points towards a momentum and field-independent mean free path of the spin excitations, contrary to theoretical expectations.     

Improved thermal relaxation method for the simultaneous measurement of the specific heat and thermal conductivity

A novel method for the simultaneous, high-resolution measurement of the specific heat c and the thermal conductivity κ is presented. A new experimental setup has been developed with special emphasis on the elimination of systematic errors arising from radiative heat loss. A self-consistent data evaluation method is implemented which takes the effects of the sample geometry on c and κ properly into account. The measurements were performed over a broad temperature regime from 3 K up to room temperature on three compounds from the family of strongly correlated electron systems. The differences in their thermal properties and their highly sample-dependent sizes and shapes demonstrate the extended scope of the proposed method.     

Anharmonic Excitations,Time Correlations and Electric Conductivity

We study the influence of anharmonic mechanical excitations of a classical ionic lattice on its electric properties. First, to illustrate salient features, we investigate a simple model, an one‐dimensional (1D) system consisting of ten semiclassical electrons embedded in a lattice or a ring with ten ions interacting with exponentially repulsive interactions. The lattice is embedded in a thermal bath. The behavior of the velocity autocorrelation function and the dynamic structure factor of the system are analyzed. We show that in this model the nonlinear excitations lead to long lasting time correlations and, correspondingly, to an increase of the conductivity in a narrow temperature region, where the excitations are supersonic soliton‐like. In the second part we consider the quantum statistics of general ion‐electron systems with arbitrary dimension and express ‐ following linear response transport theory ‐ the quantum‐mechanical conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the ion motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. An evaluation of the influenec of solitons predicts for 1D‐lattices a conductivity increase in the temperature region where most thermal solitons are excited, similar as shown in the classical Drude‐Lorentz‐Kubo framework. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electron transport in modulation-doped GaAs v-groove quantum wires

We report the growth of modulation-doped GaAs/Al_xGa_1−xAs v-groove quantum wires and structural, electrical and optical investigations of their electronic states and transport properties. By using alternative group III precursors on partially SiO₂ masked pre-patterned GaAs substrates, samples have been fabricated which permit electrical measurements of single isolated wire structures without the need for additional electron-beam lithography. Magneto-transport was measured as a function of tilt angle of the incident magnetic field to identify the formation of low-dimensional electron gases in different parts of the structure. Photoluminescence investigations reveal 1D and 2D confined states which show different carrier heating when electric fields are applied along the wire structure.     

Modification of the lattice thermal conductivity in silicon quantum wires due to spatial confinement of acoustic phonons

Lattice thermal conductivity in silicon quantum wires is theoretically investigated. The bulk of heat in silicon structures is carried by acoustic phonons within a small region in the first Brillouin zone. Our formalism rigorously takes into account modification of these acoustic phonon modes and phonon group velocities in free- and clamped-surface wires due to spatial confinement. From our numerical results, we predict a significant decrease (more than an order of magnitude) of the lattice thermal conductivity in cylindrical quantum wires with diameter D =  200 Å. The decrease is about two times stronger in quantum wires than in quantum wells of corresponding dimensions. Our theoretical results are in qualitative agreement with experimentally observed drop of the lattice thermal conductivity in silicon low-dimensional structures.     

Two-spinon and orbital excitations of the spin-Peierls system TiOCl

We combine high-resolution resonant inelastic x-ray scattering with cluster calculations utilizing a recently derived effective magnetic scattering operator to analyze the polarization, excitation energy, and momentum-dependent excitation spectrum of the low-dimensional quantum magnet TiOCl in the range expected for orbital and magnetic excitations (0-2.5?eV). Ti 3d orbital excitations yield complete information on the temperature-dependent crystal-field splitting. In the spin-Peierls phase we observe a dispersive two-spinon excitation and estimate the inter- and intradimer magnetic exchange coupling from a comparison to cluster calculations.     

Magnetic field enhancement of heat transport in the 2D Heisenberg antiferromagnet K2V3O8

The thermal conductivity and heat capacity of single crystals of the spin 1/2 quasi-2D Heisenberg antiferromagnet K(2)V(3)O(8) have been measured from 1.9 to 300 K in magnetic fields from 0 to 8 T. The zero field thermal conductivity data are consistent with resonant scattering of phonons by magnons near the zone boundary. Application of a magnetic field greater than 1 T, however, produces a new magnetic ground state with substantial heat transport by long wavelength magnons.     

Heat transfer in the plastic phases I and II of cyclopentane

Thermal conductivity of solid cyclopentane C₅H₁₀ has been measured at isochoric conditions in the plastic phases I and II for samples of different densities. Isochoric thermal conductivity is nearly constant in phase II and increases with temperature in phase I. Such behaviour is attributed to weakening of the translational orientational coupling which, in turn, leads to a decrease of phonon scattering on rotational excitations. The experimental data are described in terms of a modified Debye model of thermal conductivity with allowance for heat transfer by both low-frequency phonons and diffusive modes.     

Magnetic field dependence of the thermal conductivity in EuxSr1-xS

The thermal conductivity κ of two Eu_xSr_1-x single crystals (x = 0.25 and 0.54) was measured between 1.5 and 25 K. In magnetic fields of ≈ 7 T κ is enhanced for temperatures up to 20 K with respect to κ(B = 0). At 1.5 K, where the relative increase κ(B)/κ(0) is largest, this ratio is 1.5 for x = 0.54 and ≈ 4 for x = 0.25. Two possible mechanisms for this effect, i.e. freezing of phonon scattering by magnetic excitations in a magnetic field, and heat transport by field-induced magnons, are discussed.     

Thermal Conductivity of the Toda Lattice with Conservative Noise

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter γ. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length n of the chain according to κ(n)∼n ^α , with 0<α≤1/2. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent α of the divergence depends on γ.     

Influence of heat bath on the heat conductivity in disordered anharmonic chain

We study heat conduction in a one-dimensional disordered anharmonic chain with arbitrary heat bath by using extended Ford, Kac and Mazur (FKM) formulation, which satisfy the fluctuation-dissipation theorem. A simple formal expression for the heat conductivity κ is obtained, from which the asymptotic system-size (N) dependence is extracted. It shows κ∼N^α. As a special case we give the expression that κ∼N^1/2 for free boundaries, and κ∼ N^-1/2 for fixed boundaries, from which we can get the conclusion that the momentum conservation is a key factor of the anomalous heat conduction. Comparing with different ∇T, the heat conductivity shows large difference between the linear system and the nonlinear system.     

Low-temperature heat transport of the zigzag spin-chain compound SrEr2O4

Low-temperature thermal conductivity ($\kappa$), as well as the magnetic properties and specific heat, are studied for the frustrated zigzag spin-chain material SrEr$_{2}$O$_{4}$ by using single-crystal samples. The specific heat data indicate the long-range antiferromagnetic transition at $\sim 0.73 $ K and the existence of strong magnetic fluctuations. The magnetizations at very low temperatures for magnetic field along the $c$ axis (spin chain direction) or the $a$ axis reveal the field-induced magnetic transitions. The $\kappa $ shows a strong dependence on magnetic field, applied along the $c$ axis or the $a$ axis, which is closely related to the magnetic transitions. Furthermore, high magnetic field induces a strong increase of $\kappa $. These results indicate that thermal conductivity along either the $c$ axis or the $a$ axis are mainly contributed by phonons, while magnetic excitations play a role of scattering phonons.     

Phonon scattering by electrons and low energy excitations in a metallic glass

Measurements of the thermal conductivity of a superconducting metallic glass Zr₇₀Cu₃₀ in zero field and in a magnetic field exceeding the upper critical field allow a quantitative determination of the strength of the phonon-electron scattering for the first time in amorphous metals. The temperature dependence of the residual phonon scattering by localized low energy excitations is similar to that found in insulating glasses.