Spin Density Wave Ground State Research Articles

Overhauser’s spin-density wave in exact-exchange spin-density functional theory

The spin density wave (SDW) state of the uniform electron gas is investigated in the exact exchange approximation of noncollinear spin density functional theory (DFT). Unlike in HartreeFock theory, where the uniform paramagnetic state of the electron gas is unstable against formation of the spin density wave for all densities, in exact-exchange spin-DFT this instability occurs only for densities lower than a critical value. It is also shown that, although in a suitable density range it is possible to find a non-interacting SDW ground state Slater determinant with energy lower than the corresponding paramagnetic state, this Slater determinant is not a self-consistent solution of the Optimized Effective Potential (OEP) integral equations of noncollinear spin-DFT. A selfconsistent solution of the OEP equations which gives an even lower energy can be found using an excited-state Slater determinant where only orbitals with single-particle energies in the lower of two bands are occupied while orbitals in the second band remain unoccupied even if their energies are below the Fermi energy.

Absence of Transition in Photoexcited States across the One-Dimensional CDW–SDW Phase Boundary

We theoretically investigate how the photoexcited states change across the phase boundary between the charge density wave (CDW) and the spin density wave (SDW) states in the one-dimensional (1D) and the two-dimensional (2D) Pariser–Parr–Pople models in the strong interaction case. In the 1D case, the CDW (singlet spin pair) droplet states dominate light absorption spectrum in the SDW (CDW) ground state region near the phase boundary. These photoexcited states exhibit crossover behavior across the phase boundary, that is, the density of the CDW region gradually increases across the phase boundary from the SDW to the CDW ground state region. On the contrary, in the 2D case, the bound holon–doublon (singlet spin) pair state dominates the light absorption spectrum, and the quantum fluctuations of the CDW or the singlet spin pair domain are negligible in the dominant photoexcited state even near the phase boundary. As a result, the transition occurs in the dominant photoexcited state at the ground state phase ...

Spin‐density‐wave gap in (TMTSF)2PF6 probed by reflection‐type terahertz time‐domain spectroscopy

AbstractWe report on a development of the reflection‐type terahertz time‐domain spectroscopy system and apply it to determine the conductivity spectra of the spin density wave (SDW) ground states in (TMTSF)2PF6. We take special care over optimizing the spatial resolution of the measurement system in order to investigate the tiny sample and also for correcting the phase error of the measurement. We observe a distinct reduction of the optical conductivity below ∼65 cm–1, which is a clear indication of SDW gap formation with metal–insulator transition. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Low-frequency dielectric response in the quasi-one-dimensional organic conductor (TMTSF)2PF6

Abstract A unique and rare opportunity of revealing the nature of the spin-density-wave (SDW) fluctuation in the quasi-one-dimensional organic conductor (TMTSF) 2 PF 6 has been provided by our AC impedance measurements above the SDW transition temperature. A close resemblance of the low-frequency dielectric response in the range between 20 K and the temperature of maximum resistivity T max ∼ 80 K to that in the SDW ground state was revealed, with quite compatible exponents for their power law dependencies. The SDW fluctuation has thus been identified in the 2D Fermi liquid regime, which can be regarded as a precursor phase of the SDW ground state.

Equilibrium low temperature heat capacity of the spin density wave compound (TMTTF)2Br: effect of a magnetic field

We have investigated the effect of the magnetic field (B) on the very low-temperature equilibrium heat capacity ceq of the quasi-1 D organic compound (TMTTF)2Br, characterized by a commensurate Spin Density Wave (SDW) ground state. Below 1K, ceq is dominated by a Schottky-like contribution, very sensitive to the experimental time scale, a property that we have previously measured in numerous DW compounds. Under applied field (in the range 0.2- 7 T), the equilibrium dynamics, and hence ceq extracted from the time constant, increases enormously. For B = 2-3 T, ceq varies like B2, in agreement with a magnetic Zeeman coupling. Another specific property, common to other Charge/Spin density wave (DW) compounds, is the occurrence of metastable branches in ceq, induced at very low temperature by the field exceeding a critical value. These effects are discussed within a generalization to SDWs in a magnetic field of the available Larkin-Ovchinnikov local model of strong pinning. A limitation of the model when compared to experiments is pointed out.

Electron states and the spin density wave phase diagram in Cr(1 1 0) films

Chromium films offer an excellent system to study the impact of dimensional confinement on physical properties associated with the spin-density-wave (SDW) ground state observed in bulk materials. These properties are also of some technological importance since chromium is a common component of thin film magnetic structures. We prepared chromium (1 1 0) films of high crystalline quality on a W(1 1 0) substrate with a wedge-shaped thickness profile so that the impact of confinement can be systematically studied. We have characterized these films using a combination of low-energy electron diffraction and microscopy as well as high-resolution angle-resolved photoemission spectroscopy. We have probed the Fermi surface and the nesting vectors therein that are relevant to the SDW ground state. We find these to predict accurately the observed bulk SDW periodicity. We have also characterized the SDW periodicity in the film directly by measuring the splitting between backfolded bands, and we find that this periodicity deviates markedly from the bulk periodicity for thinner films at higher temperatures. We have systematically mapped the SDW incommensurability and phase diagram as a function of both film thickness and temperature. We find commensurate and incommensurate phases that are separated by nearly continuous transitions. Our results suggest a simple model to explain the delicate interplay between commensurate and incommensurate phases that involves a balance between SDW stabilization energy and surface and interface energetics.

Unusual magnetic field-induced transition in the low temperature (T< 1 K) SDW ground state of (TMTSF)2PF6

We have observed a strong sensitivity to low magnetic field (H<0.5T) of the low-temperature specific heat of (TMTSF)2PF6 in its spin-density wave ground state. The mostly pronounced manifestation is a sharp maximum at H = 0.2 T in the amplitude of Shottky anomaly contribution which dominates the heat capacity below 0.3 K. This effect is independent of the field direction for H // a or b' crystal axis.

Spin waves in La2CuO4: band structure and correlation effects

AbstractWe calculate the antiferromagnetic spin wave dispersion in the half‐filled (electronic density n = 1) Hubbard model for a two‐dimensional square lattice, using the random phase approximation (RPA) in a broken symmetry (spin density wave) ground state. Our results for the spin wave dispersion, ω (q), are compared with high‐resolution inelastic neutron scattering performed on La2CuO4. The effects of different band structures and different values of the on‐site Coulomb interaction on the spin wave spectrum are studied. Particular attention is put on the high energy dispersion values ω (π/2, π/2) and ω (0, π).

Long-time heat release in the quasi-1D conductor (TMTSF)2PF6 at low temperatures

We have measured the heat capacity and the heat release of the quasi-1D conductor (TMTSF)2PF6 in its spin-density wave ground state. Below 1 K the presence of low-energy excitations is at the origin of slow heat release over time scales from about 1 s up to 105 s. In a first attempt, we analyzed this behaviour with a modified version of the standard tunneling model used in the case of amorphous solids, introducing a short-time cut-off in the distribution of the relaxation times of tunneling states. A remarkable feature of the heat release in (TMTSF)2PF6 is its high absolute value, which is 3–4 orders of magnitude larger than in structural glasses. The heat capacity contains a Schottky and a quasi-linear term.

Magnetic field influence on the low temperature heat capacity and heat release of (TMTSF)2PF6

We have measured under applied magnetic field the heat capacity c p and heat release $${\dot Q}$$ of the quasi-1D conductor (TMTSF)2PF6 in its spin density wave (SDW) ground state. The low-temperature heat capacity (T < 0.5 K) is dominated by a Schottky anomaly contribution. A corresponding term was also found for the heat release. In this T-range both properties are strongly sensitive to moderate magnetic fields (i.e., below 0.5 T): their amplitudes have a sharp maximum for H c=0.2 T. We show that the corresponding density of two-level states N S undergoes a sharp maximum at H c, which rules out an extrinsic origin for the two-level states. Instead we suppose an intrinsic origin, such as defects of commensurability of the SDW, as the (slow) excitations related to the domain walls. This effect is found to be independent on the field orientations H ∥ a and H ⊥ a.

SDW in the 2D Compound CuFeTe2

In a previous work (ICAME'97) we presented the Mossbauer results for a non-stoichiometric sample of the quasi-two-dimensional (2D) dichalcogenide CuFeTe2, where a Spin Density Wave (SDW) ground state with T SDW=256±15 K was proposed. Here we report the study of the magnetic and electric properties determined by magnetic susceptibility, Mossbauer spectroscopy and resistance measurements, of an almost stoichiometric sample prepared by the vertical Bridgman growth technique. The SDW behavior is supported by the results obtained by the following different techniques: Magnetic susceptibility: A magnetic transition is observed at T SDW=308 K with a Pauli paramagnetic behavior above this temperature. Mossbauer effect: The shape of the spectra and the thermal evolution of the hyperfine field are characteristic of the SDW's in quasi-2D systems. Electrical resistance: There is a metal–semiconductor transition along the layers as the temperature decreases indicating the opening of a gap at the Fermi level.

Observation of charge-density wave domains on the Cr(110) surface by low-temperature scanning tunneling microscopy

We have studied the Cr(110) surface with low-temperature scanning tunneling microscopy at 6 to 145 K. For tunneling voltages below +/-150 mV we observe a surface charge-density wave (CDW) with a wavelength of 42 A and wave fronts aligned with the [001] in-plane direction. The observed wave pattern is identified as the surface projection of the bulk CDW's arising from the spin-density wave ground state of Cr with the Q vector parallel to [100] and [010], respectively. The bulk CDW with Q parallel to the [001] in-plane direction appears, however, to be strongly suppressed at the Cr(110) surface.

Specific heat measurementsof the lattice contribution and the spin-density-wave andanion-ordering transitions in the (TMTSF)2ClO4 salt (TMTSF≡tetramethyltetraselenafulvalene)

The specific heat of the quasi-one-dimensional organic compound (TMTSF)2ClO4 was measured between 1.9 and 35 K for two statescorresponding to the metallic/superconducting ground state and theinsulating spin-density-wave (SDW) ground state at low temperature,by varying the cooling conditions through the anion-ordering(AO) transition at 24 K. These are the first thermodynamicalmeasurements of the SDW ground state. Like in the previouslyinvestigated compounds (TMTSF)2X, with X = PF6 andAsF6, and (TMTTF)2Br (where TMTTF≡tetramethyltetrathiafulvalene), the lattice specific heat showsstrong deviations from a Debye behaviour, which can be explained bythe quasi-one-dimensional structural character. Bumps in C/T3occur at T = 3.5-4 K and 5 K for the quenched SDW and relaxedmetallic states respectively; these are in good agreement with thefrequencies of low-lying modes detected by infrared spectroscopy forthe metallic sample. In addition, analysis of the latticecontribution suggests a Tα (α = 2.7) acousticcontribution for T≳2 K, ascribed to the lowdimensionality of the structure. The SDW transition was detected atTc = 4.5 K, as expected from the high value of thequenching rate (of 3.3 K s-1) through the AO transition(the amplitude of the anomaly represents about 3% of the total heatcapacity). The AO transition was investigated either by decreasingthe temperature for the slow-cooled sample or by reheating, at asimilar rate, for the quenched sample; the specific heat anomalies areidentical for the two procedures, due to reordering annealingeffects on reheating, a phenomenon previously investigated by x-rayexperiments. Surprisingly, the entropy under the AO anomaly isRln (4/3), much lower than the Rln 2 value expected for the twopossible configurational orientations of the perchlorate ion in thedisordered state. Similar low values of the entropy have beenpreviously measured for the perrhenate (ReO4) and BF4 salts.

Full potential calculations of the spiral spin density wave ground state of ?-Fe

All previous ab initio calculations of spiral spin density waves (SSDW) have used the atomic sphere approximation (ASA) in which not only is the charge density approximated by its spherical average, but the magnetization direction is also held fixed within each Wigner–Seitz sphere. Using the Vanderbilt ultrasoft pseudopotential method, we have performed the first full potential calculations of a system with a SSDW ground state, γ-Fe. We report calculations made using the local spin density approximation (LSDA) as well as two forms of the generalized gradient approximation (GGA) for the exchange–correlation (xc) energy density functionals. These calculations were performed for SSDW wave vectors q=(2π/a)(α,0,0) and q=(2π/a)(1,γ,0) with the ground state q found close to (2π/a)(0.55,0,0) for both xc functionals. These as well as the ASA calculations failed to obtain the experimental value, q=(2π/a)(1,0.13,0). Interesting results were obtained for the angle of the magnetization vector (in the xy plane), \documentclass{article}\usepackage{amsbsy}\pagestyle{empty}\begin{document}$\varphi(\mathbf{r})=\mathbf{q}\,\boldsymbol{\cdot}\,\mathbf{r}+\hat{\varphi}(\mathbf{r})$\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$e^{i\hat{\varphi}(\mathbf{r})}$\end{document} is a periodic function of r that is calculated self-consistently. We attribute the failure to obtain the experimental ground state q to the fact that the LSDA and GGA depend upon the local magnetization and are oblivious to the variation of its direction. A term proportional to ∣∇φ(r)∣2 is derived that, when added to the LSDA, improves agreement with experiment. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 940–950, 2000

Single-particle and spin-density wave charge dynamics in (TMTSF)2PF6 and (TMTSF)2AsF6 : A comparative overview

We present the results of DC and AC (100 mHz - 1MHz) electrical transport measurements in low and lugh electric fields performed in the spin-density wave (SDW) state of the Bechagaards salts (TMTSF) 2 PF 6 and (TMTSF) 2 AsF 6 . We argue that a degree of complex structure of the SDW ground state which is unfolded in a particular experiment depends strongly on the chosen experimental probe and the crystal measured.

Anisotropy in the optical response of (TMTTF) 2X (X=PF 6 and Br) Bechgaard salts

The optical properties of the linear chain spin-Peierls (TMTTF) 2Br and spin-density-wave (TMTTF) 2PF 6 compounds were examined in a wide frequency range in their normal state and also in the spin-Peierls and spin-density wave ground state. While the low-temperature spectra along the chain direction ( E∥ a) are not affected by the onset of the various ground states, we have identified a correlation gap in the normal state due to electron–electron interactions and Umklapp scattering for both compounds. In the polarization direction perpendicular to the chains ( E∥ b′) the absence of any temperature dependence and any plasma edge in the optical spectra provide evidence for electron confinement on individual chains.

Acoustical properties of(TMTSF)2PF6in the spin-density-wave ground state

We have carried out ultrasonic investigations of ${(\mathrm{TMTSF})}_{2}{\mathrm{PF}}_{6}$ in the spin-density-wave (SDW) ground state. Some features for the elastic behavior of the SDW state are found. One of the acoustic modes shows a jump in the sound velocity at the critical temperature of the SDW transition ${(T}_{\mathrm{SDW}}\ensuremath{\approx}12\mathrm{K})$ and a relaxation peak in the attenuation of sound just below ${T}_{\mathrm{SDW}}.$ From this peak we have estimated the characteristic relaxation time of the spin fluctuations along the b axis to be ${t}_{0}=2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\mathrm{s}.$ The sound velocity of another acoustic mode changes with temperature as the square of the order parameter. Besides a maximum just below ${T}_{\mathrm{SDW}}$ the attenuation of this mode has an exponential behavior at low temperatures and yields an energy gap value equal to $2\ensuremath{\Delta}(0)\ensuremath{\approx}96\mathrm{K},$ which is much larger than the BCS value $2\ensuremath{\Delta}(0)\ensuremath{\approx}43\mathrm{K}.$ In addition there is an acoustic mode which displays a slow decrease of the sound velocity in the SDW state. We have also studied the influence of a magnetic field applied along the ${c}^{*}$ axis on the acoustic properties of ${(\mathrm{TMTSF})}_{2}{\mathrm{PF}}_{6}:$ ${T}_{\mathrm{SDW}}$ increases in the magnetic field. We discuss our experimental results in the frame of theoretical considerations which are based on the assumption that phonons influence the exchange interaction between the spins of the conducting electrons and thus couple to the SDW (magnetoelastic coupling). In our model, the temperature behavior of the sound velocity and the attenuation of sound is related to the real and imaginary parts of the dynamical spin susceptibility. This model allows us to classify the temperature behavior of different acoustic modes and to explain the observed anomalies in the sound velocity and the attenuation of sound in the SDW ground state.

Interplay of spin density wave and superconductivity with different pairing symmetry

A model study for the coexistence of the spin density wave and superconductivity is presented. With reference to the recent angle-resolved photo-emission experimental data in high- T c cuprates, presence of the nested pieces of bands is assumed. The single-band Hubbard model, therefore, when treated within the Hatree–Fock mean field theory leads to a spin density wave (SDW) ground state. The superconductivity (SC) is assumed to be due to a generalised attractive potential with a separable form without specifying to any particular origin. It therefore allows a comparative study of the coexistence of superconductivity of different order parameter symmetry with the spin density wave state. We find that the phase diagram, comprising of the amplitudes of the respective gaps (SC and SDW) vs. band filling resembles that of the high- T c cuprates only when the order parameter of the superconducting phase has d-wave symmetry. Thermal variation of different order parameters (e.g., SC and SDW) also shows interesting coexistence and reentrance behaviors that are consistent with experimental observations, specially for the borocarbides.

On the order parameter of Bechgaard salts

At low temperature the one-dimensional Bechgaard salts (TMTSF) 2X undergo phase transitions to superconducting and spin density wave (SDW) ground states depending on external pressure and magnetic field. Both phases still have a number of unresolved problems. The absorption processes can be described by a common formalism based on the BCS theory with different coherence factors applying to different broken symmetry ground states. The optical conductivity and ultrasonic attenuation in the SDW phase are discussed as examples.

Microscopic evidence for a partially gapped density wave state in α-(BEDT–TTF) 2KHg(SCN) 4 in high magnetic fields

We present NMR measurements on α-(BEDT–TTF) 2KHg(SCN) 4, in which the six inner carbon sites of BEDT–TTF are labeled with the 13C isotope, at low temperatures and in magnetic fields up to 28.8 T. We find, based on microscopic measurements which probe the center of the primary molecular orbital, that the density wave ground state of this system persists up to fields well above the so-called “kink field”, a hysteretic transition observed in transport near 23 T below 6 K. The main implication of this result is that in the low temperature limit, the ground state of this material is not fully metallic, but still partially gapped, even to 28.8 T. We obtain a BCS-like relationship between the transition temperature and the energy gap, as derived from the spin relaxation measurements using a simple model. Further, the 13C NMR spectrum is relatively insensitive to crossing the phase boundary, a result that does not support the notion that the ground state is a conventional spin density wave ground state.