Commensurate Spin Density Wave Research Articles

High-pressure ultrasonic properties of spin-density-wave Cr–Re alloy single crystals

The pressure dependence of the elastic constants ( c ij ) of Cr–Re alloy single crystals, containing 0.3 and 0.5 at.% Re, are reported. For 0.3 at.% Re the concentration ( c) is below the triple point concentration ( c t) on the ( c– T) magnetic phase diagram. This crystal therefore remains in the incommensurate (I) spin-density-wave (SDW) antiferromagnetic phase at all temperatures below the ISDW–paramagnetic (P) Néel transition temperature ( T N). The pressure derivatives of the elastic constants, d c ij /d p, were measured for the Cr+0.3 at.% Re crystal as a function of temperature through T N. The Cr+0.5 at.% Re crystal has c> c t and exhibits an incommensurate–commensurate (I–C) SDW phase transition at a temperature T IC< T N on heating. In the case of this crystal d c ij /d p was studied at temperatures close to and above T IC. The acoustic mode Grüneisen parameters ( γ n ), which quantify the lattice vibrational anharmonicity, were calculated as a function of temperature from the d c ij /d p data for each crystal. These calculations indicate much larger coupling of the SDW to the long-wavelength longitudinal phonons than to the shear modes for both Cr–Re crystals. Longitudinal mode softening under applied pressure, due to strong magnetoelastic interactions between the SDW and the longitudinal acoustic phonons, in Cr+0.3 at.% Re at T< T N, gives nearly discontinuously way to extremely large mode stiffening as the crystal is heated through T N. γ n in the CSDW and pressure-induced ISDW phases of the Cr+0.5 at.% Re crystal shows unusual behaviour with temperature. This is particularly so for the shear mode Grüneisen parameters which are relatively large and negative just above T IC, implying significant shear mode softening under applied pressure. γ n (shear) then increases on further increasing the temperature of this crystal. In comparison, γ n (shear) for both the CSDW and pressure-induced ISDW phases of other Cr alloys, with c> c t, for instance Cr–Ru and Cr–Ir alloys, is near zero, slightly positive, and remains constant with temperature. The measurements on the Cr+0.5 at.% Re crystal suggest the existence of a new phase line, separating the ISDW phase present at atmospheric pressure from that induced from the CSDW phase by applying high pressure, on the pressure–temperature magnetic phase diagrams of dilute Cr alloys with c> c t. More experimentation, particularly high pressure neutron diffraction studies, are needed to verify this point.

Antiferromagnetic order of thin epitaxial Cr layers in an Fe/Cr(110) multilayer

We investigated the magnetic properties of thin Cr(110) layers in a (110)-oriented Fe/Cr multilayer consisting of 26-nm-thick Cr layers and 1.2-nm-thick Fe layers that were grown epitaxially on a V( 110) single crystal. Neutron-diffraction data reveal that the commensurate spin-density wave of the Cr layers is stable up to a temperature of 520 K. In the temperature range from 225 K to 175 K we observe a phase transition to the incommensurate spin-density wave. Measurements on the Cr{111} reflections show that the Fe/Cr multilayer is in a multidomain state with the Cr polarization being parallel to [100], [010], or [001]. The domains do not have equal probability. They are observed with a probability of 41%, 41%, and 18%, respectively. That means that there is a probability of 90% for the Cr polarization being perpendicular to the Fe magnetization that has its easy axis along [001].

Triangular lattices of charge-and spin-density waves in chemisorbed metal monolayers on the surface of diamond structure semiconductors

The electronic spectrum of a planar triangular lattice is analyzed, and the possible occurrence of charge (CDWs) and spin density waves (SDWs) in the lattice is discussed. Commensurate CDW and SDW structures of two types are considered in the weak and strong electron-electron interaction approximations. The CDW and SDW models are applied to the specific case of chemisorbed metal monolayers on the (111) surface of diamond structure semiconductors with a coverage close to 1/3.

Static magnetic susceptibility in (TMTTF) 2Br and (TMTSF) 2AsF 6

We report on the static magnetic susceptibility in the spin density wave (SDW) phase of (TMTTF) 2Br and (TMTSF) 2AsF 6. A decrease of the differential susceptibility of (TMTSF) 2AsF 6 was observed around 4 K. This anomaly indicates a difference of the spin canting above and below the critical temperature. In the measurements of magnetic susceptibility on the commensurate SDW phase of (TMTTF) 2Br, a large decrease of the spin susceptibility was observed above T SDW and non-activated-type behavior in the b′-axis susceptibility was observed below the spin-flop field at low temperature. The data are discussed on the basis of commensurability.

Spin density waves of thin Cr layers in Fe/Cr(1 1 0) multilayers

We investigated the magnetic properties of 26 nm thick Cr layers of an (1 1 0)-oriented Fe/Cr multilayer. Neutron diffraction measurements reveal that the commensurate spin-density wave is the stable phase at 300 K with the Cr polarization being perpendicular to the Fe magnetization. In the temperature range from 225 to 175 K we observe a phase transition to the incommensurate spin-density wave.

Slow energy relaxation at low temperature in quasi-1D organic conductors

We present a study of the slow dynamics in the heat relaxation at very low temperature (T < 1 K) in the nominally commensurate SDW compound (TMTTF) 2 Br, that we compare to the incommensurate SDW-(TMTSF) 2 PF 6 . Instead of a broad distribution of relaxation times g (log τ) in the PF 6 salt typical of glassy materials, the dynamics in the Br salt reveals almost discrete bands in the relaxation spectrum. A saturation towards equilibrium is reached very rapidly (within ∼20 mn) at T ∼ 100 mK in comparison with PF 6 (more than a few days for the same temperature).

Electronic topological transition in zinc metal? A 67Zn-Mössbauer investigation

The question concerning the existence of an electronic topological transition (ETT) in Zn metal under quasi-hydrostatic pressure at ∼6.6 GPa caused a considerable controversy in the literature. We briefly review low-temperature 67Zn-Mossbauer data and scalar-relativistic augmented plane wave calculations and give a consistent interpretation in terms of an ETT. To highlight some important aspects of the controversy two theoretical and two experimental publications will be discussed in more detail. At present the existence of an ETT in Zn metal is disputed both from an experimental and from a theoretical point of view. The suggestion of a transition to a commensurate spin-density wave at ∼6.6 GPa instead of an ETT may reconcile the seemingly contradictory results of 67Zn-Mossbauer experiments at 4.2 K and of room temperature inelastic neutron scattering measurements. However, it does not explain the anomalies found in theoretical calculations performed for Zn metal in this pressure range. Considerable experimental and theoretical efforts are required to confirm - or rule out - a spin-density-wave transition.

Slow dynamics of energy relaxation in the commensurate SDW ground state of (TMTTF)2Br

We present a study, of the slow dynamics in the heat relaxation at very low temperature (T < 1 K) in the nominally commensurate SDW compound (TMTTF) 2 Br, that we compare to the incommensurate SDW-(TMTSF) 2 PF 6 . Instead of a broad distribution of relaxation times g(log τ) in the PF 6 salt, the dynamics in the Br salt reveals almost discrete bands in the relaxation spectrum. A saturation towards equilibrium is reached very rapidly (within ∼ 20 mn) at T ∼ 100 mK in comparison with PF 6 (more than 10 hr for the same temperature).

Magnetic properties of the spin-density wave in (TMTSF)2X and (TMTTF)2Br

Magnetic properties of the spin density wave (SDW) phase in (TMTSF) 2 X (X=AsF 6 , PF 6 ) and (TMTTF) 2 Br were investigated through analyses of 1 H-NMR and static magnetization measurements. A divergent peak was observed, at the temperature T * well below the SDW transition temperature, in the 1 H spin-lattice relaxation rate in the incommensurate SDW phase of (TMTSF) 2 X. A decrease of the differential magnetic susceptibility of (TMTSF) 2 X with the field parallel to the a-axis was observed around T * . This anomaly indicates a difference of the spin canting above and below T * which divides the SDW phase. In the measurements of magnetic susceptibility on the commensurate SDW phase of (TMTTF) 2 Br, a large decrease of the spin susceptibility was observed above T SDW and non-activated type behavior in the b'-axis susceptibility is observed below the spin-flop field at low temperature. The data are discussed on the basis of commensurability.

Electrical and structural properties of Cr ion-implanted thin Au films

Cr metal ions with doses of 1×10 14–1×10 15 ions/cm 2 have been implanted at 125 keV into thin Au films prepared by DC magnetron sputtering. Electron diffraction patterns have revealed that all the films remain in the f.c.c. structure, indicating the formation of Au–Cr solid solution. The resistivity of the films were studied in the temperature range 100–330 K. The results show increase in the resistivity with respect to the unimplanted film as a result of the implantation. Some samples show two different types of resistivity anomalies, which are attributed to the occurrence of the antiferromagnetically incommensurate spin density wave and commensurate spin density wave structures.

Magnetoelastic effects and spin excitations inγ−Mnalloys

A two-band model which includes the magnetoelastic interaction is used to study the magnetization and spin dynamics of {gamma}-Mn alloys. As previously believed, single (S), double (D), and triple (T) spin-density wave (SDW) states are found in fct (c{lt}a and c{gt}a) and fcc (c=a) lattices, respectively. When the magnetoelastic coupling constant {kappa} exceeds the critical value {kappa}{sub c}, both the structural and magnetic phase transitions become first order. This critical value drops to zero at the triple point, where the commensurate and incommensurate SDW phase boundaries meet. In agreement with experiments on fct MnNi and fcc FeMn alloys, we find that the gap {Delta}{sub sw}(T) in the spin-wave dispersion is proportional to the 3/2 power of the sublattice magnetization M(T). For the noncollinear D and T SDW magnetic phases observed in MnNi and FeMn alloys, we find an additional class of collective modes. This class includes a Goldstone mode which is produced by the modified dispersion of holes not directly involved in the SDW. We also find high-frequency excitations with energies of order {Delta}, where 2{Delta}{approx}2 eV is the energy gap in the quasiparticle spectrum. Although these incoherent excitations have the same frequencies in the D and T SDW phases,more » their neutron-scattering cross sections should be 33{percent} larger in the TSDW phase. {copyright} {ital 1999} {ital The American Physical Society}« less

Spin-density waves and reorientation effects in thin epitaxial Cr films covered with ferromagnetic and paramagnetic layers

We report about synchrotron and neutron-scattering studies investigating incommensurate spin-density waves (I-SDW's) in epitaxially grown thin Cr(001) films, including surface and interface effects. These studies show that thin ferromagnetic cap layers of Fe, Ni, and Co with a thickness of only 2--3 nm have a strong effect on the propagation and orientation of the I-SDW's in Cr. For thick Cr films there exist essentially only transverse I-SDW's propagating parallel to the film plane with the spins oriented normal to the plane and at right angles to the in-plane magnetization of the ferromagnetic cap layers. With decreasing Cr thickness a different transverse I-SDW grows at the expense of the in-plane ones, now propagating normal to the plane and with spins parallel or antiparallel to the film magnetization. At a Cr thickness of about 250 \AA{}, the transverse out-of-plane I-SDW completely dominates the phase diagram of Cr. All other domains are suppressed and a spin-flip transition does not occur above 10 K in strong contrast to bulk. For in-plane propagation of the I-SDW we find a coexisting commensurate spin-density wave (C-SDW) which vanishes during the reorientation to out-of-plane propagation with Cr thickness. Finally, for Cr thicknesses well below the period of the I-SDW, the Cr can only order as a C-SDW. The behavior of the SDW's in thin Cr films with ferromagnetic cap layers can be understood in terms of competing interactions at the rough interfaces inducing frustration and by finite-size and strain effects. We have also investigated the effect of Cu and Pd cap layers on the SDW. The Cu cover is similar to a Cr/vacuum interface, whereas the effect of the Pd cover is intermediate between the ferromagnetic layers and Cu.

New spin-density waves systems:: Cu and Fe selenides and tellurides

57 Fe Mössbauer absorption measurements are reported indicating that CuFeSe 2 and CuFeTe 2 have both a ground state of spin-density waves (SDW) nature. For the selenide it is a transverse commensurate SDW with T N=71 K and for the telluride it is an incommensurate SDW with T N=308 K.

Spin-density-wave effects on the vibrational anharmonicity of acoustic phonons in Cr-Ir alloy single crystals

Measurements are reported of the dependences on hydrostatic pressure (p) of the elastic constants of Cr-Ir alloy single crystals containing 0.07 at.% and 0.20 at.% Ir. For the former concentration the alloy exhibits a transition from an incommensurate (I) spin-density-wave (SDW) to a paramagnetic state at the Néel temperature was studied as a function of temperature through . The concentration of the crystal is larger than the triple-point concentration on the Cr-Ir magnetic phase diagram and for this crystal there appears a phase transition from an ISDW to a commensurate (C) SDW at was measured for this crystal as a function of temperature through . The acoustic mode Grüneisen parameters were calculated for the two crystals as a function of temperature through (for ) and through (for ). Large negative Grüneisen parameters are observed in the ISDW and CSDW phases of . The results indicate stronger magnetoelastic interactions in the CSDW than in the ISDW phase of this crystal. It is shown that the strong magnetoelastic coupling in the ISDW and CSDW antiferromagnetic phases of the Cr-Ir system takes mainly place through volume effects.

Exact results related to the extended Hubbard model with increased interaction range in D &gt; 1 dimensions

Abstract Exact results related to extended Hubbard model containing couplings up to next-nearest-neighbour terms were deduced for restricted regions of parameter space in arbitrary D > 1 dimensions at half-filling and T = 0 temperature. Different types of commensurate charge-density waves and spin-density waves, a ferromagnetic domain and a phase separation region were found, the last being for the first time signalled at the level of approximation-free results in dimensions higher than one. In connection with other presented phases we extended their stability domains in comparison with previously published data. The deduced phase diagram is complete in the localized limit. The dependences on the interaction range and dimension were studied. The obtained results emphasize the importance of next-nearest neighbour terms in the development of ordered phases within the studied system.

Variational Monte Carlo study on the superconductivity in the two-dimensional Hubbard model

The possibility of superconductivity (SC) in the ground state of the two-dimensional (2D) Hubbard model was investigated by means of the variational Monte Carlo method. The energy gain of the d-wave SC state, obtained as the difference of the minimum energy with a finite gap and that with zero gap, was examined with respect to dependences on U, electron density ρ and next nearest neighbor transfer t′ mainly on the 10×10 lattice. It was found to be maximized around U=8 (the energy unit is nearest neighbor transfer t). It was shown to sharply increase for negative values of t′ and have a broad peak for t′∼−0.10. For these value of t′ the energy gain was a smooth increasing function of ρ almost independent of the shell structure in the region starting from ∼0.76 up to the upper bound of investigation 0.92. This clearly indicates that the result is already close to the value in the bulk limit. For t′=0, the energy gain depended on the electronic shell state. This suggests the 10×10 lattice is not sufficiently large for this case, although it is highly plausible that the bulk limit value is finite. Competition between the SC and the commensurate SDW states was also investigated. When t′=0, the ground state is SDW in the range of ρ≥∼0.84. The SC region slightly extends up to ∼0.87 for t′∼−0.10. Consequently the present results strongly support an assertion that the 2D Hubbard model with t′∼−0.1 drives SC by itself in the ρ region from ∼0.76 to ∼0.87. The above features are in a fair agreement with the phase diagram of the optimally and overly hole-doped cuprates. The energy gain in the SC state with suitable parameters is found to be in reasonable agreement with the condensation energy in the SC state of YBa 2Cu 3O 7. The corresponding t– J model proves to give an order-of-magnitude larger energy gain, which questions its validity.

Susceptibility of dilutely doped CrFe alloys

For low dopant concentrations, Fe is the only impurity atom which exhibits Pauli paramagnetism below the Néel temperature of a Cr host. A series of measurements on and alloys reveal that the magnetization M is sensitive to the amplitude of the spin-density wave (SDW) below . The Fe moment also depends on the period of the SDW and is about 6% larger in the incommensurate than in the commensurate SDW state. Surprisingly, the differential susceptibility dM/dH peaks at the field , which is about 5 kOe for low temperatures and small V concentrations. While increases with the temperature, it decreases with the V and Fe concentrations. These observations may be explained by making the radical assumption that the rigidity of the Fe moment is broken by its interaction with the SDW. Whereas part of the Fe moment is bound to the SDW by the nesting free energy, the remainder experiences a weak effective field exerted by the surrounding SDW and by the ferromagnetically coupled, nearest-neighbour pairs of Fe atoms. The peak in dM/dH occurs when the external field H overcomes the antiferromagnetic field experienced by the single Fe atoms. This model explains the temperature and doping dependence of , as well as the difference between the Fe moments in the commensurate and incommensurate SDW hosts.

Local Fe moment in commensurate and incommensurate spin-density wave Cr matrix

It is well known that Fe is the only impurity atom which exhibits Pauli paramagnetism below the Néel temperature of a dilutely doped Cr host. Magnetic measurements on two complementary Cr alloys now reveal that the Fe moment is about 6% larger in the incommensurate than in the commensurate spin-density wave state. A phenomenological model is presented which explains this difference by dividing the Fe moment into bound and unbound parts.

Magnetism of thin epitaxial Cr films in sandwich structures and superlattices

The spin density wave (SDW) magnetism of thin epitaxial Cr films has recently become the focus of interest because of its mediating role in exchange coupled superlattices. While the incommensurate SDW and the Néel temperature, , are well established for bulk Cr, the question arises of how these properties are altered in thin films and superlattices with ferromagnetic boundary layers. We review here recent synchrotron and neutron scattering experiments to probe the commensurate and incommensurate SDWs in epitaxial Cr(100) layers and the phase diagrams which result from these measurements as a function of film thickness and temperature. Finally, we link the antiferromagnetic spin structure of Cr to the Fe layer magnetization vectors in exchange coupled superlattices, which provides a deeper insight for the cause of non-collinear magnetic ordering in these artificial superlattices.

Nature of the triple point in chromium alloys: Mode-softening of the incommensurate spin-density wave

The magnetic stiffness parameter, A 2, associated with the critical fluctuations in the paramagnetic phase close to the incommensurate spin-density-wave (SDW) transition of a Cr + 0.18 at% Re single crystal, when compared with that of pure chromium and dilute alloys of vanadium in chromium, indicates that the singularity responsible for the onset of the commensurate SDW phase occurs when A 2 approaches zero at a finite value of the incommensurability parameter, δ ≊ 0.017 rlu , instead of zero as usually assumed. The mode of the incommensurate SDW softens as δ approaches this critical value with rhenium doping, and conversely hardens as δ increases when vanadium is added to chromium. Also, the amplitude of the critical scattering increases as δ approaches its end point, by a factor of about two going from 0.2 and 0.5at% V to pure chromium, and by another factor near two in going from pure Cr to Cr + 0.18at%Re.