Incommensurate Spin Density Wave State Research Articles

Incommensurate Spin Density Wave in Antiferromagnetic RuO_{2} Evinced by Abnormal Spin Splitting Torque.

Since the discovery of antiferromagnetism, metallic oxide RuO_{2} has exhibited numerous intriguing spintronics properties such as the anomalous Hall effect and anisotropic spin splitting effect. However, the microscopic origin of its antiferromagnetism remains unclear. By investigating the spin splitting torque in RuO_{2}/Py, we found that metallic RuO_{2} exhibits a spatially periodic spin structure which interacts with the spin waves in Py through interfacial exchange coupling. The wavelength of such structure is evaluated within 14-20nm depending on the temperature, which is evidence of an incommensurate spin density wave state in RuO_{2}. Our work not only provides a dynamics approach to characterize the antiferromagnetic ordering in RuO_{2}, but also offers fundamental insights into the spin current generation due to anisotropic spin splitting effect associated with spin density wave.

Multi- k magnetic structure and large anomalous Hall effect in candidate magnetic Weyl semimetal NdAlGe

The magnetic structure, magnetoresistance (MR), and Hall effect of the noncentrosymmetric magnetic semimetal NdAlGe are investigated, revealing an unusual magnetic state and anomalous transport properties that are associated with the electronic structure of this compound. The magnetization and MR measurements are both highly anisotropic and indicate an Ising-like magnetic system. The magnetic structure is complex in that it involves two magnetic ordering vectors, including an incommensurate spin density wave and commensurate ferrimagnetic state in zero field. We have discovered a large anomalous Hall conductivity that reaches $\ensuremath{\approx}430\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.28em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$, implying that it originates from an intrinsic Berry curvature effect stemming from Weyl nodes found in the electronic structure. These electronic structure calculations indicate the presence of nested Fermi surface pockets with nesting wave vectors like the measured magnetic ordering wave vector and the presence of Weyl nodes in proximity to the Fermi surface. We associate the incommensurate magnetic structure with the large anomalous Hall response to be the result of the combination of Fermi surface nesting and the Berry curvature associated with Weyl nodes.

Functional renormalization group study of the two-dimensional Su-Schrieffer-Heeger-Hubbard model

We study the Hubbard model on the square lattice coupled in addition to the optical Su-Schrieffer-Heeger (SSH) phonons, using the singular-mode functional renormalization group method. At half-filling and in the absence of the Hubbard interaction $U$, we find the degenerate spin-density-wave (SDW)/charge-density-wave (CDW)/s-wave superconductivity (sSC) state at smaller electron-phonon coupling strength $\lambda$ and higher phonon frequency $\omega$, and the valence bond solid (VBS) state at larger $\lambda$ and lower $\omega$. After switching on a positive $U$, the VBS state is suppressed, while the SDW state is enhanced. At finite doping, the SSH phonon is found to favor sSC at $U=0$. With increasing positive $U$, we find d-wave superconductivity (dSC) and incommensurate SDW states. In a narrow window of moderate $U$ and $\lambda$, we also find the incommensurate VBS state. The sSC and dSC here can be naturally related to the CDW and SDW fluctuations, both of which can be triggered by the SSH phonons. In contrast, the repulsive interaction $U$ enhances SDW but suppresses CDW fluctuations. Our results at half filling are consistent with quantum Monte Carlo (QMC), and provide insights at finite doping where QMC may suffer from the minus sign problem.

Evaluating Second-Order Phase Transitions with Diagrammatic Monte Carlo: Néel Transition in the Doped Three-Dimensional Hubbard Model

Diagrammatic MonteCarlo-the technique for the numerically exact summation of all Feynman diagrams to high orders-offers a unique unbiased probe of continuous phase transitions. Being formulated directly in the thermodynamic limit, the diagrammatic series is bound to diverge and is not resummable at the transition due to the nonanalyticity of physical observables. This enables the detection of the transition with controlled error bars from an analysis of the series coefficients alone, avoiding the challenge of evaluating physical observables near the transition. We demonstrate this technique by the example of the Néel transition in the 3D Hubbard model. At half filling and higher temperatures, the method matches the accuracy of state-of-the-art finite-size techniques, but surpasses it at low temperatures and allows us to map the phase diagram in the doped regime, where finite-size techniques struggle from the fermion sign problem. At low temperatures and sufficient doping, the transition to an incommensurate spin density wave state is observed.

An enhancement ZT and spin state transition of Ca3Co4O9 with Pb doping

We reported the structural, electrical, thermal and magnetic properties of Pb-doped Ca3Co4O9 in the range of 300–5K. DTA analysis showed that the stability of the Ca3Co4O9 was increased with Pb doping. According to XRD analysis, it is found that Pb ions were successfully doped in the Ca3Co4O9 structure. The temperature of resistivity minima, Tmin, increased by increasing the Pb doping level and it is seen that incommensurate spin density wave state becomes more stable with Pb doping. The enhancement of thermopower was explained that Pb doping in Ca sites caused a decrease of Co4+ fraction such that Co4+ ions transformed into Co3+ or Co2+. The room temperature ZT value of the polycrystalline sample reaches about 16 times larger value than that of the un-doped polycrystalline sample which is the promising candidate for high temperatures in the thin film applications.According to magnetic susceptibility measurement, the increase of effective magnetic moment by Pb concentration was explained by spin state transition of Co3+ from low spin to intermediate spin and high spin state together with some orbital angular momentum contribution which comes from 5T2 term due to a decrease of the ligand field splitting energy.

Single crystal growth of antiferromagnetic Mn3Si by a two-phase RF floating-zone method

The floating-zone growth of massive intermetallic single crystals is very often unsuccessful due to unfavorable solid–liquid interface geometry and insufficient mixing of the melt which depends on the flow in the molten zone. A tailored magnetic two-phase stirrer system with radio frequency (RF) heating has been developed which enables the control of the melt flow by a significant change of the flow field. The magnetic system was used for the crystal growth of the Heusler compound Mn3Si due to their interesting properties such an itinerant antiferromagnetic and incommensurate spin-density wave state. The grown crystals were oriented and cut to samples with the crystallographic orientations (100) and (110) normal to a plane. Measurements of the temperature dependence of magnetization and specific heat are discussed in terms of contributions of other thermodynamic phases and phase transitions.

Effects of chemical doping and pressure on CaFe4As3

The effects of chemical doping by P, Yb, Co, and Cu, and hydrostatic pressure on CaFe${}_{4}$As${}_{3}$, were studied on single-crystalline samples. While the former two dopants substitute the nonmagnetic ions, the latter two partially occupy the Fe sites within the magnetic sublattice. The incommensurate spin density wave (IC-SDW) ordering at ${T}_{N}\ensuremath{\sim}$ 88 K in CaFe${}_{4}$As${}_{3}$ changes only by up to $\ensuremath{\sim}$40% with doping and applied pressure. Thus the IC-SDW state appears more robust than in the layered Fe pnictides. The commensurate SDW (C-SDW) state below ${T}_{2}\ensuremath{\sim}$ 26 K is suppressed in the Co-doped series, while it moves up in temperature in the P-, Yb-, and Cu-doped compounds. A new magnetic phase transition is observed at an intermediate temperature ${T}_{3}$ in Ca(Fe${}_{1\ensuremath{-}x}$Co${}_{x}$)${}_{4}$As${}_{3}$. Resistivity and magnetization measurements on CaFe${}_{4}$As${}_{3}$ were performed under hydrostatic pressure up to 5 GPa, showing a systematic decrease of ${T}_{N}$ and a domelike phase boundary at ${T}_{2}$ up to ${p}_{c}\ensuremath{\sim}$ 2.10 GPa. At higher pressures, a possible structural phase transition occurs, marked by a slowly increasing transition temperature. A phase diagram is shown to compare the effects of chemical doping and pressure.

Slicing the cuprate Fermi surface to reveal underlying order

A complete theoretical picture of high-Tc superconductivity in the cuprates is still lacking despite more than two decades of research. One of the central puzzles in these materials is related to the nature of the low-lying electronic excitations that seems to differ radically between the underdoped and overdoped regimes that define the edges of the superconducting dome. While there is little doubt that overdoped cuprates are bad metals with a large Fermi surface, the nature of low-lying excitations in underdoped cuprates is a matter of intensive debate. The recent discovery of quantum oscillations (QO) in the electrical resistance of the low-disorder ortho-II YBa2Cu3O6.5[1] under a magnetic field strong enough to suppress superconductivity has opened up a new direction of research in the high Tc area and re-inserted the concept of a Fermi liquid (FL) into the underdoped region, where it was long thought that fermionic coherence is completely lost. The issue of QO has been the subject of intensive debates in the literature over the last three years (see Refs. [1–5, 7–10], to name a few). The debates will surely intensify because of new quantum oscillation experiments that show more periods than before, allowing the detection of multiple oscillation frequencies, and a new interpretation of this data presented in an article in Physical Review B by Suchitra E. Sebastian and her international team of colleagues from Cambridge and Oxford universities in the UK, Los Alamos Laboratory in the US, the University of British Columbia and the Canadian Institute for Advanced Research, both in Canada, and Max-Planck-Institut fur Feskorperforschung in Stuttgart, Germany [11]. According to the standard Lifshitz-Kosevich theory [12], quantum oscillations in a FL originate from Landau quantization of closed orbits in a magnetic field. A period F of QO is related to an extreme cross section of the Fermi surface (FS) by F=nΦ0, where n is the carrier density enclosed by the FS, and Φ0 is the magnetic flux quantum. QO measurements in the overdoped Tl2Ba2CuO6+δ[6] revealed a large hole FS, consistent with photoemission [13] and with the Luttinger count for free electrons. In sharp contrast, Fermi surfaces extracted from QO measurements in underdoped YBCO are small pockets, which collectively account for only few percent of the area of the Brillouin zone (BZ). Such small pockets imply that the FS undergoes a substantial reconstruction between overdoped and underdoped regimes. FS reconstruction and small pockets are expected when the system develops a density-wave order in either spin or charge channel (spin-density wave (SDW) [14] or d-density wave (DDW) [7], respectively). In both cases, however, the reconstructed FS contains both electron and hole pockets, at least when the order parameter is not too large. The measurements of QO revealed multiple oscillation frequencies, several of them as satellites of the major peak at F∼ 530 T[3, 5]. This peak was originally identified [5] as coming from an electron pocket on the basis of required consistency with the observed negative sign of the Hall coefficient, and satellites were attributed to bilayer splitting and warping of an electron FS. Sebastian et al. have offered another interpretation of the QO data [11]. They argue that the major peak corresponds to the hole pocket located near (π/2,π/2) (the α pocket in their notations), while the two satellites at 460 T and 602 T correspond to electron γ pockets near (0,π) and symmetry-related points (see Fig.1). They further associate the high-frequency oscillation at 1650 T, which they identified earlier [3], with another, larger hole β pocket, and argue that their (α,β,γ) pocket structure is quantitatively consistent with the FS for an incommensurate SDW state. The agreement with the data becomes even better once one includes the ortho-II potential due to oxygen ordering [8].

Spin and Charge Order in the Doped Hubbard Model: Long-Wavelength Collective Modes

Determining the properties of the two-dimensional Hubbard model is an outstanding problem in physics. Applying recent advances in constrained path auxiliary-field quantum Monte Carlo techniques and simulating large rectangular supercells, we characterize the magnetic and charge properties in the ground state as a function of doping. At intermediate interaction strengths, an incommensurate spin density wave (SDW) state is found, with antiferromagnetic order and essentially homogeneous charge correlation. The wavelength of the collective mode decreases with doping, as does its magnitude. The SDW order vanishes beyond a critical doping. As the interaction is increased, the holes go from a wavelike (delocalized) to a particlelike (localized) state, and charge ordering develops which eventually evolves into stripelike states.

Transition from spin-density-wave to layered antiferromagnetic state induced by hydrogen as a test for the origin of spin-density waves in chromium

Neutron scattering experiments of Cr/V(001) superlattices are discussed, which show that the incommensurate spin-density-wave (SDW) in thick Cr layers becomes suppressed when the V spacer layers are loaded with hydrogen. The hydrogen loading triggers a transition from the incommensurate SDW state to a commensurate antiferromagnetic state. Model Hamiltonian calculations are presented, which show that this transition is not connected with the nesting property of the Cr Fermi surface. Instead, the transition is a manifestation of the antiferromagnetic ground state of Cr, which is separated from the incommensurate SDW state by an energy barrier. Hydrogen is identified as an effective trigger for reducing the activation barrier, enabling the system to relax to the ground state.

Incommensurate spin density wave state in layered cobaltites

Magnetism of misfit layered cobaltites with a triple rocksalt-type subsystem, i.e., [ A ( M 1 - y Co y ) O 3 ] x RS [ CoO 2 ( A = Ca and Sr, M = Ti , Hg, Tl and Pb, x = 0.5 – 0.7 and RS denotes the rocksalt-type subsystem) was investigated by μ + SR , using polycrystalline samples down to 1.8 K. Weak transverse-field measurements indicated the existence of a magnetic transition below ∼ 150 K ( = T c on ) . A clear muon spin oscillation was however observed only in [ Ca 2 Pb 0.4 Co 0.6 O 3 ] 0.62 RS [ CoO 2 ] below ∼ 50 K , indicating formation of an incommensurate spin density wave (IC-SDW) state. The oscillation frequency as T approaches at 0 K ( f SDW ( 0 K ) ) was ∼ 60 MHz which is comparable to that in the related compound [ Ca 2 CoO 3 ] 0.62 RS [ CoO 2 ] ( f SDW ( 0 K ) ∼ 54 MHz ) . Since the ( Pb 0.4 Co 0.6 ) O (or the Co–O) sheet is sandwiched by the two adjacent Ca–O sheets in the RS subsystem, the IC-SDW is most unlikely to form in the RS subsystem but in the CoO 2 plane. Only a fast relaxation is apparent even at 1.8 K in both [ Sr 2 Hg 0.4 Co 0.6 O 3 ] 0.57 RS [ CoO 2 ] and [ Ca 2 Ti 0.4 Co 0.6 O 3 ] 0.57 RS [ CoO 2 ] , although the Co content in the RS subsystem is equivalent to that for [ Ca 2 Pb 0.4 Co 0.6 O 3 ] 0.62 RS [ CoO 2 ] . Assuming that the RS subsystem acts as a charge reservoir as in the high T C cuprates, the present result suggests that the IC-SDW order is strongly affected by the carrier concentration in the [ CoO 2 ] plane.

Quasi-One-dimensional Spin-Density-Wave States in Presence of Two Commensurate Potentials and Interchain Misfit

The spin-density-wave (SDW) states of a quasi-one-dimensional system with an incommensurate wave vector perpendicular to the chain have been studied in the presence of two kinds of commensurate potential, which originate in a quarter-filled band and under dimerization along the chain. For the phase variance phase of the SDW order parameter, we classically treat a two-dimensional Hamiltonian, which includes both acoustic excitation with a long wavelength and a vortex excitation with a short wavelength. A phase diagram on the plane of temperature and chemical potential (where the latter corresponds to the deviation of the transverse wave vector from the commensurate one) exhibits a variety of states given by the commensurate SDW state without charge density, the commensurate SDW state with charge density, the incommensurate SDW state, and the disordered state.

Electron correlation in the two-dimensional triangular lattice of [formula omitted] with [formula omitted

Magnetism of layered cobaltites Na x CoO 2 with x = 0.6 and 0.9 has been investigated by a positive muon spin rotation and relaxation ( μ + SR) spectroscopy together with magnetic susceptibility and specific heat measurements, using single-crystal samples in the temperature range between 250 and 1.8 K. Zero-field μ + SR measurements on Na 0.9 CoO 2 indicate a transition to an incommensurate spin density wave state at 19 K ( = T SDW ) . Since Na 0.6 CoO 2 is paramagnetic down to 1.8 K, the magnitude of T SDW is found to strongly depend on x . This behavior is explained using the Hubbard model within a mean field approximation on two-dimensional triangle lattice in the CoO 2 plane. Also, both the appearance of the IC-SDW state by the change in x and the magnitude of the electronic specific heat parameter of Na 0.6 CoO 2 indicate that Na x CoO 2 is unlikely to be a typical strongly correlated electron system.

Superconducting∕ferromagnetic proximity effect mediated byCrspacer layers

We have studied the superconducting proximity effect in the thin film system $\mathrm{Fe}∕\mathrm{Cr}∕\mathrm{V}∕\mathrm{Cr}∕\mathrm{Fe}$ where the $\mathrm{Cr}$ layers play the role of screening layers between the superconducting $\mathrm{V}$-layer and the strongly pair breaking $\mathrm{Fe}$-layers. When keeping the thickness of the $\mathrm{Fe}$-layers ${d}_{\mathrm{Fe}}$ fixed and varying the thickness of the $\mathrm{Cr}$-layers ${d}_{\mathrm{Cr}}$, the superconducting transition temperature ${T}_{c}$ first rises reaching a maximum at ${d}_{\mathrm{Cr}}=40\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ and then sharply drops for larger $\mathrm{Cr}$-thickness. Keeping ${d}_{\mathrm{Cr}}$ constant and varying ${d}_{\mathrm{Fe}}$ the superconducting transition temperature becomes independent on ${d}_{\mathrm{Fe}}$ for ${d}_{\mathrm{Cr}}g40\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. The results demonstrate that the Cooper pairs penetrate into the $\mathrm{Cr}$-layer to a depth of about $40\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. From our experimental results we suggest that the $\mathrm{Cr}$-layer is nonmagnetic for ${d}_{\mathrm{Cr}}l40\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ and undergoes a transition to an incommensurate spin density wave state for ${d}_{\mathrm{Cr}}g40\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$.

The proximity effect in an Fe-Cr-V-Cr-Fe system

The proximity effect was studied in a thin-film Fe-Cr-V-Cr-Fe layered system. As the chromium layer thickness (dCr) increases at a fixed thickness of iron layers (dFe), the dependence of the superconducting transition temperature (Tc) on dCr exhibits a maximum at dCr ≃ 40 A followed by a sharp decrease. Investigation of the dependence of Tc on dFe at a fixed dCr showed that the depth of penetration of the Cooper pairs into a chromium layer does not exceed 40 A. Analysis of the results obtained suggests that, at dCr ≃ 40 A, chromium layers exhibit the transition from a nonmagnetic state to an incommensurate spin density wave state.

A common behaviour of thermoelectric layered cobaltites: incommensurate spin density wave statesin [Ca2Co4/3Cu2/3O4]0.62[CoO2] and [Ca2CoO3]0.62[CoO2

Magnetism of a misfit layered cobaltite[Ca2Co4/3Cu2/3O4]xRS[CoO2] (, RS denotes a rocksalt-type block) was investigated by a positive muon spin rotation and relaxation(μ+SR)experiment. A transition to an incommensurate (IC) spin density wave (SDW) state was found below180 K (= TCon); and a clear oscillation due to a static internal magnetic field was observed below140 K (= TC). Furthermore, an anisotropic behaviour of the zero-fieldμ+SR experiment indicated that the IC-SDW lies in thea–b plane, with oscillating moments directed along thec axis. These results were quite similar to those for the related compound[Ca2CoO3]0.62RS[CoO2], i.e.,Ca3Co4O9. Since theIC-SDW field in [Ca2Co4/3Cu2/3O4]0.62RS[CoO2] was approximately the same as those in pure and doped[Ca2CoO3]0.62RS[CoO2], it was concluded that the IC-SDW exists in the[CoO2 ] planes.

μSR studies on layered cobalt oxides

To investigate the role of magnetism on transport properties of ‘good’ thermoelectric oxides, μSR spectroscopy has been used for polycrystalline Ca 3Co 4O 9 and Na 0.7CoO 2 samples in the temperature range between 300 and 2.5 K . It was found that Ca 3Co 4O 9 exhibits a magnetic transition below T c onset ∼100 K with a transition width of ΔT c =70 K ; below T c onset, two types of relaxation were observed using a weak transverse-field μSR technique; one exhibits a fast relaxation rate on the order of 10 μs −1 and the other a slow one of about 0.1 μs −1 . Furthermore, ZF-μSR measurements suggested the existence of an incommensurate spin density wave state below T c onset (i.e. T c onset= T SDW). Since the resistivity vs. T curve exhibited a broad minimum around 80 K , the SDW transition was found to be associated with the change in the transport properties of Ca 3Co 4O 9. Similar measurements on Na 0.7CoO 2 indicated no magnetic transitions below 250 K . Considering the difference between the both crystal structures, it is concluded that the Co ions in the rocksalt-type layers of Ca 3Co 4O 9 are likely to play the dominant role in inducing the observed magnetic transitions below 100 K .

Spin-density wave controlled by the superlattice period in Cr (001)/Sn multilayers with Sn monatomic spacer layers

Exotic spin-density-wave (SDW) states in Cr (001)/Sn multilayers were studied by neutron diffraction. Six multilayers with different Cr thicknesses (tCr=4, 8, 10, 12, 14 and 16 nm) with monatomic Sn layers were synthesized on MgO (001) substrates. In the multilayers, except for tCr=4 nm, complicated incommensurate SDW states formed at low temperatures, in which the wave vectors of the SDW were controlled by the multilayer period.

Spin and Charge Excitations in Incommensurate Spin Density Waves

Collective excitations both for spin- and charge-channels are investigated in incommensurate spin density wave (or stripe) states on two-dimensional Hubbard model. By random phase approximation, the dynamical susceptibility \chi(q,\omega) is calculated for full range of (q,\omega) with including all higher harmonics components. An intricate landscape of the spectra in \chi(q,\omega) is obtained. We discuss the anisotropy of the dispersion cones for spin wave excitations, and for the phason excitation related to the motion of the stripe line. Inelastic neutron experiments on Cr and its alloys and stripe states of underdoped cuprates are proposed.

Low- and high-energy excitations in the incommensurate antiferromagnet, chromium

Dynamical susceptibility of metallic chromium (Cr) has been elucidated by using neutron magnetic scattering technique. Systematic studies in a wide energy range at various temperatures revealed that magnetic excitations in the antiferromagnetic state of Cr well below Néel temperature are not interpreted by a simple spin-wave mode like in the conventionally ordered magnet. The most prominent feature of spin dynamics in the incommensurate spin density wave (SDW) state is that magnetic excitations consist of two components having incommensurate and commensurate wave vector in the reciprocal space. Energy and temperature dependence of such magnetic excitations is also unusual, which may reflect the characteristic band structure of Cr.