Transverse Spin Density Wave Research Articles

Collective excitations of a general spin-3/2 Fermi gas

Collective excitation modes in a general 3D homogenous spin-3/2 Fermi gas with spin-dependent contact interactions are investigated by two-particle Green’s functions and diagram techniques. Energy spectra for two branches of charge-density waves and three branches of transverse spin-density waves are obtained within the random-phase approximation. All spectra are gapless and linear in the small wave vector q, with their slopes dependent on the interaction parameters. It is also found that the spin-mixing interaction has effects on the transverse spin-density waves, but not on the charge-density modes. When the system satisfies SU(4) symmetry, the two charge-density modes become degenerate and two of the three transverse spin-density modes are degenerate, too. Furthermore, static spin susceptibilities are discussed in detail. It is found that susceptibilities increase with the enhancement of all interaction parameters, and become divergent at certain points. This phenomenon is analogous to the Stoner transition in spin-1/2 fermion gas.

Spin and charge density waves in quasi-one-dimensional KMn6Bi5

AMn6Bi5 materials (A = Na, K, Rb and Cs) consisting of unique Mn-cluster chains emerge as a new family of superconductors with the suppression of their antiferromagnetic (AFM) order under high pressures. Here, we report transverse incommensurate spin density waves (SDWs) for the Mn atoms with a propagating direction along the chain axes as a ground state for KMn6Bi5 by single crystal neutron diffraction. The SDWs have a refined amplitude of ~2.46 Bohr magnetons for the Mn atoms in the pentagons and ~0.29 Bohr magnetons with a large standard deviation for Mn atoms in the center between the pentagons. AFM dominate both the nearest-neighbor Mn-Mn interactions within the pentagon and next-nearest-neighbor Mn-Mn interactions out of the pentagon (along the propagating wave). The SDWs exhibit both local and itinerant characteristics probably formed by a cooperative interaction between local magnetic exchange and conduction electrons. A significant magnetoelastic effect during the AFM transition, especially along the chain direction, has been demonstrated by temperature-dependent x-ray powder diffraction. Single crystal x-ray diffraction below the AFM transition revealed satellite peaks originating from charge density waves along the chain direction with a q-vector twice as large as the SDW one, pointing to a strong real space coupling between them. Our work not only manifests a fascinating interplay among spin, charge, lattice and one dimensionality to trigger intertwined orders in KMn6Bi5 but also provides important piece of information for the magnetic structure of the parent compound to understand the mechanism of superconductivity in this new family.

Factors Governing the Propagation Direction and Spin-Rotation Plane of Noncollinear Magnetic Structures: A Helix vs Cycloid in Doubly Ordered Perovskites NaYMnWO6 and NaYNiWO6.

The magnetic structure of NaYMnWO6 was determined by neutron powder diffraction measurements. Below 9 K, the magnetic structure is a helix to wave vector k = (0, 0.447, 1/2), in contrast with NaYNiWO6, which shows a transverse spin density wave with k = (0.47, 0, 0.49). By analyzing the differences in the spin exchanges of NaYMnWO6 and NaYNiWO6, and in the magnetic anisotropies of the Mn2+ (d5, S = 5/2) and the Ni2+ (d2, S = 1) ions, we show what factors govern the propagation direction of a noncollinear magnetic structure and whether it becomes a helix or a cycloid.

Spin-gapped phases in the frustrated Hubbard chain with transverse spin anisotropy

At weak coupling, we investigate the frustrated Hubbard chain including nearest-neighbor and next-nearest-neighbor antiferromagnetic exchange with easy-plane anisotropy J1xy and J2xy. At half filling, we obtain three different phases in the J1xy–J2xy plane: a transverse spin density wave phase, a bond order wave phase and a Luther–Emery metallic phase characterized by the coexistence of singlet superconductivity and charge density wave correlations. The frustrating exchange J2xy accounts for the spin-gapped phases.

Crystallite size effect on the monoclinic deformation of the bcc crystal structure of chromium

The modulated spin density wave magnetic orderings observed in chromium suggests that the crystal structure of chromium cannot be described by the cubic space group Im3¯m. Our experimental studies of polycrystalline and nanocrystalline chromium by synchrotron radiation (SR) and neutron powder diffraction show a hkl-dependent Bragg peak broadening which can be interpreted by the low-symmetry monoclinic space group P21/n instead of the high symmetry cubic space group Im3¯m. The monoclinic angle is βm = 90.05(1)° and 90.29(1)° for polycrystalline Cr and nanocrystalline Cr, respectively. The relative monoclinic distortion observed in chromium is 5 times larger than those reported for several oxides: BiFeO3, α-Fe2O3, Cr2O3 and calcite. The symmetry of the magnetic transverse spin density wave (TSDW) and the longitudinal spin density wave (LSDW) observed in Cr are described by using the superspace groups P21/n(0β0)00 and P21′/n′(0β0)00, respectively. These superspace groups describe both the magnetic modulations and the atomic position modulations reported in the literature. The monoclinic symmetry of chromium is a robust effect which is observed in the paramagnetic as well as in the TSDW and LSDW phases.

Magnetic structure and multiferroic coupling in pyroxeneNaFeSi2O6

By comprehensive neutron diffraction measurements we have studied the magnetic structure of aegirine $({\mathrm{NaFeSi}}_{2}{\mathrm{O}}_{6})$ in and above its multiferroic phase. Natural aegirine exhibits two magnetic transitions into incommensurate magnetic order with a propagation vector of ${\stackrel{P\vec}{k}}_{\mathrm{inc}}=(0,\ensuremath{\sim}0.78,0)$. Between 9 and 6 K, we find a transverse spin-density wave with moments pointing near the $c$ direction. Below 6 K, magnetic order becomes helical and spins rotate in the $ac$ plane. The same irreducible representation is involved in the two successive transitions. In addition, the ferroelectric polarization $\stackrel{P\vec}{P}$ appearing along the $b$ direction cannot be described by the most common multiferroic mechanism but follows $\stackrel{P\vec}{P}\ensuremath{\propto}{\stackrel{P\vec}{S}}_{i}\ifmmode\times\else\texttimes\fi{}{\stackrel{P\vec}{S}}_{j}$. Synthetic ${\mathrm{NaFeSi}}_{2}{\mathrm{O}}_{6}$ does not exhibit the pure incommensurate helical order but shows coexistence of this order with a commensurate magnetic structure. By applying moderate pressure to natural aegirine, we find that the incommensurate magnetic ordering partially transforms to the commensurate one, underlining the nearly degenerate character of the two types of order in ${\mathrm{NaFeSi}}_{2}{\mathrm{O}}_{6}$.

Versatile module for experiments with focussing neutron guides

We report the development of a versatile module that permits fast and reliable use of focussing neutron guides under varying scattering angles. A simple procedure for setting up the module and neutron guides is illustrated by typical intensity patterns to highlight operational aspects as well as typical parasitic artefacts. Combining a high-precision alignment table with separate housings for the neutron guides on kinematic mounts, the change-over between neutron guides with different focussing characteristics requires no readjustments of the experimental setup. Exploiting substantial gain factors, we demonstrate the performance of this versatile neutron scattering module in a study of the effects of uniaxial stress on the domain populations in the transverse spin density wave phase of single crystal Cr.

Influence of the crystalline microstructure on the magnetic ordering of nanocrystalline chromium

The magnetic and structural properties of nanocrystalline chromium (n-Cr) were studied by neutron powder diffraction and by synchrotron radiation diffraction techniques. The nanocrystalline Cr is composed of small-sized particles with antiferromagnetic ordering, medium-sized particles with transverse spin density wave (SDW) ordering, and large-sized particles with the same magnetic ordering as bulk Cr. The critical size ${D}_{C}$ between the small and medium-sized crystallites is $18\ifmmode\pm\else\textpm\fi{}2$ nm. The alteration of the magnetic properties of n-Cr is due to microstrain fluctuations which are correlated with the crystallite sizes rather than to the crystallite size itself. The microstrain fluctuations increase the SDW modulation length up to large values (10.5 nm for n-Cr vs 7.8 nm for bulk Cr).

PHASE DIAGRAM OF THE ONE-DIMENSIONAL t–U–J MODEL WITH ON-BOND REPULSION AT HALF FILLING

By using the bosonization approach and the renormalization group (RG) technique, we study the half-filled band one-dimensional t–U–J model with additional on-bond repulsion (W>0) in the weak-coupling regime. The presence of on-bond repulsion is responsible for realization of a metallic phase in the system, and the phase diagram is strongly controlled by the symmetry of the model. By analyzing the RG flow diagram and comparing order parameters, the phase boundaries are determined and the structure of the phase diagram is clarified. In the case of SU (2) ⊗ SU (2) symmetry, the phase diagram consists of a metallic phase characterized by a Luttinger liquid (LL) and two insulting phases characterized by the degenerate spin-density-wave (SDW) and the bond-charge-density-wave (BCDW). In the SU (2) ⊗ U(1)-symmetric case, the phase diagram contains two metallic phases: a LL and a Luther–Emery phase, and three insulating phases: the transverse SDW ( SDW ±), the longitudinal SDW ( SDW z) and the dimerized BCDW. The insulating charge-density-wave and bond-spin-density-wave (BSDW) phases are always suppressed in the ground state. In addition, the system show a long-ranged order in the BCDW and SDW z phases.

PHASE DIAGRAM OF ONE-DIMENSIONAL t–U–J MODEL WITH ANISOTROPIC ANTIFERROMAGNETIC EXCHANGE

By using the bosonization approach and the weak-coupling renormalization group (RG) techniques, we study the phase diagram of one-dimensional half-filled t–U–J model parametrized by exchange anisotropy λ (0 ≤ λ ≤ 2) in the weak-coupling regime. In the case of anisotropic antiferromagnetic exchange (J > 0) and on-site repulsion (U > 0), the ground state is characterized by the spin-density-wave (SDW) and bond-charge-density-wave (BCDW) insulating phases. We identify the SDW correlation corresponding to the transverse SDW± phases with a gapless spin excitation (Δs=0) for λ < 4/3 and to the longitudinal SDWz phase with a spin gap (Δs > 0) for λ > 4/3, respectively. The charge excitation is always gapped (Δc > 0) in the whole regime, and the BCDW and SDWz phases show a long-range order. We also examine effects of the nonlocal Umklapp scattering of parallel-spin electrons, which play a role to weaken the BCDW phase and to enhance the SDW phase slightly. The results demonstrate that the properties of our model are not identical with those of the conventional t–U–J model.

Electromagnon excitations in modulated multiferroics

The phenomenological theory of ferroelectricity in spiral magnets presented in [M. Mostovoy, Phys. Rev. Lett. 96, 067601 (2006)] is generalized to describe consistently states with both uniform and modulated-in-space ferroelectric polarizations. A key point in this description is the symmetric part of the magnetoelectric coupling since, although being irrelevant for the uniform component, it plays an essential role for the nonuniform part of the polarization. We illustrate this importance in generic examples of modulated magnetic systems: longitudinal and transverse spin-density wave states and planar cycloidal phase. We show that even in the cases with no uniform ferroelectricity induced, polarization correlation functions follow the soft magnetic behavior of the system due to the magnetoelectric effect. Our results can be easily generalized for more complicated types of magnetic ordering, and the applications may concern various natural and artificial systems in condensed matter physics (e.g., magnon properties could be extracted from dynamic dielectric response measurements).

Resonant X-ray magnetic scattering studies of the TmNi 2B 2C spin density wave

We report on polarisation resolved, resonant X-ray magnetic scattering (RXMS) studies of the spin density wave (SDW) formed in the TmNi 2B 2C superconductor. From this high wave-vector resolution investigation, we find the incommensurate magnetic SDW propagation vector to be ( 0 ± τ 0 ± τ 0 ) with τ = 0.096 rlu , slightly larger than the value previously deduced from magnetic neutron studies ( τ = 0.093 rlu ). The widths of the SDW peaks at 1 K are consistent with long-range magnetic order and we have deduced a magnetic correlation length of ∼1200 Å. When the incident photons are tuned to the Tm L 3 absorption edge, the RXMS energy response consists of a double peak feature, arising from both dipole (E1) transitions, probing the 5d conduction band polarisation, and quadrupole (E2) transitions, probing the Tm 4f magnetic moments. The RXMS wave-vector dependences of the (0± τ 0± τ L) SDW satellites are consistent with the transverse spin-density wave structure, with moments orientated along the crystallographic c-axis, originally proposed from neutron-scattering measurements. Our RXMS data are also in good agreement with the magnetic neutron-scattering response for the thermal evolution of the magnetic moments down to 1 K and in deducing a Nèel temperature of T N = 1.5 K . However, the RXMS probe reveals a small shift of the magnetic propagation vector of the order 3×10 −3 rlu along the (1 1 0) direction, on decreasing temperature below T N. Using very high-resolution X-ray studies with a conventional Si(1 1 1) analyser, no change in width or position is found below T N or T c. We have also not observed any charge modulation peaks at 2 τ , indicating that the SDW does not couple to the lattice.

Neutron diffraction study of anomalous high-field magnetic phases inTmNi2B2C

We present a $(B,T)$-phase diagram of the magnetic superconductor ${\mathrm{TmNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ obtained by neutron scattering. The measurements were performed in magnetic fields up to 6 T applied along the crystalline a axis. The observed phases are characterized by three ordering vectors, ${\mathbf{Q}}_{\mathrm{F}}=(0.094,0.094,0),{\mathbf{Q}}_{\mathrm{AI}}=(0.483,0,0),$ and ${\mathbf{Q}}_{\mathrm{AII}}=(0.496,0,0),$ all with the magnetic moment along the c axis. In zero and low fields the Tm $4f$-moments order in a long wavelength transverse spin density wave with $\mathbf{Q}={\mathbf{Q}}_{\mathrm{F}}.$ The magnetic ${\mathbf{Q}}_{\mathrm{AI}}$ structure is stabilized by an applied field of 1 T and a transition to ${\mathbf{Q}}_{\mathrm{AII}}$ is observed at 4 T. For both transitions there is a broad temperature and field range of overlap between the different states. Surprisingly, we observe that the ${\mathbf{Q}}_{\mathrm{A}}$ phases persist to increasingly higher temperatures when the field is increased. Doping with Yb has been introduced to partly suppress superconductivity. In $({\mathrm{Tm}}_{0.90}{\mathrm{Yb}}_{0.10}){\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ the ${\mathbf{Q}}_{\mathrm{F}}\ensuremath{\rightarrow}{\mathbf{Q}}_{\mathrm{AI}}$ phase transition is also observed but at a larger transition field compared to the undoped compound. In $({\mathrm{Tm}}_{0.85}{\mathrm{Yb}}_{0.15}){\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ the ${\mathbf{Q}}_{\mathrm{F}}$ phase persists up to at least 1.8 T. The magnetic correlation length of the ${\mathbf{Q}}_{\mathrm{AI}}$ phase in ${\mathrm{TmNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ measured parallel and perpendicular to the magnetic field, is constant within 10% at all fields and temperatures.

Oscillatory exchange bias due to an antiferromagnet with incommensurate spin-density waves.

Oscillatory exchange bias in both magnitude and in sign has been observed in epitaxial (100)Cr/Ni(81)Fe19 bilayers due to the incommensurate spin-density waves in antiferromagnetic (100)Cr layers. Salient effects due to the spin-flip transition between longitudinal and transverse spin-density waves as well as that of expanding wavelength have been observed.

Fincher-Burke excitations in single-Q chromium

The low-energy excitations of incommensurate antiferromagnetic Cr have been investigated by means of high-resolution, inelastic neutron scattering with unpolarized, cold neutrons within an energy range E<9 meV. In agreement with previous measurements we observe Fincher–Burke excitations in the transverse spin density wave phase that appear between the unresolved spin-wave peaks at the incommensurate positions Q±=(1±δ,0,0). In contrast to the previous measurements, our high-resolution data shows that the Fincher–Burke modes do not follow a linear dispersion. Therefore, they have nothing in common with the acoustic phonon branch. The major part of the scattering is concentrated in the range 4 meV<E<8 meV.

Magnetic ordering in electrodeposited nanocrystalline chromium particles

The magnetic ordering and thermal lattice expansion of nanocrystaline chromium (n-Cr) are studied by neutron powder diffraction. Nanocrystalline Cr with a volume-averaged crystallite size of 27 nm has been obtained by electrodeposition. Between room temperature and 240 K there is a simple antiferromagnetic ordering. At 240 K the magnetic ordering changes and a part of the material adopts a transverse spin-density-wave (TSDW) ordering. The spin-flip transition from the TSDW to the longitudinal LSDW ordering is supressed and about 40% of the volume has the TSDW ordering stabilized down to 2 K. The thermal lattice expansion of the material becomes negative around the magnetic phase transition near 240 K. The values of the magnetic moments of the simple antiferromagnetic and TSDW orderings observed at 2 K are in agreement with the magnetic moments observed in single crystals and polycrystalline Cr.

Influence of strain on the anti-ferromagnetic ordering in epitaxial Cr(001) films on MgO

The influence of epitaxial strain on the anti-ferromagnetic ordering was studied in a 450-nm-thick Cr film grown on a MgO(001) substrate by molecular beam epitaxy. The anti-ferromagnetic nature of the films was probed by neutron diffraction. A detailed structural characterization of the film was carried out by atomic force microscopy, Rutherford backscattering/channeling spectrometry, and X-ray diffraction. At low temperatures a transverse spin density wave with propagation vector in the film plane is detected, and is attributed to the presence of epitaxial strain. Crystal defects in the sample lead to the appearance of the commensurate anti-ferromagnetic state at higher temperatures.

Phase transitions in a magnetic field inV2−yO3(y=0and0.04)

The effect of a magnetic field on the two long-range-ordered magnetic phases, the collinear insulating antiferromagnetic (AFI) and the incommensurate metallic transverse spin density wave (SDW), is investigated for the vanadium sesquioxide system. A field of 18 T has little effect on the AFI phase of a nominal ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ sample. The transverse SDW phase of ${\mathrm{V}}_{1.96}{\mathrm{O}}_{3}$ can be suppressed by a 4.6(3)-T magnetic field applied in the plane of spiraling spins, while the same magnetic field applied along the spiral axis has little effect on the SDW phase.

Depth-dependent investigation of the distribution of the spin density waves in thin chromium films with surface X-ray and neutron scattering

For thin epitaxial Cr(0 0 1) films capped with a ferromagnetic Fe layer a transverse spin density wave (SDW) is expected which propagates in the out-of-plane direction with the Cr spins aligned parallel to the film plane in the direction of the Fe magnetization vector. Synchrotron and neutron scattering experiments show, however, that the SDW wave propagates parallel to the film plane with spins oriented out-of-plane. In addition, a commensurate antiferromagnetic phase is found. The re-orientation of the SDW is caused by a frustrated Fe–Cr exchange coupling introduced by monoatomic steps at the Fe–Cr interface. Complete re-orientation takes place over some distance close to the interface reducing severely the coherence length of the SDW structure. With the surface scattering method we have measured the coherence length of the SDW as a function of depth. Furthermore, we have investigated the role of the commensurate antiferromagnetic phase near the Fe–Cr interface. We find no scattering from a commensurate order, implying a layering of the two phases with the incommensurate phase on top.

Spin-density-wave antiferromagnetism of Cr in Fe/Cr(0 0 1) superlattices

The antiferromagnetic spin-density-wave (SDW) order of Cr layers in Fe/Cr(0 0 1) superlattices was investigated by neutron scattering. For Cr thicknesses from 51 to 190 Å, a transverse SDW is formed for all temperatures below the Néel temperature with a single wave vector Q normal to the layers. A coherent magnetic structure forms with the nodes of the SDW near the FeCr interfaces. For thinner Cr layers, the magnetic scattering can be described by commensurate antiferromagnetic order.