Incommensurate Magnetic Order Research Articles

Magnetic-Field-Enhanced Incommensurate Magnetic Order in the Underdoped High-Temperature SuperconductorYBa2Cu3O6.45

We present a neutron-scattering study of the static and dynamic spin correlations in the underdoped high-temperature superconductor YBa2Cu3O6.45 in magnetic fields up to 15 T. The field strongly enhances static incommensurate magnetic order at low temperatures and induces a spectral-weight shift in the magnetic-excitation spectrum. A reconstruction of the Fermi surface driven by the field-enhanced magnetic superstructure may thus be responsible for the unusual Fermi surface topology revealed by recent quantum-oscillation experiments.

Magnetic phase evolution in the spinel compoundsZn1−xCoxCr2O4

We present the magnetic properties of complete solid solutions ofZnCr2O4 andCoCr2O4: two well studied oxide spinels with very different magnetic ground states.ZnCr2O4, with non-magneticd10 cations occupying theA site and magnetic d3 cations on the B site, is a highly frustrated antiferromagnet.CoCr2O4, withmagnetic d7 cations (three unpaired electrons) on the A site as well, exhibits Néel ferrimagnetism as wellas commensurate and incommensurate non-collinear magnetic order. More recently,CoCr2O4 has been studied extensively because of its polar behavior which arises fromconical magnetic ordering. Gradually introducing magnetism on the A site ofZnCr2O4 results in a transition from frustrated antiferromagnetism to glassy magnetism at lowconcentrations of Co, and eventually to ferrimagnetic and conical ground states at higherconcentrations. Real-space Monte Carlo simulations of the magnetic susceptibility suggestthat the first magnetic ordering transition and features of the susceptibility acrossx are captured by near-neighbor self-couplings and cross-couplings between the magnetic Aand B atoms. We present, as a part of this study, a method for displaying the temperaturedependence of magnetic susceptibility in a manner which helps distinguish betweencompounds possessing purely antiferromagnetic interactions from compounds where otherkinds of ordering are present.

Character of magnetic instabilities inCaFe2As2

The density-functional spin susceptibility has been analyzed in different phases of CaFe{sub 2}As{sub 2} and compared with similar data for pure d metals. The conditions for the 'no local-moment' itinerant state with large frustrations are found for the 'collapsed' phase. This itineracy determines the instability versus the incommensurate magnetic order for the narrow region of wave vectors. For the ambient pressure phase, the local moments on Fe atoms with much less frustrated antiferromagnetic interactions are stabilized and a magnetic short-range or long-range order is developed. The system is close to the point of magnetic instability and spin fluctuations should be included to describe properties of this system.

Magnetic Correlations inLa2−xSrxCoO4Studied by Neutron Scattering: Possible Evidence for Stripe Phases

Spin correlations in La2-xSrxCoO4 (0.3 < or = x < or = 0.6) have been studied by neutron scattering. The commensurate antiferromagnetic order of La2CoO4 persists in a very short range up to a Sr content of x = 0.3, whereas small amounts of Sr suppress commensurate antiferromagnetism in cuprates and in nickelates. La2-xSrxCoO4 with x > 0.3 exhibits incommensurate spin ordering with the modulation closely following the amount of doping. These incommensurate phases strongly resemble the stripe phases observed in cuprates and nickelates, but incommensurate magnetic ordering appears only at larger Sr content in the cobaltates due to a reduced charge mobility.

MicroscopicA75sNMR study of the effect of impurities on the first-order spin-density-wave transition inBaFe2As2

We report an $^{75}\text{A}\text{s}$ NMR study of ${\text{BaFe}}_{2}{\text{As}}_{2}$ in both single crystals and polycrystal forms. We find that Sn impurities in the single crystal dramatically alter the low energy spin fluctuations and suppress the ordering temperature from 138 to 85 K. In contrast to Sn-free samples, we find that the temperature dependence of the $^{75}\text{A}\text{s}$ NMR spectra and spin-lattice relaxation rates reveal a second-order phase transition to a state of incommensurate magnetic order.

Diagonal and collinear incommensurate spin structures in underdopedLa2−xBaxCuO4

We have studied incommensurate spin ordering in single-crystal underdoped ${\text{La}}_{2\ensuremath{-}x}{\text{Ba}}_{x}{\text{CuO}}_{4}$ with $x\ensuremath{\sim}0.08$, 0.05, and 0.025 using neutron-scattering techniques. Static incommensurate magnetic order is observed in the ${\text{La}}_{2\ensuremath{-}x}{\text{Ba}}_{x}{\text{CuO}}_{4}$ ($x=0.05$ and 0.025) compounds with ordering wave vectors which are rotated by $45\ifmmode^\circ\else\textdegree\fi{}$ about the commensurate (0.5,0.5,0) position, with respect to that in the superconducting $x=0.08$ material. These spin modulations are one dimensional in the $x=0.05$ and 0.025 samples, with ordering wave vectors lying along the orthorhombic ${b}^{\ensuremath{\ast}}$ direction. Such a rotation in the orientation of the static spin ordering as a function of increasing Ba doping, from diagonal to collinear, is roughly coincident with the transition from an insulating to a superconducting ground state and is similar to that observed in the related ${\text{La}}_{2\ensuremath{-}x}{\text{Sr}}_{x}{\text{CuO}}_{4}$ system. This phenomenon is therefore a more generic property of underdoped La-214 cuprates.

Magnetic Ground State and Transition of a Quantum MultiferroicLiCu2O2

Based on resonant soft x-ray magnetic scattering, we report that LiCu2O2 exhibits a large interchain coupling which suppresses quantum fluctuations along spin chains, and a quasi-2D short-range magnetic order prevails at temperatures above the magnetic transition. These observations unravel the fact that the ground state of LiCu2O2 possesses long-range 2D-like incommensurate magnetic order rather than being a gapped spin liquid as expected from the nature of quantum spin-1/2 chains. In addition, the spin coupling along the c axis is found to be essential for inducing electric polarization.

Incommensurate Spin-Density Modulation in a Copper Oxide Chain Compound with Commensurate Charge Order

Neutron diffraction has been used to determine the magnetic structure of Na8Cu5O10, a stoichiometric compound containing chains based on edge-sharing CuO4 plaquettes. The chains are doped with 2/5 hole per Cu site and exhibit long-range commensurate charge order with an onset well above room temperature. Below TN=23 K, the neutron data indicate long-range collinear magnetic order with a spin-density modulation whose propagation vector is commensurate along, and incommensurate perpendicular to, the chains. Competing interchain exchange interactions are discussed as a possible origin of the incommensurate magnetic order.

Pressure-induced phase transitions inPrB6: Electrical resistivity measurements

We have studied the electrical resistivity of ${\text{PrB}}_{6}$ under pressure up to $P=0.8\text{ }\text{GPa}$, with magnetic fields applied along the [001] and [111] directions. The commensurate (C) magnetic ordered phase is significantly stabilized by pressure, and another extra phase (denoted phase A) is observed under a low pressure of $\ensuremath{\sim}0.3\text{ }\text{GPa}$. This phase appears above the transition temperature ${T}_{\text{IC}1}=7\text{ }\text{K}$ at which the incommensurate magnetic order sets in at the ambient pressure. The magnetic phase diagram for $H\ensuremath{\parallel}[111]$ changes drastically under pressure. Short-range interactions, which are strongly dependent on the Pr-Pr distances, are likely to play a dominant role in the relative stability of the different phases.

Magnetic order and multipole interactions inCexPr1−xB6solid solutions

Magnetic ordering phenomena in ${\text{Ce}}_{x}{\text{Pr}}_{1\ensuremath{-}x}{\text{B}}_{6}$ solid solutions have been studied using both powder and single-crystal neutron diffraction. A variety of magnetic structures are observed depending on temperature and Ce concentration. Over a broad composition range $(x\ensuremath{\le}0.7)$, Pr-Pr interactions play a dominant role, giving rise to incommensurate structures with wave vectors of the form ${\mathbf{k}}_{\text{IC}1}=(1/4\ensuremath{-}\ensuremath{\delta},1/4,1/2)$ or ${\mathbf{k}}_{\text{IC}2}=(1/4\ensuremath{-}\ensuremath{\delta},1/4\ensuremath{-}\ensuremath{\delta},1/2)$. The crossover to a ${\text{CeB}}_{6}$-like regime takes place near $x=0.7--0.8$. For the latter composition, the antiferroquadrupolar phase transition observed in transport measurements precedes the onset, at lower temperature, of a commensurate magnetic order similar to that existing in ${\text{CeB}}_{6}$. However, unlike in the pure compound, an incommensurate magnetic order is formed at even higher temperature and persists in the antiferroquadrupolar phase down to the lock-in transition. These results are shown to reflect the interplay between various type of dipole exchange and higher multipole interactions in this series of compounds.

Incommensurate spin ordering and fluctuations in underdopedLa2−xBaxCuO4

By using neutron scattering techniques, we have studied the incommensurate spin ordering as well as the low energy spin dynamics in single crystal underdoped ${\text{La}}_{2\ensuremath{-}x}{\text{Ba}}_{x}{\text{CuO}}_{4}$ with $x\ensuremath{\sim}0.095$ and 0.08, which are high temperature superconductors with ${T}_{C}\ensuremath{\sim}27$ and 29 K, respectively. Static two dimensional incommensurate magnetic order appears below ${T}_{N}=39.5\ifmmode\pm\else\textpm\fi{}0.3\text{ }\text{K}$ in ${\text{La}}_{2\ensuremath{-}x}{\text{Ba}}_{x}{\text{CuO}}_{4}$ $(x=0.095)$ and a similar temperature for $x=0.08$ within the low temperature tetragonal phase. The spin order is unaffected by either the onset of superconductivity or the application of magnetic fields of up to 7 T applied along the $c$ axis in the $x=0.095$ sample. Such a magnetic field independent behavior is in marked contrast to the field induced enhancement of the staggered magnetization observed in the related ${\text{La}}_{2\ensuremath{-}x}{\text{Sr}}_{x}{\text{CuO}}_{4}$ system, which indicates that this phenomenon is not a universal property of cuprate superconductors. Surprisingly, we find that the incommensurability $\ensuremath{\delta}$ is only weakly dependent on doping relative to ${\text{La}}_{2\ensuremath{-}x}{\text{Sr}}_{x}{\text{CuO}}_{4}$. Dispersive excitations in ${\text{La}}_{2\ensuremath{-}x}{\text{Ba}}_{x}{\text{CuO}}_{4}$ $(x=0.095)$ at the same incommensurate wave vector persist up to at least 60 K. The dynamical spin susceptibility of the low energy spin excitations saturates below ${T}_{C}$ in a similar manner to that seen in the superconducting state of ${\text{La}}_{2}{\text{CuO}}_{4+y}$.

Neutron powder diffraction study of the magnetic and crystal structures of SrFe 2(PO 4) 2

The crystal and magnetic structures of SrFe 2+ 2(PO 4) 2 have been determined by neutron powder diffraction data at low temperatures (space group P2 1/ c (no. 14); Z=4; a=9.35417(13) Å, b=6.83808(10) Å, c=10.51899(15) Å, and β=109.5147(7)° at 15 K). Two magnetic phase transitions were found at T 1=7.4 K (first-order phase transition) and T 2=11.4 K (second-order phase transition). The transition at T 2 was hardly detectable by dc and ac magnetization measurements, and a small anomaly was observed by specific heat measurements. At T 1, strong anomalies were found by dc and ac magnetization and specific heat. The structure of SrFe 2(PO 4) 2 consists of linear four-spin cluster units, Fe2–Fe1–Fe1–Fe2. Below T 1, the propagation vector of the magnetic structure is k=[0,0,0]. The magnetic moments of the inner Fe1–Fe1 atoms of the four-spin cluster unit are ferromagnetically coupled. The magnetic moment of the outer Fe2 atom is also ferromagnetically coupled with that of the Fe1 atom but with spin canting. The four-spin cluster units form ferromagnetic layers parallel to the [−101] plane, while these layers are stacked antiferromagnetically in the [−101] direction. Spin canting of the outer Fe2 atoms provides a weak ferromagnetic moment of about 1 μ B along the b-axis. The refined magnetic moments at 3.5 K are 4.09 μ B for Fe1 and 4.07 μ B for Fe2. Between T 1 and T 2, a few weak magnetic reflections were observed probably due to incommensurate magnetic order.

Erratum: Landau analysis of the symmetry of the magnetic structure and magnetoelectric interaction in multiferroics [Phys. Rev. B76, 054447 (2007)

This paper presents a detailed instruction manual for constructing the Landau expansion for magnetoelectric coupling in incommensurate ferroelectric magnets, including ${\mathrm{Ni}}_{3}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$, $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_{3}$, $\mathrm{Mn}\mathrm{W}{\mathrm{O}}_{4}$, $\mathrm{Tb}{\mathrm{Mn}}_{2}{\mathrm{O}}_{5}$, $\mathrm{Y}{\mathrm{Mn}}_{2}{\mathrm{O}}_{5}$, $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_{2}$, and $\mathrm{Rb}\mathrm{Fe}{(\mathrm{M}{\mathrm{O}}_{4})}_{2}$. The first step is to describe the magnetic ordering in terms of symmetry adapted coordinates which serve as complex-valued magnetic order parameters whose transformation properties are displayed. In so doing, we use the previously proposed technique to exploit inversion symmetry, since this symmetry has seemingly been universally overlooked. Inversion symmetry severely reduces the number of fitting parameters needed to describe the spin structure, usually by fixing the relative phases of the complex fitting parameters. By introducing order parameters of known symmetry to describe the magnetic ordering, we are able to construct the trilinear magnetoelectric interaction which couples incommensurate magnetic order to the uniform polarization, and thereby we treat many of the multiferroic systems so far investigated. In most cases, the symmetry of the magnetoelectric interaction determines the direction of the magnetically induced spontaneous polarization. We use the Landau description of the magnetoelectric phase transition to discuss the qualitative behavior of various susceptibilities near the phase transition. The consequences of symmetry for optical properties such as polarization induced mixing of Raman and infrared phonons and electromagnons are analyzed. The implication of this theory for microscopic models is discussed.

X-ray scattering study of the order parameters in multiferroicTbMnO3

We report on an extensive investigation of the multiferroic compound TbMnO3 using x-ray scattering techniques. Nonresonant x-ray magnetic scattering NRXMS was used to characterize the domain population of the single crystal used in our experiments. This revealed that the dominant domain is overwhelmingly A type. The temperature dependence of the intensity and wave vector associated with the incommensurate magnetic order was found to be in good agreement with neutron scattering data. X-ray resonant scattering experiments were performed in the vicinity of the Mn K and Tb L3 edges in the high-temperature collinear phase, the intermediate temperature cycloidal and ferroelectric phase, and the low-temperature phase. In the collinear phase, where according to neutron diffraction only the Mn sublattice is ordered, resonant E1-E1 satellites were found at the Mn K edge associated with A-type but also F-type peaks. Detailed measurements of the azimuthal dependence of the F-type satellites and their absence in the NRXMS experiments leads us to conclude that they are most likely nonmagnetic in origin. We suggest instead that they may be associated with an induced charge multipole. At the Tb L3 edge, resonant A- and F-type satellites were observed in the collinear phase again associated with E1-E1 events. We attribute these to a polarization of the Tb 5d states by the ordering of the Mn sublattice. On cooling into the cycloidal and ferroelectric phase, a new set of resonant satellites appear corresponding to C-type order. These appear at the Tb L3 edge only. In addition to a dominant E1-E1 component in the - channel, a weaker component is found in the preedge with - polarization and displaced by −7 eV with respect to the E1-E1 component. Comprehensive calculations of the x-ray scattering cross section were performed using the FDMNES code. These calculations show that the unrotated - component of the Tb L3 C-type peaks appearing in the ferroelectric phase contains a contribution from a multipole that is odd with respect to both space and time, known in various contexts as the anapole. Our experiments thus provide tentative evidence for the existence of a type of anapolar order parameter in the rare-earth manganite class of mulitferroic compounds.

Occurrence of magnetism in [formula omitted] ( [formula omitted], Ir)

The physical properties of CeM ( In 1 - x Hg x ) 5 ( M = Rh , Ir) including specific heat and magnetic susceptibility are reported. Two magnetic phases exist in CeRhIn ( In 1 - x Hg x ) 5 with some evidence of a change from incommensurate magnetic order to a commensurate structure near 10% nominal Hg substitution. In CeIr ( In 1 - x Hg x ) 5 , an antiferromagnetic quantum critical point near x = 3 % (followed by robust long-range antiferromagnetism for x > 5 % ) appears to be separated from superconductivity in CeIrIn 5. The multitude of magnetic ground states observed in the CeM ( In 1 - x Hg x ) 5 materials is quite sensitive to doping and magnetic fields.

A nonfrustrated magnetoelectric with incommensurate magnetic order in magnetic field

We discuss a model nonfrustrated magnetoelectric in which a sufficiently strong magnetoelectric coupling produces an incommensurate magnetic order leading to ferroelectricity. Properties of the magnetoelectric in the magnetic field directed perpendicular to the wave vector describing the spin helix are considered in detail. Analysis of the classical energy shows that in contrast to the naive expectation, the onset of ferroelectricity occurs at a field H c1 that is lower than the saturation field H c2. We have H c1 = H c2 at large enough magnetoelectric coupling. We show that at H = 0, ferroelectricity occurs at T = T FE < T N. A qualitative discussion of the phase diagram in the H-T plane is presented within the mean-field approach.

Landau analysis of the symmetry of the magnetic structure and magnetoelectric interaction in multiferroics

This paper presents a detailed instruction manual for constructing the Landau expansion for magnetoelectric coupling in incommensurate ferroelectric magnets, including ${\mathrm{Ni}}_{3}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$, $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_{3}$, $\mathrm{Mn}\mathrm{W}{\mathrm{O}}_{4}$, $\mathrm{Tb}{\mathrm{Mn}}_{2}{\mathrm{O}}_{5}$, $\mathrm{Y}{\mathrm{Mn}}_{2}{\mathrm{O}}_{5}$, $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_{2}$, and $\mathrm{Rb}\mathrm{Fe}{(\mathrm{M}{\mathrm{O}}_{4})}_{2}$. The first step is to describe the magnetic ordering in terms of symmetry adapted coordinates which serve as complex-valued magnetic order parameters whose transformation properties are displayed. In so doing, we use the previously proposed technique to exploit inversion symmetry, since this symmetry has seemingly been universally overlooked. Inversion symmetry severely reduces the number of fitting parameters needed to describe the spin structure, usually by fixing the relative phases of the complex fitting parameters. By introducing order parameters of known symmetry to describe the magnetic ordering, we are able to construct the trilinear magnetoelectric interaction which couples incommensurate magnetic order to the uniform polarization, and thereby we treat many of the multiferroic systems so far investigated. In most cases, the symmetry of the magnetoelectric interaction determines the direction of the magnetically induced spontaneous polarization. We use the Landau description of the magnetoelectric phase transition to discuss the qualitative behavior of various susceptibilities near the phase transition. The consequences of symmetry for optical properties such as polarization induced mixing of Raman and infrared phonons and electromagnons are analyzed. The implication of this theory for microscopic models is discussed.

Incommensurate helical magnetic order in LiCu2O2 and NaCu2O2 quasi-one-dimensional compounds

The results of the measurements of the 6, 7Li and 23Na nuclear magnetic resonance (NMR) and 63, 65Cu nuclear quadrupole resonance in LiCu2O2 and NaCu2O2 quasi-one-dimensional compounds with a spin chains in the paramagnetic and magnetically ordered states are presented. The shape of the NMR line below Tc = 24 and 13 K for LiCu2O2 and NaCu2O2, respectively, is characteristic of the incommensurate static modulation of the local magnetic field matching with the incommensurate spiral modulation of the magnetic moments. The differences in the shape of the NMR spectra of 23Na and 7Li are discussed in terms of the features of the crystal structure of LiCu2O2 and NaCu2O2.

Stripeless incommensurate magnetism in strongly correlated oxideLa1.5Sr0.5CoO4

We studied the nanoscale structure of the short-range incommensurate magnetic order in ${\text{La}}_{1.5}{\text{Sr}}_{0.5}{\text{CoO}}_{4}$ by elastic neutron scattering. We find that magnetic diffuse scattering is isotropic in the $a\text{\ensuremath{-}}b$ plane, in contrast with the naive expectation based on the popular stripe model. Indeed, charge segregation into lines favoring certain lattice direction(s) would facilitate linear stacking faults in an otherwise robust antiferromagnetism of undoped material, leading to anisotropic disorder with a characteristic symmetry pattern present in the neutron scattering data.

Magnetic-order-induced ferroelectricity in orthorhombic perovskite manganites

We studied the ferroelectricity of magnetic oxides, in which its emergence coincides with the onset of a second incommensurate magnetic order. We solved for the wave function of ${e}_{g}$ electrons in the presence of magnetic orders. The coupling between the magnetic and electric orders is provided by the spin-orbit interaction. It was found that the net electric dipole moment of the system came from the bond between the transition metal and oxygen atoms. The anisotropy of $d$ orbitals also played an important role. Finally, the form of the coupling leads us to the conclusion that it is an improper ferroelectricity.