Incommensurate Magnetic Structures Research Articles

Neutron diffraction studies under zero and finite magnetic fields of the 12 quantum magnetization plateau compound Ni2V2O7

We performed powder neutron diffraction experiments on a $\frac{1}{2}$ quantum magnetization plateau compound ${\mathrm{Ni}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{7}$ for magnetic fields in the range 0--10 T. The incommensurate magnetic structures with the propagation vector $({k}_{x}\ensuremath{\sim}0.45,0,0)$ were determined at 0 T and at 6.0 K (between ${T}_{\mathrm{N}1}=6.7$ K and ${T}_{\mathrm{N}2}=5.7$ K) and 2.3 K. Consequently, the Ni1 and Ni2 moments were disordered and ordered at 6.0 K, respectively, indicating a partially disordered state. The magnetic structure of Ni2 moments was a spin density wave structure with moments ordered parallel to the $b$ axis and perpendicular to the propagation vector. Both Ni1 and Ni2 moments exhibited ellipsoidal cycloidal incommensurate magnetic structures at 2.3 K. These moments lay in the $ab$ plane. The maximum magnitudes of Ni1 and Ni2 moments [1.62(16) and 2.50(6) ${\textmu{}}_{\mathrm{B}}$] at 2.3 K were sufficiently smaller and slightly larger than the value ($\ensuremath{\sim}2.2\phantom{\rule{0.28em}{0ex}}{\textmu{}}_{\mathrm{B}}$) expected from the classical picture. Further, we evaluated the field-induced magnetic moments as follows: ${m}_{1}=0.3$ and ${m}_{2}=1.9\phantom{\rule{0.28em}{0ex}}{\textmu{}}_{\mathrm{B}}$ at Ni1 and Ni2 sites, respectively, at 10 T and 1.9 K, where the $\frac{1}{2}$ quantum magnetization plateau was observed. The results indicating both the ordered moment at 0 T and the field-induced moment at 10 T being small and large at Ni1 and Ni2 sites, respectively, were consistent with results expected in the $\text{dimer}+\text{monomer}$ model that was proposed by J. J. Cao et al. [Phys. Rev. B 106, 184409 (2022)].

Enumeration and tabulation of magnetic (3+d)-dimensional superspace groups.

A magnetic superspace group (MSSG) simultaneously constrains both the magnetic and non-magnetic (e.g. displacive, occupational, rotation and strain) degrees of freedom of an incommensurately modulated magnetic crystal. We present the first enumeration and tabulation of all non-equivalent (3+d)-dimensional magnetic superspace groups for d = 1, 2 and 3 independent incommensurate modulations, along with a number, symbol and reference setting for each group. We explain the process for generating an exhaustive set of inequivalent magnetic superspace groups, describe several examples, and show how the tables can be accessed via the ISO(3+d)D interface within the ISOTROPY Software Suite. We recommend that published incommensurate magnetic structures indicate a magnetic superspace-group number and symbol from these tables, as well as the transformation matrix from the published group setting to the reference setting used in these tables.

Ellipsoidal Cycloidal Magnetic Structures in Cr1−xMoxB2 Revealed by Neutron Diffraction and Polarimetry Experiments

We examined incommensurate magnetic structures in Cr1−xMoxB2 (\(x = 0,0.15\)) by neutron diffraction experiments. Single crystals of Cr1−xMoxB2 were grown by the floating zone method. Using unpolar...

Chiral properties of the zero-field spiral state and field-induced magnetic phases of the itinerant kagome metal YMn6Sn6

Applying a magnetic field in the hexagonal plane of YMn$_6$Sn$_6$ leads to a complex magnetic phase diagram of commensurate and incommensurate phases, one of which coexists with the topological Hall effect (THE) generated by a unique fluctuation-driven mechanism. Using unpolarized neutron diffraction, we report on the solved magnetic structure for two previously identified, but unknown, commensurate phases. These include a low-temperature, high-field fan-like phase and a room-temperature, low-field canted antiferromagnetic phase. An intermediate incommensurate phase between the fan-like and forced ferromagnetic phases is also identified as the last known phase of the in-plane field-temperature diagram. Additional characterization using synchrotron powder diffraction reveals extremely high-quality, single-phase crystals, which suggests that the presence of two incommensurate magnetic structures throughout much of the phase diagram is an intrinsic property of the system. Interestingly, polarized neutron diffraction shows that the centrosymmetric system hosts preferential chirality in the zero-field double-flat-spiral phase, which, along with the THE, is a topologically non-trivial characteristic.

Analysis of Incommensurate Magnetic Structures of Rare-Earth Intermetallides Tb3Ni and Ho7Rh3 Using the Magnetic Supersymmetry Group Formalism

Complex incommensurate magnetic structures of Tb3Ni and Ho7Rh3 compounds have been analyzed using the magnetic superspace group approach. It has been established that the high-temperature incommensurate magnetic structure of Tb3Ni is described by the magnetic superspace group P1121/a1'(ab0)0ss and the incommensurate magnetic structure of Ho7Rh3 is described by the magnetic superspace group $$P{{6}_{3}}1{\kern 1pt} '\left( {00g} \right)hs.$$ Using the example of the Tb3Ni and Ho7Rh3 compounds, it is shown that the magnetic superspace groups formalism is the most efficient approach when establishing and describing complex incommensurate magnetic structures.

Zinc blende and wurtzite CoO polymorph nanoparticles: Rational synthesis and commensurate and incommensurate magnetic order

On the nanoscale, CoO can have different polymorph crystal structures, zinc blende and wurtzite, apart from rock salt, which is the stable one in bulk. However, the magnetic structures of the zinc blende and wurtzite phases remain virtually unexplored. Here we discuss some of the main parameters controlling the growth of the CoO wurtzite and zinc blende polymorphs by thermal decomposition of cobalt (II) acetylacetonate. In addition, we present a detailed neutron diffraction study of oxygen deficient CoO (CoO0.70–0.75) nanoparticles with zinc blende (∼15nm) and wurtzite (∼30nm) crystal structures to unravel their magnetic order and its temperature evolution. The magnetic order of the zinc blende nanoparticles is antiferromagnetic and appears at the Néel temperature TN∼203K. It corresponds to the 3rd type of magnetic ordering in a face-centered cubic lattice with magnetic moments aligned along a cube edge. The magnetic structure in the wurtzite nanoparticles turned out to be rather complex with two perpendicular components. One component is incommensurate, of the longitudinal spin wave type, with the magnetic moments confined in the ab-plane. In the perpendicular direction, this magnetic order is uncorrelated, forming quasi-two-dimensional magnetic layers. The component of the magnetic moment, aligned along the hexagonal axis, is commensurate and corresponds to the antiferromagnetic order known as the 2nd type in a wurtzite structure. The Néel temperature of wurtzite phase is estimated to be ∼109K. The temperature dependence of the magnetic reflections confirms the reduced dimensionality of the incommensurate magnetic order. Incommensurate magnetic structures in nanoparticles are an unusual phenomenon and in the case of wurtzite CoO it is probably caused by structural defects (e.g., vacancies, strains and stacking faults).

On the symmetry of incommensurate magnetic structures

On the symmetry of incommensurate magnetic structures

The multi-purpose three-axis spectrometer (TAS) MIRA at FRM II

The cold-neutron three-axis spectrometer MIRA is an instrument optimized for low-energy excitations. Its excellent intrinsic Q-resolution makes it ideal for studying incommensurate magnetic systems (elastic and inelastic). MIRA is at the forefront of using advanced neutron focusing optics such as elliptic guides, which enable the investigation of small samples under extreme conditions. Another advantage of MIRA is the modular assembly allowing for instrumental adaption to the needs of the experiment within a few hours. The development of new methods such as the spin-echo technique MIEZE is another important application at MIRA. Scientific topics include the investigation of complex inter-metallic alloys and spectroscopy on incommensurate magnetic structures.

Magnetic structures of rare earth intermetallic compounds RCuAs2 (R = Pr, Nd, Tb, Dy, Ho, and Yb)

Neutron scattering studies have been carried out on polycrystalline samples of a series of rare earth intermetallic compounds RCuAs2 (R = Pr, Nd, Dy, Tb, Ho and Yb) as a function of temperature to determine the magnetic structures and the order parameters. These compounds crystallize in the ZrCuSi2 type structure, which is similar to that of the RFeAsO (space group P4/nmm) class of iron-based superconductors. PrCuAs2 develops commensurate magnetic order with K = (0, 0, 0.5) below TN = 6.4(2) K, with the ordered moments pointing along the c-axis. The irreducible representation analysis shows either a Γ12 or Γ13 representation. NdCuAs2 and DyCuAs2 order below TN = 3.54(5) K and TN = 10.1(2) K, respectively, with the same ordering wave vector but the moments lying in the a-b plane (with a Γ29 or Γ210 representation). TbCuAs2 and HoCuAs2 exhibit incommensurate magnetic structures below TN = 9.44(7) and 4.41(2) K, respectively. For TbCuAs2, two separate magnetic ordering wave vectors are established as K1(Tb) = (0.240,0.155,0.48) and K2(Tb) = (0.205, 0.115, 0.28), whereas HoCuAs2 forms a single K(Ho) = (0.121, 0.041, 0.376) magnetic structure with 3rd order harmonic magnetic peaks. YbCuAs2 does not exhibit any magnetic Bragg peaks at 1.5 K, while susceptibility measurements indicate an antiferromagnetic-like transition at 4 K, suggesting that either the ordering is not long range in nature or the ordered moment is below the sensitivity limit of ≈0.2 μB.

Determination of the magnetic structure of CePt2In7 by means of neutron diffraction

The magnetic structure of the heavy fermion antiferromagnet CePt$_2$In$_7$ is determined using neutron diffraction. We find a magnetic wave vector $\mathbf{q}_M = (1/2,1/2,1/2)$, which is temperature independent up to $T_N =$ 5.5 K. A staggered moment of 0.45(1)$\mu_B$ at 2 K resides on the Ce ion. The nearest-neighbor moments in the tetragonal basal plane are aligned antiferromagnetically. The moments rotate by 90$^\circ$ from one CeIn$_3$ plane to another along the $c$ axis. A much weaker satellite peak with an incommensurate magnetic wave vector $\mathbf{q}_M = (1/2,1/2,0.47)$ seems to develop at low temperature. However, the experimental data available so far are not sufficient to draw a definitive conclusion about the possible co-existence of commensurate and incommensurate magnetic structures in this material.

MAGNDATA: towards a database of magnetic structures. II. The incommensurate case

A free web page under the name MAGNDATA, which provides detailed quantitative information on more than 400 published magnetic structures, has been made available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). It includes both commensurate and incommensurate structures. In the first article in this series, the information available on commensurate magnetic structures was presented [Gallego, Perez-Mato, Elcoro, Tasci, Hanson, Momma, Aroyo & Madariaga (2016). J. Appl. Cryst. 49, 1750–1776]. In this second article, the subset of the database devoted to incommensurate magnetic structures is discussed. These structures are described using magnetic superspace groups, i.e. a direct extension of the non-magnetic superspace groups, which is the standard approach in the description of aperiodic crystals. The use of magnetic superspace symmetry ensures a robust and unambiguous description of both atomic positions and magnetic moments within a common unique formalism. The point-group symmetry of each structure is derived from its magnetic superspace group, and any macroscopic tensor property of interest governed by this point-group symmetry can be retrieved through direct links to other programs of the Bilbao Crystallographic Server. The fact that incommensurate magnetic structures are often reported with ambiguous or incomplete information has made it impossible to include in this collection a good number of the published structures which were initially considered. However, as a proof of concept, the published data of about 30 structures have been re-interpreted and transformed, and together with ten structures where the superspace formalism was directly employed, they form this section of MAGNDATA. The relevant symmetry of most of the structures could be identified with an epikernel or isotropy subgroup of one irreducible representation of the space group of the parent phase, but in some cases several irreducible representations are active. Any entry of the collection can be visualized using the online tools available on the Bilbao server or can be retrieved as a magCIF file, a file format under development by the International Union of Crystallography. These CIF-like files are supported by visualization programs like Jmol and by analysis programs like JANA and ISODISTORT.

Static and quasielastic properties of the spiral magnetBa2CuGe2O7studied by neutron resonance spin echo spectroscopy and neutron Larmor labeling

We provide a route to use elastic and quasielastic neutron spin echo spectroscopy (Larmor labeling) for a unified approach to study both the static and dynamic properties of incommensurate magnetic structures with small propagation vectors. The archetypal noncentrosymmetric spiral magnet ${\mathrm{Ba}}_{2}{\mathrm{CuGe}}_{2}{\mathrm{O}}_{7}$ serves as a model system for our study. We show how Larmor labeling can efficiently decouple instrumental wavelength resolution and effective-$\stackrel{P\vec}{Q}$ resolution and give high-precision access to the structural properties of the incommensurate domains of ${\mathrm{Ba}}_{2}{\mathrm{CuGe}}_{2}{\mathrm{O}}_{7}$.

Flat and conical incommensurate magnetic structures in the two-subsystem partially frustrated Heisenberg ferrimagnet

The phase transitions into flat and conical incommensurate magnetic structures are considered for a ferrimagnet with the dominant nonfrustrated exchange between the spins in one crystallographic position, competing exchanges between the spins in another position and frustrated exchange between the spins in different positions. The appearance conditions and the temperatures of the second order phase transitions are analytically obtained in the mean field approximation. The first order phase transition between these states is studied and the phase diagrams of temperature vs frustrated exchanges are calculated by the numerical minimization of free energy.

Linear spin wave theory for single-Q incommensurate magnetic structures

Linear spin wave theory provides the leading term in the calculation of the excitation spectra of long-range ordered magnetic systems as a function of . This term is acquired using the Holstein–Primakoff approximation of the spin operator and valid for small δS fluctuations of the ordered moment. We propose an algorithm that allows magnetic ground states with general moment directions and single-Q incommensurate ordering wave vector using a local coordinate transformation for every spin and a rotating coordinate transformation for the incommensurability. Finally we show, how our model can determine the spin wave spectrum of the magnetic C-site langasites with incommensurate order.

Field effects withH∥bon the incommensurate magnetic structures of multiferroicMnWO4studied within the superspace formalism

We investigate the magnetic-field-induced $(H\ensuremath{\parallel}b)$ transition in the reference improper multiferroic $\mathrm{MnW}{\mathrm{O}}_{4}$ using superspace formalism. The distinct superspace group symmetries are determined from single-crystal neutron diffraction. The study of the full magnetic symmetry of the incommensurate magnetic phases under field provides the keys for understanding its magnetic and ferroelectric behavior up to 12 T. At moderate fields, below the transition, the magnetic modulations of the two Mn sites in the simple cell are independent. At the field-induced transition between multiferroic phases, the electric polarization undergoes a flip from the monoclinic $b$ axis to the $ac$ plane. An additional component in the polarization is predicted along the $c$ axis, due to a point symmetry change from ${2}_{y}{1}^{\ensuremath{'}}$ to ${m}_{y}{1}^{\ensuremath{'}}$. In contrast with the low-field phase, above the transition the influence of the magnetic field results in the coupling between the magnetic modulations of the two Mn sites of the original monoclinic cell.

ChemInform Abstract: Field‐Induced Spin‐Flop in Antiferromagnetic Semiconductors with Commensurate and Incommensurate Magnetic Structures: Li2FeGeS4 (LIGS) and Li2FeSnS4 (LITS).

AbstractThe title compounds are characterized by synchrotron powder XRD, neutron powder diffraction, 57Fe and 119Sn Moessbauer spectroscopy, UV/VIS/NIR diffuse reflectance spectroscopy, and magnetic measurements.

Sheding light on the multiferroicity in Mn1-xCoxWO4using superspace formalism

The use of the superspace symmetry formalism allows to rationalize the physical properties induced by an incommensurate magnetic ordering [1]. The incommensurate magnetic structures (ICMS) in Mn1-xCoxWO4 have been studied in the light of this formalism. MnWO4 is a multiferroic material in which the magnetic order of one of its magnetic phases induces ferroelectricity. Like most multiferroic materials MnWO4 is extremely sensitive to small perturbations such as chemical substitution. It turned out that doping with Co2+ is particularly interesting since it strongly stabilizes the multiferroic phase at low temperatures, and moreover, by increasing the cobalt amount in the crystals the orientation of the electric polarization flops from the b axis to the ac plane [2]. This change of orientation is linked to a symmetry change. The ICMS of the x = 0 and x = 0.10 compounds, which exhibit completely different behavior, have been studied thoroughly using superspace formalism. We have found, not only the symmetry of the magnetic structures and their intrinsic restrictions, but also information about the tensor properties of each incommensurate phase, such as ferroelectric and magnetostructural properties [3]: in the paramagnetic state, there is a unique independent magnetic atom in the crystallographic unit cell in both cases, but when the system enters into the multiferroic phase, this is no-longer true. In the multiferroic phase of MnWO4, the two Mn atoms in the unit cell become symmetry independent, whereas in the x = 0.10 substituted compound, they are still symmetry-related. This difference is related to the change of the electric polarization.

Incommensurate Magnetic Structures in the Rhombohedrally Distorted Cubic Lattice

The ground state of a rhombohedrally distorted magnetic cubic lattice with frustrated exchange in the thriangular base plane of spins and competition of exchanges between the nearest and next nearest planes was investigated. The dependence of helix vector components on the exchange parameters was calculated. The phase diagram of ground state was obtained.

Incommensurate magnetic structures in rhombohedral Heisenberg antiferromagnet

The phase diagram of the ground state has been calculated for a rhombohedral antiferromagnet of the R3m symmetry with frustrated exchange in the base plane and competition of exchanges between the nearest and next-nearest planes. The diagram contains phases of collinear antiferromagnetic ordering of various types separated by five incommensurate magnetic states of the helicoidal type, differing in the ordering type and in the direction of the modulation vector. The commensurate and incommensurate phases converge at multi-critical points lying on a line corresponding to an antiferromagnet with an undistorted simple cubic lattice.

Field-induced phase transitions and phase diagrams in BiFeO3-like multiferroics

The incommensurate magnetic structures and phase diagrams of multiferroics has been explored on the basis of accurate micromagnetic analysis taking into account the spin flexoelecric interaction (Lifshitz invariant). The objects of the study are BiFeO_3-like single crystals and epitaxial films grown on the <111> substrates. The main control parameters are the magnetic field, the magnetic anisotropy, and the epitaxial strain in the case of films. We predict novel quasi-cycloidal structures induced by external magnetic field or by epitaxial strain in the BiFeO_3-films. Phase diagrams representing the regions of homogeneous magnetic states and incommensurate structures stability are constructed for the two essential geometries of magnetic field (magnetic field oriented parallel to the principal crystal axis C_3 and perpendicular to this direction C_3). It is shown that the direction of applied magnetic field substantially affects a set of magnetic phases, properties of incommensurate structures, character of phase transitions. Novel conical type of cycloidal ordering is revealed during the transition from incommensurate cycloidal structure into homogeneous magnetic state. Elaborated phase diagrams allow estimate appropriate combination of control parameters (magnetic field, magnetic anisotropy, exchange stiffness) required to the destruction of cycloidal ordering corresponding to the transition into homogeneous structure. The results show that the magnitude of critical magnetic field suppressing cycloid is lowered in multiferroics films comparing to single crystals, it can be also lowered by the selection of orientation of magnetic field. Our results can be useful for strain engineering of new multiferroic functional materials on demand.