Zero-field Magnetic Structure Research Articles

Stripe antiferromagnetic ground state of the ideal triangular lattice compound KErSe2

Rare earth triangular lattice materials have been proposed as a good platform for the investigation of frustrated magnetic ground states. KErSe$_2$ with the delafossite structure, contains perfect two-dimensional Er$^{3+}$ triangular layers separated by potassium ions, realizing this ideal configuration and inviting study. Here we investigate the magnetism of KErSe$_2$ at miliKelvin temperatures by heat capacity and neutron powder diffraction. Heat capacity results reveal a magnetic transition at 0.2 K in zero applied field. This long-range order is suppressed by an applied magnetic field of 0.5 T below 0.08 K. Neutron powder diffraction suggests that the zero-field magnetic structure orders with $k=(\frac{1}{2},0,\frac{1}{2})$ in a stripe spin structure. Unexpectedly, Er is found to have a reduced moment of 3.06(1) $\mu_B$/Er in the ordered state and diffuse magnetic scattering, which originates at higher temperatures, is found to persist in the ordered state potentially indicating magnetic fluctuations. Neutron diffraction collected under an applied field shows a metamagnetic transition at $\sim$ 0.5 T to ferromagnetic order with $k$=(0,0,0) and two possible structures, which are likely dependent on the applied field direction. First principle calculations show that the zero field stripe spin structure can be explained by the first, second and third neighbor couplings in the antiferromagnetic triangular lattice.

Evolution of spin correlations in SrDy2O4 in an applied magnetic field

The development of short- and long-range magnetic order induced in a frustrated zig-zag ladder compound SrDy2O4 by an applied field is studied using neutron diffraction techniques. In zero field, SrDy2O4 lacks long-range magnetic order down to temperatures as low as 60 mK, and the observed powder neutron diffraction (PND) patterns are dominated by very broad diffuse scattering peaks. Single crystal neutron diffraction reveals that the zero-field magnetic structure consists of a collection of antiferromagnetic chains running along the c axis and that there is very little correlation between the chains in the ab plane. In an applied magnetic field, the broad diffuse scattering features in PND are gradually replaced by much sharper peaks, however, the pattern remains rather complex, reflecting the highly anisotropic nature of SrDy2O4. Single crystal neutron diffraction shows that a moderate field applied along the b axis induces an up-up-down magnetic order associated with a 1/3-magnetisation plateau, in which magnetic correlation length in the ab plane is significantly increased, but it nevertheless remains finite. The resolution limited k = 0 peaks associated with a ferromagnetic arrangement appear in powder and single crystal neutron diffraction patterns in fields of 2.5 T and above.

High-temperature series expansion for spin-1/2 Heisenberg models

We present a high-temperature series expansion code for spin-1/2 Heisenberg models on arbitrary lattices. As an example we demonstrate how to use the application for an anisotropic triangular lattice with two independent couplings J1 and J2 and calculate the high-temperature series of the magnetic susceptibility and the static structure factor up to 12th and 10th order, respectively. We show how to extract effective coupling constants for the triangular Heisenberg model from experimental data on Cs2CuBr4. Program summaryProgram Title: LCSEProgram Files doi:http://dx.doi.org/10.17632/vygxnfjt8b.1Licensing provisions: Apache-2.0.Programming language: C++11, MPI for parallelization, Mathematica for analysis of results.Nature of problem: Calculation of thermodynamic properties (mag- netic susceptibility and static structure factor) for quantum magnets on arbitrary lattices. A particularly hard problem pose quantum magnets on so frustrated lattice geometries, as they cannot be solved efficiently by Quantum Monte Carlo methods.Solution method: High-temperature series expansions employing a linked-cluster expansion allow to obtain a high-order series in the inverse temperature for thermodynamic quantities in the thermodynamic limit. The resulting high-temperature series are exact up to the expansion order. We implement the calculation of high-temperature series for the zero-field magnetic susceptibility and static magnetic structure factor for the spin-1/2 Heisenberg model on arbitrary infinite lattices in arbitrary dimension.External routines/libraries: ALPS [13,14], GMP [29]

Determination of the zero-field magnetic structure of the helimagnet MnSi at low temperature

Below a temperature of approximately 29 K the manganese magnetic moments of the cubic binary compound MnSi order to a long-range incommensurate helical magnetic structure. Here we quantitatively analyze a high-statistic zero-field muon spin rotation spectrum recorded in the magnetically ordered phase of MnSi by exploiting the result of representation theory as applied to the determination of magnetic structures. Instead of a gradual rotation of the magnetic moments when moving along a $\ensuremath{\langle}111\ensuremath{\rangle}$ axis, we find that the angle of rotation between the moments of certain subsequent planes is essentially quenched. It is the magnetization of pairs of planes which rotates when moving along a $\ensuremath{\langle}111\ensuremath{\rangle}$ axis, thus preserving the overall helical structure.

Magnetic structure and dynamics of a strongly one-dimensionalcobaltIImetal-organic framework

We investigate the magnetism of the ${\text{Co}}^{\mathrm{II}}$${}_{4}$(OH)${}_{2}$(${\text{C}}_{10}$${\text{H}}_{16}$${\text{O}}_{4}$)${}_{3}$ metal-organic framework, which displays complex inorganic chains separated from each other by distances of 1 to 2 nm and orders at 5.4 K. The zero-field magnetic structure is determined using neutron powder diffraction: it is mainly antiferromagnetic but possesses a ferromagnetic component along the c axis. This magnetic structure persists in presence of a magnetic field. Alternating current susceptibility measurements confirm the existence of a single thermally activated regime over seven decades in frequency ($E/{k}_{B}\ensuremath{\approx}64$ K), whereas time-dependent relaxation of the magnetization after saturation in an external field leads to a two times smaller energy barrier. These experiments probe the slow dynamics of domain walls within the chains: we propose that the ac measurements are sensitive to the motion of existing domain walls within the chains, while the magnetization measurements are governed by the creation of domain walls.

Growth and micromagnetism of self-assembled epitaxial fcc(111) cobalt dots

We develop the self-assembly of epitaxial submicrometer-sized face-centered-cubic (fcc) Co(111) dots using pulsed laser deposition. The dots display atomically flat facets, from which the ratios of surface and interface energies for fcc Co are deduced. Zero-field magnetic structures are investigated with magnetic force and Lorentz microscopies, revealing vortex-based flux-closure patterns. A good agreement is found with micromagnetic simulations.

Correlation between crystallographic superstructure and magnetic structures in finite magnetic fields: A neutron study on a single crystal ofHo2PdSi3

We present results of neutron-diffraction experiments on a ${\text{Ho}}_{2}{\text{PdSi}}_{3}$ single crystal in the magnetically ordered state at $T=1.5\text{ }\text{K}$ for magnetic fields applied in the easy $(0,0,L)$ direction. Moderate fields of less than 0.8 T are sufficient to wipe out the antiferromagnetic order in the basal plane of the ${\text{AlB}}_{2}$-type hexagonal lattice structure. Concurrently strong magnetic reflections along the $(0,0,L)$ direction develop with increasing fields that are closely related to the nuclear superstructure reflections found in the single crystal at all temperatures. The field dependence of the intensity of these reflections is rather unusual: after a maximum at 0.6 T and a shallow minimum at 2 T a further increase in intensity for fields up to 5 T is observed. A phase transition into a field induced, saturated ferromagnetic state is expected only at very high fields $(g13\text{ }\text{T})$ as inferred from magnetization data. For the origin of the high-field magnetic structure two models are proposed and the corresponding model calculations are compared to our experimental results. Furthermore, the experimental data in low fields $(l0.8\text{ }\text{T})$ are used to clarify the hitherto unsolved zero-field magnetic structure of ${\text{Ho}}_{2}{\text{PdSi}}_{3}$. The relevance of our findings with respect to other members of the ${R}_{2}{\text{PdSi}}_{3}$ series ($R=\text{Tb}$, Er, Tm, and others) is emphasized.

Determination of the magnetic structure ofYb3Pt4:k=0local-moment antiferromagnet

We have used neutron-diffraction measurements to study the zero-field magnetic structure of the intermetallic compound ${\text{Yb}}_{3}{\text{Pt}}_{4}$, which was earlier found to order antiferromagnetically at the N\'eel temperature ${T}_{\text{N}}=2.4\text{ }\text{K}$, and displays a field-driven quantum-critical point at 1.6 T. In ${\text{Yb}}_{3}{\text{Pt}}_{4}$, the Yb moments sit on a single low-symmetry site in the rhombohedral lattice with space group $R\overline{3}$. The Yb ions form octahedra with edges that are twisted with respect to the hexagonal unit cell, a twisting that results in every Yb ion having exactly one Yb nearest neighbor. Below ${T}_{\text{N}}$, we found new diffracted intensity due to a $\mathbit{k}=0$ magnetic structure. This magnetic structure was compared to all symmetry-allowed magnetic structures and was subsequently refined. The best-fitting magnetic-structure model is antiferromagnetic and involves pairs of Yb nearest neighbors on which the moments point almost exactly toward each other. This structure has moment components within the $ab$ plane as well as parallel to the $c$ axis although the easy magnetization direction lies in the $ab$ plane. Our magnetization results suggest that besides the crystal-electric-field anisotropy, anisotropic exchange favoring alignment along the $c$ axis is responsible for the overall direction of the ordered moments. The magnitude of the ordered Yb moments in ${\text{Yb}}_{3}{\text{Pt}}_{4}$ is $0.81{\ensuremath{\mu}}_{\text{B}}/\text{Yb}$ at 1.4 K. The analysis of the bulk properties, the size of the ordered moment, and the observation of well-defined crystal-field levels argue that the Yb moments are spatially localized in zero field.

Magnetic order in CePdAl single crystal: Effect of magnetic field

Our neutron diffraction experiments on CePdAl single crystal down to 0.36 K do not reveal any additional magnetic reflections except those which apper below T N=2.78 (4) K and can be indexed with the propagation vector q=(0.5 0 τ). The component τ decreases with lowering temperature and stays constant below 1.9 K. Application of field up to 5.5 T directed along the easy magnetization c-axis shows that geometrical magnetic frustration present in zero field can be lifted. The magnetization process is hysteretic and in agreement with bulk measurements. The observed three field-induced transitions are complicated with signs of domain re-population. The zero-field magnetic structure established after application of field has slightly different magnetic periodicity with respect to the zero-field cooled state.

Neutron diffraction investigations of zero-field and field-induced magnetic structures of DyNiSn single crystal

Single crystal neutron diffraction studies have been performed on the rare-earth ternary compound, DyNiSn. This crystal exhibits an incommensurate magnetic structure expressed by the propagation vector, Q = (0.662 0.352 0) with its third harmonics at low temperatures. In an external magnetic field applied along the c-axis DyNiSn shows incommensurate modulation with Q = (1 0.315 0) at 1.6 K, while along the easy magnetization direction of the b-axis a commensurate modulation with Q = (2/3 0 0) develops at 2 K. The results along the b-axis are fully consistent with the magnetization curve.

Quadrupolar and dipolar magnetic order inDyPd3S4: A neutron scattering and muon spin rotation and relaxation investigation

The quadrupolar and dipolar magnetic phases in polycrystalline ${\mathrm{DyPd}}_{3}{\mathrm{S}}_{4}$ have been investigated by neutron scattering and muon spin rotation/relaxation $(\ensuremath{\mu}\mathrm{SR})$ technique. The transition from paramagnetic to antiferroquadrupolar state at ${T}_{Q}=3.4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ as well as two successive dipolar magnetic phase transitions at ${T}_{N1}\ensuremath{\approx}1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and ${T}_{N2}\ensuremath{\approx}0.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ are evidenced by anomalies in the observed relaxation rates in the zero-field $\ensuremath{\mu}\mathrm{SR}$ measurements. In addition, measurements in longitudinal external magnetic field showed clear evidence for field-induced dipolar magnetic moments below ${T}_{Q}$. In inelastic neutron scattering measurements the transition to an ordered lattice of the Dy quadrupole moments at ${T}_{Q}$ is observed by a temperature dependent splitting of the ground-state crystal-field multiplet below ${T}_{Q}$. Neutron diffraction revealed the induced magnetic structure in the quadrupolar phase of ${\mathrm{DyPd}}_{3}{\mathrm{S}}_{4}$ to be of the canted antiferromagnetic type with a canting angle close to perpendicular, similar to the spontaneous zero-field magnetic structures below $1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

Zero-field magnetic structure inCeB6reinvestigated by neutron diffraction and muon spin relaxation

The zero-field magnetic structure of ${\mathrm{Ce}}^{11}{\mathrm{B}}_{6}$ has been revised from neutron powder and single-crystal diffraction including neutron spherical polarimetry. The crystal structure remains cubic in the antiferroquadrupolar (AFQ) ordered state ${(T}_{Q}=3.3\mathrm{K},$ ${\mathbf{k}}_{Q}=[1/2,1/2,1/2])$ and in the antiferromagnetic (AFM) ordered state ${(T}_{N}=2.3\mathrm{K},$ ${\mathbf{k}}_{1}=[1/4,1/4,0],$ ${\mathbf{k}}_{2}=[1/4,\ensuremath{-}1/4,0],$ ${\mathbf{k}}_{1}^{\ensuremath{'}}=[1/4,1/4,1/2],$ ${\mathbf{k}}_{2}^{\ensuremath{'}}=[1/4,\ensuremath{-}1/4,1/2])$ within the precision of the experiment. The model of Effantin et al. [J. Magn. Magn. Mater. 47-48, 145 (1985)] fits our 60-mK high-intensity neutron powder diffraction data rather poorly and therefore a model of the AFM multi-$\mathbf{k}$ structure has been developed. It is a 2 ${\mathbf{k}\mathbf{\ensuremath{-}}\mathbf{k}}^{\ensuremath{'}}$ transverse sine-wave structure with the Ce magnetic moments strictly along $[1\ensuremath{-}10]$ and [110] and orthogonal arrangement of the nearest moments. Ce atoms located at the $z=0$ and $z=1$ layers have significantly different magnetic moment values. In addition there is a modulation of the moment value in each layer. The resulting ordered magnetic Ce moments reach $0.744(16){\ensuremath{\mu}}_{B},$ $0.543(16){\ensuremath{\mu}}_{B}$ at $z=1$ and only $0.01{\ensuremath{\mu}}_{B},$ $0.138(7){\ensuremath{\mu}}_{B}$ at $z=0$ at 60 mK. This complex AFM structure is due to competition between the established AFQ order and the dipolar and octupolar AFM order developing at lower temperatures. The model is consistent with the $\ensuremath{\mu}\mathrm{SR}$ zero-field results [R. Feyerherm et al., J. Magn. Magn. Mater. 140-144, 1175 (1995)] and suggests a highly inhomogeneous conduction electron spin polarization and anisotropic RKKY interactions below ${T}_{N}.$

Interdependence of magnetism and superconductivity in the borocarbide TmNi2B2C

We have discovered a new antiferromagnetic phase in TmNi2B2C by neutron diffraction. The ordering vector is Q(A) = (0.48,0,0) and the phase appears above a critical in-plane magnetic field of 0.9 T. The field was applied in order to test the assumption that the zero-field magnetic structure at Q(F) = (0.094,0.094,0) would change into a c-axis ferromagnet if superconductivity were destroyed. We present theoretical calculations which show that two effects are important: a suppression of the ferromagnetic component of the RKKY exchange interaction in the superconducting phase and a reduction of the superconducting condensation energy due to the periodic modulation of the moments at Q(A).

Neutron diffraction and x-ray resonant exchange-scattering studies of the zero-field magnetic structures ofTbNi2Ge2

The zero-field magnetic structures of the rare-earth intermetallic compound ${\mathrm{TbNi}}_{2}{\mathrm{Ge}}_{2}$ have been determined using conventional magnetic neutron diffraction and high-resolution x-ray resonant exchange scattering techniques. There are two distinct magnetic phase transitions in this material: one is from the high-temperature paramagnetic state to a long period antiferromagnetic phase at the N\'eel temperature ${(T}_{N}=16.8 \mathrm{K}),$ and the other is at a lower temperature ${(T}_{t}=9.3 \mathrm{K}),$ where the system locks into a commensurate phase. The structure above ${T}_{t}$ is described by a longitudinal, amplitude modulated, sinusoidal wave with propagation vector ${\mathit{\ensuremath{\tau}}}_{1}\ensuremath{\approx}(000.758\ifmmode\pm\else\textpm\fi{}0.002)$ in reciprocal-lattice units (r.l.u.). As the temperature is lowered below ${T}_{t},$ ${\mathit{\ensuremath{\tau}}}_{1}$ locks at $(0 0 \frac{3}{4})$ and additional magnetic Bragg reflections corresponding to ${\mathit{\ensuremath{\tau}}}_{2}=(\frac{1}{2} \frac{1}{2} 0)$ and ${\mathit{\ensuremath{\tau}}}_{3}=(\frac{1}{2} \frac{1}{2} \frac{1}{2})$ develop. A weak modulation ${\mathit{\ensuremath{\tau}}}_{1}^{\ensuremath{'}}=(0 0 \frac{1}{4}),$ related to ${\mathit{\ensuremath{\tau}}}_{1}$ also appears indicating a squaring-up of the low-temperature structure. In this equal moment structure all Tb moments have the saturation value of ${\ensuremath{\mu}}_{s}=9.0\ifmmode\pm\else\textpm\fi{}0.2{\ensuremath{\mu}}_{\mathrm{B}}.$ Both the phases are uniaxial with Tb moments parallel to the $\mathbf{c}^$ axis of the tetragonal unit cell.

Spherical neutron polarimetry study of the zero-field magnetic structures of neodymium using Cryopad II

Due to their complex nature, an investigation of the zero-field magnetic structures of Nd has been started using CRYOPAD, the ILL zero-field neutron polarimeter available on IN20. Having set the incident polarisation to any desired direction, CRYOPAD then analyses the magnitude and direction of the polarisation vector of the scattered beam to a precision of 3° at a given momentum transfer. We have confirmed that the moments in the 2- q phase, which order solely on the hexagonal sites of the DHCP structure, are confined to the basal plane at 11.2 K. This was also found to be the case for the moments at the hexagonal sites at 7.6 K in the 3- q phase. Below 8.3 K, the moments on the cubic sites become ordered and we observe both a c-axis and basal plane component. We observe for the first time that the angle between these moments and the basal plane increases continuously with cooling through the 3- q phase.

X-ray scattering study of the interplay between magnetism and structure in CeSb

The chemical and magnetic structures of CeSb have been investigated using high-resolution x-ray scattering techniques. Experiments performed in the non-resonant regime (x-ray energy of E = 9.4 keV) showed that when the sample was cooled below its Néel temperature of , peaks appeared with commensurate wave vectors q. From their polarization and wave-vector dependence, the peaks are deduced to arise mainly from a periodic lattice distortion. In the resonant regime, when the x-ray energy was tuned to the L absorption edges of Ce, weak, resonantly enhanced magnetic scattering was observed at the edge (E = 6.164 keV), with no scattering found at either or . Of the six possible zero-field commensurate magnetic structures reported in earlier neutron experiments, we found the phases with and only, with the domain that has moments perpendicular to the surface absent. Neutron scattering experiments on the same single crystal confirm that the absence of the other phases is a bulk property of that particular crystal, but the absence of the domain is a feature of the near-surface region. These results are discussed in terms of the currently accepted model of the magnetic structure of CeSb.

Magnetic phase diagram and low-dimensional excitations of hexagonal UNi4B

The hexagonal antiferromagnet UNi4B (TN = 20 K) exhibits highly unusual magnetic properties, such as huge anisotropy and increasing electronic specific heat and susceptibility below TN. New high-field magnetization, magnetoresistance and thermoelectric power measurements are analyzed using the recently resolved zero-field magnetic structure [1], which consists of six ordered and three paramagnetic spins.

Magnetism of synthetic and natural annite mica: ground state and nature of excitations in an exchange-wise two-dimensional easy-plane ferromagnet with disorder

We have studied the magnetism of annite mica (the Fe-end-member layer silicate having ideal structural formula: {K +}[Fe 3 2+] <Al 3+Si 3 4+〉 O 10 2-(OH -) 2) using SQUID magnetometry, Mössbauer spectroscopy, and neutron d iffraction on well characterized samples of both a synthetic powder and a natural single crystal. In disagreement with previous predictions, we find T c > 10 K and as large as T c = 58 K in the true end member and a metamagnetic ground state spin structure (predominantly ferromagnetic layers with in-plane moments, stacked antiferromagnetically along the c ∗-axis) that is stable despite significant amounts of Fe 3+, diamagnetic octahedral ions, and Mn 2+ in the natural sample. We propose that the antiferromagnetic stacking is part of the intrinsic zero-field magnetic domain structure and that it is entirely due to dipole-dipole forces. The most striking features are that a paramagnetic Fe 2+ temperature dependent fraction persists far below T c and that the Fe 3+ moments abruptly disorder significantly below T c, with the tetrahedral Fe 3+ going first as temperature is increased. Plausible causes for the latter intrinsic features are discussed.

The magnetic structure of metamagnetic Co(pyr)2Cl2

The zero-field magnetic structure of Co(pyr)2Cl2 is obtained by means of nuclear magnetic resonance. The low temperature crystallographic structure must be described by the α structure. Field induced phases are proposed, and the resulting magnetizations are compared with experiment.

NMR Study of the Magnetic Phase of EuSe

The Eu 153 NMR in EuSe has been observed as a function of temperature and applied magnetic field. NMR results in zero applied field support the magnetic structure proposed by Fischer et al. ; EuSe has a structure of the NNSS-type in the antiferromagnetic region (from 4.6 K down to about 2.5 K) and a structure in which there coexist the NNS-and NSNS-types in the ferrimagnetic region (below about 2.5 K). As the applied field is increased, the zerofield magnetic structure changes into an intermediate one and finally into the ferromagnetic one (NNN). The coexistence of a canted spin structure and a ferrimagnetic one is proposed for the intermediate phase.