Spherical Neutron Polarimetry Research Articles

On the sign of the linear magnetoelectric coefficient in Cr2O3

We establish the sign of the linear magnetoelectric (ME) coefficient, α, in chromia, Cr2O3. Cr2O3 is the prototypical linear ME material, in which an electric (magnetic) field induces a linearly proportional magnetization (polarization), and a single magnetic domain can be selected by annealing in combined magnetic (H) and electric (E) fields. Opposite antiferromagnetic (AFM) domains have opposite ME responses, and which AFM domain corresponds to which sign of response has previously been unclear. We use density functional theory (DFT) to calculate the magnetic response of a single AFM domain of Cr2O3 to an applied in-plane electric field at zero kelvin. We find that the domain with nearest neighbor magnetic moments oriented away from (towards) each other has a negative (positive) in-plane ME coefficient, α⊥ , at zero kelvin. We show that this sign is consistent with all other DFT calculations in the literature that specified the domain orientation, independent of the choice of DFT code or functional, the method used to apply the field, and whether the direct (magnetic field) or inverse (electric field) ME response was calculated. Next, we reanalyze our previously published spherical neutron polarimetry data to determine the AFM domain produced by annealing in combined E and H fields oriented along the crystallographic symmetry axis at room temperature. We find that the AFM domain with nearest-neighbor magnetic moments oriented away from (towards) each other is produced by annealing in (anti-)parallel E and H fields, corresponding to a positive (negative) axial ME coefficient, α∥ , at room temperature. Since α⊥ at zero kelvin and α∥ at room temperature are known to be of opposite sign, our computational and experimental results are consistent.

Anomalous Hall effect and magnetic structure of the topological semimetal ( Mn0.78Fe0.22)Ge3

Me$_{3+\delta}$Ge, being a Weyl semimetal, shows a large anomalous Hall effect (AHE), which decreases slowly with an increase in $\delta$ from 0.1 to 0.4. However, AHE in this compound remains significantly large in the whole range of $\delta$ because of the robust nature of the topology of bands. To explore the possibility of tuning the anomalous transport effects in Weyl semimetals, we have studied the single-crystal hexagonal-(Mn$_{0.78}$Fe$_{0.22}$)$_3$Ge compound. Magnetization of this compound shows two magnetic transitions at 242 K ($T_{\text{N1}}$) and 120 K ($T_{\text{N2}}$). We observed that the AHE persists between $T_{\text{N2}}$ - $T_{\text{N1}}$ and vanishes below $T_{\text{N2}}$. Further, we performed single-crystal neutron diffraction experiments (using spherical neutron polarimetry and unpolarized neutron diffraction) to determine the magnetic structures of (Mn$_{0.78}$Fe$_{0.22}$)$_3$Ge at different temperatures. Our neutron diffraction results show that the sample possesses a collinear antiferromagnetic structure below $T_{\text{N2}}$. However, the magnetic structure of the sample remains noncollinear antiferromagnetic, the same as Mn$_3$Ge, between $T_{\text{N1}}$ to $T_{\text{N2}}$. The presence of AHE, and noncollinear magnetic structure in (Mn$_{0.78}$Fe$_{0.22}$)$_3$Ge, between $T_{\text{N1}}$ and $T_{\text{N2}}$, suggest the existence of Weyl points in this temperature regime. Below $T_{\text{N2}}$, AHE is absent, and the magnetic structure also changes to a collinear antiferromagnetic structure. These observations signify a strong link between the magnetic structure of the sample and AHE.

Advanced polarization analysis capability on the very small-angle neutron scattering instrument at the NIST Center for Neutron Research

The Very Small Angle Neutron Scattering (VSANS) diffractometer at the National Institute of Standards and Technology has been commissioned and is in the user program. A large available space of nearly 2 m along the beam in the sample area not only enhances the existing SANS polarization analysis capability, but also makes it possible for implementation of other polarization analysis capabilities which would not be easily available on existing SANS instruments, including grazing-incidence small-angle neutron scattering with polarization analysis and spherical neutron polarimetry. We present two polarized setups, one for high magnetic sample fields and the other for low magnetic sample fields, together with a versatile and flexible operational platform for polarized beam experiments. The design of a magnetostatic cavity device that provides better field homogeneity and thus longer 3He polarization relaxation time is discussed. It consists of an end-compensated magnetic shielded solenoid with non-identical holes to accommodate the divergent scattered beam in a constrained distance. Significant improvement in polarized neutronic performance, 3He polarization relaxation time, and an extended momentum transfer range for polarization analysis are presented. Improved neutron polarizing devices, double V-shaped supermirror polarizer, adiabatic radio-frequency spin flipper, and a 3He spin analyzer have yielded an initial instrumental flipping ratio of 100, allowing for higher sensitivity to detection of weak magnetic features in the sample.

Single E -type collinear spin state in orthorhombic YMnO3

We studied the ferroelectricity and magnetic ordering of multiferroic orthorhombic perovskite ${\mathrm{YMnO}}_{3}$ using magnetic and dielectric measurements and polarized/unpolarized neutron diffraction experiments with a single crystal. The ferroelectric polarization of a relatively large value $P\ensuremath{\simeq}0.55\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{C}/{\mathrm{cm}}^{2}$ was observed below $T=29\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The magnetic $\mathbit{k}$ vector was identified as $\mathbit{k}=(0,0.487,0)$ in the low-temperature ferroelectric phase. Based on the spherical neutron polarimetry experiment, the magnetic structure was determined to be of collinear $E$-type ordering with spins along the $b$ axis. The $E$-type state did not coexist with other states in the low-temperature ferroelectric phase. A simple domain structure model indicated that a single collinear $E$-type structure with a small incommensurability can be realized as the magnetic ground state of ${\mathrm{YMnO}}_{3}$.

Magnetic structure of the topological semimetal Co3Sn2S2

${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ has recently been predicted to be a Weyl semimetal in which magnetic order is key to its behavior as a topological material. Here, we report unpolarized neutron diffraction and spherical neutron polarimetry measurements, supported by magnetization and transport data, which probe the magnetic order in ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ below ${T}_{\text{C}}=177$ K. The results are fully consistent with ferromagnetic order in which the spins on the Co atoms point along the crystal $c$ axis, although we cannot rule out some canting of the spins. We find no evidence for a type of long-ranged $(\mathbf{k}=\mathbf{0})$ in-plane ${120}^{\ensuremath{\circ}}$ antiferromagnetic order which had previously been considered as a secondary phase present at temperatures between $\ensuremath{\sim}$90 K and ${T}_{\text{C}}$. A discontinuous change in bulk properties and neutron polarization observed at $T=125$ K when samples are cooled in a field and measured on warming is found to be due to a sudden reduction in ferromagnetic domain size. Our results lend support to the theoretical predictions that ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ is a magnetic Weyl semimetal.

Magnetic surface reconstruction in the van der Waals antiferromagnet Fe1+xTe

Fe$_{1+x}$Te is a two dimensional van der Waals antiferromagnet that becomes superconducting on anion substitution on the Te site. The parent phase of Fe$_{1+x}$Te is sensitive to the amount of interstitial iron situated between the iron-tellurium layers displaying collinear magnetic order coexisting with low temperature metallic resistivity for small concentrations of interstitial iron $x$ and helical magnetic order for large values of $x$. While this phase diagram has been established through scattering [see for example E. E. Rodriguez $\textit{et al.}$ Phys. Rev. B ${\bf{84}}$, 064403 (2011) and S. R\"ossler $\textit{et al.}$ Phys. Rev. B ${\bf{84}}$, 174506 (2011)], recent scanning tunnelling microscopy measurements [C. Trainer $\textit{et al.}$ Sci. Adv. ${\bf{5}}$, eaav3478 (2019)] have observed a different magnetic structure for small interstitial iron concentrations $x$ with a significant canting of the magnetic moments along the crystallographic $c$ axis of $\theta$=28 $\pm$ 3$^{\circ}$. In this paper, we revisit the magnetic structure of Fe$_{1.09}$Te using spherical neutron polarimetry and scanning tunnelling microscopy to search for this canting in the bulk phase and compare surface and bulk magnetism. The results show that the bulk magnetic structure of Fe$_{1.09}$Te is consistent with collinear in-plane order ($\theta=0$ with an error of $\sim$ 5$^{\circ}$). Comparison with scanning tunnelling microscopy on a series of Fe$_{1+x}$Te samples reveals that the surface exhibits a magnetic surface reconstruction with a canting angle of the spins of $\theta=29.8^{\circ}$. We suggest that this is a consequence of structural relaxation of the surface layer resulting in an out-of-plane magnetocrystalline anisotropy. The magnetism in Fe$_{1+x}$Te displays different properties at the surface when the symmetry constraints of the bulk are removed.

Origin of the large ferroelectric polarization enhancement under high pressure for multiferroic DyMnO3 studied by polarized and unpolarized neutron diffraction

Using unique experimental setups allowing spherical neutron polarimetry (SNP) and unpolarized neutron diffraction at pressure up to 8 GPa, this collaboration of authors from Japan, France, and the UK investigates pressure- and magnetic field induced gigantic ferroelectricity in multiferroic DyMnO${}_{3}$. This work reveals that the exchange striction for rare-earth and Mn bonds is strongly related to the ferroelectric polarization enhancement in DyMnO${}_{3}$. It also proves the feasibility of the SNP experiment under high pressure, which will encourage researchers to investigate pressure-induced magnetic ordering.

Ground-state magnetic structure of Mn3Ge

We have used spherical neutron polarimetry to investigate the magnetic structure of the Mn spins in the hexagonal semimetal Mn$_3$Ge, which exhibits a large intrinsic anomalous Hall effect. Our analysis of the polarimetric data finds a strong preference for a spin structure with $E_{1g}$ symmetry relative to the $D_{6h}$ point group. We show that weak ferromagnetism is an inevitable consequence of the symmetry of the observed magnetic structure, and that sixth order anisotropy is needed to select a unique ground state.

Direct control of magnetic chirality in NdMn2O5 by external electric field

Detailed investigation of the incommensurate magnetic ordering in a single crystal of multiferroic NdMn2O5 has been performed using both non-polarized and polarized neutron diffraction techniques. Below TN = 30.5 K magnetic Bragg reflections corresponding to the non-chiral type magnetic structure with propagation vector k1 = (0.5 0 kz1) occurs. Below about 27 K a new distorted magnetic modulation with a similar vector kz2 occurs, which is attributed to the magnetization of the Nd3+ ions by the Mn-sub-lattice. Strong temperature hysteresis in the occurrence of the incommensurate magnetic phases in NdMn2O5 was observed depending on the cooling or heating history of the sample. Below about 20 K the magnetic structure became of a chiral type. From spherical neutron polarimetry measurements, the resulting low-temperature magnetic structure kz3 was approximated by the general elliptic helix. The parameters of the magnetic helix-like ellipticity and helical plane orientation in regard to the crystal structure were determined. A reorientation of the helix occurs at an intermediate temperature between 4 K and 18 K. A difference between the population of right- and left-handed chiral domains of about 0.2 was observed in the as-grown crystal when cooling without an external electric field. The magnetic chiral ratio can be changed by the application of an external electric field of a few kV/cm, revealing strong magnetoelectric coupling. A linear dependence of the magnetic chirality on the applied electric field in NdMn2O5 was found. The results are discussed within the frame of the antisymmetric super-exchange model for Dzyaloshinsky-Moria interaction.

Proof of the elusive high-temperature incommensurate phase in CuO by spherical neutron polarimetry.

CuO is the only known binary multiferroic compound, and due to its high transition temperature into the multiferroic state, it has been extensively studied. In comparison to other prototype multiferroics, the nature and even the existence of the high-temperature incommensurate paraelectric phase (AF3) were strongly debated-both experimentally and theoretically-since it is stable for only a few tenths of a kelvin just below the Néel temperature. Until now, there is no proof by neutron diffraction techniques owing to its very small ordered Cu magnetic moment. Here, we demonstrate the potential of spherical neutron polarimetry, first, in detecting magnetic structure changes, which are not or weakly manifest in the peak intensity and, second, in deducing the spin arrangement of the so far hypothetic AF3 phase. Our findings suggest two coexisting spin density waves emerging from an accidental degeneracy of the respective states implying a delicate energy balance in the spin Hamiltonian.

A strategy for handling aberration in Spherical Neutron Polarimetry

We present a strategy for identifying and correcting for aberration effects in Spherical Neutron Polarimetry. The transformation of the neutron beam polarization vector due to scattering from a material is determined with Spherical Neutron Polarimetry. This neutron scattering technique measures the three cardinal components of the scattered polarization for any chosen cardinal direction of the incident polarization for a given Bragg reflection. As a consequence, the instrumentation required for this technique is desired to be capable of measuring the three-dimensional polarization vector over the sphere. As with all instrumentation, the field of measurement is subject to aberration which must be characterized.

Developing Wide Angle Spherical Neutron Polarimetry at Oak Ridge National Laboratory

The Spherical Neutron Polarimetry (SNP) Technique probes complex magnetic structures which are inaccessible by other methods. This technique is achieved by combining a zero-field sample chamber with full control of incoming and outgoing neutron polarization. While wide-angle SNP capability has been fully implemented in Europe, it is still in development in the US. At Oak Ridge National Laboratory, we are developing a wide-angle SNP capability suited for multiple neutron beamlines. The design is based on the basic concept of SNP while utilizing high-Tc superconducting films and Mu-metal. In this article we report our recent development of the SNP capability and its future applications.

Unambiguous determination of the commensurate antiferromagnetic structure of HoNi2B2C in the superconducting ground state

Crystal and magnetic structures of the intermetallic ${\mathrm{HoNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ have been investigated using different single-crystal diffraction techniques at both room and low temperatures (superconducting phase). Combined refinement of the neutron and x-ray diffraction data performed at room temperature shows that the crystal structure of ${\mathrm{HoNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ is well described in the tetragonal space group $I4/mmm$, in agreement with the literature. The magnetic ordering at low temperatures is accompanied by a structural phase transition to the orthorhombic space group $Fmmm$. However, only noncharacteristic orbits are occupied in this space group, and the symmetry reduction is entirely due to a lifting of the symmetry-induced restrictions on the anisotropic displacement parameters. Based on magnetic symmetry analysis, two types of commensurate antiferromagnetic structures with different magnetic space groups (MSGs) are found below ${T}_{\mathrm{N}}\ensuremath{\approx}5.2$ K: MSG ${P}_{I}nnm$ (Ho spins are along the [100] direction of the parent structure) and MSG ${C}_{A}mca$ (Ho spins are along [110] of the parent structure). Both models agree well with conventional unpolarized neutron diffraction data at low temperature (2.4 K) with ordered magnetic moments of 9.16(9) ${\ensuremath{\mu}}_{\mathrm{B}}$/${\mathrm{Ho}}^{3+}$ atom. Spherical neutron polarimetry, on the other hand, allowed us to unambiguously solve the magnetic structure (MSG ${C}_{A}mca$) as well as to determine the population of two types of ${90}^{\ensuremath{\circ}}$ antiferromagnetic domains (0.45/0.55).

Small-angle neutron polarimetry apparatus (SANPA): Development at the NIST Center for Neutron Research

Spherical neutron polarimetry directly measures the rotation of the neutron polarization after scattering from materials with magnetic structure. It is an under utilized measurement technique that is capable of measuring all nine elements of the polarization tensor of a material. In this article, we describe our new cryogen-free small-angle neutron polarimetry apparatus and infrastructure at the NIST Center for Neutron Research. The resulting apparatus is capable of continuous operation and is designed for measurements at low temperatures (4-8 K) using niobium Meissner shielding and mu-metal shielding to produce a zero-field (≤1 μT) cooling sample environment.

Mag2Pol: a program for the analysis of spherical neutron polarimetry, flipping ratio and integrated intensity data

Mag2Pol is a graphical user interface program which is devoted to the treatment of data from polarized neutron diffractometers with spherical polarization analysis. Nuclear and magnetic structure models can be introduced using space-group symbols and individual symmetry operators, respectively, and viewed in an OpenGL widget. The program calculates nuclear/magnetic structure factors, flipping ratios and polarization matrices for magnetic Bragg reflections, taking into account structural twins and magnetic domains. Spherical neutron polarimetry data can be analyzed by refining a magnetic structure model including magnetic domain populations in a least-squares fit and can also be correlated with an integrated intensity data set in a joint refinement. Further features are the simultaneous refinement of nuclear and magnetic structures with integrated intensity data and the analysis of flipping ratios either with tabulated magnetic form factors or using a multipole expansion of the magnetization density.

Development of Hybrid-Anvil-Cell for Polarized and Unpolarized Neutron Diffraction Study

We developed a hybrid anvil high-pressure cell (HAC) for neutron diffraction experiments with multi-extreme conditions, including high pressure, a high magnetic field, and low temperature, and for spherical neutron polarimetry analysis under pressure. By using the HAC, we successfully conducted neutron diffraction experiments under high-pressure (5.0 GPa) and high-magnetic-field (8 T) conditions, and conducted spherical neutron polarimetry analysis at up to 4.0 GPa. This review introduces the technical development of the HAC and recent experimental results for multiferroic materials.

The fourth ferroic order: Current status on ferrotoroidic materials

We review the topic of ferrotoroidicty and the inorganic solids proposed to exhibit this most elusive category of primary ferroic orders. We first define how ferrotoroidic order fits in with the other well known ferroic orders: ferromagnetism, ferroelectricity, and ferroelasticity. Since the order parameter is a toroidal moment, which is a moment of magnetization, these materials have been difficult to characterize. We present some of the symmetry constraints for an extended solid to exhibit ferrotoroidic order, and the most prominent characterization tools to measure the order parameter, which include magnetoelectric measurements, spherical neutron polarimetry, and second-harmonic generation optical spectroscopy and microscopy. In addition to being primary ferroics, ferrotoroidic materials also display the secondary effect known as magnetoelectricity. The magnetically ordered state must display long-range order with a k=0 structure, that is a magnetic unit cell that is the same size as the chemical unit cell. Of the 122 known Heesch-Shubnikov (or colored) point groups, only 31 allow ferrotoroidicity. With these preliminaries covered, we then review the leading candidates for ferrotoroidicity including the metal orthophosphates with the triphylite-type structure such as LiCoPO4, the pyroxene germanates and silicates such as LiFeSi2O6, and a few other systems. Common to the various solid state compounds is a first-row transition metal with some orbital degree of freedom that may not be completely quenched. From a crystal chemistry point of view, many include transition metals in an octahedral crystal field arranged in motifs separated by oxoanions such as phosphate or silicate groups.

Spherical neutron polarimetry under high pressure for a multiferroic delafossite ferrite

The analysis of three-dimensional neutron spin polarization vectors, using a technique referred to as spherical neutron polarimetry (SNP), is a very powerful means of determining complex magnetic structures in magnetic materials. However, the requirement to maintain neutrons in a highly polarized state has made it difficult to use this technique in conjunction with extreme experimental conditions. We have developed a high pressure cell made completely of nonmagnetic materials and having no effect on neutron polarizations. Herein, we report the first SNP analyses under high pressure up to 4.0 GPa in the magnetoelectric multiferroic delafossite CuFeO2. This study also determined the complex spiral magnetic structures in these pressure-induced phases, by measuring the full neutron polarization matrix. The results presented herein demonstrate that the SNP measurements are feasible under high pressure conditions, and that this method is a useful approach to study pressure-induced physical phenomena.

Complex magnetic structure of the swedenborgite CaBa(Co3Fe)O7 derived by unpolarized neutron diffraction and spherical neutron polarimetry

Complex magnetic structure of the swedenborgite CaBa(Co₃Fe)O₇ derived by unpolarized neutron diffraction and spherical neutron polarimetry

The fourth ferroic: ferrotoroidic materials and spherical neutron polarimetry

The fourth ferroic: ferrotoroidic materials and spherical neutron polarimetry