Institute Quantum Phenomena in Novel Materials

The Flat-Cone Diffractometer E2

The flat-cone diffractionmeter E2 was operated at the BER II research reactor until December 11, 2019. The data is in principle available for analysis of the principell proposer (and also for subsequent use in accordance with the data policy). At the moment, the former instrument manager Jens-Uwe Hoffmann must be contacted to get the data until the ICAT system is back in operation.

This page contains all the necessary information and software required to utilize the data. It is structured as follows:

• TVneXus
• Nexus
• E2 Instrument Parameter
• Flat-Cone Geometry
• Scientific Highlights

TVneXus

The software package TVneXus  (Windows 64 Application) is able to visualise and analyze one and two-dimensional intensity distributions. The program is designed especially for data  determined by neutron experiments using diffractometer equipped with 2D multidetector and can be used for single crystal and for powder experiments as well by using the Nexus file format.

TVneXus screen shot

Download Area

• Download for Win64 TVneXusLight 1.01
• Visual C++ Redistributable for Visual Studio 2012 Update 4

Nexus

NeXus is a common data format for neutron, x-ray, and muon science. It is being developed as an international standard by scientists and programmers representing major scientific facilities in order to facilitate greater cooperation in the analysis and visualization of neutron, x-ray, and muon data. A reference paper The NeXus data format was published 2015.

The design idea:

• Complete data for typical use
• Extendable, add additional data as you please
• Self describing
• Easy automatic plotting
• Platform independent, public domain, efficient
• Suitable for a wild variety of applications

Please visit the official NeXus-Website for current information.

NXinstrument - Nexus configuration tool (screen shot)

E2 Instrument Parameter

The original design of the instrument is based on the Weissenberg geometry with a linear detector. The last state of the instrument used four 300 x 300 mm² area detectors without energy analysis. Each detector window had a size of 10° x 10° (30 mSr). The wavelength could be set with a monochromator changer to l = 0.9 Å (qmax = 10.8 Å^-1), 1.2 Å (qmax = 8.1 Å^-1) and 2.4 Å (qmax = 4.1 Å^-1) with in-pile collimations of 15’, 30’ or 60’. In the optimum configuration the resolutions was dq/q < 10-2. An oscillating radial collimator in front of the detector had reduced the background intensity. The maximum tilting angle in the flat-cone mode was µ = 18°.

Flat-Cone Geometry

The flat-cone technique is a special case of the Weissenberg techniques which were developed for X-ray diffractometry with photographic detectors (e.g. Buerger, 1942). In these methods a single crystal is rotated around a crystal axis. Then the reciprocal-lattice planes normal to this axis will diffract in planes or cones, i.e. all reflections of one reciprocal plane or layer are recorded along straight lines on a cylindrical film. If only one line is selected by putting a layer-line screen before the film, then a two-dimensional lattice plane can be mapped on the two-dimensional film by coupling the crystal rotation and the film translation.

The same procedure can be realized with a twodimensional (electronic) multidetector which is placed along one layer line. For each rotational angle of the crystal a separate measurement has to be made. In comparison with the film and the first linear detector system there was of course a loss in resolution perpendicular to the layer line. With the new two dimensional detector system can be measured a cylindrical range of the reciprocal space.

The sample table is equipped with a special cradle system which allows a turntable (φ axis) to be tilted by an angle (0 < µ < 20 °) around the shaft of the lift up system of the detector bank. The detector with its shielding can be tilted by the same amount around the axis which is perpendicular to the direction of the incident beam in most of our experiments.

Normal beam setting

The cradles angles CHI1 and CHI2 have to be on zero, and one cradle is parallel to the monochromatic beam, e.g. OMGS = 0.0. The detector starting point has to be at TTHS = 0°, then the detector lifting axis is at 2θ = 90°.

An upper layer:

e.g. (c* vertical) the layer (h,k,x) can be scanned if you incline

1. the cradle which is parallel to the beam by an angle µ and
2. the detector by an angle µ

The x.-layer is then scanned by PHIS. μ can be calculated by the formula if

c* = 1/c

sin (µ) = xc*/k = x λ/c

Generalized flat-cone setting

Instead OMGS = 0°, we can put OMGS = ν, then TTHS = ν

And μ follows from

sin (µ) = (xc*)/(k cos(v)) = (x λ)/(c cos(ν))

 In this way, higher 2θ values can be recorded.

Scientific Highlights

The flat-cone diffractometer was specialized to investigate complex and short-range order in single crystals and for in-situ experiments. The wavelength of 2.4 Å is optimal for magnetic scattering research with temperatures down to 30 mK and applied magnetic fields up to 6T on topical scientific subjects. With the computer controlled flat-cone-option in combination with the off-scattering information of the 2D-detectors it was possible to scan a broad slice of the three dimensional reciprocal space.

Materials with complex order and interaction between multiple competing components such as multifunctional oxides and highly frustrated magnets are of outstanding technological and scientific importance.

Presentation: Scientific Case (pdf).

Materials with complex order and interaction between multiple competing components such as multifunctional oxides and highly frustrated magnets are of outstanding technological and scientific importance. They present particular challenges which E2 is increasingly developed to address, and in particular the need to undertake comprehensive measurements of the short-range and complex ordering in 3D reciprocal space under diverse in situ conditions. Access to short range order and competing/topological phases provide the motivation and the combination of new analysis methods with full 3D mapping using neutrons and x-rays has been identified as a direction where substantial progress can be made. E2 is one of the few instruments worldwide where these studies can be undertaken and the application to magnetic studies are particularly important as these are controllable via field and have simpler interactions.

Dirac Strings and Magnetic Monopoles in the Spin Ice Dy₂Ti₂O₇

Morris et al., Science 326 (5951): 411-414 (2009)

The spin-ice state is argued to be well described by networks of aligned dipoles resembling solenoidal tubes - classical, and observable, versions of a Dirac string. Where these tubes end, the resulting defects look like magnetic monopoles. It was possible with the flat-cone-diffractometer E2, to observe the presence of such strings in the spin ice dysprosium titanate (Dy₂Ti₂O₇). The experiment required unique capabilities of E2 in combining 3D diffuse scattering mapping, milliKelvin temperatures, and applied fields. New theoretical methods for the description of diffuse scattering (taken from statistical field theory) were used. These in combination with thermodynamic measurements confirmed that monopoles deconfined in dysprosium titanate.

Patterning of sodium ions and the control of electrons in sodium cobaltate

M.Roger et. al, Nature 445, 631-634 (8 February 2007)

Sodium cobaltate (Na_xCoO₂) has emerged as a material of exceptional scientific interest due to the potential for thermoelectric applications, and because the strong interplay between the magnetic and superconducting properties has led to close comparisons with the physics of the superconducting copper oxides. The density x of the sodium in the intercalation layers can be altered electrochemically, directly changing the number of conduction electrons on the triangular Co layers. Recent electron diffraction measurements reveal a kaleidoscope of Na⁺ ion patterns as a function of concentration. Here we use single-crystal neutron diffraction supported by numerical simulations to determine the long-range three-dimensional superstructures of these ions. We show that the sodium ordering and its associated distortion field are governed by pure electrostatics, and that the organizational principle is the stabilization of charge droplets that order long range at some simple fractional fillings. Our results provide a good starting point to understand the electronic properties in terms of a Hubbard Hamiltonian that takes into account the electrostatic potential from the Na superstructures. The resulting depth of potential wells in the Co layer is greater than the single-particle hopping kinetic energy and as a consequence, holes preferentially occupy the lowest potential regions. Thus we conclude that the Na⁺ ion patterning has a decisive role in the transport and magnetic properties.

Magnetic phase control by an electric field

Th. Lottermoser et. al, Nature 430, 541-544 (29 July 2004)

The quest for higher data density in information storage is motivating investigations into approaches for manipulating magnetization by means other than magnetic fields. This is evidenced by the recent boom in magnetoelectronics and 'spintronics', where phenomena such as carrier effects in magnetic semiconductors and high-correlation effects in colossal magnetoresistive compounds are studied for their device potential. The linear magnetoelectric effect—the induction of polarization by a magnetic field and of magnetization by an electric field—provides another route for linking magnetic and electric properties. It was recently discovered that composite materials and magnetic ferroelectrics exhibit magnetoelectric effects that exceed previously known effects by orders of magnitude, with the potential to trigger magnetic or electric phase transitions. Here we report a system whose magnetic phase can be controlled by an external electric field: ferromagnetic ordering in hexagonal HoMnO₃ is reversibly switched on and off by the applied field via magnetoelectric interactions. We monitor this process using magneto-optical techniques and reveal its microscopic origin by neutron and X-ray diffraction. From our results, we identify basic requirements for other candidate materials to exhibit magnetoelectric phase control.

Electronic Structure and Nesting-Driven Enhancement of the RKKY Interaction at the Magnetic Ordering Propagation Vector in Gd₂PdSi₃ and Tb₂PdSi₃

D.S. Inosov et. al, Phys. Rev. Lett. 102, 046401 (2009)

Measurements of the low-energy electronic structure in Gd₂PdSi₃ and Tb₂PdSi₃ by means of angle-resolved photoelectron spectroscopy reveal a Fermi surface consisting of an electron barrel at the Γ point surrounded by spindle-shaped electron pockets originating from the same band. The calculated momentum-dependent RKKY coupling strength is peaked at the 1/2ΓK wave vector, which coincides with the propagation vector of the low-temperature in-plane magnetic order observed by neutron diffraction, thereby demonstrating the decisive role of the Fermi surface geometry in explaining the complex magnetic ground state of ternary rare earth silicides.