International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.8, pp. 183-186

Section 2.8.3.3. Diffraction under a magnetic field

H. Ehrenberg,a* M. Hinterstein,a A. Senyshynb and H. Fuessc

aInstitut für Angewandte Materialien (IAM-ESS), Karlsruhe Institut für Technologie (KIT), Eggenstein-Leopoldshafen, Germany,bTechnische Universität München, Garching b. München, Germany, and cTechnische Universität Darmstadt, Darmstadt, Germany
Correspondence e-mail:  helmut.ehrenberg@kit.edu

2.8.3.3. Diffraction under a magnetic field

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2.8.3.3.1. General remarks

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The majority of synchrotron and neutron experiments are currently limited to superconducting magnets with fields of 5–16 T. When higher fields are required there are essentially two possible solutions: pulsed resistive or steady-field resistive (or hybrid: resistive inner coil, superconducting outer coil) magnets. Pulsed fields are often used when signals are strong and the signal-to-noise ratio is good, whereas steady fields are primarily used for techniques with relatively long counting times and many data points. The relatively short pulse duration (from microseconds to milliseconds) along with the rather large sample volume required severely limit the use of pulsed magnetic fields in powder diffraction applications as well as more exotic methods of achieving high magnetic fields, e.g. magnetic flux compression or single-turn coils (Schneider-Muntau et al., 2006[link]). Furthermore, because of the large stresses, the lifetime of a resistive/pulsed magnet is finite: pulsed magnets have typical lifetimes of 500 shots at 95% of the design field, and their lifetimes are virtually independent of pulse duration.

At present, the maximum field for technical superconductors is 23 T and modern developments in superconductor design along with robust magnet manufacturing techniques have made possible high-flux-density magnets for neutron scattering studies up to 16 T. For resistive magnets, there are in principle no limitations to the generation of the highest continuous fields apart from economics, as approximately 1 MW of electric power is consumed per 1 T field strength. Therefore, in order to reduce the running costs (i.e. the required power per unit magnetic field), hybrid magnets are becoming increasingly popular. In this context we mention the joint developments between the National High Magnetic Field Laboratory (Tallahassee, FL, USA), the Spallation Neutron Source (Oak Ridge, TN, USA) and Helmholtz-Zentrum Berlin (Germany) in the development of high-steady-field (25 T with a 4 MW resistive insert, 30 T with an 8 MW resistive insert) hybrid magnets for neutron scattering (Bird et al., 2009[link]). A high-field magnet has been installed and is in routine user operation (Fig. 2.8.13[link]) at the Extreme Environment Diffractometer (HFM-EXED) of Helmholtz-Zentrum Berlin (Prokhnenko et al., 2015[link]).

[Figure 2.8.13]

Figure 2.8.13 | top | pdf |

The High Magnetic Field Facility for Neutron Scattering at the Helmholtz-Zentrum Berlin has two main components: the High Field Magnet (HFM) and the Extreme Environment Diffractometer (EXED). Courtesy of Dr O. Prokhnenko.

On the other hand, it is quite simple to produce magnetic flux density uniformity or homogeneity over the required sample volume down to the p.p.m. level with a solenoid magnet. However, the majority take the form of split-pair solenoids. With this setup, the access to the sample environment (along the magnetic axis) can be orthogonal to the beam-access plane. The split-coil setup is the most popular in neutron scattering, but the geometry constraints imposed by the neutron aperture make the creation of very uniform flux density much more difficult. In general, for a typical neutron-scattering sample volume of 1 cm3, the magnetic field homogeneity is normally limited to the range 0.1 to 5%. As the available current density for a given conductor decreases with increasing flux density, the flux density seen by the superconductor inside the magnet windings is greater than the `nominal' central value. This is particularly the case for split-pair magnets, where the ratio of the two can be large, e.g. for a central value of 9 T, a ratio of 1.6 gives a maximum flux density of 14.3 T (Brown, 2010[link]).

As already pointed out, diffraction studies under a magnetic field are almost always performed with neutrons. However, Mitsui et al. (2009[link]) have developed a device that includes a cryo-cooled split-pair NbTi superconducting magnet and a sample furnace, for high fields and temperatures above room temperature, respectively, which can be installed on a laboratory X-ray diffractometer. The magnetic field generated goes up to 5 T at the centre of a 50 mm vertical and 10 mm horizontal bore, with a field homogeneity of 0.1%. The first results of studies on the martensitic phase transition in the shape memory system Ni40Co10Mn34Al16 in a field of 5 T and at temperatures up to 473 K have been reported for powders (Mitsui et al., 2009[link]).

Synchrotron radiation can be used to study specific properties such as orbital contributions and their separation from the spin values. Diffraction studies with unpolarized neutrons are common at a constant field to elucidate simple magnetic structures: no confident conclusion about the spin direction can be obtained if the configurational symmetry is cubic, and in the case of uniaxial symmetry (either tetragonal, hexagonal or rhombohedral) only the angle with the unique axis of the magnetic structure can be defined (Shirane, 1959[link]). The sensitivity of non-polarized neutron powder diffraction (the magnetic detection limit) is by a few orders of magnitude less than that of superconducting quantum interference device (SQUID) magnetometry, muon spin rotation or magnetic dichroism spectroscopy. In an antiferromagnetically ordered system the determination of magnetic moments below 0.1 µB per magnetic atom presents severe challenges, which become even more pronounced for the localization of weak ferromagnetic components. Less frequent are in situ investigations to determine magnetic phase diagrams. The use of powder samples at high magnetic fields is often limited by the redistribution of grains and texture effects.

Experiments with polarized neutrons are normally performed with single crystals. Out of the variety of compounds that have been studied, we have chosen materials with particular properties and report on in situ studies of them under magnetic fields.

2.8.3.3.2. Frustrated magnetic systems

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Multiferroic systems (or more precisely magnetoelectric materials) have gained considerable attention because of their potential applications in devices. In fact, the efficient control of magnetism by an electric field allows magnetic information to be written electrically (with low energy consumption) and read magnetically. A real application, however, requires both phenomena to occur at room temperature. There are very few compounds that fulfil this requirement; examples include BiFeO3 and β-NaFeO2.

Magnetoelectric properties have been observed in many compounds with different structures and chemical compositions. However, they all have a geometrical magnetic frustration in common, which induces competition among multiple magnetic ground states. Furthermore, a magnetic phase transition is thought to be an essential ingredient for realizing a non-linear colossal response in the electric properties. In the colossal effect, the two properties not only coexist but couple strongly in their order parameter. Most novel multiferroic materials exhibit a cycloidal component to the magnetic structure; this has been considered as a guiding principle for tailoring new materials based on the non-collinearity of the spins. Many cycloidal compounds exhibit a small ferromagnetic component in their antiferromagnetic order, giving rise to the Dzyaloshinskii–Moriya interaction. We shall concentrate here on two systems linked by frustration in the magnetic ordering, namely ortho­vanadates and the manganites of the rare earths.

2.8.3.3.2.1. Kagomé staircase systems

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Among the orthovanadates of 3d metals, Co3V2O8 and Ni3V2O8 have been identified as kagomé staircase magnetic structures, which exhibit a considerable number of phase transitions at low temperature. Their crystal structure was determined by Fuess et al. (1970[link]) as orthorhombic (space group Cmca). Ferromagnetic order was found for the cobalt compound and an indication of antiferromagnetism for the nickel compound at 4.2 K. The crystal structure is characterized by edge-sharing CoO6 octahedra forming buckled layers of corner-sharing triangles, called kagomé staircases, separated by VO4 tetrahedra. The magnetic ions (Co or Ni) are situated at the corners of triangles, thus leading to spin frustration. Therefore, if a small amount of energy is supplied by an external magnetic field, a whole sequence of magnetic phase transitions can be introduced. The previously determined ferromagnetic order as the ground state for Co3V2O8 was confirmed by Wilson et al. (2007[link]). They also reported field-dependent neutron powder diffraction studies under a field of 8 T at 2 and 9 K (Fig. 2.8.14[link]). At 9 K the system has an incommensurate magnetic structure. At a field as low as 0.5 T, new magnetic peaks indexed in a commensurate structure occur, accompanied by a shift in the position of others. The incommensurate ordering disappears completely at a higher field and a purely ferromagnetic behaviour is observed, similar to the low-temperature ground state at zero field. At 2 K and 8 T no additional magnetic reflections are observed but changes in the intensity of several existing ones are seen. The refinement of the magnetic structure based on these data indicated a change of the spin direction in the ferromagnetic arrangement as compared with the zero-field low-temperature structure. Furthermore, the magnetic moments on the two different Co sites in the structure are aligned under the field and reach the same value of 3.15 µB on both sites, which is similar to the spin-only moment of cobalt.

[Figure 2.8.14]

Figure 2.8.14 | top | pdf |

Neutron powder diffraction data for Co3V2O8 at 9 K (left) and 2 K (right) under magnetic fields of 0, 0.5, 1.5, 2.5, 4.0 and 8.0 T. Data from a bank of detectors situated at the scattering angle 35° are shown. The arrows indicate the changes between the data at different fields. Individual curves are offset arbitrarily for display purposes. Reprinted with permission from Wilson et al. (2007[link]). Copyright (2007) by the American Physical Society.

The reorientation of spins and the complete magnetic field versus temperature (HT) phase diagram of the multiferroic Ni3V2O8 has been reported (Kenzelmann et al., 2006[link]). The inversion symmetry of space group Cmca is broken at low temperature and a commensurate phase is observed. Thus, over a narrow temperature range a macroscopic polar vector leads to a multiferroic behaviour. As this study was based on single-crystal neutron measurements, no further details are given here. Frustrated triangular-lattice Ising antiferromagnets have degenerate magnetic ground states, which give rise to very complex magnetic structures. As there are only small differences in the competing exchange interaction in such frustrated triangular-lattice compounds, a sequence of phase transitions is introduced by changes in temperature or magnetic field. The compound Ca3Co2O6 is another example of a frustrated system. Field-dependent powder diffraction patterns were reported for the doped system Ca3Co1.8Fe0.2O6 by Yusuf et al. (2013[link]). They distinguished the short-range magnetic order (SRO), reflected in the half-width of the Bragg reflections (Fig. 2.8.15[link]), from the long-range order as given by the Bragg positions. They stated that even under magnetic fields up to 4 T the broadening of Bragg reflections indicates the persistence of SRO. In a field of 2 T, the observed change in the structure from incommensurate to commensurate indicates a reduction of spin frustration. In fields of 4 T, a ferrimagnetic system is introduced, followed by a ferromagnetic one above 5 T.

[Figure 2.8.15]

Figure 2.8.15 | top | pdf |

The observed Bragg reflection 100 (open circles) under an applied field of (a) 0 T, (b) 2 T and (c) 4 T at 4.2 K and (d) 0 T, (e) 2 T and (f) 4 T at 16 K (taken from Yusuf et al., 2013 [link]). Copyright IOP Publishing. Reproduced with permission. All rights reserved.

2.8.3.3.2.2. Manganite systems

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Like the vanadates, in the class of rare-earth manganites of the type RMn2O5 successive magnetic phase transitions between commensurate (CO) and incommensurate phases (ICP) can occur. Intensive investigations have been undertaken to understand the relationship between their magnetic and dielectric properties. The spontaneous electric polarization is induced by a magnetic transition. Thus the primary order parameter is magnetic rather than structural. Among the rare-earth compounds, those containing Nd or an element lighter than Nd do not exhibit ferroelectricity. In all these materials a broken magnetic symmetry at lower temperatures leads to a polar symmetry group. In addition, a cycloidal component indicates a common underlying mechanism. The Mn3+ and Mn4+ ions are fully charge-ordered. Neutron diffraction studies of these phases have been performed by Radaelli & Chapon (2008[link]), who also analysed the possible exchange pathways. In TbMn2O5 the HT phase diagram of the commensurate–low-temperature–incommensurate (CO–LT–ICP) magnetic transitions shows an upward jump in the transition temperature from ∼25 K at zero field to 27 K at 9 T. The low-temperature ICP phase is stabilized under an external field for TbMn2O5 and the dielectric constant is enhanced. It was concluded that Tb and Mn order independently, implying the absence of coupling terms between them. Strong support for this suggestion was provided by an in-field neutron study on the analogue YMn2O5. Neither the positions nor the intensities of the magnetic Bragg reflections were affected by the magnetic field (Fig. 2.8.16[link]). The magnetic low-temperature ICP phase in the Tb compound was stabilized under a magnetic field. This is in contrast to observations on HoMn2O5 by Kimura et al. (2007[link]), using single crystals. In both cases, however, the neutron data correlate directly with the results obtained by dielectric measurements under a magnetic field. The difference in the behaviours is thus confirmed. The two studies also reveal different magnetic order at low temperatures. The same magnetic sequence at low temperatures as for Tb was observed in YMn2O5, which does not contain a magnetic rare-earth element. Under fields up to 8 T the positions and the intensities of the magnetic Bragg reflections remained unchanged, showing that the antiferromagnetic structure of the manganese sublattice is extremely stable. As in the vanadates, the main reason for the sequence of magnetic structures is frustration of the manganese spins. Without going too deeply into the details of the different exchange pathways and orbital occupancies, one factor behind this behaviour is the Jahn–Teller effect of the Mn3+ ion, which is also relevant in the multiferroic TbMnO3 as part of the RMnO3 family (Kimura et al., 2003[link]). Another feature often found in multiferroic systems is the small ferromagnetic component caused by small spin canting due to Dzyaloshinskii–Moriya interactions. This property strongly influences the low-temperature magnetism in RMn2O5 (Kimura et al., 2009[link]).

[Figure 2.8.16]

Figure 2.8.16 | top | pdf |

Time-of-flight diffraction patterns of YMn2O5 at 1.6 K under magnetic fields between 0 and 8 T (taken from Radaelli & Chapon, 2008 [link]). Copyright IOP Publishing. Reproduced with permission. All rights reserved.

2.8.3.3.3. Additional systems and scattering techniques

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Information about the anisotropy of the local magnetic susceptibility at different magnetic sites has been extracted from diffraction patterns for a Tb2Sn2O7 powder measured using polarized neutrons under magnetic fields of 1 and 5 T (Gukasov & Brown, 2010[link]). No magnetic contribution to the diffracted intensities was observed at 2 K in the absence of an external field. However, applying a field led to considerable changes in the diffraction pattern (Fig. 2.8.17[link]). At 100 K and 5 T, the intensities of the reflections that are allowed for the cubic space group [Fd{\overline 3} m] increase considerably. Furthermore, they were found to depend strongly on the polarization of the incoming neutrons, as shown by the difference pattern in Fig. 2.8.17[link]. At a field of 1 T, new reflections appear (Fig. 2.8.17[link]a) that are forbidden for the occupied sites in [Fd{\overline 3} m] symmetry, such as 200, 222 and 240. The intensities of these new reflections do not change with the polarization of the neutrons, as demonstrated in the difference plot, hence they are purely magnetic. In conclusion, information on local anisotropic magnetic susceptibility at different sites can be obtained by using a combination of unpolarized and polarized neutron powder patterns. This demonstrates the usefulness of polarized neutron scattering, even for polycrystalline samples.

[Figure 2.8.17]

Figure 2.8.17 | top | pdf |

Polarized neutron diffraction patterns for Tb2Sn2O7 at 2 K and 1 T (a) and 100 K and 5 T (b). I+ and I are the intensities for spin-up and spin-down neutrons, respectively. Taken from Gukasov & Brown (2010) [link]. Copyright IOP Publishing. Reproduced with permission. All rights reserved.

We now return to X-ray investigations of magnetic materials. A laboratory device for fields up to 5 T and temperatures above room temperature was mentioned in Section 2.8.3.3.1[link]. The corresponding low-temperature apparatus (Koyama et al., 2013[link]) has produced results on magneto-caloric compounds of MnFeP-type materials. Substitution of P in MnFeP1−xZx with Z = As or Ge produces materials that exhibit a large magneto-caloric effect and thus allows control of the Curie temperature by chemical composition. Studies under magnetic fields are mandatory, as the refrigerants are working under a field. For two different compositions of the As compound the lattice parameters change drastically and the cell volume decreases with increasing magnetic field strength. In MnFeP0.78Ge0.22 a field-induced ferromagnetic phase was observed near the Curie temperature at 280 K. This phase is, however, not identical to the low-temperature ferromagnetic one (Koyama et al., 2013[link]).

2.8.3.3.4. Concluding remarks

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Despite some shortcomings, powder diffraction studies as a function of magnetic fields are valuable for the qualitative and sometimes even quantitative interpretation of magnetic materials. Unpolarized neutrons are used in most experiments, but the additional information from polarized neutrons has also been exploited. X-rays do not interact directly with the magnetic moments, but structural changes as a consequence of magnetic phase transitions have been observed in several cases. In situ powder diffraction under magnetic fields reaching 4 T on an X-ray diffractometer with a rotating anode revealed details of lattice parameters and atomic positions in rare-earth alloys with a higher precision than that accessible by neutron diffraction (Pecharsky et al., 2007[link]). Furthermore, the two test-case compounds studied, Gd5Ge4 and DyCo2, contain the rare-earth elements Gd and Dy with the highest absorption cross sections for neutrons in their natural isotope abundance. The data were used to refine the underlying structure models by Rietveld analysis. Advances in X-ray and neutron sources and optics delivered higher resolution and flux to the samples, which in combination with rapid computing made real-time experiments feasible.

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