Diamond Annual Review 2020/21

62 63 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 0 / 2 1 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 0 / 2 1 Absolute determination of crystal andmagnetic chiralities in an iron-based langasite Related publication: Qureshi N., Bombardi A., Picozzi S., Barone P., Lelièvre-Berna E., Xu X., Stock C., McMorrowD. F., Hearmon A., Fabrizi F., Radaelli P. G., Cheong S.W. & Chapon L. C. Absolute crystal andmagnetic chiralities in the langasite compound Ba 3 NbFe 3 Si 2 O 14 determined by polarized neutron and x-ray scattering. Phys. Rev. B 102 , 54417 (2020). DOI: 10.1103/PhysRevB.102.054417 Publication keywords: Antiferromagnetism; Chirality; XRMS C hirality is a concept first proposed by Lord Kelvin in the 19th century, referring to objects that do not coincidewith their mirror image. Chirality can be thought of as ‘handedness’, with themost obvious example being a pair of human hands. Theoretical models suggest that chiral materials will give rise to exotic physical phenomena. Langasite (lanthanumgallium silicate) is a piezoelectric crystal with optoelectronic applications. An international teamof researchers used X-ray scattering and polarised neutrons to investigate the magnetic and structural chirality in a langasite crystal. The crystal has a chiral atomic arrangement. When it orders magnetically, it forms a triangular arrangement of magnetic helices. The triangular configuration adopted by the spins, the rotational direction of the helices and their relationship with the structural chirality were unclear. DiamondLightSource’sMaterialsandMagnetismbeamline(I16)wasperfectforthisstudy.Itallowsfullcontroloftheenergyandpolarisation of the X-ray beamand analysis of the final polarisation of the diffracted beam. These features are all necessary to study the chiral properties of a crystal. The research team determined the system’s absolute structural and magnetic chirality and the unusual mechanism controlling the direction of rotation of the magnetic helix. Chirality is an elusive property to measure. However, it is robust and can be associated to topological properties. In future, it may be possible to use topologically chiral objects to store information. Chirality, from the ancient Greek χείρ-hand, is an embodied characteristic of humans that appear during the embryonic development and is shared across bilaterians from snails to vertebrate. Such morphological characteristic was recently loosely associated to the existence of functional lateralisation in our daily actions 1 . This feature makes us perfect detectors to discriminate between left and right handed objects through our interaction with them, so we can easily distinguish not only between a left and right shoe, but also between the smell of spearmint and cumin. Chirality is not only an essential ingredient of life. It appears amongst the subatomic particles properties and it can give origin to amazing novel magnetic and electronic properties in chiral crystals. In magnetic crystals, the absence of inversion symmetry leads to helical magnetic exchange paths and allows antisymmetric magnetic exchange interactions. Examples of chiral systems in condensed matter systems include magnetic skyrmions, whose topological charge can be manipulated and potentially used to store information. Likewise, chiral magnetic domains can be manipulated by electric fields in systems belonging to the so-called ferroaxial groups supporting magnetically induced ferroelelectricity 2,3 . In this combined polarised neutron and X-ray scattering experiment, the relationship between the structural and magnetic chiralities in two enantiopure iron-based langasite single crystals was investigated. Langasites crystallise in the chiral P321 space group (Fig. 1). The magnetic moments associated to the Fe ions form a triangular network in the basal plane and order in a helical spiral out of plane below TN = 27 K 4 . The first task of this investigation was to establish the absolute structural and magnetic chiralities of two samples of opposite structural chirality. The second task was to understand what stabilises a given magnetic handedness. The experimental results together with simple energy considerations reveal that it is not the antisymmetric Dzyaloshinskii-Moriya (DM) interaction but the local Fe single-ion anisotropy (SIA) which plays a key role in stabilising one of the two magnetic helices. Determining structural chirality in a transparent crystal can be done directly by optical rotation, measuring the angular deviation of linearly polarised light transmitted through the medium. But surprisingly, given MagneticMaterials Group Beamline I16 our ability to immediately identify chiral objects, chirality is not directly observable, and we can only make use of small effects to discriminate amongst different handedness. In the domain of the X-ray, determining the structural chirality is routinely achieved by collecting the integrated intensity from many reflections and including the anomalous form factor in the data analysis. In our I16 study we pushed this approach to the extreme by measuring the intensity variation of few reflections across the Fe K absorption edge. In this region, the energy dependent part of the form factor starts to dominate and the different interferences given by the mirror related arrangement of the crystal ions in the two enantiomers lead to large contrast on some reflections across the Fe K-edge (Fig. 2). Once all the conventions were carefully checked we established a uniform left structural chirality for our specimen across the whole surface. The determination of the absolute magnetic chirality can not be obtained in a similar manner and requires not only the full brightness of synchrotron radiation, but also full control over the incident polarisation of the light to create a chiral probe. The horizontally linearly polarised photon was tuned at 5.0 keV, to minimise the noise due to the edges of all the chemical elements present in Ba 3 NbFe 3 Si 2 O 14 . Circular polarisation of the beamwas achieved by transmission through a 100 μm thick diamond plate. The diamond crystal was aligned close to the (111) reflection in the Laue scattering geometry. Under these precise geometrical conditions, the crystal behaves as a quarter-wave plate producing circular light. The handedness of the light is determined by precise orientation of the diamond, which was calculated by dynamical scattering theory and confirmed through experimental absolute calibration of the beamline by measuring the X-ray dichroism of a standard ferromagnet. The magnetic chirality was investigated at T = 5K. A large area of the sample was mapped with respect to its magnetic chirality, revealing the same character, from which we can deduce that it is magnetically enantiopure. The results are reported in Fig. 3 and are based on a L-handed spiral clearly showing that the magnetic chirality follows the structural one. For an opposite magnetic chirality, the calculated curves would be reversed. Finally, an azimuthal investigation of few reflections confirms the elliptical modulation of the magnetic helix with Sh/Se = 0.94(2), where Sh and Se are the spin components along the hard and easy axis of the magnetic envelope. Theoretical calculations including SIA effect indicates that there is no energetic advantage to distort the circular modulation in the cases of negative triangular chirality (εT = -1) , whereas an energetic gain is obtained, independently of the spin-orbit coupling, for εT= +1. This selection mechanism of chirality where the SIA in the planar triangular arrangement, in itself not ‘chiral’, not only distorts the helix but it chooses the global magnetic chirality almost independently from the strength of the spin orbit coupling and hence of the DM chiral term appearing in the microscopic Hamiltonian. In conclusion, the capability of tuning the energy and controlling of the X-ray polarisation available on the I16 beamline were essential in determining absolutely and simultaneously the sign of all the microscopic chiral elements appearing in the system. References: 1. Brandler W. M. et al. The genetic relationship between handedness and neurodevelopmental disorders. Trends Mol. Med. 20 , 83–90 (2014). DOI: 10.1016/j.molmed.2013.10.008 2. Johnson R. D. et al. Giant improper ferroelectricity in the ferroaxial magnet CaMn 7O 12. Phys. Rev. Lett. 108 , 67201 (2012). DOI: 10.1103/ PhysRevLett.108.067201 3. Hearmon A. J. et al. Electric field control of the magnetic chiralities in ferroaxial multiferroic RbFe(MoO 4 ) 2 . Phys. Rev. Lett. 108 , 237201 (2012). DOI: 10.1103/PhysRevLett.108.237201 4. Marty K. et al. Single domain magnetic helicity and triangular chirality in structurally enantiopure Ba 3 NbFe 3 Si 2 O 14 . Phys. Rev. Lett. 101 , 247201 (2008). DOI: 10.1103/PhysRevLett.101.247201 Funding acknowledgement: We acknowledge Diamond Light Source for time on Beamline I16 under Proposals mt4073-1, mt1803-1, and 17569. The work at Rutgers University was supported by the DOE under Grant No. DOE: DE-FG02-07ER46382. Work in London was supported by the Engineering and Physical Sciences Research Council, UK (Grant No. EP/N027671/1). Corresponding author: Dr Alessandro Bombardi, Diamond Light Source, alessandro.bombardi@diamond.ac.uk Figure 1: Four different chiral configurations which all yield the same nuclear and magnetic structure factors and therefore are indistinguishable by unpolarised X-rays diffraction. The structural crystal chirality (L/R), the helical (hc) and triangular (tc) magnetic chiralities are also shown. Figure 2: The behaviour of four noncoplanar reflections shows great contrast in the simulations for the left-handed (red lines) and right-handed (blue lines) enantiomers. As is immediately evident, only simulations with the left-handed structure match the trend of the experimental data. No attempt was made to simulate the subtle feature shown by the experimental data across the transition. Figure 3: The X-ray dichroic intensity as a function of the deviation angle η of the linear polarisation analyser from the scattering plane for four different magnetic Bragg reflections at T = 5K. Red circles represent data taken with a photon beam of left-handed polarisation; blue squares, data measured with a photon beam of right-handed polarisation. The calculated intensities are based on a left-handed enantiomer and are shown as solid lines in the corresponding colours.