The word “chiral”, introduced by Lord Kelvin in 1904, refers to an object whose image in a plane mirror does not coincide with itself [1]. One intuitive example is the left and right hands, which are mirror images of each other but are not superimposable. The two forms of a chiral object are called enantiomorphs or enantiomers for molecules. The chirality is a key property which is found in all branches of science, from biology to physics and at different scales, from microscopic to macroscopic objects. For instance, in biology, the notion of chirality is crucial for living organisms and plays a critical role in molecular recognition [2]. In parallel, in fundamental physics, the chirality is also an important property, as shown by the example of the weak interaction, not invariant under mirror symmetry [3], which only interacts with left-chiral fermions or right-chiral anti-fermions. The chirality can also be found in solid state physics, in crystallography where it refers to the concept of spatial inversion symmetry rather than mirror symmetry, or again in magnetism, where it refers to the sense of rotation of the spins on oriented loops [4].

In this talk, I will focus on the concept of chirality in magnetic ordered systems. I will present the archetype chiral magnetic compound, Ba₃NbFe₃Si₂O₁₄, which hosts three different types of chirality. This system belongs to the family of langasite materials providing interesting geometrically frustrated spin lattices. It crystallizes in the non-centrosymmetric P321 space group and displays a structural chirality. The magnetic Fe³⁺ ions form an original triangular network in the (a,b) planes, stacked along the c-axis (see Figure 1). Below T_N ~ 27 K, the system orders magnetically with a 120° spins structure within each triangle, in the (a,b) planes, and presents a helical modulation along the perpendicular direction, i.e. the c-axis, with a period of ~ 7 lattice parameters (see Figure 1) [5]. Surprisingly, this magnetic ground state displays a unique sense of rotation of the spins within the triangles (triangular chirality) as well as a unique sense of rotation of the spins along the helices (helical chirality). This multi-chiral magnetic ground state is correlated to the structural chirality through a twist of the inter-plane exchange interactions (see Figure 1) [5-7]. I will present the scientific arguments that led to the discovery of such complex multi-chiral magnetic structure and the consequences on its physical properties. I will conclude by presenting our last results focusing on the critical regime and the nature of the phase transition toward this peculiar multi-chiral magnetic order.

[1] Lord Kelvin, (1904). Baltimore Lectures. London: C. J. Clay and Sons 619.

[2] Inaki, M., Liu, J., & Matsuno, K., (2016). Phil. Trans. R. Soc. B 371, 20150403.

[3] Lee, T. D. & Yang, C. N., (1956). Phys. Rev. 104, 254. Lee, T. D., Oehme, R. & Yang, C. N., (1957). Phys. Rev. 106, 340.

[4] Simonet, V., Loire, M. & Ballou, R., (2012). Eur. Phys. J. Spec. Top. 213, 5.

[5] Marty, K., Simonet, V., Ressouche, E., Ballou, R., Lejay, P. & Bordet, P., (2008). Phys. Rev. Lett. 101, 247201.

[6] Loire, M., Simonet, V., Petit, S., K. Marty, Bordet, P., Lejay, P., Ollivier, J., Enderle, M., Steffens, P., Ressouche, E., Zorko, A. & Ballou, R., (2011). Phys. Rev. Lett. 106, 207201.

[7] Chaix, L., Ballou, R., Cano, A., Petit, S., de Brion, S., Ollivier, J., Regnault, L.-P., Ressouche, E., Constable, E., Colin, C. V., Zorko, A., Scagnoli, V., Balay, J., Lejay, P., & Simonet, V., (2016). Phys. Rev. B 93, 214419.

In metallic heavy fermion materials the magnetic ground state is often a spin density wave (SDW) phase in which the magnetization vary periodically with a period that is usually incommensurate with the parent structure lattice. These phases are associated to the itinerant character of the f-electron present in the system and are intimately related to the electronic structure near the fermi energy.

This is the case in the tetragonal heavy-fermion compound CeAuSb₂ which shows the development of a SDW phase below T_N~6.5 K with a propagation vector k₁ = (0.136, 0.136, 0.5) [1-2]. This phase is very sensitive to external stimuli and, indeed, the systems shows two metamagnetic phase transitions with magnetic field applied along the [001] direction [1-2]. An additional parameter which can tune the magnetic ground state is the application of a uniaxial stress, for example along the [010] direction. Extensive transport and thermodynamic measurements [2, 3, 4] indicate a sudden and anisotropic jump of the resistivity at an induced strain along the axis of compression of 0.5% indicating a first order transition.

In this talk we present single crystal time of flight neutron diffraction data collected under the application of a [010] uniaxial stress to characterize the magnetic phases of CeAuSb₂. The neutron data indicate a change of the propagation vector from k₁ at low stress to k₂ = (0, 0.25, 0.5) at high stress. Even with the geometrical constrains imposed from the experiment sample environment, which allows to collect only a limited number of magnetic reflections, we will show that it is possible to determine and refine the magnetic structure with the support of group theory calculations and magnetic symmetry analysis. The commensurate nature of the propagation vector is attributed to the presence of a lock in invariant in the free energy and we will show that the magnetic ground state under compressive stress is characterized by the presence of two primary order parameters related to different irreducible representations of the parent structure.

[1] Marcus, G. G., Kim, D.-J., Tutmaher, J. A., Rodriguez-Rivera, J. A., Birk, J. O., Niedermeyer, C., Lee, H., Fisk, Z., Brohol, C. L. (2018). Phys. Rev. Lett. 120, 097201

[2] Zhao, L., Yelland, E. A., Bruin, J. A. N., Sheikin, I., Canfield, P. C., Fritsch, V., Sakai, H., Mackenzie, A. P., Hicks, C. W. (2016). Phys. Rev. B 93, 195124.

[3] Park, J., Sakai, H., Erten, O., Mackenzie A. P., Hicks, C. W. (2018). Phys. Rev. B 97, 024411 [4] Park, J., Sakai, H., Mackenzie A. P., Hicks, C. W. (2018). Phys. Rev. B 98, 024426.

[4] Park, J., Sakai, H., Mackenzie A. P., Hicks, C. W. (2018). Phys. Rev. B 98, 024426.

Magnetic interactions are the fundamental components for the fascinating variety of complex magnetic structures and properties found in many functional materials. Identifying, understanding, and finally predicting these interactions is an essential step towards their utilization in novel devices. One of these basic interactions is the Dzyaloshinskii-Moriya interaction (DMI) – an antisymmetric exchange coupling favouring a perpendicular arrangement of magnetic moments, and thus a canting in otherwise collinear structures [1,2]. The DMI, originally introduced in the late 1950s to explain ‘weak ferromagnets’ (not perfectly collinear antiferromagnets), regained the interest in current condensed matter research as it was found to be the driving force to stabilize various novel topological noncollinear magnetic structures, such as spin spirals [3], magnetic skyrmions [4], magnetic soliton lattices [5] and others. In particular for spintronic applications, the DMI shows promising characteristics towards the development of next-generation devices [6]. Although the magnitude of the DMI-induced canting is usually small, the direction can have a fundamental impact on the spin chirality and the resulting magnetic and multiferroic properties [7]. Here, we present polarized neutron diffraction (PND) as an efficient technique for the determination of the absolute direction of the DMI in weak ferromagnetic materials, as recently established by us [8].

We provide the basic formalism for a symmetry analysis of the DMI in crystal structures and show how to relate the measured PND data with the absolute DMI direction. We exemplify this approach in weak ferromagnetic MnCO₃ and identify the magnetic moment configurations for a positive or negative sign of the DMI with an applied magnetic field as shown in Fig. 1. Using PND [9], we can distinguish even from the measurement of a single suitable Bragg reflection between the two configurations and unambiguously reveal a negative DMI sign in MnCO₃. This is in agreement with previous results obtained by resonant magnetic X-ray scattering and thus, validates the method [10]. We demonstrate the generality of our method by providing further examples of topical magnetic materials with different symmetries and support our findings with ab-initio calculations, which reproduce the experimental results.

Figure 1. The local environment of the z=0 manganese atom in the hexagonal unit cell of MnCO₃. The six nearest-neighbour manganese atoms of the other magnetic sublattice are shown as light and dark blue spheres located above and below the central atom, respectively. The oxygen atoms between these manganese layers are shown as small yellow spheres. Panels (a) and (b) show the two possible magnetic moment configurations stabilized dependent on the sign of the D_z DMI component by applying an external magnetic field along the [110] direction aligning the weak ferromagnetic moment.

[1] V. E. Dzyaloshinskii, Sov. Phys. - JETP 5(6), 1259 (1957)

[2] T. Moriya, Phys. Rev. 120(1), 91 (1960)

[3] M. Bode et al., Nature 447, 190 (2007)

[4] S. Heinze et al., Nat. Phys. 7, 713 (2011)

[5] Y. Togawa et al., Phys. Rev. Lett. 108, 107202 (2012)

[6] S. S. P. Parkin et al., Science 320, 190 (2008)

[7] J. Cho et al., J. Phys. D: Appl. Phys. 50, 425004 (2017)

[8] H. Thoma et al., Phys. Rev. X 11, 011060 (2021)

[9] H. Thoma et al., J. Appl. Crystallogr. 51, 17 (2018)

[10] V. E. Dmitrienko et al., Nat. Phys. 10, 202 (2014)

Ca₂RuO₄ (CRO), the close neighbour of the famous superconductor Sr₂RuO₄ displays surprisingly different behaviour to its neighbour, exhibiting insulating behaviour below an irreversible metal-insulator transition at T_MI = 357K. In the insulating state CRO displays orbital ordering at T_OO = 260K and antiferromagnetic ordering below T_N = 110K. This material has been extensively investigated but still questions remain regarding the nature of the insulating state and whether Mott gaps are opened only on certain orbitals, or whether the insulating state is a result of purely structural change. While recent publications have tended towards the latter of these possibilities, previous results observing varying orbital concentrations with temperature have not been explained. Here we will show new resonant elastic x-ray scattering (REXS) results from the Ruthenium absorption edge made on the synchrotron beamline I16 at Diamond. The resonant spectra provide a unique way of looking at the ordered magnetic and orbital structure of this material and we will present a systematic approach to understanding the different contributions to these signals.

Binary rare-earth intermetallic compounds of R₇Rh₃ type attract possess complex magnetic phase diagrams and rich variety of magnetic structure transitions. In particular, three temperature induced magnetic phase transitions were observed at T_N = 32 K, T_t1 = 21 K, and T_t2 = 9 K [1, 2]. In this work, a comprehensive study of the low-temperature magnetic state of Ho₇Rh₃ was carried out using neutron diffraction and nonlinear AC magnetic susceptibility.

Analysis of the neutron diffraction data and the temperature dependence of the harmonics χ_nω'(T) and χ_nω''(T) (n = 1, 2, 3) (Fig. 1) showed that the magnetic phase transition at a temperature T_N = 32 K is associated with emergence of an incommensurate magnetic structure of spin density wave type described by the magnetic superspace group Cmc2₁1'(00g)0sss. Upon further cooling below the temperature T_t1 ~ 21 K, a "squaring-up" process begins reflecting evolution of the amplitude modulated incommensurate magnetic structure towards a rectangular structure of the "antiphase domains" type. At T<T_t2 ~ 9 K, the magnetic structure can be described by the magnetic supersymmetry groups Cm'c2₁'(00g)ss0 or Cmc'2₁'(00g)000, which are subgroups of index i = 2 of the Cmc2₁1'(00g)0sss magnetic superspace group. Symmetry breaking associated with {1’|0 0 0 1/2} operation lost at the transition allows the emergence of a spontaneous magnetization confined in the basal plane of the hexagonal structure Ho₇Rh₃ while magnetic structure keeps its incommensurate character. Measurements of the linear and nonlinear AC magnetic susceptibility revealed that emergence of the weak spontaneous magnetization in the sample are accompanied by pronounced anomalies in the temperature dependencies of the 2nd and 3rd harmonics of the AC susceptibility ascribed to a symmetry breaking due to the loss of the time inversion symmetry {1’|0 0 0 1/2}.

[1] Tsutaoka, T., et al, (2003). Physica B. 327, 352-356.

[2] Tsutaoka, T., et al, (2016). J. of Alloys and Compounds. 654, 126-132.