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Adding electrons to switch magnetic chirality

The Dzyloshinskii-Moriya interaction (DMI) was first introduced in 1957 to explain ‘weak ferromagnetism’. It causes a twisting of the pattern of atomic magnets, and is now considered to be the driving force behind the exotic magnetic vortexes called Skyrmions. A predictive theory hadn’t been developed, however, as until now a detailed study of the amplitude and sign of the DMI hadn’t been carried out.

A team of researchers has used the Materials and Magnetism beamline (I16) to carry out a systematic study of the DMI in a series of magnetic crystals. I16 offers the very high X-ray flux needed to observe the tiny signals associated with magnetism. Even more importantly, it has the space and versatility to allow the development and testing of novel techniques. For these experiments, the researchers installed a movable magnet to drag around the whole magnetic pattern without moving the sample, yielding data of much higher quality than traditional scans. Their novel technique could be applied to small crystal grains, with one of the samples (NiCO3) being around 50 microns in size.

Their results showed a spectacular change in the magnitude and sign of the DMI as electrons were added to 3d shells, confirming theoretical calculations and a simple model based on the number of electrons carried by the magnetic ion. The study brings us a step closer to systematic prediction of important material properties. The possibility of controlling and changing the sign of the DMI is an essential step towards finding suitable materials for spintronics applications.

Magnetic order at the atomic scale is ruled by exchange interactions, which are mostly symmetric upon exchange of the spins. In 1957, Dzyaloshinskii introduced an antisymmetric part to explain the weak ferromagnetism observed in a some crystals¹. This new term, known as the Dzyaloshinskii-Moriya interaction (DMI), is a key ingredient in many modern magnetic phases, such as multiferroics and skyrmions. Despite the intense research effort on these materials, the DMI still lacks a simple understanding at the microscopic level, in particular because many experimental studies on the DMI address only its magnitude, not its sign. The sign of the magnetic twist is accessible in a handful of long-period magnetic structures, with complex phase diagrams that defy systematic investigations versus band filling.

: Figure 1: Local atomic and magnetic structures in the series of weak ferromagnets. The ions of the two magnetic sublattices are represented by blue (site 1) and red (site 2) spheres, with black arrows denoting the direction of their spins. Oxygen atoms between the two adjacent transition metal layers are represented as yellow spheres. The dotted circles highlight the twist of the oxygen layer. The left and right panels show the two possible magnetic configurations which depend on the sign of the DMI, for an applied magnetic field pointing toward the bottom of the figure.

Weak ferromagnets with the carbonate structure offer an opportunity to perform such a systematic study: MnCO₃, FeBO₃, CoCO₃ and NiCO₃ share the same crystal structure and the same low temperature magnetic ground state: weak ferromagnetism due to a small canting of the spins away from the collinear antiferromagnetic arrangement (Fig. 1). The main difference is the nature of the transition metal ions, which carry the magnetic moments, and it is expected that the number of valence electrons has a large influence on the DMI. The sign of the DMI in these crystals is directly connected to the direction of the canting of the spins with respect to the antiferromagnetic sequence (Fig. 1), but the determination of this direction is not straightforward. Specifically, the canting direction can easily be driven in any direction of the basal plane by a small magnetic field, which is convenient to ensure a single magnetic domain in the sample, but the phase of the antiferromagnetic structure is needed to extract the sign of the DMI.

A new diffraction method was developed for this purpose2. Magnetic scattering encodes the magnetic structure, but the measurement of pure magnetic reflections cannot capture its phase and therefore the pattern of stacking of the canted moments. Interference was needed with a reference wave independent of the magnetic structure: here Resonant Elastic X-ray Scattering (REXS) is used, which contributes to the same ‘crystallographically forbidden’ reflections as the antiferromagnetic structure. The sign of the REXS amplitude must of course be known. Despite the rather exotic nature of the REXS amplitude in this case (pure electronic quadrupole scattering), it can be reliably modelled with a modern X-ray spectroscopy software.

$Figure 2: X-ray diffraction experiment: schematic view and main results. Normalised experimental values of the diffraction intensity versus magnet angle η, for the series of weak ferromagnets. The blue curves are measured away from the resonance and show the pure magnetic scattering intensity, which is symmetric and insensitive to the scattering phase. The red curves are on resonance and include a strong interference term that breaks the symmetry and gives the phase of the magnetic scattering, revealing the sign of the DMI. Experimental data (symbols) are shown with their fits (plain lines) against the model given in Beutier et al.3.$: Figure 2: X-ray diffraction experiment: schematic view and main results. Normalised experimental values of the diffraction intensity versus magnet angle η, for the series of weak ferromagnets. The blue curves are measured away from the resonance and show the pure magnetic scattering intensity, which is symmetric and insensitive to the scattering phase. The red curves are on resonance and include a strong interference term that breaks the symmetry and gives the phase of the magnetic scattering, revealing the sign of the DMI. Experimental data (symbols) are shown with their fits
(plain lines) against the model given in Beutier et al.3.

The measurements were performed at beamline I16, with a monochromatic X-ray beam tuned to the K absorption edge of the transition metal of each sample. The ‘spacegroup forbidden’ 009 reflection, allowed for the antiferromagnetic structure and quadrupole resonant scattering, was measured in the low temperature magnetic phase. In order to exploit the interference effect, a weak magnetic field was rotated in the basal plane of the sample, dragging the whole magnetic structure without moving the sample. The interference intensity varied in proportion to σ sin(η), where σ is the sign of the DMI and η is the azimuthal angle of the magnetic field in the basal plane. This simple scan yields directly the sign of the DMI, as shown in Figure 2. It is characterised by the deviation of the measured intensity toward η = 90° or η = 270°, i.e., whether the red rings in Figure 2 go up or down. The results are remarkably clear: the sign of the DMI is the same in FeBO₃ and MnCO₃, which are both opposite to CoCO₃ and NiCO₃. More precisely, the canting angle is negative (Fig. 1, left) in FeBO₃ and MnCO₃, and positive (Fig. 1, right) in CoCO₃ and NiCO₃. These signs represent the missing information from the absolute values of the canting angles that are reported in the literature and complete our knowledge of the relative strength of the DMI in this series of materials. The experimental signed values of the canting angles are in agreement with state-of-the-art first-principle calculations within local density approximation taking into account the on-site Coulomb interaction U and spin-orbit coupling (LDA + U + SO).

: Figure 3: Experimental and theoretical values of the canting angle (φ) against the filling of the 3d band. The experimental signs and the ab initio values are taken from this work. The sign of the canting angle corresponds to the sign of the DMI. N3d is the number of the 3d electrons per transition metal ion obtained from first-principles calculations.

The results³ show a nearly monotonic variation of the canting angle (and the DMI) as a function of the filling of the 3d band, with a change of sign between FeBO₃ and CoCO₃. This can be understood with a simple model based on partial inter-orbital contributions to the DMI (IO-DMI), following the super-exchange-based approach developed by Moriya⁴: considering two interacting ions, one considers each of the partial contributions for DMI between one orbital of one ion and one orbital of the other ion. By changing the occupation of the 3d states we change the balance between empty and fully occupied channels for the IO-DMI. It results in the change of sign and magnitude of the total DMI.

This work, relying on a novel diffraction method, provides thus a simple microscopic understanding of the DMI in insulator systems.

References:

Dzyaloshinsky I. A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. Journal of Physics and Chemistry of Solids 4(4), 241-255, doi: 10.1016/0022-3697(58)90076-3 (1958).
Dmitrienko, V. E. et al. Measuring the Dzyaloshinskii–Moriya interaction in a weak ferromagnet. Nature Physics 10, 202–206, doi:10.1038/nphys2859 (2014).
Beutier, G. et al. Band Filling Control of the Dzyaloshinskii-Moriya Interaction in Weakly Ferromagnetic Insulators. Phys. Rev. Lett. 119, 167201, doi:10.1103/PhysRevLett.119.167201 (2017).
Moriya, T. Anisotropic Superexchange Interaction and Weak Ferromagnetism, Phys. Rev. 120, 91, doi:10.1103/PhysRev.120.91 (1960).

Funding acknowledgement: We acknowledge Diamond Light Source for time on Beamline I16 under Proposals No. 7703 and 11751, and ESRF for time on Beamline BM28 (XMaS) under Proposal BM28-01-966. The work of V. V. M. is supported by the grant of the President of Russian Federation Grant No. MD-6458.2016.2. A. I. L. acknowledges the support of Grant No. DFG SFB-668 and the excellence cluster CUI. M. I. K. acknowledges support from ERC Advanced Grant No. 338957 FEMTO/NANO. Y. O. K. acknowledges the computational resources provided by the Swedish National Infrastructure for Computing (SNIC) and Uppsala Multidisciplinary Center for Advanced Computational Science (UPPMAX).

Corresponding authors: Dr Guillaume Beutier, SIMAP, guillaume.beutier@ grenoble-inp.fr and Prof Steve P. Collins, Diamond Light Source, [email protected]

Related publication

Beutier G, Collins SP, Dimitrova OV, Dmitrienko VE, Katsnelson MI, Kvashnin YO, Lichtenstein AI, Mazurenko VV, Nisbet AGA, Ovchinnikova EN, Pincini D. Band Filling Control of the Dzyaloshinskii-Moriya Interaction in Weakly Ferromagnetic Insulators. Physical Review Letters 119, 167201, doi:10.1103/PhysRevLett.119.167201 (2017).

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Adding electrons to switch magnetic chirality

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