Dzyaloshinskii-Moriya interaction and the magnetic ground state in magnetoelectric ${\mathrm{LiCoPO}}_{4}$

Dzyaloshinskii-Moriya interaction and the magnetic ground state in magnetoelectric ${LiCoPO}_{4}$

Ellen Fogh, Oksana Zaharko, Jürg Schefer, Christof Niedermayer, Sonja Holm-Dahlin, Michael Korning Sørensen, Andreas Bott Kristensen, Niels Hessel Andersen, David Vaknin, Niels Bech Christensen, and Rasmus Toft-Petersen

Phys. Rev. B 99, 104421 – Published 20 March 2019

Abstract

Magnetic structures are investigated by means of neutron diffraction to shine a light on the intricate details that are believed to be key to understanding the magnetoelectric effect in ${LiCoPO}_{4}$ . At zero field, a spontaneous spin canting of $φ = 7 {(1)}^{\circ}$ is found. The spins tilt away from the easy $b$ -axis toward $c$ . Symmetry considerations lead to the magnetic point group $m_{z}^{'}$ , which is consistent with the previously observed magnetoelectric tensor form and weak ferromagnetic moment along $b$ . For magnetic fields applied along $a$ , the induced ferromagnetic moment couples via the Dzyaloshinskii-Moriya interaction to yield an additional field-induced spin canting. An upper limit to the size of the interaction is estimated from the canting angle.

Received 19 November 2018
Revised 8 March 2019

DOI:https://doi.org/10.1103/PhysRevB.99.104421

Physics Subject Headings (PhySH)

Antiferromagnetism Magnetic order Magnetic phase transitions

3-dimensional systems Antiferromagnets Single crystal materials

Magnetization measurements Neutron diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ellen Fogh^1,*, Oksana Zaharko², Jürg Schefer², Christof Niedermayer², Sonja Holm-Dahlin^2,3, Michael Korning Sørensen¹, Andreas Bott Kristensen¹, Niels Hessel Andersen¹, David Vaknin⁴, Niels Bech Christensen¹, and Rasmus Toft-Petersen¹

¹Department of Physics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
²Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, Villigen CH-5232, Switzerland
³Nano-Science Center, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
⁴Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

^*elfogh@fysik.dtu.dk

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Vol. 99, Iss. 10 — 1 March 2019

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Figure 1
Schematic of temperature dependencies of the ME tensor elements, $α_{⊥}$ and $α_{∥}$ , for the lithium orthophosphates as measured by Mercier [19]. Values of $Δ g / g$ [20] are listed for each compound as well as maximum absolute values of the ME coefficients [21, 22].
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Figure 2
Neutron diffraction data from RITA-II. (a)–(c) Rocking curves of $(3, 0, 1), (1, 0, 0)$ , and (0,1,0) at 18 or $2 K$ (black circles) and $25 K$ (blue diamonds), all at $0 T$ . The solid lines are Gaussian fits from which the integrated intensities are obtained. The canting angle of the zero-field structure is estimated from the intensity ratio between the magnetic contributions of (3,0,1) and (1,0,0). (d) Integrated magnetic intensity of (3,0,1) (circles) and (1,0,0) (squares) as a function of temperature at $0 T$ (black symbols) and $10 T$ along $b$ (green symbols). The intensities have been normalized to the value of (3,0,1) at the lowest temperature, and the intensity of (1,0,0) has been multiplied by 20 for a better comparison of the temperature profiles. Backgrounds at $25 K$ have been subtracted. The solid lines show fits to a power law, $I \propto {(T - T_{N})}^{β}$ , for $T > 17 K$ at $0 T$ and $T > 13 K$ at $10 T$ . The transition temperature, $T_{N}$ , and critical exponent, $β$ , were fitted collectively for the two peaks. (e) Spontaneous canting angle calculated from the intensity ratio of (1,0,0) and (3,0,1) for measurements done at $0 T$ (black symbols) and $10 T$ (green symbols). The horizontal line shows the value of the weighted mean of all data points, $φ = 7 {(1)}^{\circ}$ .
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Figure 3
Projections in the $(b, c)$ plane of the magnetic structures of ${LiCoPO}_{4}$ at (a) zero field and for (b) $H ∥ a$ . For clarity, only the four magnetic ions of the unit cell are shown and all angles are largely exaggerated. The ion positions deviate slightly from the high-symmetry positions (dashed circles). The applied field yields asymmetric total canting angles.
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Figure 4
Magnetization, field-induced canting angle, and integrated neutron intensity of (0,2,1) for magnetic fields applied along $a$ . (a) Magnetization (thick black line) and field-induced canting angle (green circles) calculated from the neutron intensity of (0,2,1) as a function of applied field. Both are to a good approximation linearly proportional to the field strength. The solid line shows a linear fit to the canting angle, whereas the dashed line shows the angle as calculated from the magnetization with $M_{s} = 3.6 μ_{B}$ /ion. (b) and (c) Integrated intensity (blue diamonds) of (0,2,1) as a function of applied field at $2 K$ and as a function of temperature at $12.2 T$ , respectively. The field dependence in (b) and the temperature dependence in (c) have been fitted to a quadratic and a Curie-Weiss law squared, respectively (solid lines). The black symbols in (b) show intensities for (0,1,2) (circles) and (0,0,1) (stars) at 0 and $12.2 T$ . Note that the intensities for these peaks are scaled to appear together with the intensity of (0,2,1) in order to demonstrate that they show no or only little field dependence.
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Physical Review B

covering condensed matter and materials physics

Dzyaloshinskii-Moriya interaction and the magnetic ground state in magnetoelectric ${LiCoPO}_{4}$

Ellen Fogh, Oksana Zaharko, Jürg Schefer, Christof Niedermayer, Sonja Holm-Dahlin, Michael Korning Sørensen, Andreas Bott Kristensen, Niels Hessel Andersen, David Vaknin, Niels Bech Christensen, and Rasmus Toft-Petersen

Phys. Rev. B 99, 104421 – Published 20 March 2019

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Physical Review B

covering condensed matter and materials physics

Dzyaloshinskii-Moriya interaction and the magnetic ground state in magnetoelectric LiCoPO4

Ellen Fogh, Oksana Zaharko, Jürg Schefer, Christof Niedermayer, Sonja Holm-Dahlin, Michael Korning Sørensen, Andreas Bott Kristensen, Niels Hessel Andersen, David Vaknin, Niels Bech Christensen, and Rasmus Toft-Petersen

Phys. Rev. B 99, 104421 – Published 20 March 2019

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Dzyaloshinskii-Moriya interaction and the magnetic ground state in magnetoelectric ${LiCoPO}_{4}$