Weak ferromagnetism in perovskite oxides

J.-S. Zhou, L. G. Marshall, Z.-Y. Li, X. Li, and J.-M. He

Phys. Rev. B 102, 104420 – Published 16 September 2020

Abstract

Weak ferromagnetism has been widely found in antiferromagnetic systems, including the technically important orthorhombic perovskites $R Fe O_{3}$ ( $R = rare earth$ ) owing to spin canting associated with crystal symmetry. Antisymmetric exchange interaction (AEI) and single-ion anisotropy (SIA) are the essential mechanisms responsible for the development of noncollinear structures in antiferromagnetic systems. AEI and SIA share the same structural restriction to facilitate the spin canting. While both AEI and SIA originate from the spin-orbit coupling effect, they have sharply different dependences on the local structure. Consideration of the structural dependence of a canted spin motivates us to revisit the orthoferrite family. The spin canting along the $c$ axis measured on precisely oriented crystals increases monotonically from $La Fe O_{3}$ to $Lu Fe O_{3}$ . Based on Moriya's model, AEI is sensitive to the octahedral-site distortion in the perovskite structure. However, the site distortion does not exhibit a monotonic change with the rare-earth substitution. Instead, a linear relationship has been found in both the octahedral rotation and the spin canting angle versus the rare-earth ionic radius, which indicates that SIA plays a significant role leading the spin canting in orthoferrites.

Received 13 May 2020
Revised 7 July 2020
Accepted 30 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.104420

Physics Subject Headings (PhySH)

Dzyaloshinskii-Moriya interaction Ferromagnetism Magnetic order

Ferrites Perovskites

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J.-S. Zhou^*, L. G. Marshall ^†, Z.-Y. Li, X. Li , and J.-M. He

Materials Science and Engineering Program, Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA

^*jszhou@mail.utexas.edu
^†Present address: VitalFlo Inc., 310 S. Harrington St., Raleigh, NC 27603.

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Vol. 102, Iss. 10 — 1 September 2020

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Images

Figure 1
The magnetic phase diagram of orthoferrites.
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Figure 2
The $M - H$ loops at different temperatures for (a) $LuFe O_{3}$ and (b) $YbFe O_{3}$ . The plot on the side of (a) shows schematically the magnetization switching along the $c$ axis. Instead of changing the magnetic domain boundary, the sharp magnetization switching is made possible by simply flipping spins by 180°. Blue circles denote oxygen, solid yellow circles $F e^{3 +}$ , and red arrows spins at $F e^{3 +}$ .
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Figure 3
Temperature dependence of the residual moment $M_{res}$ obtained from the $M$ ( $H$ ) loops at $H_{a} = 0$ for $R Fe O_{3}$ ; lines are the fitting results to the Brillouin function for the diamagnetic rare earths or the function of Eq. (1) in the text for the magnetic rare earths. The abrupt drop of the canted moment at low temperatures for the $R Fe O_{3}$ with $R = Nd$ , Dy, Er, and Tm is due to the spin reorientation at $T_{SR}$ . Below $T_{SR}$ , the formula of Eq. (2) is invalid for the fitting in these cases.
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Figure 4
Reduced spin canting angle $θ_{r}$ and the octahedral-site rotation angle $β_{r}$ versus IR of orthoferrite $R Fe O_{3}$ ; solid lines are drawn as a guide to the eyes. The dot-dash line is a schematic drawing for the spin canting angle based on the change of the local crystal structure. The solid blue circles denote the reduced angle for the $R Fe O_{3}$ with nonmagnetic rare earth. The hollow blue circles are for those $R Fe O_{3}$ with magnetic rare earths; the dashed line is a guide to the eyes, which is drawn within the data points for the $R Fe O_{3}$ with the rare earths having odd numbers of $4 f$ electrons. The data of the reduced angle in the figure represent the change of the canting moment of $R Fe O_{3}$ relative to that in $LaFe O_{3}$ . On the other hand, the DMI theory predicts that the canting moment is proportional to the correction of the Landé factor in the crystal field. The correction is inversely proportional to the bond length splitting. Therefore, the data in the figure show the relative change of the canted moment from the experiment and the prediction of the DMI model as a function of the rare-earth radius.
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Figure 5
Upper panel: Three Fe-O bond lengths versus IR in orthoferrites; dashed lines are guides to the eyes. Lower panel: the orthorhombic vibration modes $Q_{2} = (l_{x} - l_{y})$ and $Q_{3} = (2 l_{z} - l_{x} - l_{y}) / \sqrt 3$ , where $l_{x}$ denotes the Fe-O bond length, and the magnitude of local bond length splitting $ρ = {(Q_{2}^{2} + Q_{3}^{2})}^{1 / 2}$ versus IR. The structural data are after Refs. [11, 27].
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Figure 6
Schematic structural model and the spin structure of orthoferrites. Left: the orthorhombic perovskite structure of $LaFe O_{3}$ ; Right: Octahedron in a-b plane projected along the $c$ axis. The preferred crystallographic direction is represented by red arrows inside the octahedra.
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