Possible topological contribution to the anomalous Hall effect of the noncollinear ferromagnet ${\mathrm{Fe}}_{3}{\mathrm{Sn}}_{2}$

Possible topological contribution to the anomalous Hall effect of the noncollinear ferromagnet ${Fe}_{3} {Sn}_{2}$

Christopher D. O'Neill, Andrew S. Wills, and Andrew D. Huxley

Phys. Rev. B 100, 174420 – Published 18 November 2019

Abstract

The magnetization, magnetoresistance, and Hall effect of the kagome structured material ${Fe}_{3} {Sn}_{2}$ is reported for high-quality single crystals. Previous investigations of ${Fe}_{3} {Sn}_{2}$ polycrystals detected ferromagnetism at $T_{c} \approx 657 K$ with moments along the easy $c$ axis and a moment rotation towards the $a - b$ plane upon cooling that culminates in moments freezing to form a spin glass at $T_{F} \approx 80 K$ . The results presented here for single crystals show the lower value of $T_{F} = 70 \pm 2.5 K$ , most likely due to the increased sample quality. Above $T_{F}$ we identify a topological contribution to the Hall resistivity coinciding with an anomalous magnetoresistance. This supports recent proposals that the magnetic structure contains magnetic skyrmions in this temperature range.

Received 8 May 2019
Revised 1 August 2019

DOI:https://doi.org/10.1103/PhysRevB.100.174420

Physics Subject Headings (PhySH)

Anomalous Hall effect Ferromagnetism Hall effect Magnetoresistance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Christopher D. O'Neill^1,*, Andrew S. Wills^2,3, and Andrew D. Huxley¹

¹School of Physics and Astronomy and CSEC, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
²Chemistry Department, UCL, 20 Gordon Street, London WC1H 0AJ, United Kingdom
³London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom

^*chris.oneill@ed.ac.uk

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Vol. 100, Iss. 17 — 1 November 2019

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Figure 1
(a) The crystal structure of ${Fe}_{3} {Sn}_{2}$ with the crystallographic axes shown as colored arrows. The blue Fe atoms form kagome planes made up of two sizes of equilateral triangles, 2.732 and $2.582 Å$ , shown in blue and red, respectively. (b) The kagome planes are bilayered where the $2.582 - Å$ Fe-Fe triangles form octahedra and the green Sn atoms sit within the kagome planes and between bilayers. (c) A typical hexagonal crystal of ${Fe}_{3} {Sn}_{2}$ showing the directions of the crystallographic axes along with a scale for comparison.
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Figure 2
(a) Curves of magnetic DC susceptibility ( $M / H$ ) versus temperature, for $μ_{0} H = 0.01$ and $0.05 T$ applied parallel to the $a$ axis (left axis) and $c$ axis (right axis), respectively. The maximum in ( $M / H$ ) attributed to $T_{F} = 70 K$ is indicated. (b) The $1 T \to 0 T$ segment of hysteresis curves for $μ_{0} H$ parallel to the $a$ axis at a series of temperatures. (c) The full magnetic hysteresis curve at $120 K$ between $\pm 4 T$ , for $μ_{0} H$ parallel to the $c$ axis. No notable hysteresis is observed. (d, e) The $4 T \to 0 T$ segment of hysteresis curves at a series of temperatures for $μ_{0} H$ parallel to the $c$ axis.
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Figure 3
(a) The zero-field resistivity, $ρ_{x x} (0)$ , of ${Fe}_{2} {Sn}_{3}$ measured in the $a - b$ plane of the crystal. (b, c) Curves of the change in resistivity relative to the zero-field value versus $μ_{0} H$ for a range of temperatures between 270 and 30 K.
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Figure 4
(a–c) Curves of Hall resistivity, $ρ_{x y}$ , versus $μ_{0} H$ , between 270 and 30 K. Dashed black lines are calculated fits based on Eqs. (1) and (2) discussed in the text. Black arrows indicate the region where an extra contribution to the Hall resistivity, $Δ ρ_{x y}$ , exists.
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Figure 5
(a) Values of $n$ (left axis) and $S_{H}$ (right axis) from fits to the Hall resistivity as a function of the temperature. Dashed horizontal lines are guides for the eye to demonstrate the temperature independence of $n$ and $S_{H}$ above $T_{F}$ . (b, c) Curves of the change in resistivity relative to the zero-field value versus $μ_{0} H$ for 250 and $120 K$ , respectively. (d, e) The corresponding $Δ ρ_{x y}$ curves. Dashed vertical lines are guides for the eye showing that $Δ ρ_{x y}$ exists over the same $μ_{0} H$ range as the anomaly seen in magnetoresistance. (f) The magnitude of the peak maximum $| Δ ρ_{x y} |$ averaged for both positive and negative fields as a function of the temperature from $270 K$ to $T_{F}$ .
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Figure 6
The $μ_{0} H - T$ phase diagram of ${Fe}_{3} {Sn}_{2}$ with $μ_{0} H$ parallel to the $c$ axis. The green region represents the spin-glass phase below $T_{F} = 70 K$ determined from the magnetic susceptibility, shown as gray triangles outlined in red. Gray circle and diamond markers are derived from the anomaly in magnetoresistance, as described in the text. The blue area depicts the R-state region of noncollinear moments, while the yellow area represents moment saturation with $μ_{0} H$ and the shaded blue/yellow area represents the crossover region.
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Physical Review B

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Possible topological contribution to the anomalous Hall effect of the noncollinear ferromagnet ${Fe}_{3} {Sn}_{2}$

Christopher D. O'Neill, Andrew S. Wills, and Andrew D. Huxley

Phys. Rev. B 100, 174420 – Published 18 November 2019

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Physical Review B

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Possible topological contribution to the anomalous Hall effect of the noncollinear ferromagnet Fe3Sn2

Christopher D. O'Neill, Andrew S. Wills, and Andrew D. Huxley

Phys. Rev. B 100, 174420 – Published 18 November 2019

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Possible topological contribution to the anomalous Hall effect of the noncollinear ferromagnet ${Fe}_{3} {Sn}_{2}$