Probing short-range magnetic order in a geometrically frustrated magnet by means of the spin Seebeck effect

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Probing short-range magnetic order in a geometrically frustrated magnet by means of the spin Seebeck effect

Changjiang Liu, Stephen M. Wu, John E. Pearson, J. Samuel Jiang, N. d'Ambrumenil, and Anand Bhattacharya

Phys. Rev. B 98, 060415(R) – Published 28 August 2018

Abstract

The spin Seebeck effect (SSE) is a phenomenon where a spin current is generated from thermal excitations in magnetic materials. It is believed that magnetic long-range order (LRO) is not required for SSE, while short-ranged order (SRO) plays an important role. However, a definitive experimental demonstration of the connection between the SSE and SRO has been missing. Here, we show that the SSE is able to probe a specific SRO in a model geometrically frustrated magnet ${Gd}_{3} {Ga}_{5} O_{12}$ (GGG). A field-induced SRO in GGG is detected by the SSE in the temperature range 2–5 K. The origin of the SRO is verified by comparing the SSE data directly to existing neutron scattering measurements at much lower temperatures ( $T < 0.9$ K), where field-induced LRO exists. Our theoretical calculations of the magnetic structure further confirm the anisotropic field dependence of the SRO in GGG. These findings establish that the SSE can serve as an effective probe of SRO in geometrically frustrated magnets.

Received 29 March 2018

DOI:https://doi.org/10.1103/PhysRevB.98.060415

Physics Subject Headings (PhySH)

Ferrimagnetism Frustrated magnetism Magnetic order Magnons Spin Seebeck effect

Ferrimagnets Kagome lattice Magnetic insulators

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Changjiang Liu¹, Stephen M. Wu^1,2, John E. Pearson¹, J. Samuel Jiang¹, N. d'Ambrumenil³, and Anand Bhattacharya^1,*

¹Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
²Department of Electrical and Computer Engineering, University of Rochester, Rochester, New York 14627, USA
³Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

^*anand@anl.gov

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Issue

Vol. 98, Iss. 6 — 1 August 2018

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Images

Figure 1
GGG hyperkagome lattice and schematics of the SSE device. (a) Illustration of geometrical frustration of antiferromagnetically coupled spins on a triangular lattice. The kagome lattice is a realization of such frustration in two-dimensional space. When extended to three dimensions, corner-sharing triangles form the hyperkagome lattice. For GGG, the two interpenetrating corner-sharing triangular sublattices are shown in purple and orange, respectively. (b) Device design of an on-chip heated SSE device. The upper left panel shows the vertical structure of the fabricated device. A cross-sectional view of the simulated temperature profile in GGG is shown in the bottom panel.
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Figure 2
SSE measurement results and modulations in the SSE response. (a) SSE measurement results at temperatures below 5 K with magnetic field applied along the [100] crystal axis. (b) Derivative of SSE voltage with respect to magnetic field $(d V / d H)$ showing extra field-dependent modulations in the SSE signal. (c), (d) Modulations in the SSE voltage plotted directly in the field range $- 35 kOe < H < 35$ kOe after subtracting a linear background from the SSE signal at $T = 2$ and 3 K, respectively.
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Figure 3
Anisotropic behavior of the modulation in SSE response. (a) SSE signals measured with magnetic field applied along different directions in the (001) plane, with $ϕ = 0^{\circ}$ being along the [100] crystal axis. (b) Magnitude of the slope of the linear part of the SSE signal satisfies cosine angular dependence. The inset shows the corresponding measurement geometry. $H$ is the applied in-plane magnetic field. (c)–(f) Modulations in SSE voltage from $T = 2$ to 5 K. Data in red and blue correspond to field applied along the [100] and [110] directions, respectively. Notice that the modulation in SSE signal can be resolved at temperatures up to 5 K. In these measurements, the SSE devices were fabricated on the (001) surface of GGG single crystals.
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Figure 4
Comparison between the SSE response and intensity of the [002] AFM order, and theoretical calculation of the spin configurations. (a) and (b) Magnetic field dependencies of the modulation in the SSE signal and the intensity of [002] AFM order measured by neutron diffraction with corresponding fields applied along the [100] and [110] crystal axes, respectively. Vertical dashed lines in both (a) and (b) indicate the same peak positions in the SSE data and neutron diffraction results. (c) and (d) Calculated spin configurations in one GGG primitive cell at an applied field $H = 17$ kOe aligned along the [100] and [110] crystal axes, respectively. The magnetic field points out of the page, and the spin orientation of ${Gd}^{3 +}$ ions is represented by a small arrow at each Gd site. Notice that most spins are canted away from the applied field. In (c) the net spin components in horizontal direction are zero, while the total horizontal components in (d), indicated by large arrows on the right, form an alternating AFM pattern with [002] wave vector.
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