Electronic transport on the Shastry-Sutherland lattice in Ising-type rare-earth tetraborides

Linda Ye, Takehito Suzuki, and Joseph G. Checkelsky

Phys. Rev. B 95, 174405 – Published 3 May 2017

Abstract

In the presence of a magnetic field frustrated spin systems may exhibit plateaus at fractional values of saturation magnetization. Such plateau states are stabilized by classical and quantum mechanisms including order by disorder, triplon crystallization, and various competing order effects. In the case of electrically conducting systems, free electrons represent an incisive probe for the plateau states. Here we study the electrical transport of Ising-type rare-earth tetraborides $R B_{4}$ ( $R = Er$ , Tm), a metallic Shastry-Sutherland lattice showing magnetization plateaus. We find that the longitudinal and transverse resistivities reflect scattering with both the static and the dynamic plateau structure. We model these results consistently with the expected strong uniaxial anisotropy on a quantitative level, providing a framework for the study of plateau states in metallic frustrated systems.

Received 7 March 2017
Revised 14 April 2017

DOI:https://doi.org/10.1103/PhysRevB.95.174405

Physics Subject Headings (PhySH)

Frustrated magnetism Transport phenomena

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Linda Ye^*, Takehito Suzuki, and Joseph G. Checkelsky

Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*lindaye@mit.edu

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Issue

Vol. 95, Iss. 17 — 1 May 2017

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Images

Figure 1
Shastry-Sutherland lattice and magnetization plateaus in ${ErB}_{4}$ and ${TmB}_{4}$ . (a) SSL model with diagonal bond $J_{1}$ and square bond $J_{2}$ . (b, c) Spin configuration for antiferromagnetic ground states in ${ErB}_{4}$ and ${TmB}_{4}$ , respectively. Exchange couplings $J_{1}$ , $J_{2}$ , $J_{3}$ , and $J_{4}$ and the unit cell (dashed line) are shown. (d) Magnetization as a function of the field $μ_{0} H_{eff}$ applied along the $c$ axis for ${ErB}_{4}$ and ${TmB}_{4}$ . Inset: Magnified view near the $(1 / q) M_{s}$ phase in ${TmB}_{4}$ . Light blue (dark blue) curves represent scans with an increasing (a decreasing) field between $\pm 5$ T. The plateau values (defined at the midpoint of the plateau) for the two scan directions are 0.121 $M_{s}$ ( $q ≃ 8.3$ ) and 0.132 $M_{s}$ ( $q ≃ 7.6$ ), respectively.
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Figure 2
Magnetic phase diagram of ${ErB}_{4}$ and ${TmB}_{4}$ . (a) Resistivity $ρ$ as a function of temperature $T$ for the SSL plane of ${ErB}_{4}$ and ${TmB}_{4}$ single crystals. (b) Volume magnetic susceptibility $χ$ measured along the $c$ axis for ${ErB}_{4}$ and ${TmB}_{4}$ . Triangles denote transition temperatures. (c, d) Phase diagram in the $H − T$ plane for ${ErB}_{4}$ and (trained) ${TmB}_{4}$ , respectively. The boundaries determined from transport are represented by triangles; those determined from magnetization, by circles. (e) Magnetic-field dependence of the longitudinal resistivity $ρ_{x x} (B)$ at selected $T$ for ${TmB}_{4}$ and ${ErB}_{4}$ .
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Figure 3
Magnetic scattering in ${ErB}_{4}$ . (a) Detailed magnetic-field dependence of the longitudinal resistivity $ρ_{x x} (B)$ of ${ErB}_{4}$ at $T < T_{N}$ . (b) Magnetic contribution to resistivity $Δ ρ_{x x}$ (see text). Inset: Possible configuration of the half-plateau state, with AFM stripes marked in gray. Here the black (white) circles represent spins parallel (antiparallel) to $H$ . Dashed square frames enclose two types of unit cells for the $M_{s} / 2$ phase. (c) Magnetic energy $E_{0}$ as a function of $B$ . The hatched area represents regions with phase coexistence and the dashed line is a linear fit to the FIP phase. Left inset: Mean-field fitting to the magnetic susceptibility of ${ErB}_{4}$ . Right inset: Fitting of $Δ ρ_{x x} (T)$ at selected $B$ .
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Figure 4
Hall effect in ${ErB}_{4}$ . (a) Field dependence of the transverse resistivity $ρ_{y x} (B)$ for ${ErB}_{4}$ . Dashed lines represent the singularities observed in $ρ_{x x}$ . (b) Relative relaxation time $τ (B) / τ_{0}$ as a function of $B$ . (c) Longitudinal conductivity $σ_{x x}$ and (d) transverse conductivity $σ_{x y}$ fit with the modified two-band model using $τ (B) / τ_{0}$ [Eqs. (3) and (4)]. The legend is the same for both panels.
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Figure 5
Magnetotransport in ${TmB}_{4}$ . (a) Longitudinal resistivity $ρ_{x x}$ for ${TmB}_{4}$ at low $T$ . The $T = 3$ K and $T = 5$ K curves are offset for clarity. (b) Transverse resistivity of ${TmB}_{4}$ at low $T$ . (c) Magnetic contribution to resistivity $Δ ρ_{x x}$ and possible magnetic configurations [16, 26]. Inset: $σ_{x x}$ and $σ_{x y}$ fit with Eqs. (3) and (4). For clarity, only scans from negative to positive $B$ are shown.
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