Asymmetric melting of a one-third plateau in kagome quantum antiferromagnets

Takahiro Misawa, Yuichi Motoyama, and Youhei Yamaji

Phys. Rev. B 102, 094419 – Published 16 September 2020

Abstract

Asymmetric destruction of the one-third magnetization plateau upon heating is found in the spin- $\frac{1}{2}$ kagome Heisenberg antiferromagnets by using the typical pure quantum state approach. The asymmetry originates from a density of states of low-lying excited states of $N_{s}$ spin systems with magnetization $(1 / 3 - 2 / N_{s})$ that is larger than the density of states of low-lying states with magnetization $(1 / 3 + 2 / N_{s})$ . The enhanced specific heat and entropy that reflect the larger density of states in the lower-field side of the plateau are detectable in candidate materials of the kagome antiferromagnets. We discuss how the asymmetry originates from the unprecedented preservation of the ice rule around the plateau.

Received 16 January 2018
Revised 17 August 2020
Accepted 28 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.094419

Physics Subject Headings (PhySH)

Frustrated magnetism Quantum statistical mechanics Spin liquid

Kagome lattice

Numerical techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Takahiro Misawa ¹, Yuichi Motoyama¹, and Youhei Yamaji^2,3

¹Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan
²Department of Applied Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
³JST, PRESTO, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

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Vol. 102, Iss. 9 — 1 September 2020

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Images

Figure 1
Finite-temperature magnetization process of the spin- $\frac{1}{2}$ antiferromagnetic Heisenberg model (a) on the kagome lattice and (b) the triangular lattice. The magnetization at $T = 0$ is also shown by a solid line. In the left insets, the lattice structures for a 36-site kagome lattice and a 27-site triangular lattice are shown. The one-third plateau region ( $m = 1 / 3$ within error bars) at $T / J = 0.05$ is shown by the shaded region. The arrow shows the region where the one-third plateau appears at zero temperature for $N_{s} = 36$ (kagome lattice) and $N_{s} = 27$ (triangular lattice). In the right insets, we show $| m - 1 / 3 |$ around the plateaus for both lattices.
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Figure 2
(a) Temperature dependence of the magnetization in the kagome lattice (36-site clusters) for several different magnetic fields. Around $h / J = 1.2$ , magnetization saturates to $1 / 3$ . Slightly above the one-third plateau, we also find the signature of another apparent plateau around $h / J = 1.6$ . However, we conclude that this plateau is induced by the finite-size effects, as we discuss in the main text. (b) Temperature dependence of the magnetization around the $1 / 3$ plateau. For $h / J = 1.1$ , 1.2, and 1.3, the magnetizations converge to 1/3 at low temperatures. (c) Size dependence of the magnetization at $T / J = 0.05$ for different magnetic fields. We take $N_{s} = 24$ , 27, 30, and 36 clusters. In the insets, the shapes of the used clusters are shown. The size-dependent error bars around the 1/3 plateau may originate from the peculiar degeneracy in the 1/3 plateau.
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Figure 3
(a) Low-energy spectrum around the one-third magnetization plateau for the 27-site cluster. We plot $\tilde{E} (m, h) = E (m) - h \times (m - 1 / 3)$ for $m = 7 / 27, 9 / 27 = 1 / 3, 11 / 27$ . Dotted lines show the position of the crossing points of the lowest energies. The arrow indicates the width of the plateau at zero temperature. In the inset, we show the lowest 128 eigenenergies for 27-site clusters ( $m = 5 / 27, 7 / 27, 9 / 27, 11 / 27$ ) and the lowest 16 eigenenergies for 36-site clusters ( $m = 10 / 36, 12 / 36, 14 / 36$ ). The eigenenergies are measured from the ground-state energy $E_{GS}$ . (b) Spin structure factors in the extended Brillouin zone for the 36-site cluster at $m = 1 / 3$ for the ground state (left panel) and the third excited state (right panel), where ${\tilde{q}}_{α} = q_{α} \times \frac{3}{π} (α = x, y)$ . In the ground state, there are sharp peaks at $\vec{q} = (\pm 4 π / 3, 0), (\pm 2 π / 3, \pm 2 π / \sqrt{3})$ , which correspond to the $\sqrt{3} \times \sqrt{3}$ order. In contrast with that, we find no significant peaks in the spin structure factor in the third excited state whose energy difference is given by $E_{third} - E_{GS} \sim 0.04 J$ .
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Figure 4
(a) Temperature dependence of the specific heat for several different magnetic fields. (b) Magnetic-field dependence of the entropy $S$ for several different temperatures. The region where the one-third plateau appears at $T / J = 0.05$ is represented by the shaded region. In the inset, we show the probability of the ice rule $P_{ice}$ for 128 eigenstates in 27-site clusters. $P_{ice}$ is defined in Appendix pp2. (c) Magnetic-field dependence of the specific heat $C / T$ for several different temperatures. At $T / t = 0.05$ , we find that $C / T$ has peaks at both the sides of the one-third plateau. We note that the finite-size effects are small around the one-third plateau for both $S$ and $C / T$ . Solid curves are guides for the eyes.
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Figure 5
Temperature dependence of the energy obtained by the TPQ method (blue circles) and the full diagonalization (red curve). For the TPQ calculations, we perform five independent runs and regard its standard deviation as error bars. In the inset, we show the geometry used in the calculation.
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