High-temperature magnetic anomaly in the Kitaev hyperhoneycomb compound $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$

High-temperature magnetic anomaly in the Kitaev hyperhoneycomb compound $β べーた − {Li}_{2} {IrO}_{3}$

Alejandro Ruiz, Vikram Nagarajan, Mayia Vranas, Gilbert Lopez, Gregory T. McCandless, Itamar Kimchi, Julia Y. Chan, Nicholas P. Breznay, Alex Frañó, Benjamin A. Frandsen, and James G. Analytis

Phys. Rev. B 101, 075112 – Published 12 February 2020

Abstract

We report the existence of a high-temperature magnetic anomaly in the three-dimensional Kitaev candidate material, $β べーた − {Li}_{2} {IrO}_{3}$ . Signatures of the anomaly appear in magnetization, heat capacity, and muon spin relaxation measurements. The onset coincides with a reordering of the principal axes of magnetization, which is thought to be connected to the onset of Kitaev-like correlations in the system. The anomaly also shows magnetic hysteresis with a spatially anisotropic magnitude that follows the spin-anisotropic exchange anisotropy of the underlying Kitaev Hamiltonian. We discuss possible scenarios for a bulk and impurity origin.

Received 28 May 2019
Revised 8 November 2019
Accepted 9 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.075112

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Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Alejandro Ruiz^1,2, Vikram Nagarajan^1,2, Mayia Vranas^1,2, Gilbert Lopez^1,2, Gregory T. McCandless³, Itamar Kimchi⁴, Julia Y. Chan⁵, Nicholas P. Breznay⁶, Alex Frañó⁷, Benjamin A. Frandsen⁸, and James G. Analytis^1,2

¹Department of Physics, University of California, Berkeley, California 94720, USA
²Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³Department of Chemistry and Biochemistry, The University of Texas at Dallas, Richardson, Texas 75080, USA
⁴JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
⁵Department of Chemistry, The University of Texas at Dallas, Richardson, Texas 75080, USA
⁶Department of Physics, Harvey Mudd College, Claremont, California 91711, USA
⁷Department of Physics, University of California, San Diego, California 92093, USA
⁸Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA

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Vol. 101, Iss. 7 — 15 February 2020

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Figure 1
(a) Three-dimensional structure of $β べーた − {Li}_{2} {IrO}_{3}$ , where the red, green, and blue colors correspond to orthogonal compass directions of the Kitaev model. The two triangles, situated $70^{\circ}$ apart, show the possible environments for a magnetic ion in $β べーた − {Li}_{2} {IrO}_{3}$ , and determine the $g$ -factor anisotropy. Also shown is a site vacancy which can trap flux excitations in a Kitaev spin liquid, creating a large local moment. (b) The anisotropic magnetic susceptibility of $β べーた − {Li}_{2} {IrO}_{3}$ for an applied magnetic field of $0.1 T$ . At $T_{I} = 38 K$ , the system transitions into an incommensurate spiral state with noncoplanar, counter-rotating moments. When a small magnetic field is applied ( $H < 0.5 T$ ), a magnetic anomaly is also observed at $100 K$ . Inset shows inverse susceptibility, clearly showing a reordering of the principal axes of susceptibility at $\sim 100 K$ . (c) Comparison of the inverse $\hat{b}$ -axis susceptibility for $1.0 T$ and $0.1 T$ . The low-field data shows two distinct behaviors: a linear response above $100 K$ and a strong deviation from Curie-Weiss behavior $100 > T > 40 K$ .
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Figure 2
(a)–(c) Hysteresis behavior was observed in $β べーた − {Li}_{2} {IrO}_{3}$ below $T_{η いーた} = 100 K$ . The figure insets show the data after the linear background corresponding to the high-field susceptibility is subtracted to indicate the isotropy of the anisotropic field $H_{a}$ along the three principal axes.
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Figure 3
(a) Angular dependent torque, ${τ たう}_{a} = 1 / 2 ({χ かい}_{b} - {χ かい}_{c}) H^{2} sin 2 {θ しーた}_{a b}$ , also shows hysteretic behavior below $T_{η いーた}$ for an applied field $H = 0.35 T$ . (b),(c) Hysteresis is observed for rotations in the $a b$ and $b c$ planes, but not in the $a c$ plane. This behavior disappears at high fields, as it is evident in the data presented for $80 K$ . In this case $θ しーた = 0$ corresponds to $H ∥ b$ for rotations in the $b c$ and $a b$ planes. (d) The anisotropy field $H_{a}$ was extracted from $M (H)$ and $τ たう / H (θ しーた$ ) measurements. $H_{a}$ appears to be indifferent to the low temperature phase boundary, and it terminates $H_{a} (0) \sim H^{*} (0)$ , suggesting the incommensurate and magnetic anomaly might share a common energy scale (see SM, Sec. S4 for low temperature determination).
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Figure 4
(a) Inset shows the field-cooled (FC) and zero-field-cooled (ZFC) magnetization with a $0.1 T$ field applied along the $b$ axis, while the main panel shows the magnetic irreversibility $Δ でるた M = M_{FC} - M_{ZFC}$ for all three axes. (b) dc heat capacity was measured on a powder sample of $β べーた − {Li}_{2} {IrO}_{3}$ (blue points). The figure inset shows the area of attention from 90 to 110 K. No sharp transition was detected. A nonmagnetic isostructure, $β べーた − {Li}_{2} {PtO}_{3}$ , was also measured to isolate the magnetic contribution to the heat capacity (black points). The two curves start to deviate below $100 K$ . Moreover, $β べーた − {Li}_{2} {IrO}_{3}$ has a nonzero intercept at low temperature, $γ がんま = 0.02 J / mol K^{2}$ . (c) The magnetic entropy was calculated by taking the difference between the two data sets in (b), and integrating over temperature, $d S = C_{p} / T d T$ . At $T_{η いーた}$ , the magnetic entropy reaches $\sim 1 / 4$ $R ln 2$ .
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Figure 5
(a) $μ みゅー SR$ asymmetry, $A (t)$ , spectra at selected temperatures measured in zero field (ZF) and a $50 G$ longitudinal field (LF). The ZF relaxation rate shows a clear increase below $T_{η いーた}$ . This relaxation can be decoupled with a very modest LF, indicating the development of weak, static magnetism. Solid lines are Gaussian fits to the data. (b) The asymmetry $A (t) = a_{o} e^{- t^{2} ({σ しぐま}_{1}^{2} + {σ しぐま}_{2}^{2}) / 2}$ has two contributions: a $T$ -independent nuclear contribution ${σ しぐま}_{1}$ and a $T$ -dependent electronic contribution ${σ しぐま}_{2}$ . The $T$ -dependent ${σ しぐま}_{2}$ evolves like an order parameter below $T_{η いーた}$ . (c) A model independent metric, $Δ でるた A^{2} (T) = \sum_{i} \frac{{(A_{i}^{150 K} - A_{i}^{T})}^{2}}{{(A_{i}^{150 K})}^{2}}$ , confirms the results of the fits in panel (b). (d) Ruthenium substituted samples show a clear effect of disorder: just as the incommensurate transition is suppressed, so too is the transition at 100 K, which is observed by the difference of zero-field-cooled (ZFC) and field-cooled (FC) magnetization curves taken with $0.01 T$ . Note that substitution amounts are given in nominal values. Actual values are significantly lower, below the resolution of our EDX measurements. Nevertheless, the systematics show clear trends.
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Physical Review B

covering condensed matter and materials physics

High-temperature magnetic anomaly in the Kitaev hyperhoneycomb compound $β べーた − {Li}_{2} {IrO}_{3}$

Alejandro Ruiz, Vikram Nagarajan, Mayia Vranas, Gilbert Lopez, Gregory T. McCandless, Itamar Kimchi, Julia Y. Chan, Nicholas P. Breznay, Alex Frañó, Benjamin A. Frandsen, and James G. Analytis

Phys. Rev. B 101, 075112 – Published 12 February 2020

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Physical Review B

covering condensed matter and materials physics

High-temperature magnetic anomaly in the Kitaev hyperhoneycomb compound βべーた−Li2IrO3

Alejandro Ruiz, Vikram Nagarajan, Mayia Vranas, Gilbert Lopez, Gregory T. McCandless, Itamar Kimchi, Julia Y. Chan, Nicholas P. Breznay, Alex Frañó, Benjamin A. Frandsen, and James G. Analytis

Phys. Rev. B 101, 075112 – Published 12 February 2020

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High-temperature magnetic anomaly in the Kitaev hyperhoneycomb compound $β べーた − {Li}_{2} {IrO}_{3}$