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Spin-Lattice Decoupling in a Triangular-Lattice Quantum Spin Liquid

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Spin-Lattice Decoupling in a Triangular-Lattice Quantum Spin Liquid ARTICLE DOI: 10.1038/s41467-018-04005-1 OPEN Spin-lattice decoupling in a triangular-lattice quantum spin liquid Takayuki Isono1,3, Shiori Sugiura 1, Taichi Terashima 1, Kazuya Miyagawa2, Kazushi Kanoda 2 & Shinya Uji1 A quantum spin liquid (QSL) is an exotic state of matter in condensed-matter systems, where the electron spins are strongly correlated, but conventional magnetic orders are suppressed down to zero temperature because of strong quantum fluctuations. One of the most pro- 1234567890():,; minent features of a QSL is the presence of fractionalized spin excitations, called spinons. Despite extensive studies, the nature of the spinons is still highly controversial. Here we report magnetocaloric-effect measurements on an organic spin-1/2 triangular-lattice anti- ferromagnet, showing that electron spins are decoupled from a lattice in a QSL state. The decoupling phenomena support the gapless nature of spin excitations. We further find that as a magnetic field is applied away from a quantum critical point, the number of spin states that interact with lattice vibrations is strongly reduced, leading to weak spin–lattice coupling. The results are compared with a model of a strongly correlated QSL near a quantum critical point. 1 National Institute for Materials Science, Tsukuba, Ibaraki 305-0003, Japan. 2 Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113- 8656, Japan. 3Present address: Condensed Molecular Materials Laboratory, RIKEN, Wako, Saitama 351-0198, Japan. Correspondence and requests for materials should be addressed to T.I. (email: [email protected]) or to S.U. (email: [email protected]) NATURE COMMUNICATIONS | (2018) 9:1509 | DOI: 10.1038/s41467-018-04005-1 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-04005-1 quantum spin liquid (QSL) is an intriguing exception for Conversely, Arrhenius behavior of the thermal conductivity fi Δ k 17 Athe Landau theory of phase transitions; at suf ciently low suggests the presence of a small gap, / B ~ 0.5 K . There have temperatures, condensed-matter systems form an ordered been many debates about the spinon excitations not only in κ- state characterized by broken symmetries and corresponding (BEDT-TTF)2Cu2(CN)3, but also in the other QSL candidates 18,19 order parameters. However, the order can be suppressed when such as a triangular-lattice system, YbMgGaO4 , and a fl 20,21 there exist strong quantum-mechanical uctuations enhanced by kagome-lattice system, ZnCu3(OH)6Cl2 (refs. ). low dimensionality and/or geometrical frustration. The resulting Here we report magnetocaloric-effect (MCE) measurements on κ exotic quantum liquids such as the QSL are not described by any -(BEDT-TTF)2Cu2(CN)3, which unveils a characteristic thermal broken symmetry or order parameter1. The QSL is also of great relaxation of the QSL state. At very low temperatures in a mag- interest in connection with a mechanism of high-temperature netic field, the thermal relaxation time between the electron spins superconductivity2 and application to quantum computation3. and lattice is dramatically increased, indicating that the spins are A spin-1/2 triangular-lattice antiferromagnet with nearest- decoupled from the lattice bath. The spin–lattice decoupling can neighbor (NN) antiferromagnetic (AF) exchange interactions J is explain the seeming discrepancy in the nature of the spin- one of the most typical example of two-dimensional frustrated excitation spectrum; the spin excitations are gapless. Moreover, spin systems, in which Anderson first proposed a QSL ground we show by combining the present MCE results with our recent state more than 40 years ago4. Although the ground state of the magnetic-susceptibility study that as a zero-field quantum critical triangular-lattice Heisenberg AF system is now known to be 120° point (QCP) is approached, the number of spin states is strongly AF order5, its ordered state can be suppressed by ring-exchange enhanced. This is compatible with a model of a strongly corre- interactions6, next NN interactions7, or a spatial distribution of lated QSL near a QCP. an exchange coupling constant8, consequently leading to QSL ground states. One of the most fundamental properties of a QSL Results is the presence of charge neutral excitations carrying spin-1/2 Magnetocaloric effect. In the present study, we have measured quantum number, spinons. These fractional excitations are clearly the MCE to resolve the discrepancy between the gapped and distinct from spin-1 magnon excitations in magnetically ordered gapless features of the spin excitations in κ-(BEDT- ΔT states. Depending on the theoretical model, the spinon excitations TTF)2Cu2(CN)3. The MCE, , is a thermal response of a sample may be gapped or gapless, and may obey Bose or Fermi fi H t – to magnetic- eld changes, d /d , given by statistics1,6,9 11. ΔT T H ∂S In 2003, the first evidence of a QSL was reported in an organic ΔT τ dð Þ d ; κ ¼À t À K t ∂H ð1Þ triangular-lattice antiferromagnet, -(BEDT-TTF)2Cu2(CN)3 d B d T (ref. 12), where BEDT-TTF stands for bis(ethylenedithio)tetra- thiafulvalene. In this material, a spin-1/2 is located on a (BEDT- where K represents the thermal conductance between the sample þ B TTF)2 dimer, which is arranged on a triangular lattice. Despite and heat bath. The second term in Eq. (1) describes heating or J k the large NN AF interactions, / B ~ 250 K, no magnetic long- cooling of the sample by the magnetic entropy change, dS/dH. 12–14 range order happens down to T ∼ 30 mK , which is four When S decreases (increases) with increasing field, the sample is J k orders of magnitude lower than / B. This suggests that the QSL heated up (cooled down). Resulting ΔT is relaxed with the κ τ = C K fi C state is realized in -(BEDT-TTF)2Cu2(CN)3. The nature of the relaxation time, / B, as described in the rst term. Here, magnetic excitations of the QSL state, spinons, has been inten- represents the heat capacity of the sample. Figure 1a, b show sively studied and discussed. A finite value of the specific heat heating and relaxation processes of the sample at the bath tem- divided by temperature C/T for T → 0, and Pauli-like magnetic perature, T , of 0.26 K (see also Supplementary Fig. 1). As the 15,16 B susceptibility are hallmarks of gapless spin excitations . field increases up to 0.8 T (t < 10 s) (Fig. 1a), the sample a c 2 10 Spin heating, Lattice heating, 1 0H = 0.8 T 5 0H = 0.8 T (mK) (mK) T T 0 0 0 20 40 60 0 10 20 30 t (s) t (s) b d 1.5 10 Spin heating, Lattice heating, 1.0 H = 3 T H = 3 T 0 5 0 (mK) 0.5 (mK) T T 0.0 0 –0.5 0 100 200 300 0 10 20 30 t (s) t (s) Fig. 1 Thermal relaxation curve at the temperature of 0.26 K. Thermal relaxation curve for the spin (magnetocaloric) heating, when the magnetic field is swept up from a 0.6 to 0.8 T, and b 2 to 3 T. The thermal relaxation curve for the lattice (Joule) heating at c μ0H = 0.8 T and d 3 T. In each figure, the solid line represents a single exponential decay, ΔT = A exp(−t/τ), with the relaxation time, τ, and a constant, A 2 NATURE COMMUNICATIONS | (2018) 9:1509 | DOI: 10.1038/s41467-018-04005-1 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-04005-1 ARTICLE a b 103 102 T = 0.92 K 10 T –1.3 1 3 10 102 (s) τ 1.5 0 10 (s) τ 101 0.1 T 2 10 T = 0.51 K 1 10 0 (s) 10 τ 6 8 2 4 6 8 2 100 0.1 1 T (K) 103 c T = 0.26 K 2 10 ) 100 1.5 T –1.3 1 K (s) 10 τ 3 50 –1 0 (s –1 10 –1 10 ) 1.3 –1 0 T τ 10 0 1 2 3 4 ( 10 10–2 4 6 8 2 4 6 8 2 6 8 2 4 6 8 2 1 10 0.1 1 0H (T) T (K) Fig. 2 Magnetic field and temperature dependence of the relaxation time. a Magnetic-field dependence of the relaxation time, τ, for the spin heating at various temperatures. The dashed line represents constant τ of 2.1 s. At low fields, τ is shorter than 2.1 s (thick arrows). The thin arrows indicate the onset field of the τ increase, H*, which is determined based on the linear-scale plot, shown in the inset. b Temperature variation in τ for the spin heating at various magnetic fields. The black- and purple-dashed lines denote the power-law behavior with an exponent of −1.3, and constant τ of 2.1 s, respectively. At each field, τ is shorter than 2.1 s above the temperature indicated by the thick arrows. c Temperature dependence of (τT1.3)−1 at various magnetic fields. The τT1:3 À1 dashed line represents a zero-temperature extrapolation of the low-temperature data, ð Þ0 − temperature increases, ΔT > 0 K. We observe positive ΔT in the behavior, τ ~ T 1.3, in the wide temperature range. Figure 2c − whole field and temperature range up to 17 T between 0.1 and 1.6 shows the temperature dependence of (τT1.3) 1. As the − K, indicating that the magnetic entropy is monotonously sup- temperature goes to zero, (τT1.3) 1 approaches a constant value pressed by applying a magnetic field.
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