Randomness-induced universal quantum spin liquids in frustrated magnets — Cooperation of frustration and randomness in quantum magnets —

正理 渡邊, Masari Watanabe

Kazuki Uematsu, Toshiya Hikihara, Hikaru Kawamura

Recent studies have revealed that the randomness-induced quantum spin liquid (QSL)-like state is stabilized in certain frustrated quantum magnets in two and three dimensions. In order to clarify the nature of this gapless QSL-like state, we investigate both zero- and finite-temperature properties of the random-bond one-dimensional (1D) $s=12$ Heisenberg model with the competing nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions, $J_1$ and $J_2$, by means of the exact diagonalization, density-matrix renormalization-group and Hams--de Raedt methods. We find that, on increasing the frustration $J_2$, the gapless nonmagnetic state stabilized in the unfrustrated model with $J_2=0$, the {\it unfrustrated\} random-singlet (RS) state, exhibits a phase transition into different gapless nonmagnetic state, the {\it frustrated\} RS state. This frustrated RS state in 1D has properties quite similar to the randomness-induced QSL-like state recently identified in 2D and 3D frustrated magnets exhibiting the $T$-linear low-temperature ($T$) specific heat, while the unfrustrated RS state is more or less specific to the unfrustrated 1D system exhibiting the $\sim 1(\log T)^3$ low-$T$ specific heat. Universal features and the robustness against perturbations of the frustrated RS state are emphasized.

Frédéric Mila

Kazuki Uematsu, Hikaru Kawamura

We investigate the ground-state and finite-temperature properties of the bond-random $s=1/2$ Heisenberg model on a honeycomb lattice with frustrated nearest- and next-nearest-neighbor antiferromagnetic interactions, $J_1$ and $J_2$, by the exact diagonalization and the Hams--de Raedt methods. The ground-state phase diagram of the model is constructed in the randomness versus the frustration ($J_2/J_1$) plane, with the aim of clarifying the effects of randomness and frustration in stabilizing a variety of distinct phases. We find that the randomness induces the gapless quantum spin liquid (QSL)-like state, the random-singlet state, in a wide range of parameter space. The observed robustness of the random-singlet state suggests that the gapless QSL-like behaviors might be realized in a wide class of frustrated quantum magnets possessing a certain amount of randomness or inhomogeneity, without fine-tuning the interaction parameters. Possible implications to recent experiments on the honeycomb-lattice magnets Ba$_3$CuSb$_2$O$_9$ and 6HB-Ba$_3$NiSb$_2$O$_9$ exhibiting the gapless QSL-like behaviors are discussed.

Subir Sachdev A

Masari Watanabe

In frustrated magnets, the experimental realization of a quantum disordered ground state (QDGS), especially quantum spin liquid (QSL) ground state, is a central topic in condensed matter physics.Several promising candidates were reported, and a number of QSL-like behavior, such as excitation continuum, Tlinear specific heat, and so on, were observed.However, whether the QSL-like behavior is owing to the synergy between spin frustration and quantum fluctuation or bond randomness effects has not been clarified yet.Several theoretical studies have demonstrated that the synergy effect between the magnetic frustration and the bond randomness suppresses magnetic ordering and induces a QSL-like state.This QSL-like state was proposed to be a random-singlet (RS) state, where not only nearest-neighbor spins but also distant spins form singlet pairs with random coupling energy.Since thermodynamic properties of RS and QSL are predicted to be similar to each other, it is important to elucidate the microscopic nature of randomness-induced QDGSs.However, its experimental verifications are still insufficient due to a lack of model materials.In this work, I synthesized polycrystalline samples of SrLaCuSbO 6 (SLCSO) and SrLaCuNbO 6 (SLCNO) by a solid-state reaction.Magnetic Cu 2+ ions with S = 1/2 Heisenberg spins form a square lattice with nearest-neighbor (J 1 ) and next-nearest-neighbor (J 2 ) exchange interaction.Thus, SLCSO and SLCNO were magnetically described as quasi-two-dimensional S = 1/2 J 1 -J 2 square lattice Heisenberg antiferromagnet (SLHAF).The temperature dependence of the magnetic susceptibilities of both compounds shows a broad maximum characteristic of an S = 1/2 SLHAF.However, both compounds undergo magnetic phase transitions at T N = 13.6 and 15.7 K for SLCSO and SLCNO, respectively, due to weak inter-layer interactions.Neutron powder diffraction measurements reveal contrasting spin structures in both compounds.The spin structures of SLCSO and SLCNO below T N are Néel antiferromagnetic and collinear antiferromagnetic, respectively.This result demonstrates that the nearest-neighbor interaction is dominant in SLCSO, whereas the next-nearest-neighbor interaction is dominant in SLCNO.The magnitude of the ordered moment was evaluated at 3.5 K to be m = 0.39(3) µ B for SLCSO and 0.37(1) µ B for SLCNO, which are significantly reduced from 1µ B expected in the classical spin case.The shrink of the ordered magnetic moment was caused by not only magnetic frustration effects but also bond randomness effects arising from the site disorder of Sr 2+ and La 3+ ions.Next, I synthesized the mixed system SrLaCuSb 1-x Nb x O 6 with 0.1 ≤ x ≤