arXiv 2109.087992021-09-18cond-mat.str-el

阻挫烧绿石磁体Tb $_{2+x}$ Ti $_{2-x}$ O $_{7+y}$中三自旋相互作用的自旋和四极关联

Spin and quadrupole correlations by three-spin interaction in the frustrated pyrochlore magnet Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$

Hiroaki Kadowaki, Mika Wakita, Björn Fåk, Jacques Ollivier, Seiko Ohira-Kawamura

备注：: 28 pages, 25 figures
DOI：: 10.1103/PhysRevB.105.014439

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摘要：

我们研究了在阻挫烧绿石磁体Tb $_{2+x}$ Ti $_{2-x}$ O $_{7+y}$中观察到的以调制波矢量$\boldsymbol{k} \sim (\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})$为特征的磁偶极关联$\langle σ_{\boldsymbol{Q}}^z σ_{\boldsymbol{-Q}}^z \rangle$的起源。这种磁短程有序不能通过在量子烧绿石磁体的最近邻赝自旋- $\tfrac{1}{2}$哈密顿量中加入更远的近邻交换相互作用来解释。利用经典的Monte Carlo模拟和基于热纯量子态的量子模拟，我们证明了在低温下与$\boldsymbol{k} \sim (\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})$的自旋关联是由$σ_{\boldsymbol{r}}^{\pm} σ_{\boldsymbol{r}^{\prime}}^z σ_{\boldsymbol{r}^{\prime \prime}}^z $形式的三自旋相互作用引起的，这是对低晶场激发下哈密顿量的修正.利用TPQ态的模拟表明，自旋关联与电四极关联$\langle σ_{\boldsymbol{Q}}^α σ_{\boldsymbol{-Q}}^β \rangle$（$α, β= x, y$）和$\boldsymbol{k} \sim \boldsymbol{0}$共存。这些结果表明，TbPDMATHABMOTiPDMATHABMPOPDMATHABMQ的量子自旋液态在经典近似下位于自旋冰态、四极有序态和磁有序态的相界附近，三自旋相互作用导致了自旋和四极关联的量子无序基态.

英文摘要：

We have investigated the origin of the magnetic dipole correlations $\langle σ_{\boldsymbol{Q}}^z σ_{\boldsymbol{-Q}}^z \rangle$ characterized by the modulation wave vector $\boldsymbol{k} \sim (\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})$ observed in the frustrated pyrochlore magnet Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$. This magnetic short-range order cannot be accounted for by adding further-neighbor exchange interactions to the nearest-neighbor pseudospin-$\tfrac{1}{2}$ Hamiltonian for quantum pyrochlore magnets. Using classical Monte Carlo simulation and quantum simulation based on thermally pure quantum (TPQ) states we have shown that the spin correlations with $\boldsymbol{k} \sim (\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})$ are induced at low temperatures by a three-spin interaction of a form $σ_{\boldsymbol{r}}^{\pm} σ_{\boldsymbol{r}^{\prime}}^z σ_{\boldsymbol{r}^{\prime \prime}}^z $, which is a correction to the Hamiltonian due to the low crystal-field excitation. Simulations using TPQ states have shown that the spin correlations coexist with electric quadrupole correlations $\langle σ_{\boldsymbol{Q}}^α σ_{\boldsymbol{-Q}}^β \rangle$ ($α, β= x, y$) with $\boldsymbol{k} \sim \boldsymbol{0}$. These results suggest that the putative quantum spin liquid state of Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ is located close to phase boundaries of the spin-ice, quadrupole-ordered, and magnetic-ordered states in the classical approximation, and that the three-spin interaction brings about a quantum disordered ground state with both spin and quadrupole correlations.

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