Magnon Pairs and Spin-Nematic Correlation in the Spin Seebeck Effect

Investigating exotic magnetic materials with spintronic techniques is effective at advancing magnetism as well as spintronics. In this work, we report unusual field-induced suppression of the spin Seebeck effect (SSE) in a quasi-one-dimensional frustrated spin-$\frac{1}{2}$ magnet ${\mathrm{LiCuVO}}_4$, known to exhibit spin-nematic correlation in a wide range of external magnetic field $B$. The suppression takes place above $|B|\gtrsim 2\mathrm{T}$ in spite of the $B$-linear isothermal magnetization curves in the same $B$ range. The result can be attributed to the growth of the spin-nematic correlation while increasing $B$. The correlation stabilizes magnon pairs carrying spin 2, thereby suppressing the interfacial spin injection of SSE by preventing the spin-1 exchange between single magnons and conduction electrons at the interface. This interpretation is supported by integrating thermodynamic measurements and theoretical analysis on the SSE.

Figure 1

(a) Theoretical ground-state phase diagrams of a purely 1D frustrated $J_1\text{−}{J}_2$ spin-$\frac{1}{2}$ chain [32, 33] (top) and a quasi-1D one with an interchain exchange interaction [36] (bottom). $B$ denotes external magnetic field. (b) Spin chain in ${\mathrm{LiCuVO}}_4$ composed of ${\mathrm{Cu}}^{2+}$ and ${\mathrm{O}}^{2-}$ ions. (c) Magnetic field ($B$)—temperature ($T$) phase diagram of ${\mathrm{LiCuVO}}_4$, obtained while applying $B$ in the $c$ axis. Triangular data points were taken in this study: the sky-blue ones from the $T$ dependence of the magnetization $M$, the orange ones from the $B$ dependence of $M$. The circular data points were adapted from Ref. [42]. (d) Experimental setup for detecting the spin-Seebeck effect in a ${\mathrm{LiCuVO}}_4/\mathrm{Pt}$ system. $J_1$ and $J_2$, respectively, denote the nearest and next-nearest-neighboring exchange interactions in the spin chain of ${\mathrm{LiCuVO}}_4$; $\nabla T$ a temperature gradient along the spin chain; $t$ and $l$, respectively, the thickness and the length of the ${\mathrm{LiCuVO}}_4$.

Figure 2

(a),(b) $B$ dependence of the transverse thermopower $S$ at several $T$. (c) Comparison between $B$ dependences of $S$ and $M$ at $T=4\mathrm{K}$.

Figure 3

(a) $B$ dependences of the magnon-pair binding energy $E_{\mathrm{bind}}$ and the calculated magnetic moment per site $m=2⟨S_j^z⟩$ for a 1D frustrated spin chain with $J_1/J_2=-1$ [see also Eq. (1)] [36]. The inset shows the $B$ dependences up to $B/B_{\mathrm{s}}=1$ with $B_{\mathrm{s}}$ being the saturation field. (b) $B$ dependence of the calculated spin current ${\tilde{J}}_{\mathrm{s}}$ injected into a metal by single magnons which have an energy gap equal to the magnon-pair binding energy. The $B$ dependence of $S$ is also shown as data points for comparison. $B$ is normalized by $B_s=93\mathrm{T}$ for ${\tilde{J}}_s$, calculated with $J_1/J_2=-1$ and $J_2=50\mathrm{K}$ while by $B_s\sim 43\mathrm{T}$ for $S$ [45, 59]. ${\tilde{J}}_s$ and $S$ are, respectively, normalized by their maximum values ${\tilde{J}}_{\mathrm{s},\max }$ and $S_{\max }$.

Figure 4

(a) $T_{\mathrm{ave}}$ dependence of $S$ at several $B$. Datasets are shifted by multiples of $0.1\mathrm{A}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$. (b) $T$ dependence of the calculated spin current ${\tilde{J}}_s$ that is injected into a metal by single magnons with an energy gap equal to the magnon-pair binding energy. $m=2⟨S_j^z⟩$ is the magnetic moment per site.