Slow spin-glass and fast spin-liquid components in quasi-two-dimensional ${\mathrm{La}}_2(\mathrm{Cu},\mathrm{Li}){\mathrm{O}}_4$

In conventional spin glasses, magnetic interaction is not strongly anisotropic and the entire spin system is believed to be frozen below the spin-glass transition temperature. In ${\mathrm{La}}_2{\mathrm{Cu}}_{0.94}{\mathrm{Li}}_{0.06}{\mathrm{O}}_4$, for which the in-plane exchange interaction dominates the interplane one, only a fraction of spins with antiferromagnetic correlations extending to neighboring planes become spin glass. The remaining spins with only in-plane antiferromagnetic correlations remain spin liquid at low temperature. Such a partial spin freezing out of a two-dimensional spin liquid observed in this cold neutron scattering study is likely due to a delicate balance between disorder and quantum fluctuations in the quasi-two-dimensional $S=1∕2$ Heisenberg system.

Figure 1

(Color) Measured SANS cross section in the 10 pixels wide rectangle shown in the inset at 3 (squares) and 30 K (diamonds), and the difference of the intensity between 3 and 30 K (circles) as a function of wave vector transfer $q$. Lines are guide to the eye. Inset: the SANS pattern at 30 and 3 K, with the intensity color scale at the left.

Figure 2

Representative magnetic quasielastic and elastic scattering along (a) an in-plane direction and (b) the interlayer direction between 1.5 and 180 K. Open squares in (b) were measured at $(1.06,k,0)$ and represent background. The solid lines are resolution convoluted $S^{3D}(\mathbf{q},E)+S^{q3D}(\mathbf{q},E)$ in Eq. (3, 4).

Figure 3

(Color) Measured $S(\mathbf{q},E)$ as a function of $E$ and interlayer $k$ at 1.5 K with a logarithmic intensity scale, showing three color-coded magnetic components in Eq. (5). $S^{3D}(\mathbf{q},E)$ (red) and $S^{q3D}(\mathbf{q},E)$ (blue) are energy-resolution limited at $E=0$, representing very slow spin dynamics which is associated with the spin-glass freezing. They are modulated along the interlayer $k$ direction. The spin-liquid component, $S^{2D}(\mathbf{q},E)$ (green), has a finite energy scale of about 1 meV below 50 K, and $0.18k_{B}T$ above 50 K (Ref. 25). It is flat along the $k$ direction. A few representative scans at 1.5 K are shown with yellow symbols. The black surface indicates background of $\sim 1.3\text{counts}∕\min$.

Figure 4

(Color) Temperature dependence of spectral weights $I^{2D}$ (green), $I^{q3D}$ (blue) and $I^{3D}$ (red) in the same unit for three experimentally separable antiferromagnetic components in Eq. (5). $I^{3D}+I^{q3D}$ is the total spectral weight of the spin-glass component. $I^{2D}$ is the spectral weight of the spin-liquid component within $\mid E\mid <10\mathrm{meV}$, thus the lower limit of its total spectral weight. The orange circles represent squared static order parameter of the spin-glass transition, which was measured by $\mu \mathrm{SR}$[5] and equals to $I^{3D}+I^{q3D}$ at $T=0$.