Disorder-induced spin-cluster magnetism in a doped kagome spin liquid candidate

Abstract

The search for new quantum spin liquid materials relies on systems with strong frustration such as spins on an ideal kagome lattice. However, lattice imperfections can have substantial effects which are as yet not well understood. In recent work, the two-dimensional kagome system YCu$_3$(OH)$_6$[(Cl$_x$Br$_{(1-x)}$)$_{3-y}$(OH)$_y$] has emerged as a leading candidate hosting a Dirac spin liquid which appears to survive at least for x<0.4, associated with alternating-bond hexagon (ABH) disorder. Here in magnetic samples with x=0.58, y=0.1 we report unusual in-plane ferromagnetic canting (FM) of the in-plane antiferromagnet (AFM), with an unusually wide regime of short-ranged order, and propose theoretical models to explain this behavior. First, we show that Kitaev type exchanges naturally arise on the kagome lattice to second order in the known Dzyaloshinskii-Moriya exchanges, and that these interactions can produce the unusual in-plane FM canting from antichiral AFM. Second, we propose a phenomenological model of weakly-FM-canted spin clusters to describe the short-ranged regime and analyze quantum fluctuations in an ABH toy model to show how ABH disorder can stabilize this regime. The combination of experimental observation and theory suggests that kagome-Kitaev interactions and ABH disorder are necessary for describing the magnetic fluctuations in this family of materials, with potential implications for the proposed proximate spin liquid phase.

Figures (11)

• Figure 1: Temperature dependence of the magnetization, $M$, for the 58% chlorine doped sample under FC and ZFC conditions (main panel) for a field of 50 Oe in the kagome plane (perpendicular to $c$). The hysteresis with strong FC-ZFC separation is visible below the $M(T)$ peak showing long range order below $T_L \approx 6.5$ K. Additionally, a slight separation between the two curves is visible from 10--12 K and slowly increases down to $T_L$, which suggests formation of ferromagnetic clusters across this temperature range $T_L < T < T_*$. The inset is the same data on an expanded scale to demonstrate that the deviation from paramagnetic behavior sets in at $T_* \sim 14$ K.
• Figure 2: Magnetization ($M$) isotherms (as a function of magnetic field $M(B)$ at fixed temperature $T$) here shown at three different temperatures below $T_*$. For B in the plane ($\perp c$) (red dot-space-dot upper curves) a clear ferromagnetic response, suggesting some saturation at a fairly low field, is visible. The low field region has a larger slope compared to the high field linear response with a smaller slope. At low $T$ the ordered moment per site is of the order 0.01 $\mu_B$. As $T$ increases towards $T \rightarrow T_*$ the low field response shrinks and is absent above $T_*$. For B$\parallel$c-axis (blue dot-dot lower curves) no such ferromagnetic behavior is seen. Together, this suggests $T_L < T < T_*$ formation of spin clusters with in-plane FM moments, as shown below (Fig. \ref{['fig_spinclusters']}).
• Figure 3: Implied in-plane ferromagnetic moment as obtained from an extrapolation of the high field (in-plane field $\perp c$) linear behavior to obtain a $B=0$ intercept. The data implies a net ordered moment in the plane.
• Figure 4: Magnetic ordering in kagome lattice due to Heisenberg and DM interaction. (a) kagome network with dilute alternating-bond-hexagon (ABH) defects shown with thick red/green bonds hosting stronger/weaker exchange couplings respectively. (ABH also appear with red/green interchanged, i.e. 2$\pi/6$ rotated.) The blue arrows show in-plane DM vectors on each bond. The blue dots denote the out-of-plane DM vector on the surrounding bonds. To define the sign of DM vectors, bonds are oriented counterclockwise around each hexagon, or equivalently, clockwise around each triangle. (b) Chiral magnetic order for $D_z>0$. Inset shows the ferromagnetic canting due to in-plane DM coupling. (c) Antichiral magnetic order for $D_z<0$. This is the magnetic order considered below and relevant to the material, which has no out-of-plane canting.
• Figure 5: Various AFM antichiral spin configurations (black) and associated FM canting (blue) arising by adding Kitaev interactions with AFM (a) or FM (b) sign. The black arrows on the sites (kagome vertices) show the spins of the corresponding antichiral order. The blue arrow on the center of each triangle represents the net moment of the corresponding triangle. The canting due to AFM (a) and FM (b) Kitaev interaction differ by the sign reversal of the canted moment (blue arrows). The four figures on each panel show four representative configurations (or domains) of the antichiral order (and the associated different configurations of the canting moment) given by $\phi_1=~\pi/2,~5\pi/6,~\pi,~3\pi/2$. Though at the classical level $\phi_1$ has an emergent $U(1)$ symmetry, which is moreover preserved by the Kitaev exchanges, we choose these values because we expect higher order quantum fluctuations to break the emergent $U(1)$ down to the discrete microscopic lattice symmetry of $2\pi/6$ rotations. The four domains with rotated spin angle $\phi_1$ show the unusual feature of the canting (Eqn. \ref{['eqn:canted']}): under rotations of the ordered spin moments, the net canted moment $m$ rotates oppositely.