From frustration to glassiness via quantum fluctuations and random tiling with exotic entropy

When magnetic moments (spins) are regularly arranged in a geometry of a triangular motif, the spins may not satisfy simultaneously their interactions with their neighbors. This phenomenon, called frustration, leads to numerous energetically equivalent magnetic states (ground states), which results in exotic states such as spin liquid and spin ice. Here we report an alternative situation: a system that, classically, is to be a liquid in the clean limit freezes into a glassy state induced by quantum fluctuations. The case in point is a frustrated magnet in which spins are arranged in a triangular network of bi-pyramids. When taking into account quantum corrections, the classical degeneracy is broken into a set of local minima in a rugged energy landscape, which are separated by large energy barriers, over a finite number of degenerate, periodic, ground states. The appearance of large barriers is due to the absence of local zero-energy modes that are typical in spin-liquid candidate systems. We establish this by mapping the set of local energy minima states into a tiling with colored hexagonal tiles. We show that the system exhibits a large number of aperiodic tessellations. The configuration entropy of the local minima is extremely sensitive to boundary conditions, scaling with the boundary length rather than its volume. The low temperature ther-modynamics is also discussed to compare it with other glassy materials. 2 It is well known, since the classical work of Pauling on ice [1], that certain systems can exhibit an extensive number of energetically equivalent ground states, leading to finite entropy at low temperatures. In a spin ice, states are separated by local single ionic energy barriers, and the spins freeze into one of the equivalent states at low enough temperatures [2, 3]. In pyrochlore with large spins, locally confined zero energy motions of spins are possible, which can lead to a classical spin liquid state [4]. When quantum effects are taken into account, for small spins, such systems may settle into a super-position of states, forming a quantum spin-liquid[5], as suggested by Anderson [6]. A closely related but distinct type of systems is glassy systems. One example is amorphous alloys in which the atoms are arranged in a disordered way [7, 8]. Another is spin glass systems in which low concentration of magnetic impurities interact via random long-range interactions [9, 10]. In such systems randomness (or quenching) is the driving force for the freezing phenomena. The …