Specific-heat anomaly in frustrated magnets with vacancy defects

Abstract

Motivated by frustrated magnets and spin-liquid-candidate materials, we study the thermodynamics of a 2D geometrically frustrated magnet with vacancy defects. The presence of vacancies imposes significant constraints on the bulk spins, which freeze some of the degrees of freedom in the system at low temperatures. With increasing temperature, these constraints get relaxed, resulting in an increase in the system's entropy. This leads to the emergence of a peak in the heat capacity $C(T)$ of the magnet at a temperature $T_\text{imp}$ determined by the concentration of the vacancy defects. The entropy associated with this peak comes from the lowest-energy degrees of freedom in the material. To illustrate the emergence of such an anomaly, we compute analytically the heat capacity of the antiferromagnetic (AFM) Ising model on the triangular lattice with vacancy defects. The presence of the vacancy leads to a peak in $C(T)$ at the temperature $T_\text{imp}=-4J/\ln n_\text{imp}$, where $J$ is the AFM coupling between the spins and $n_\text{imp}$ is the fraction of the missing sites.

Figures (5)

• Figure 1: The heat capacity of a 2D frustrated magnet in an impurity-free system (green line) and in a system with vacancy impurities (blue line). Vacancy defects lead to an anomaly that manifests itself as a peak at a temperature $T_\text{imp}$ of the order of expression \ref{['ImpurityTemperature']}, which is in general distinct from the other temperature scales in the system. The entropy $\int_\text{peak} \left[C_\text{vac}(T)/T\right]dT \sim \left( N N_\text{imp}\right)^\frac{1}{2}$ associated with the impurity-induced peak comes predominantly from the low-energy states: the ground states in the case of the Ising model or the states that lead to low-temperature peaks RamirezSyzranov:reviewPoppRamirezSyzranov in Heisenberg models. In a generic frustrated system, the illustrated heat-capacity peaks may partially merge.
• Figure 2: A closed loop of bonds of length $r=12$ on the triangular lattice. At each site, the direction of the loop rotates by angle $\phi$, which is taken into account when evaluating the contribution of the loop to the partition function \ref{['PartitionLoop']}. The orange arrows show six possible directions for each bond of the loop.
• Figure 3: Spin configuration around a vacancy in a triangular lattice showing the alternating pattern at the sites next to the vacancy.
• Figure S1: Nearest neighbor position relationship in the triangular lattice.
• Figure S2: The state of the antiferromagnetic Ising model on the triangular lattice with two "fractionalized" excitations. A black (open) circle at a node represents the "up" ("down") state at this node. A "fractionalized" excitation has an energy of $2J$ and corresponds to a triangle of three unsatisfied bonds. The other triangles, where the excitations are absent, have one satisfied and two unsatisfied bonds.