Metamagnetic Phase Transition of the Antiferromagnetic Heisenberg Icosahedron

The observation of hysteresis effects in single molecule magnets like ${\mathrm{Mn}}_{12}$-acetate has initiated ideas of future applications in storage technology. The appearance of a hysteresis loop in such compounds is an outcome of their magnetic anisotropy. In this Letter we report that magnetic hysteresis occurs in a spin system without any anisotropy, specifically where spins mounted on the vertices of an icosahedron are coupled by antiferromagnetic isotropic nearest-neighbor Heisenberg interaction giving rise to geometric frustration. At $T=0$ this system undergoes a first-order metamagnetic phase transition at a critical field $B_{\mathrm{c}}$ between two distinct families of ground state configurations. The metastable phase of the system is characterized by a temperature and field dependent survival probability distribution.

Figure 1

Hysteresis behavior of the classical icosahedron in an applied magnetic field obtained by classical spin dynamics simulations (thick lines) as well as by analytical stability analysis (gray lines). The curves match perfectly.

Figure 2

Schematic representation of two minimal energy curves $E_1(M)$ and $E_2(M)$, whose minimum $E_{\min }(M)$ is not convex. Their common tangent (solid line) has a slope of $B_{\mathrm{c}}$.

Figure 3

Magnetization curves for $T=0$ and various values of the intrinsic spin quantum number $s$: the magnetization plateaus of smallest width are highlighted on each curve. At $s=4$ a magnetization jump of $\Delta M=2$ occurs, marked by the arrow. At $s=3$ a tiny plateau persists. The solid curve shows that the field values that bisect the smallest plateaus converge to the classical transition field (dashed line).

Figure 4

Survival probability $P_{\mathrm{s}}(t)$ for the metastable decagon phase subject to an external field $B/B_{\mathrm{sat}}=0.27$ for temperatures $k_{B}T/J=0.025$, 0.015, 0.005, 0.0005 (left to right). Time is given in units of Planck’s constant divided by the coupling. Inset: example trajectory of the system’s time evolution at finite temperature.