Enhanced magnetocaloric effect in frustrated magnetic molecules with icosahedral symmetry

We investigate the magnetocaloric properties of certain antiferromagnetic spin systems that have already been or very likely can be synthesized as magnetic molecules. It turns out that the special geometric frustration which is present in antiferromagnets that consist of corner-sharing triangles leads to an enhanced magnetocaloric effect with high cooling rates in the vicinity of the saturation field. These findings are compared with the behavior of a simple unfrustrated spin ring as well as with the properties of the icosahedron. To our surprise, also for the icosahedron large cooling rates can be achieved but due to a different kind of geometric frustration.

Figure 1

(Color online) The curves show isentropes of the antiferromagnetically coupled dimer of two spins with $s=1∕2$. The straight lines represent isentropes of a paramagnet. Compared to a paramagnet, the cooling rate of the antiferromagnetic dimer can be smaller (a), about the same (b), much bigger (c), or even negative (d).

Figure 2

(Color online) Low-lying energy levels $E_{\nu }\left(B\right)$ of the cuboctahedron with $s=1∕2$ (dashes) and $s=1$ (× symbols) at the saturation field $B=B_{\mathrm{sat}}$ versus total magnetic quantum number $M$. The attached numbers give the multiplicities $d_M$ of the lowest $M$ levels. The energy scale ($y$ axis) is organized in such a way that at $B=B_{\mathrm{sat}}$ the lowest, i.e., ground-state levels are at zero and all other levels above.

Figure 3

(Color online) Isentropes of the cuboctahedron with $s=1∕2$ and $s=1$. The entropies here and in the following are given in units of Boltzmann’s constant $k_B$; from the upper left to the lower right the values of $S∕k_B$ are 0.01, 1.01, 2.01, 3.01, and 4.01, respectively. $B_{\mathrm{sat}}=\left(12s\mid J\mid \right)∕\left(g{\mu }_B\right)$.

Figure 4

(Color online) Isentropes of a bipartite, i.e., nonfrustrated spin ring with $N=12$ spins $s=1∕2$ and $s=1$. $B_{\mathrm{sat}}=\left(8s\mid J\mid \right)∕\left(g{\mu }_B\right)$.

Figure 5

(Color online) Isentropes of the icosahedron with $s=1∕2$ and $s=1$. $B_{\mathrm{sat}}=\left(14.472s\mid J\mid \right)∕\left(g{\mu }_B\right)$.

Figure 6

Low-lying energy levels of the icosahedron with $s=1∕2$. The attached numbers give the multiplicity $d_M$ of each $M$ level. Note that the energies are rescaled in each sector of total spin $S$.

Figure 7

(Color online) Isentropes with $S=2k_B$ of the cuboctahedron, the icosahedron, and the ring with $N=12$ with spins $s=1∕2$ (lhs) and $s=1$ (rhs).

Figure 8

(Color online) Isentropes of the icosidodecahedron with $s=1∕2$ and $s=5∕2$. $B_{\mathrm{sat}}=\left(12s\mid J\mid \right)∕\left(g{\mu }_B\right)$.

Figure 9

(Color online) Isentropes of a distorted cuboctahedron with $s=1∕2$. Each coupling $J_{ij}$ between spins at sites $i$ and $j$ was modified by a random distortion of maximally $\pm 5\%$.

Figure 10

Three-dimensional projection of the cuboctahedron (Ref. 30). The vertices are spin sites and the lines denote the antiferromagnetic coupling with exchange parameter $J$. Each spin has four nearest neighbors.

Figure 11

Three-dimensional projection of the icosidodecahedron (Ref. 30). The vertices are spin sites and the lines denote the antiferromagnetic coupling with exchange parameter $J$. Each spin has four nearest neighbors.

Figure 12

Three-dimensional projection of the icosahedron (Ref. 30). The vertices are spin sites and the lines denote the antiferromagnetic coupling with exchange parameter $J$. Each spin has five nearest neighbors.