#### Abstract

We report a combined experimental and theoretical study of the spin $S=\frac{1}{2}$ nanomagnet Cu${}_{5}$(OH)${}_{2}$(NIPA)${}_{4}\xb7$10H${}_{2}$O (Cu${}_{5}$-NIPA). Using thermodynamic, electron spin resonance, and ${}^{1}$H nuclear magnetic resonance measurements on one hand, and *ab initio* density-functional band-structure calculations, exact diagonalizations, and a strong-coupling theory on the other, we derive a microscopic magnetic model of Cu${}_{5}$-NIPA and characterize the spin dynamics of this system. The elementary fivefold Cu${}^{2+}$ unit features an hourglass structure of two corner-sharing scalene triangles related by inversion symmetry. Our microscopic Heisenberg model comprises one ferromagnetic and two antiferromagnetic exchange couplings in each triangle, stabilizing a single spin $S=\frac{1}{2}$ doublet ground state (GS), with an exactly vanishing zero-field splitting (by Kramers' theorem), and a very large excitation gap of $\Delta \simeq 68$ K. Thus, Cu${}_{5}$-NIPA is a good candidate for achieving long electronic spin relaxation (${T}_{1}$) and coherence (${T}_{2}$) times at low temperatures, in analogy to other nanomagnets with low-spin GS's. Of particular interest is the strongly inhomogeneous distribution of the GS magnetic moment over the five Cu${}^{2+}$ spins. This is a purely quantum-mechanical effect since, despite the nonfrustrated nature of the magnetic couplings, the GS is far from the classical collinear ferrimagnetic configuration. Finally, Cu${}_{5}$-NIPA is a rare example of a $S=\frac{1}{2}$ nanomagnet showing an enhancement in the nuclear spin-lattice relaxation rate $1/{T}_{1}$ at intermediate temperatures.

- Received 8 April 2013

DOI:https://doi.org/10.1103/PhysRevB.87.214417

©2013 American Physical Society