The discovery of magnetic bistability in Mn$_{12}$ more than 20 years ago marked the birth of molecular magnetism, an extremely fertile interdisciplinary field and a powerful route to create tailored magnetic nanostructures. However, the difficulty t
o determine interactions in complex polycentric molecules often prevents their understanding. Mn$_{12}$ is an outstanding example of this difficulty: although it is the forefather and most studied of all molecular nanomagnets, an unambiguous determination of even the leading magnetic exchange interactions is still lacking. Here we exploit four-dimensional inelastic neutron scattering to portray how individual spins fluctuate around the magnetic ground state, thus fixing the exchange couplings of Mn$_{12}$ for the first time. Our results demonstrate the power of four-dimensional inelastic neutron scattering as an unrivaled tool to characterize magnetic clusters.
Inelastic neutron scattering is used to measure the spin excitation spectrum of the Heisenberg $S=1/2$ ladder material (C$_7$H$_10$N)$_2$CuBr$_4$ in its entirety, both in the gapped spin-liquid and the magnetic field induced Tomonaga-Luttinger spin l
iquid regimes. A fundamental change of the spin dynamics is observed between these two regimes. DMRG calculations quantitatively reproduce and help understand the observed commensurate and incommensurate excitations. The results validate long-standing quantum field theoretical predictions, but also test the limits of that approach.
Molecular nanomagnets are among the first examples of spin systems of finite size and have been test-beds for addressing a range of elusive but important phenomena in quantum dynamics. In fact, for short-enough timescales the spin wavefunctions evolv
e coherently according to the an appropriate cluster spin-Hamiltonian, whose structure can be tailored at the synthetic level to meet specific requirements. Unfortunately, to this point it has been impossible to determine the spin dynamics directly. If the molecule is sufficiently simple, the spin motion can be indirectly assessed by an approximate model Hamiltonian fitted to experimental measurements of various types. Here we show that recently-developed instrumentation yields the four-dimensional inelastic-neutron scattering function S(Q,E) in vast portions of reciprocal space and enables the spin dynamics to be determined with no need of any model Hamiltonian. We exploit the Cr8 antiferromagnetic ring as a benchmark to demonstrate the potential of this new approach. For the first time we extract a model-free picture of the quantum dynamics of a molecular nanomagnet. This allows us, for example, to examine how a quantum fluctuation propagates along the ring and to directly test the degree of validity of the N{e}el-vector-tunneling description of the spin dynamics.
We investigate the magnetic properties of three Mn$_6$ single molecule magnets by means of inelastic neutron scattering and frequency domain magnetic resonance spectroscopy. The experimental data reveal that small structural distortions of the molecu
lar geometry produce a significant effect on the energy level diagram and therefore on the magnetic properties of the molecule. We show that the giant spin model completely fails to describe the spin level structure of the ground spin multiplets. We analyze theoretically the spin Hamiltonian for the low spin Mn$_6$ molecule (S=4) and we show that the excited $S$ multiplets play a key role in determining the effective energy barrier for the magnetization reversal, in analogy to what was previously found for the two high spin Mn6 (S=12) molecules [S. Carretta et al., Phys. Rev. Lett. 100, 157203 (2008)].
Inelastic neutron scattering has been used to determine the microscopic Hamiltonian describing two high-spin variants of the high-anisotropy Mn$_6$ nanomagnet. The energy spectrum of both systems is characterized by the presence of several excited to
tal-spin multiplets partially overlapping the S=12 ground multiplet. This implies that the relaxation processes of these molecules are different from those occurring in prototype giant-spin nanomagnets. In particular, we show that both the height of the energy barrier and resonant tunnelling processes are greatly influenced by low-lying excited total-spin multiplets.
We use inelastic neutron scattering to study the crystalline electric field (CEF) excitations of Ce$^{3+}$ in CeFeAsO$_{1-x}$F$_{x}$($x=0,0.16$). For nonsuperconducting CeFeAsO, the Ce CEF levels have three magnetic doublets in the paramagnetic state
, but these doublets split into six singlets when Fe ions order antiferromagnetically. For superconducting CeFeAsO$_{0.84}$F$_{0.16}$ ($T_c=41$ K), where the static AF order is suppressed, the Ce CEF levels have three magnetic doublets at $hbaromega=0,18.7,58.4$ meV at all temperatures. Careful measurements of the intrinsic linewidth $Gamma$ and the peak position of the 18.7 meV mode reveal clear anomaly at $T_c$, consistent with a strong enhancement of local magnetic susceptibility $chi^{primeprime}(hbaromega)$ below $T_c$. These results suggest that CEF excitations in the rare-earth oxypnictides can be used as a probe of spin dynamics in the nearby FeAs planes.
Inelastic neutron scattering has been applied to the study of the spin dynamics of Cr-based antiferromagnetic octanuclear rings where a finite total spin of the ground state is obtained by substituting one Cr(III) ion (s = 3/2) with Zn (s = 0), Mn (s
= 5/2) or Ni (s = 1) di-cations. Energy and intensity measurements for several intra-multiplet and inter-multiplet magnetic excitations allow us to determine the spin wavefunctions of the investigated clusters. Effects due to the mixing of different spin multiplets have been considered. Such effects proved to be important to correctly reproduce the energy and intensity of magnetic excitations in the neutron spectra. On the contrary to what is observed for the parent homonuclear Cr8 ring, the symmetry of the first excited spin states is such that anticrossing conditions with the ground state can be realized in the presence of an external magnetic field. Heterometallic Cr7M wheels are therefore good candidates for macroscopic observations of quantum effects.
Combining recent and new inelastic neutron scattering data for the molecular cyclic cluster Cr8 produces a deep understanding of the low lying excitations in bipartite antiferromagnetic Heisenberg rings. The existence of the L-band, the lowest rotati
onal band, and the E-band, essentially spin wave excitations, is confirmed spectroscopically. The different significance of these excitations and their physical nature is clearly established by high-energy and Q-dependence data.
