Session H50: Single-Molecule Magnets and Q-bits

Strategies towards High-Temperature Lanthanide-Based Single-Molecule Magnets

Lanthanide-based single-molecule magnets are leading materials for achieving magnetization blocking at the level of one molecule. In this presentation, the physical requirements for efficient magnetization blocking in single-ion complexes will be examined and the design principles for achieving very high magnetization blocking barriers in lanthanide-based compounds will be identified$^{\mathrm{1}}$. It will be shown that the key condition is the preponderant covalent binding of the Ln ion to one of the ligand atoms, tremendously enhancing the axial crystal field. I will also make an overview of practical schemes for the implementation of this principle$^{\mathrm{2}}$. These are (1) the effective lowering of the coordination number via displacement of the Ln ion to one of the atoms in the coordination polyhedron, (2) the design of two-coordinated complexes, and (3) the stabilization of diatomic compounds in cages and on surfaces. The last proposal is appealing in connection to spintronics applications, especially via the exploration of robust and highly anisotropic [LnX] units displaying multilevel blocking barriers of thousands of Kelvin and prospects for room-temperature magnetization blocking. Finally, the effect of exchange and magnetic dipolar interactions of lanthanide with other magnetic centers on the magnetization blocking will be shortly discussed$^{\mathrm{3}}$. The conditions allowing to achieve highly opaque blocking barrier due to these interactions will be revealed. $^{\mathrm{1}}$ L. F. Chibotaru, ``Theoretical understanding of anisotropy in molecular nanomagnets," Struct. Bond. 164, 185-229 (2015). $^{\mathrm{2}}$ L. Ungur and L. F. Chibotaru, Inorg. Chem. 55, 10043 (2016). $^{\mathrm{3\thinspace }}$L. F. Chibotaru, ``Exchange interaction in lanthanides", J. Phys.: Cond. Matter, in preparation.   

Forbidden coherent transfer observed between two realizations of quasi-harmonic spin systems

Using a multi-level quantum system, we demonstrate Rabi oscillations between states belonging to different realizations of quasi-harmonic oscillators. The Mn ions diluted in a MgO matrix have tunable equally-spaced Sz spin states \footnote{Bertaina et al, \textbf{PRL} 102 (2009), \textbf{PRB} 84 (2011),\textbf{PRB} 92 (2015)}. The hyperfine field is large enough to separate sets of states $\{I_z, S_z=-5/2…+5/2\}$ of consecutive $I_z$ values. Due to the combined action of the hyperfine and crystal-field operators, such sets are coupled. If this coupling is strong enough and the coherence times of the electro-nuclear states are large enough, a level repulsion of corresponding dressed states is to be observed. Experimentally, we have been able to implement a two-tone technique allowing us to excite the multi-level system at any detuning, and then read it with a resonant pulse. This technique allows us to achieve a strong coupling regime when a splitting between Rabi oscillations of the electro-nuclear states is observable, although the states belong to different $I_z$ values. This demonstrates the possibility of including long-lived nuclear states as a degree of freedom in quantum computing based on multi-level systems.   

THz spectroscopy of one-dimensional Ising chain compound CoNb$_2$O$_6$ near the quantum critical point

One-dimensional Ising spin chain is a novel example of an interacting quantum many body system. The Ising chain in a transverse field is a good candidate to study quantum phase transitions because its low dimensionality increases its tendency to exhibit interesting quantum effects. We studied the one-dimensional ferromagnetic Ising chain material CoNb$_2$O$_6$ using far infrared spectroscopy in high magnetic fields up to 17\,T and down to 0.3\,K using a dilution refrigerator. Special attention is paid to the spectral region near the quantum critical point near 5.5\,T.   

Enhancement of spin relaxation times by dilution and by an avoided crossing in the molecular nanomagnet Cr$_7$Mn

We report an increase in the spin relaxation times of dilute samples of the spin $S=1$ molecular nanomagnet [(CH$_3$)$_2$NH$_2$][Cr$_7$MnF$_8$((CH$_3$)$_3$CCOO)$_{16}$] (``Cr$_7$Mn") in the vicinity of an avoided crossing. We study both 100\% and dilute samples, with the dilution achieved by co-crystallizing Cr$_7$Mn with Ga$_7$Zn, a diamagnetic isostructural analogue. We perform parallel-mode electron-spin resonance (ESR) spectroscopy using a loop-gap resonator (LGR), allowing us to probe the zero-field avoided crossing. With the resonant frequency of the LGR tuned to the tunnel splitting of Cr$_7$Mn, $\sim4$ GHz, we observe an ESR peak centered at zero field. We measure the saturation of that peak with pulsed ESR experiments in a pump-probe configuration, and find that $T_1$ increases from $\sim450$ ns for a non-dilute sample to $\sim15$ $\mu$s for a 10\% dilute sample. The dramatic effect that dilution has on the measured $T_1$ value indicates that there is substantial spin diffusion taking place. We can estimate $T_2^*$ from the saturation data and $T_1$ values and find it to be $\sim20$ ns and largely independent of dilution. The results of spin-echo experiments to measure $T_2$, currently in progress, will also be discussed.   

Development in the DFT estimates of magnetic couplings in chromium-based molecular rings from an optimally-tuned range separated hybrid functional

The Cr$_{8}$ molecule, as well as its homo- and hetero-metallic derivatives, belongs to a class of molecular nanomagnets which are extensively studied for a number of fundamental aspects and envisaged applications. However, estimating accurately their magnetic couplings from first principles calculations has proven to be difficult. Here we present progress in this area for two prototypical molecular rings, Cr$_{8}$ and Cr$_{7}$Ni$^{-}$, using density functional theory with an optimally-tuned range separated hybrid (OT-RSH) functional. This approach has been shown to allow for an accurate description of the electronic structure in a variety of more simple molecular systems. Here, we show that it is also capable of producing highly accurate magnetic exchange parameters for both molecules despite their complexity, while improving the overall description of the electronic structure, especially with respect to the energy of the frontier orbitals. For the Cr$_{7}$Ni$^{-}$ ring, the values of the magnetic couplings found are distinguished by a unique site distribution and lead to excellent agreement with experiment.   

Relating Symmetry to Magnetic Anisotropy in a Trigonal Mn(III) Complex Using EPR

The design of single-molecule magnets (SMMs) relies on the ability to tune the structure that gives rise to magnetic anisotropy. In the absence of an applied magnetic field, this anisotropy lifts the degeneracy of spin states, generating an energy barrier separating spin-up and down. In such cases, magnetic information can be stored in the polarization state of the molecule provided the barrier is large compared to k$_{B}$T, and tunneling through the barrier can be avoided. Both of these properties are strongly influenced by molecular structure/symmetry, thus motivating detailed studies of structure-property relations. One approach to creating SMMs involves assembling multiple paramagnetic ions with appreciable magnetic anisotropy into larger high-symmetry molecules. In this regard, trigonal molecules provide interesting insights into the effects of molecular symmetry and local single-ion anisotropy on the overall molecular anisotropy. In this study, electron paramagnetic resonance measurements were performed on a trigonal Mn(III)$_{3}$ molecule, containing rigorous C$_{3\, }$symmetry, using a vector magnet. Unlike similar molecules studied in the past, the principle axes of the individual Mn(III) sites are tilted such that there is a significant suppression of the 2nd order anisotropy. This allows for a rare, yet precise, characterization of the higher order trigonal anisotropy that emerges within the coupled spin Hamiltonian.   

High Pressure EPR for Probing the Magnetic Anisotropy in Single Molecule Magnets

Single-molecule magnets (SMM) are potential candidates for nanoscale magnetic information storage, and a platform for studying classical and quantum behaviors at the mesoscopic scale. Varying the structures of these molecules by chemical modification can give rise to changes in their magnetic properties. However, this approach can be unpredictable, leaving very little control via chemical synthesis. An alternate approach is to exert physical pressure. This convenient tool can be used to vary crystal packing, local coordination geometries, as well as inter-ion and intermolecular interactions without changing the chemical composition of a SMM. Moreover, pressure in combination with Electron Paramagnetic Resonance (EPR), can be employed to better understand the factors that control magnetic anisotropy, both at the single-ion level and in exchange-coupled molecules. Here we present a microwave cavity integrated with a diamond anvil cell with a pressure range up to 1.5 GPa. As an example we show results from single crystal high field EPR experiments performed on an exchange coupled system, [Fe$_{8}$O$_{2}$(OH)$_{12}$(tacn)$_{6}$]Br$_{8}$.9H$_{2}$O, better known as Fe$_{8}$ with a giant spin of S$=$10. The obtained pressure-dependent results will be discussed.   

Precision ESR Measurements of Transverse Anisotropy in the Single-molecule Magnet Ni$_4$

We present a method to precisely determine the transverse anisotropy in a single-molecule magnet (SMM) through electron-spin resonance measurements of a tunnel splitting that arises from the anisotropy via first-order perturbation theory. We demonstrate the technique using the SMM Ni$_4$ diluted via co-crystallization in a diamagnetic isostructural analogue. At 5\% dilution, we find markedly narrower resonance peaks than are observed in undiluted samples. Ni$_4$ has a zero-field tunnel splitting of $\sim4$ GHz, and we measure that transition at several nearby frequencies using custom loop-gap resonators, allowing a precise determination of the tunnel splitting. Because the transition under investigation arises due to a first-order perturbation from the transverse anisotropy, and lies at zero field, we can relate the splitting to the transverse anisotropy independent of any other Hamiltonian parameters. This method can be applied to other SMMs with zero-field tunnel splittings arising from first-order transverse anisotropy perturbations.   

Field and temperature dependent cavity coupling for highly sensitive on-chip spin detection.

Probing spin-photon interaction in single molecule magnets using Electron Spin Resonance is of great interest due to possible application as a molecular quantum memory\footnote{M. Blencowe,\textbf{Nature} 468, 2010}. Here we will present a method to tune the coupling of a Nb superconducting cavity\footnote{N. Groll et al, \textbf{PRB} 81, 2010} operating at $\sim$20GHz using losses induced by temperature and field. The effects are studied on a cavity empty first empty, then loaded with the molecular magnet V$_{15}$. This system has shown Rabi oscillations as well as spin-orbit dependence of the coherence time\footnote{M. Martens et al, arxiv:1505.03177}. From the zero-field temperature dependence of the resonance frequency of the empty cavity we have observed that thermally induced losses have the effect of decreasing the resonance frequency, while reaching critical coupling at a well-defined temperature. Loading the cavity shifts the critical coupling parameters which are tunable by a magnetic field in plane and/or perpendicular to the cavity. V$_{15}$ spectroscopy at critical coupling will be presented.   

EPR Study of Radical-Lanthanide Interactions in a Terbium(III) Molecular Spin Qubit

The well-separated crystal field states of mononuclear lanthanide molecular magnets make them suitable candidates for the basis of quantum information processing. However, the effective shielding of the magnetic 4f sub-shells by the 5p and 6s orbitals in such compounds poses challenges in terms of the development of molecular spintronics devices that enable electrical readout of the qubit. A promising approach involves the use of paramagnetic linkers, such as organic radicals, which can provide a more direct magnetic coupling to the lanthanide. Here we report EPR studies of lanthanide-radical interactions by probing the magnetic anisotropy of an organic radical coupled to a $Tb^{3+}$ ion. Ligand oxidation of $[Tb(Pc)_{2}]^{-}$ results in a neutral complex with an unpaired electron delocalized over the ligands and the $Tb^{3+}$ ion (with spin-orbit coupled angular momentum J=6) [1,2]. Due to the weak mixing of the $m_{J}=\pm$6 states of the Tb ion, transition within its ground doublet cannot be observed directly via EPR. However, the anisotropic coupling between the lanthanide and the radical can be monitored through EPR transitions involving the latter. This anisotropy can be explained by a simple model which can be extended to similar compounds containing different $Ln^{3+}$ion.   

Electron Spin Resonance measurements based on micro-SQUID detection and coplanar waveguide excitation

Sensitive detection of spin resonance is of paramount importance for the field of spin-based quantum computing. We combine the sensitivity of a high field, weak link SQUID\footnote{L. Chen et al, \textbf{Nanotechnology} 21, 405504 (2010)} with the versatility of an on-chip coplanar waveguide. The SQUID is in close proximity of an antenna from a coplanar waveguide and the studied spin system. Both the SQUID and the waveguide are fabricated from a Nb film on top of a Si substrate, such that the setup works in high magnetic field applied parallel to device plane. This setup has the benefit of potential wide bandwidth microwave capability compared with the cavity based ESR setup, and has taken the advantage of the micro-SQUID technique which has high sensitivity due to the direct measurement on the magnetization of the sample. The technique will be implemented to study coherence properties of quantum spins in single ions or molecular magnets\footnote{M. Martens et al, \textbf{arxiv:1505.03177}}. We report preliminary results on diluted spins distributed in a non-magnetic matrix.   

Coupling molecular spin centers to microwave resonators: steps towards the implementation of molecular qubits for hybrid quantum circuits

Hybrid spin-photons quantum bits can be obtained under strong coupling regime between microwave photons and a spin ensemble, where coherent exchange of photons is realized. Molecular spins systems, thanks to their tailorable magnetic properties, are retained promising candidates for hybrid qubits. We present an experimental study of the coupling regimes between a high critical temperature YBCO superconducting resonator [1,2] and different molecular spin ensembles. Three mononuclear compounds, (PPh4)$_{2}$[Cu(mnt)$_{2}$], [ErPc2]$^{-}$TBA$^{+}$ , Dy(trensal) and two organic radicals, DPPH and PyBTM [3], are studied. Strong coupling is found in radicals thanks to exchange narrowing. Possible strategies to achieve strong coupling with mononuclear compounds are discussed, and several hints in the design of molecular spins are given [1]. [1] C. Bonizzoni, A. Ghirri, K. Bader, J. Van Slageren, M. Perfetti, L. Sorace, Y. Lan, O. Fuhr, M. Ruben and M. Affronte Dalton Transactions (2016), 45, 16596-16603 [2] A. Ghirri, C. Bonizzoni, D. Gerace, S. Sanna, A. Cassinese and M. Affronte Appl. Phys. Lett. 106 (2015) 184101 [3] A. Ghirri, C. Bonizzoni, F. Troiani, N. Buccheri, L. Beverina, A. Cassinese and M. Affronte Phys. Rev. A 93 (2016) 063855