Quantum Nanomagnets

Past and Current Research

  • Fig. 1: Molecular structures of prominent SMMs and their energy barriers (see text).Fig. 1: Molecular structures of prominent SMMs and their energy barriers (see text).
  • Fig. 1: Molecular structures of prominent SMMs and their energy barriers (see text).
  • Fig. 2: Energy spectrum of the [Mn12] SMM (S = 10).
  • Fig. 3: Investigation of SMM behaviour by SQUID magnetometry.

Quantum nanomagnets - On the way towards miniaturization of data storage and manipulation systems a prominent group of compounds raising hopes for future applications are those displaying a single-molecule magnet (SMM) property - where single molecules are able to behave as magnets. The spectrum of these prospects is even wider, including spintronics, magnetic refrigeration and models for metal enzymes.

The crystal structure of the first SMM, a mixed-valence [Mn12] complex (fig. 1), was reported in 1980 [1]. This prototype SMM has been modified and studied in a variety of directions - therefore it has been termed as a "Drosophila" (fruit fly) of SMMs [2]. After some controversies about its magnetic properties [3], the correct interpretation was published in 1993 [4]. The spin ground state of this system is 10, corresponding to a total antiferromagnetic coupling of the MnIII and MnIV centers.

Requirements
SMMs possess a negative axial anisotropy which is the source of an energy barrier to spin reversal (fig. 2). This anisotropy, apart from a bistable electronic ground state, is required for observation of an SMM property. As a result, a specific distribution of states describes the system, separated by a characteristic effective energy barrier Ueff [4]. This energy barrier is defined as S2|D| or (S2-1/4)|D| for integer and half-integer S systems, respectively, where D is the axial zero-field splitting constant. Once an external magnetic field is switched on under a certain blocking temperature, the system is magnetized. Upon switching off this field the magnetization relaxes slowly. The thermal-assisted relaxation is an Orbach process and follows the Arrhenius equation τ = τoexp(Ueff/kBT) with relaxation times denoted as τ. Additional processes, such as Raman and quantum tunneling, are also possible. For practical applications in data storage the energy barriers to spin reversal and the blocking temperatures still have to be increased as illustrated by the current record values cited below.

Magnetic anisotropy is the dominating factor affecting the height of the energy barrier.

This anisotropy is a combined effect of single-ion contributions and exchange coupling. The single-ion contributions are connected, e.g., in the case of lanthanides, with unquenched orbital momentum, strong spin-orbit coupling, hyperfine interactions of electrons with the nuclei [5]. The exchange interaction gets stronger when less localized orbitals are involved, e.g., actinide 5f orbitals are favoured over the lanthanide 4f orbitals [6].

Observation in Manganese and Other Complexes
The energy barrier estimated as 41.7-44.5 cm-1 for the archetypic [Mn12] complex was the highest value until 2007 when an oxime-bridged [MnIII6] complex was reported, raising this value to 59.8 cm-1 [7]. For this class of compounds a magnetostructural correlation has been established, showing that the overall coupling of the metal centers can be switched from antiferro- to ferromagnetic by means of an Mn-N-O-Mn torsion angle.

Apart from manganese complexes, SMM behaviour has been discovered in many other transition metal compounds, including 3d, such as Co, Fe, V, Ni and 3d-4d/5d (Ru / Re, Os) systems. The majority of these complexes are polynuclear. Among mononuclear metal complexes, SMM behaviour has been recently found in complexes of metal ions with rare coordination spheres, e.g., FeL2 with bulky ligands L in a linear arrangement [8], displaying E barriers up to 228 cm-1.

As expected, higher E barriers have been found for mononuclear complexes of lanthanides, starting with Ishikawa's breakthrough-discovery of Tb(pc)2-based SMMs (pc: phtalocyanine) [9]. In these compounds the dominating role is played by the single-ion anisotropy; a smaller effect is imposed by the ligand field effects and exchange interactions. The most prominent group of lanthanide-based SMMs are Dy and Tb complexes. Dy, being a Kramers-ion, is more likely to yield an SMM property, but the magnetic anisotropy of the Tb ion is higher, therefore higher energy barriers are observed in Tb-based SMMs [9]. Actinide-based SMMs include U, Np complexes and the recently introduced first Pu SMM [10].

Combination of lanthanides with transition metals helped to exploit the exchange anisotropy effects. For instance, in a group of oxime-bridged [LnIII2MnIII6] complexes a remarkably high E barrier was found for the Tb compound (71.6 cm-1) [11a]. This value has been recently increased to 88.3 cm-1 with the report on a [CoII2DyIII2] complex [11b].

Exchange coupling effects have also been employed to afford record blocking temperatures in radical-bridged [Ln2] complexes up to 14 K based on hysteresis loops observed at field sweep rate of 0.9 mT/s [12]. Impact of radical ligands has also been studied for actinide complexes, such as a mononuclear U(III) complex displaying a zero-field slow magnetic relaxation, reported by Coutinho et al. [13].

For a single-ion magnet the record values have been so far reported for a mononuclear [ErIII(COT)2]- complex (COT: cyclooctatetraene) with hysteresis loops observed at temperatures up to 12 K [14]. The largest energy barriers of 216 and 331 cm-1 have been recently demonstrated for the organometallic [Cp*2Ln(BPh4)] (Cp*: pentamethylcyclopentadienyl; Ln: Tb or Dy, respectively) compounds [15].

The highest-nuclearity SMM is a wheel-like [MnIII84] complex [16], whereas the highest spin of 83/2 was reported for a mixed-valence [MnII7MnIII2] compound [17]. In these complexes the energy barriers for spin reversal are low or none, respectively, which underlines the role of magnetic anisotropy in the design of SMMs.

Characterization
The most important role in characterization of SMM behaviour plays SQUID magnetometry (fig. 3). Equilibrium magnetization of SMMs is normally studied by dc measurements. First indication of slow relaxation of magnetization is provided by zero-field cooling (ZFC) and field-cooling (FC) experiments showing a difference in magnetization data.

Dynamics of the magnetization in SMMs can be probed by ac susceptibility studies. An additional small field changing with a given frequency (usually 1-1500 Hz) is used [18], inducing a time-dependent moment in the studied sample. At very low frequencies this is equivalent to a dc study. For higher frequencies the sample magnetization cannot follow the oscillating field. An ac susceptibility χ is measured along with the phase shift, thus, a complex representation into χ´ and χ´´ can be defined. The χ´T vs T curve allows assessing the ground spin state of the system, which can be proven by a corresponding fit of the M/NμB vs H/T data. The presence of a maximum on the χ´´ vs T curves indicates slow relaxation of magnetization in the investigated sample. In these maxima the magnetization relaxation rate is equal to the angular frequency of the oscillating ac field. Thus an Arrhenius plot can be reconstructed. On the other hand, in ferromagnets this kind of behavior can be explained in terms of the domain walls movement.

Multiple relaxation processes can be identified by means of Cole-Cole plots of χ´ vs χ´´. The blocking temperature estimated from ac susceptibility studies is dependent on the applied frequency. A uniform definition was proposed by Gatteshi et al. [19] as temperature at which the magnetic relaxation time is 100 s, but so far not universally adopted in literature. Ac susceptibility studies are also helpful in studying other materials, such as spin glasses, superparamagnetic nanoparticles or superconductors.

Magnetization vs field curves recorded for SMMs show saturation effects and a hysteretic behavior of molecular origin. Steps often observed in these curves indicate quantum tunneling of magnetization [20]. An important parameter here is the coercive field defined as the magnetic field required to eliminate the remnant magnetization [20]. The temperature at which the hysteresis curves are observed is dependent on the sweep rate of the magnetic field. Therefore more reliable values for comparison of different SMMs are the energy barriers.

Other techniques for characterization of an SMM behavior include inelastic neutron scattering, Mössbauer spectroscopy, multi-frequency EPR or magnetic circular dichroism spectroscopy (MCD).

Mössbauer spectroscopy is a useful tool to probe the anisotropy of the investigated systems. Apart from iron complexes, 57Fe spectroscopy can indirectly differentiate between TbIII and DyIII in heterometallic Fe-Ln complexes, based on the differences in their ground states anisotropies [21]. Inelastic neutron scattering and multi-frequency EPR are powerful methods to determine exchange and anisotropy parameters. MCD provides an alternative sensitive technique to probe magnetization of samples in solution [22].

Concluding Remarks
In spite of still unsolved fundamental problems, efforts are also being directed towards manipulation and future applications of SMMs. For instance, Tb(pc')2 SMMs (pc': derivative of phtalocyanine) have been incorporated in supramolecular valve devices [23]. SMM research is still a rapidly developing area, bringing new insights into the underlying quantum phenomena every year. The quantum computing is already present on the market as introduced by the Company D-wave systems, yet, still dramatic developments are expected.

Acknowledgement
The author gratefully acknowledges Prof. Dr. Stefanie Dehnen for her generous support and helpful discussions, as well as the DFG for financial support (project no. HO 5055/3-1).

References are available from the author

 

 

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Philipps University of Marburg

35032 Marburg
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