Condensed-matter physics

Two bodies are better than one

Single-molecule magnets can change their spin states through quantum tunnelling. A more complete picture of the interactions occurring in a system of such magnets must include two-body transitions.

To avoid the complexity of the macroscopic world and get at the fundamental mechanisms of nature, physicists prefer to study ensembles of simple, identical objects, such as quantum dots or single molecules. In time, these objects may become the elementary parts that are assembled into functionalized devices: as Richard Feynman said, physical laws do not imply any limitation on our ability to construct and assemble objects at the atomic scale.

Although single atoms can be handled relatively easily, manipulation of the quantum properties of spin systems must be achieved if the potential of quantum-spin devices is to be realized. As well as having applications in 'spintronics', spin manipulation is a bridge to understanding a basic problem in quantum mechanics — how the quantum properties of spins are affected by their environment1.

Another step towards understanding a quantum spin in its environment has been taken by Wernsdorfer et al.2 with their study of single-molecule magnets (SMMs), published in Physical Review Letters. SMMs carry a well-defined spin, S, and can be arranged in model systems so as to minimize the magnetic interactions between them3. Spin reversal can then occur through the quantum process of tunnelling4,5.

Typically, SMMs have a large uniaxial magnetic anisotropy — that is, the directions of their spins are oriented either one way or the other (usually represented as '+' and '−'). In their study, Wernsdorfer et al.2 used an SMM with the chemical formula Mn4O3(OSiMe3)(OAc)3(dbm)3 — known simply as Mn4 — that, in its ground state, has spin S = 9/2. In a magnetic field, the energy levels associated with the different spin states of the SMM suffer 'Zeeman splitting' (Fig. 1a): the spin states split into positive and negative values, and the energy of the −9/2 state becomes higher than that of the +9/2 state, and similarly for the other spin states available to the SMM (±7/2, ±5/2, ±3/2 and ±1/2, a total of (2S + 1) energy states).

Figure 1: Spin states and energy levels.
figure1

a, In a magnetic field, the energy levels in an Mn4 single-molecule magnet (SMM) become split, and the splitting increases with the strength of the applied field. States with negative spin values have higher energy; states with positive spin values have lower energy. Two individual SMMs may make simultaneous transitions between states, as shown, that are equal and opposite in magnitude, and overall energy is conserved. b, The actual scheme of energy levels for a coupled two-molecule system is more complex. The transitions seen by Wernsdorfer et al.2 are indicated. These 'spin–spin cross-relaxations' occur at the crossing of lines representing different spin states: because the energy levels of these states coincide, the SMMs can change state by quantum tunnelling. (Graphs derived from ref. 2.)

At low temperature, where thermal fluctuations are negligible, an SMM can reverse its spin (from a positive to a negative value, or vice versa) by tunnelling through the energy barrier between the potential wells of two spin states4,5. For the conservation of energy to hold, the energy levels associated with each state must coincide. This tunnelling process is now familiar for single molecules, but Wernsdorfer et al.2 saw evidence of more spin transitions that cannot be attributed to the usual single-molecule process. It seems that these extra transitions, which are much smaller than single-molecule transitions, result from simultaneous changes of state of interacting molecular spins.

In their crystalline samples of Mn4 (between 10 and 500 µm in size), Wernsdorfer et al.2 pinpointed three particular transitions corresponding to simultaneous changes in the spin of two SMMs: spins equal to −9/2 and −9/2 become −7/2 and 9/2, or −7/2 and 7/2; and spins −9/2 and 9/2 become 7/2 and 7/2 (Fig. 1b). In each case, only one spin tunnels (changes its sign), while the other spin makes a transition within the same well (the value changes, but not the sign). This phenomenon is an example of spin–spin cross-relaxation (an effect originally described for a situation without an energy barrier6), and is called exchange-bias tunnelling, because the value of the magnetic field at which this tunnelling occurs is shifted to restore energy conservation. Simultaneous changes of state between interacting spins have already been seen7,8 in an ensemble of Ho3+ (holmium) ions diluted in a crystalline matrix of LiYF4. But in this case the effect was observed at relatively high temperatures, in the thermally activated tunnelling regime of Ho3+ ions. Wernsdorfer et al.2 have now shown that exchange-bias tunnelling is also at work at low temperature in SMMs.

These additional transitions affect the broadening of spectral lines that is observed in SMMs. When an atom or molecule in a magnetic material changes energy state, a phonon is emitted whose energy corresponds to the size of the transition. But the existence of extra exchange-bias tunnelling transitions (and related 'co-tunnelling' transitions, in which both spins change sign7,8) means that the possible transitions for the system get closer and closer together, to the extent that the multi-spin transitions could eventually fill in the space between single-spin transitions. But, for co-tunnelling transitions, going from a single spin to two interacting spins means that there is a rapid decrease in the tunnelling probability: put simply, it's harder to change 2S to −2S than to change S to −S. If the number of spins involved is increased further, the tunnelling probability decreases exponentially.

Wernsdorfer and colleagues' study of two-molecule interactions2 has produced a more complete picture of a spin system. But further studies of multi-spin transitions in the tunnelling regime of both molecules and ions are needed if the consequences of spin manipulation are to be completely understood — and if networks of quantum spins are to be viable as the bits of a quantum computer.

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Correspondence to Bernard Barbara.

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Barbara, B. Two bodies are better than one. Nature 421, 32–33 (2003). https://doi.org/10.1038/421032a

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