Quadratic transverse anisotropy term due to dislocations in Mn12-Ac directly obtained by EPR spectroscopy

High-Sensitivity Electron Paramagnetic Resonance experiments have been carried out in fresh and stressed Mn12-Acetate single crystals for frequencies ranging from 40 GHz up to 110 GHz. The high number of crystal dislocations formed in the stressing process introduces a E(S_x^2-S_y^2) transverse anisotropy term in the spin hamiltonian. From the behaviour of the resonant absorptions on the applied transverse magnetic field we have obtained an average value for E = 22 mK, corresponding to a concentration of dislocations per unit cell of c = 10^-3.

explains the quantum behaviour of Mn 12 -Ac in terms of dislocations existing in the crystals.
They propose that crystal dislocations introduce quadratic terms on S x and S y , producing tunneling in a lower order of perturbation theory than the transverse-field. Unpublished experimental results seem to support this new theory [20][21][22][23]. In this paper we will show a new experimental approach which indicates that dislocations formed in a strongly stressed single crystal introduce the E(S 2 x − S 2 y ) term suggested by Chudnovsky and Garanin, where E is the transverse anisotropy constant.
The Mn 12 -Ac organometallic cluster forms a molecular crystal of tetragonal symmetry with the lattice parameters a = 1.732 nm and c = 1.239 nm [24]. The unit cell contains two Mn 12 O 12 molecules surrounded by four water molecules and two acetic acid molecules.
In the crystallization process point defects usually appear in a low number along the whole crystal. It has been shown experimentally that dislocations can be created in a Mn 12 -Ac single crystal by rapid thermal cycles, in which the high change of temperature in a low scale of time produces radial and tangential tensions between the core and the surface of the crystal [21,22]. It is easy to visualize that tensions and pressure forces produced by mechanical distortion of the crystal may generate the same kind of dislocations in a single crystal. This is exactly what we have done with a Mn 12 -Ac single crystal. When a dislocation is created inside the crystal it has produced a disorder of the molecules in the vicinity of the dislocation. As the number of dislocations in the crystal grows the disorder extends over the whole crystal converting it in a mosaic crystal. The mosaicity is related to the number of dislocations existing in the crystal and can be determined experimentally by analyzing the width of the X-ray difraction peaks [25][26][27].
In our experiments we have used two single crystals: a) fresh single crystal and b) strongly stressed single crystal. To distort the crystal we put it in a glue by one of the extremities.
Then a gradually increasing force was applied to the other extreme, perpendicular to the longer length, until the the crystal fractured. Then, the longer resulting part of the crystal was adequately cleaned and tested by X-ray diffraction to be sure that it was a single crystal.
Both samples were characterized by X-ray analysis before making the EPR experiments. To obtain a fine check of the variation of the mosaicity between fresh and stressed crystals we have used low angle difraction peaks in order to minimize the widening associated to the lack of monochromaticity of the K α1 and K α2 X-ray emission lines of Mo element. We used a four-circle single-crystal X-ray diffractometer (Enraf-Nonius CAD4, MoKa radiation) in the characterisation. Reflections (± 2,± 2,± 2) were studied for both fresh and stressed single crystals. Peak intensities of the stressed crystal were normalised according to the measured volume of the studied fragment. Figure 1 shows ∆ω − ∆(2θ) plot of (2,2,-2) reflection for the fresh (left) and stressed crystal (right). An enlargement of the peak width along the ω direction is clearly observed although there is not a significant change along the 2θ direction (see inset of figure 1). Assuming that the distance between dislocations is inversely related to the widening of the reflection peak in the ω direction [21,25] we can conclude that the stressed crystal has a larger mosaicity than the fresh one. As the ω peak-width in the stressed crystal is a factor about 2 higher than in the fresh crystal, we can conclude that the number of dislocations increases about one order of magnitude in the distortion process.
The high frequency resonance experiments have been carried out using the AB millimeter wave vector network analyzer (MVNA) [28]. The base frequency obtained from this source (range 8 -18 GHz) is multiplied by Q, V and W Schottkey's diodes to obtain frequency range used in our experiment (37 -109 GHz). The sample, a single Mn 12 -Ac crystal, is placed on the bottom of the cylindrical resonant cavity, halfway between its axis and perimeter.
The applied dc magnetic field is parallel to the cavity axis and approximately perpendicular to the easy (c) axis of the crystal. The experiment frequencies are TE 0np (n, p = 1, 2, 3, ...) which are the resonant frequencies for the cavity used. Resonance Q-factor varies from 20000 at TE 011 mode (41.6 GHz) to a few thousand at higher frequencies. Due to the high sensitivity at resonance, there is an increase over conventional EPR of almost 3 order of magnitude, allowing for the detaction of the absorption peaks suggested theoretically by the diagonalization of the corresponding spin Hamiltonian.
The spin Hamiltonian used to explain the experimental data obtained in the last years where D, B, and C parameters have been experimentally obtained by EPR, Neutron spectroscopy and magnetic relaxation experiments [1][2][3][4][5][6]9,10,[29][30][31][32].  [18,19]. This term introduces the hardest anisotropy along the x-axis, while y-axis remains as a medium anisotropy axis. For this reason, different directions of the applied field give different values of each quantum splitting, ∆ m,ϕ . This is the same behaviour observed in the powder sample of Fe 8 molecular clusters [33][34][35]. The angular dependence of ∆ (ϕ) at a fixed value of the transverse component of the field is not monotonic. Because of the shape of the function ∆ (ϕ), for a sample with hard axis oriented at random, that is with not preference for any angle ϕ, there are two values of ∆ for which the density of states has a peak. These are the values of the splitting corresponding to ϕ = 0 and ϕ = π 2 (see references [34] and [35]). In the absence of dissipation, the contribution of each Mn 12 molecule to the imaginary part of the susceptibility is proportional to δ(ω − ∆[ϕ,H ⊥ ] h ). However, the total imaginary part of the susceptibility is, where g(ϕ) is the distribution of molecules on ϕ. For a fresh crystal, having no significant number of dislocations, there is an equivalence between x and y-axes as the Hamiltonian (1) has no preference for any transverse direction. Due to this, the splitting does not depend on φ and the amplitude A of the absorption of electromagnetic radiation must have only one peak corresponding to ∆[H ⊥ ] = hf , as it can be seen in figures 2 and 3A. On the contrary, in a strongly stressed single crystal of Mn 12 the dislocations are randomly affecting the magnetic structure of the molecular clusters, introducing the term E(S 2 x − S 2 y ) in different manner for each molecule [18,19]. That is, the fact that the effect of the dislocations existing in a single crystal depends on its direction along the crystal and on the distance to a given molecule may be considered as a random generation of a x-hard-axis for each molecule.
For this reason, a Mn 12 -Ac single crystal with a large mosaicity can be aproximated as a powder sample with x-axis of the molecules oriented at random. In this case, Eq. (2) can be rewritten as crystals. It may be also possible that the the combined effect of a heavy X-ray irradiation dose and subsequent thermal stressing treatment create a large number of new defective sites and extends the original ones. These sites will necessarily have a lower symmetry and effect of lattice defects on magnetization tunneling has been detected recently [20][21][22]. We also note that an EPR line-broadening effect of naturally present defects in Mn 12 and Fe 8 single crystals has been reported recently [36]. Additional investigations are thus needed in order to clearly understand the origin of the newly found EPR peaks in the present work.