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8.2.1 Time Dependence

Time dependence in systems without inherent randomness or impurities is rare on an appreciable timescale to be measured by neutron diffraction. However, such a time dependence was recently observed in the compound CeIr3Si2, where there are two

magnetic transitions within 1 K of each other. The time dependence was observed when the compound was rapidly cooled to a low temperature (2 K), leading to a time dependent lock-in transition between the incommensurate and commensurate magnetic phases [58]. Ca3Co2O6has also been reported to exhibit a time dependent

lock-in transition in a low applied magnetic field [155]. However, neither of these reports involves a magnetic phase with an entirely different propagation vector such as the one discussed here.

In order to study the time dependence of the conversion of the SDW to the CAFM phase in Ca3Co2O6, the sample was warmed above TN and allowed to

thermalise to erase the magnetic history. It was then thermalised again at 18 K and cooled rapidly to 2 K at a rate of approximately 2 K/min. It was then warmed to the required temperature. To evaluate the time dependent behaviour the data were binned into 15 minute intervals. The phase fractions of the different magnetic phases in Ca3Co2O6 were evaluated at each 15 minute interval by refinement of the

scale factors.

The time dependence of the data collected at 8 K is shown in the top panel of figure 8.5. The resulting curves for the SDW and CAFM phases were then fitted using stretched exponentials, defined in section 2.4.3, where the order parameter is the phase fraction (given as a percentage) of each of the magnetic phases. Using this method, the characteristic relaxation timeτ was found to be 4.4_±0.9 hrs at 8 K. Equilibrium values of 28_±5 % and 24_±5 % were found for the SDW and CAFM phases respectively, showing that within error bar the equilibrium percentages of the two phases are equal. The phase fraction of the short-range component increases slightly in the first hour of measurement before reaching a relatively stable value of

∼35 %.

The time dependence of the magnetic phases in Ca3Co2O6 was also measured

0 1 2 3 4 5 6 0 20 40 60 80 100 SDW phase Short range phase CAFM phase P h a s e F r a c t i o n ( % ) Time (Hours) T = 8 K 0 1 2 3 4 5 6 7 0 20 40 60 80 100 T = 10 K SDW phase Short range phase CAFM phase P h a s e F r a c t i o n ( % ) Time (Hours)

Figure 8.5: Time dependence of the phase fractions of the SDW, short-range and CAFM phases in Ca3Co2O6 at 8 and 10 K. The data has been binned into 15 minute

intervals, with the first measurement assigned a time of 15 minutes allowing for the fact that some time had passed before the measurement had started. The solid lines are fits to the data, described in the text.

the relaxation to equilibrium is faster than at 8 K, with a characteristic relaxation time ofτ = 1.4 _±0.2 hrs. However, at 10 K the equilibrium values of the SDW and CAFM phases are no longer comparable, and are 66.6 _± 0.6 % and 23.3 _± 0.4 % respectively. The phase fraction of the short-range component oscillates around a constant value of _∼17.4 %. It is the reduced number of short-range correlations that causes the equilibrium percentage for the SDW phase to be higher at this temperature. The diffraction patterns collected at 2 K with counting times up to 4 hours show no appreciable time dependence, and it is believed that the timescale for relaxation at this temperature is too long to feasibly measure using neutron diffraction.

8.2.2 Temperature Dependence

The time dependent evolution of the SDW to form the CAFM phase in Ca3Co2O6

is reproducible. That is, if warmed above 12 K the peaks corresponding to the CAFM phase disappear and the peaks corresponding to the SDW phase increase in intensity and become resolution limited. The temperature dependence of the magnetic phases after the CAFM phase has been allowed to evolve at 8 K is shown in figure 8.6. The phase fraction of the CAFM phase appears to increase slightly from 15 % to 20 % between 8 and 10 K before decreasing rapidly above 10 K until it disappears at 13 K. The phase fraction of the short-range phase also decreases steadily as the temperature is increased from 8 to 13 K.

Figure 8.6: The tempera- ture dependence of the phase fractions of the SDW, short- range and CAFM phases, af- ter the CAFM phase has been allowed to reach equi- librium at 8 K. The dashed lines are guides to the eye.

8 9 10 11 12 13 0 20 40 60 80 100 SDW phase Short range phase CAFM phase P h a s e F r a c t i o n ( % ) Temperature (K)

The increased preference for the CAFM phase at the expense of the SDW phase as the temperature is decreased suggests the CAFM phase may well be the true magnetic ground state of Ca3Co2O6. Calculations including next-neighbour

super-superexchange interactions in the model for the magnetic behaviour of the compound have also shown that the CAFM phase has a lower exchange energy that the SDW phase [144], supporting this theory. Above 12 K we have shown that

the SDW phase is preferred and this is attributed to a difference in configurational entropy between the two phases. This is because the SDW phase has greater entropy, containing regions with nearly zero ordered moment, whereas in the CAFM phase every magnetic site is fully ordered. However, it is evident from the competition between the SDW and CAFM phases and the lack of a clear preference of the system towards one particular configuration as the temperature is reduced that the two phases are nearly degenerate. The incomplete nature of the magnetic transition between the two phases is attributed to defects and pinning centres such as domain walls which should have already established themselves at higher temperatures.

It has previously been noted [140, 141] that there is an anomalous dip in the intensity of the Bragg peaks corresponding to the SDW phase at temperatures below 18 K. Our measurements indicate a broadening of the peaks corresponding to the SDW phase as the temperature is reduced implying a corresponding reduc- tion in the magnetic correlation length from 500 to 300 ˚A. Variations in widths of both the CAFM and SDW phases with changes in temperature implies that the interconversion process is due to an intergrowth of the magnetic phases rather than magnetic phase separation. It is believed that the peak broadening, coupled with the presence of short-range order and the emergence of the CAFM phase, fully ex- plain the anomalous dip in intensity of the peaks belonging to the SDW which was previously not fully accounted for [141].

The measurements made on GEM also showed that it is possible to ‘freeze in’ the CAFM phase if the sample is rapidly cooled to 2 K after the phase has been allowed to evolve at a higher temperature such at 8 or 10 K. This history dependence will be further discussed in the next section.