Magnetization

The results of field intensity dependent mass magnetization (M) measurements are presented in Figure 3.12, made on a powdered BFCO sample. At all temperatures a degree of hysteresis can be seen at low field. This is consistent with commonly reported spontaneous spin canting, which persists in many orthoferrites334 _{and disordered doped BFO}335, 336_{. There is also a non-} linear response at all fields which does not saturate, typical of an antiferromagnetic system. Calculating the net moment from the magnetization at the highest field and 300 K, the result is 0.053 μB per formula unit. This is far lower than could be reasonably expected from O-phase BFCO, indicating again that this is a D-phase canted antiferromagnetic system.

Figure 3.12. Field dependent magnetization of BFCO at five different temperatures. A near linear, non-saturating response is observed with a small inner hysteresis (inset), suggesting antiferromagnetic ordering with a possible weak spin canting. Figure adapted from ref. [328_] with permission.

Figure 3.13 shows the temperature dependence of χ (M/H) for a powdered sample of BFCO under a field of 10 kOe. There is a notable difference in the FC and ZFC curves at low temperature which indicates there is a component of ‘ferromagnetism’ in this sample, contributing to a hysteretic effect, again likely attributable in part to spin canting. Though due to the fact that the BFCO is more than likely iron rich, this may also be related to an imbalance of ions not causing full cancellation of moments. The curves show quite a complex response at very low temperature and there is another notable broad feature at ~ 100 K. A number of related materials exhibit similar features which are attributed to spin reorientation transitions337, 338 _{and in some cases spin state transitions}339_.

Figure 3.13. Temperature dependence of χ for BFCO at 10 kOe, showing some ZFC/FC hysteresis at low temperatures, and convergence above room temperature indicating an approach to a critical transition. Low temperature features are complex. Figure adapted from ref. [328_{] with permission.}

At high temperatures the curves begin to converge indicating an approach to a transition temperature. Figure 3.14 shows high temperature measurements made on the sample using an oven option. Due to the nature of the instrument, there is a limitation to the field applied but there does appears to be an inflection point near 400 K to indicate a transition of some kind. It should be acknowledged that the technique used to obtain this data is very sensitive to impurities and so is likely to be affected by the presence of the antiferromagnetic Cr2O3 impurity identified in the neutron experiment. This phase has a TN of ~ 308 K meaning that inflexions above this temperature are likely attributable to the bulk BFCO material, but the magnitude may be affected by background from this phase. In order to make sure this study grasps the bulk behaviour of BFCO and not the impurities, the material was subjected to Muon Spin Resonance spectroscopy (μSR).

Figure 3.14. Temperature dependent field-cooled magnetisation, measured in the high temperature range under a field of 175 Oe, showing an inflection near 400 K indicating transition behaviour. Figure adapted from ref. [328_{] with permission.}

3.3.1.2 Muon Spin Resonance Spectroscopy

The μSR technique can much better probe the behaviour of the majority component of the sample due to its low flux and local binding nature. Muons are spin polarised on implantation, become coupled to internal magnetic moments in the samples, de-phase and then decay over a period of nanoseconds. The speed and directionality of the decay is associated with the internal magnetic field in the sample. Therefore, by monitoring the asymmetry and relaxation rate of the muons passing through the sample with respect to temperature can give valuable information about the magnetic behaviour inside the main phase of the material.

Fitting the raw data with the following function can be done to obtain asymmetry and relaxation rate information:

𝐺𝐺(𝑡𝑡) =𝐴𝐴𝑝𝑝−𝜆𝜆𝑠𝑠_+𝐴𝐴

0 (3.1)

where A is the asymmetry, A0 is the baseline asymmetry (from instrumental setup, 11.7%) and

λ is the relaxation rate.

In the raw asymmetry plot with respect to time ((Figure 3.15 (a)) a large ‘missing fraction’ is noted at low temperatures. Missing fractions occur when a strong internal magnetic field quickly dephases the muons outside of the measurable time scale. Further investigating this though fitting, very low asymmetry can be seen up until near 300 K where is starts to climb and is recovered after 375 K (Figure 3.15 (b)). This implies that the internal magnetic field is lost somewhere in this range, consistent with what was seen in the magnetization measurements. Additionally, the relaxation shows a peak at low temperature near 200 K (Figure 3.15 (b)) which indicates a fluctuating magnetic process within the sample that has a

comparable time scale to the muon probe. This may correspond to the 100 K feature in the magnetization, but is frequency dependent and shows a shift to high temperatures in response to the fast muon probe. In addition, the relaxing asymmetry at 100 K was observed to be almost 1/3 of that at 400 K. Given that a powdered sample will have a 1/3 + 1/3 + 1/3 directional average in the magnetization, this observation suggests an ordered magnetic phase in the sample below room temperature.

Figure 3.15. In (a), raw data showing an asymmetry difference between low and high temperatures is presented, and (b) shows fitted data with clear recovery of a missing fraction above room temperature (and an implied loss of magnetic ordering). A peak in relaxation rate at low temperature suggests a possible frequency dependent dynamic process. Figure adapted from ref. [328_{] with permission.}

Importantly, these measurements are consistent with the bulk phase being magnetically ordered at room temperature which is compatible with the earlier proposed antiferromagnetically ordered, chemically disordered model. The combined suite of magnetic measurements and neutron diffraction analyses support the assignment of D-phase BFCO with a TN ~ 400 K when produced in the bulk. Whether or not multiferroism and photoresponsiveness was retained in bulk BFCO was also unclear from the literature, and so further characterisations were conducted and are presented in the following section.