In the INS study of Pr1/2Ca1/2MnO3, crytal micro-twinning is THE MOST crucial issue (much more complex, by showing 6 instead of 2 twins than in all INS studies so far restricted to 2D-provskites), but it is certainly not dealt as accurately as Aladinsane's diffraction analysis who was working ON THE SAME CRYSTAL! WHILST the authors pertinently knew this AND followed closely all the diffraction result!

In between the lines, I am guessing that the INS analysis is in fact made in two steps. The first step fits a selected number (~20) of single 1D cuts (which I believe, because neither any fit reliability factors (Chi^2) nor any graphical representation if the fits is shown, are chosen in ways that they are assumed to contain individual twins contribution to scattering) meant to be refined with 20 data dependent and not 6 sample related scale factors: twinning is therefore not accounted for at all, for the fit of exchange constants. Even if my guess is wrong it might be like in the second step not fully taken into account anyway: the extracted exchange values are indeed used to make simulations of 2D plots (momentum transfer, Energy) compared to symetrically averaged spin wave spectra. Such symetrical averaging is a "standard" procedure applied to TOF data on UNTWINNED samples to get more statistics, for a TWINNED crystal, this assumes the equipopulation of the crystal twin fractions, which diffraction data proves to be far from realistic.

In the final version of the article (July 2016), the "symetrical averaging" of data vaguely said to account for twinning in the arxiv-v1 (Jan 2015), has been JUSTIFIED with an posteriori "analysis" combining simulation (that are strangely nullifying twin fraction depending on the region of the data explored) completed with fitting tests whose combination The conclusion is made, a clear-cut as the model discrimination in the rest in the article, I'll let you imagine, how the discrepancy wiht reality, may apply to the whole intro-discusssion-interperetation made!

"We found that, irrespective of the initial values of the fit parameters chosen, within the error [not given, but coming from least square fit, certainly] on the fit parameters the populations of all six twin were essentially equal"

In contrast, my on-goig unpublished neutron single crystral diffraction structural analysis refines those twin fractions, and, as criteria to discriminate the models, gives quantitative reliability factors for the relevant (superstructure line intensity fit) information. ALL twin fraction are refined together with the model (structure and/or magnetic strucutre), and here are the 6 twin domain fraction such determined at RT (Bragg factors obtained of Rb=2.87% but that's the whole difficulty, getting worse because of increased splitting of twin contribs inthe CO state, i.e Rb= 7%, still giving the same fractions showing how robust is the procedure!!!).  I guess, the number coming from diffraction speak for themselves...

c-orth axis along

    a-cub                  b-cub                 c-cub

INS (essentially the same means...):
16.66% 16.66% 16.66% 16.66% 16.66% 16.66%

DIFF, experimentally "refined quantitatively" form the data
 8.72%  13.81%  9.9%  19.23%  25.43%  22.89%

Those fractions have been obtained on a cut FROM THE SAME rod (i.e much smaller than the INS sample) so, twinning being microscopic, it would be a MIRACLE that the large disparity of twin population in the small diffraction sample averages to the advocated "essentially equal populations", in the bigger sample cut for INS from the same rod. Those twinn fraction speak for themselves, about being ALL, but "essentially equal"... from a serious Structural determination involving a least square Fit procedure giving Reliability factors, not on an "analysis" based on loose combination fiddling around between simulations and fits all made with hypotheses, but one solid & verifiable structural determination (most reliable at RT but also invaribly consitent with ~4 data collections at other temperatures AND consistent between two different 4-circle diffractometers!
 
The whole INS analysis therefore self-justify a LIE, and do not account in reality for the real twin fractions (I recall... WHICH the authors know from me!), the procedure, is admitted to seemingly lead to apparent model degeneracy between the exchange model of Fig1b and 1d at some point, and a final model discrimination is then "designed" to show only ONE single selected 1D fit that may represent <1% of the data (and not accounting for twinning! most probably...) to finish... That model discrimination, admitted in the abstract to be subtle in the INS work, is from this respect  unambiguous, in the STANDARD (except for twinning) analysis of the competing SYMMETRIES, in the diffraction data.