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It is all really such a shame.... because INS turns out to be the key technique that can confirm or not the newly suggested exchnage model at x=0.5 However, as we will lenghtly detail, either the sign of the exchange predicted by the GKA rules,  or the symmetry constrains, have been completely overlooked by Toby Perring forever  who decided to never cite them, in spite of our long term "collaboration".

The overated reference to DDEX theories roots Toby perring preconception that the ZPO model is wrong at x=0.5, but that conviction was hiding (to me...) the fact Perring never had any clue (because the DDEX theory simply does not clarify THIS key point) about the Heisenberg exchange model associated to the ZP ordering model (intently, a truly localised electron model where JT modes are essential to justify the use of GKA rules) for what, he needed my help.

Not a single INS work carried by Perring et al started from the 1st neigbors models matching  this published ZP symmetry,CENSORING either the JMMM-ZP readaptation of the GKA rules or symetry constrains imposed by ZPO symetry: for example, the GKA rules are well applied, but the symetry constrain error is present in the first ISIS/ILL collaborative proposal back in 2006 : in reality, symmetry constrains impose Jf1=Jf2...

The final and published work 10 YEAR LATER... thus failed to prove that the the right  ZPO 1st Neighbor Heisenberg magnetic exchange model could capture his data.  Perring et al actually do capture the gap by considerering in the wrong ZP model (fig 1d) TWO alternating weak Super exchange and strong F-interactions building the ZP/dimer  along the zigzag. In the righ ZP ordering Heisenberg model never ever considered by Peering,  there are THREE different F-interaction (two grey and black Superexchange interactions, and the one binding the ZP), all 1st neighbor along the zigzag: this true and yet untested ZP model constitute therefore an alternative model that can not only capture the gap in INS excitations, but that's importantly and potentially constituting a more physical & minimal exchange model  proving that the ground state of half-doped manganites is like the Original Goodenough Model, that of a Heisenberg model consisting of 1st neighbor interaction only, NOT a Double Exchange Model:

Relying hence on a mix of preconceptions (that the ZPO model is wrong, that the DDEX theory is encompassing, and that diffraction is "controversial), yet perfectly conscious of the overlook/plagiarism/falsification of structural info I can bring, 


in particular, COMPLICATIONS are added, by inserting developements of the advocated DDEX model (Effremov/Khomski 2004), which considered a posteriori structural distortion also: the introduction of the published INS PCMO work is indeed referring to "extensions to the DDEX model that incorporate interaction with the lattice, Jahn-Teller distortions (which couple with the eg orbital occupancies) and alternating modulation of MnO-Mn bond angles [claiming they] also lead to different intra and interdimer exchange ". However, this sentence is an example of how the references to theories is systematically overrated if not falsified: but you need go to to read the theoretical paper, to realise why the sentence is untrue. This sentence is referring to the plethora of thoeretical papers (Ref 30-33 and Ref 40) not cited in the first version of the paper which I've carefully checked, are all mainly concerned with the calculation of the electric polarization & motivarted by the "Multiferoicity due to CO" concept born from Effremov/Khomski original proposal, but none of them include JT distortions excepted Ref 31, and for sure none of them is about the clarification or the calculation of magnetic exchange.

The reason for making so many (in fact off subject!) references to thoeretical work motivated by ZPO/CO-OO induced multiferroicity comes clear much ahead in the article: the aim is to consider orbital ordering at length [i.e have a good reason to apply the GKA rules, consider the ZPO structure more seriously, all the things I complained about after the publication on bi-layered half-doped manganites...], yet by continuing to make extremely confused references to different DDEX/theoretical works: "[we assume a DDEX description, where the concept of Goodenough Super Exchange is excluded but...] In order to anticipate  the likely signs of the weaker superexchange exchange interactions between zig-zags  we need to consider the orbital character on the Mn sites. [and for that, we'll refer to here to...] Model calculations for extensions to the DDEX Hamiltonian31,40 that include on-site Coulomb repulsion, MnO6 tilting and Jahn-Teller distortions, [which] consider the Mn orbitals to be a superposition of dy2−z 2 (dx2−z2 ) and d3x2−r 2 (d3y2−r2 ) character, where the x and y directions point along the two perpendicular Mn-Mn directions along the zig-zags. When the parameters of the  model [DDEX, not ab-initio] yield dimers there is a qualitatively closer resemblance to the latter on all sites [here, the sentence makes in fact implicit referrence to the pictures already provided in Effremov/Khomski work cited in Ref 17 and 18 the citation of ref 31 and 40 is unecessary; ref 31 is a work that is recuperated, since it is actually fairly motivated/supporting ZP ordering as buckling instability confirming the importance of one of the main characteristic of the experimental ZP structure, the Mn-O-Mn angle increase toward 180° within Zener pairs!!!]. At the corner sites along the zig-zags the resemblance is less pronounced and tends to equal character (i.e. no orbital ordering) as the dimerization vanishes."

Notice well here, how the inclusion of this verbosing paragraph in the published work, is remarkably different to the first version of the article, where the "dimer exchange model" was set without talking at all about ordital ordering but only a vague mention about the parallel and orthogonal arrangement of dimers, before laconically saying that "The Mn–O–Mn bond angles in PCMO are not far from 180◦ (refs. 12 and 15), so following the Goodenough-Kanamori rules10,33 we expect AFM coupling between nearest-neighbor Mn ions in parallel dimers, and FM coupling between nearest-neighbor Mn ions in perpendicular dimers" wihtout any justification/discussion/description of the orbital order at all.


Another remarkable discrepancy  between the published version and the first draft (compare v1 and v2 on arixv) in this last PCMO work,  is STRUCTURAL : the Mn site couloring of Fig 1d: it speaks for itself about how much authors are struggling to understand - or do not care about-  the ZP symetry and underlying OO. First there is a fundamental mistake in the cell doubling due to OO/CO in the Fig1 (it is along b, not along a). Supposing this is corrected, the colouring of Mn sites of Fig 1d is right in the first version (alternation of double stripes), but it is changed again and actually wrong in the published version (i.e it is back to a checkerboard arrangement)!

This major modifications of the published version 2 that were meant to justify the OO  from DDEX/theory (when in fact it is the reverse! the DDEX theory tried to get the OO expected from the ZPO experimental structure!) All this was done in order to justify the use of the GKA rules to DDEX inspired orbital structures in the modelling of a more realistic ZP model (Fig 1d), than the arbitrary "dimer" model considered in previous work on the bi-layered PCSMO compound (Fig 1c). However, repeating here what I said in the introduction, it is a conceptual misconception and an oxymoron to pretend to apply GKA rules to a DDEX deduced band electronic structure anyway... adding all the theoretical references most of them fairly motivated by the multiferroic aspect of ZPO problematic in the second pubished version is not meant to bring more insight into magnetic exchange, but to muddy the water, blank out the ZP-JMMM work and my numerous attempts to make it considered.The  reference to theoretical work in Perring's work is part of the systematic denial of the published ZP structure/magnetic exchange model REFUSING to refer to an experimental structure where the underlying dz2 OO character is obvious from octahedral elongations and COVERING UP this omission by an indigest pot-pourri reference to theories.

After such fiddling around orbital ordering verbosly quoting theoretical work, rather than simple phenomenology,  the INS article proposes the "shift" from the model of fig 1) c) to that of fig 1) d), which is in fact an unadmited failed attempt to correct the model fig 1c toward the true ZPO related exchange model. This Fig 1c is recalling the  "dimer model" studied in the bilayer compound but  in this ultimate  PCMO work,  notice well how this model of Fig 1 c) becomes I quote from the Fig 1 caption:  " As originally proposed the model was purely phenomenological without reference to an electronic model, and the orbitals should be considered purely schematic in this panel" i.e admitting that the orbital order, the fact it could be different in a ZPO structure adapted to layered material, had been overlooked and simply did not matter at the time !!!

Authors can then re-appropriate in PCMO50 the change I HAVE TOLD THEM THEY MUST MAKE end of 2012 afeter the publication of the PCSMO study, which is to replace the antiferromagnetic JA2 inter zigzag coupling (fig. 1.c in the PCMO paper) into what the ZP Orbital order and GKA rules (not DDEX...) predict to be a ferromagnetic JW2 (fig. 1.d). Author comply in the caption of Fig 1, "The orbital character together with Goodenough-Kanamori rules lead to FM JFW2, and AFM JA, different to the model shown in (c)" .  Last, author claim the most arrogantly, that anyway and a posteriori , the sign of that exchange parameter is not constrained in fits I quote "This model differs from that proposed by Johnstone et al, in which it was assumed JA2 ≡JFW2 < 0. Note that although we [now correctly, and thanks me!] use the Goodenough-Kanamori rules to anticipate the signs of JA and JFW2, we do not actually constrain the signs in our modelling. Consequently, the dimer model shown in Fig. 1(c) is a limiting case of the more general model shown in Fig. 1(d)", and they are admitting therefore explicitely here, that the previous work on bi-layered material was not general...

But most importantly, even after having at least "corrected" the orbital order jiggling with theories instead of relying simply onto the ZP structural phenomenology so authors finaly got the signs of exchange right as I've urged them TO DO (though I insist, GKA rules cannot be applied by conception to the advocated DDEX derived band electronic structure!), authors yet again demonstrate their complete overlook of the P 21 n m symetry of the ZPO structure, and still fail to apply a symmetry constrain expected from the 21 axis & glide plane present in this symetry: to be consistent with the ZPO phenomenology AND its symetry, it is not sufficient to invoke GKA rules and to replace JA2 by a ferromagnetic JW2, the P21 n m symetry of the ZPO  impose in addition the constrain JW1=JW2=J and in the more complete picture of the Fig1d in the v1 of the article, J'W1=J'W2=J', where J and J' correspond to the grey and black F-interaction in the blanked out JMM-ZP exchange model. However, the authors use the wrong JW1=J'W1 and JW2=J'W2 constrain, and that is because they let JW1=J'W1 follow the F zigzag and  JW2=J'W2 couple differrent zigzag - i.e they rely and get mislead by constrains suggested by the magnetic order missing by doing so, the right SYMETRY constrains expected from the ZPO. This is why they are not surprised but should have noticed if they knew/cared about the traget symetry, that they experimentally inconsistently obtain  unphysically very different values (JW1>>JW2) for couplings of atoms that are in symetrically equivalent orbital configuration in the ZPO symetry.