In their recent letter, Tamion et al.1 present a Stoner-Wohlfarth based analysis whereby they simultaneously “triple fit” the field-cooled (FC), zero-field cooled (ZFC), and high temperature magnetic response curves (m(H) at 300 K) of a magnetic nanogranular sample to determine, in a self-consistent way, the magnetic diameter distribution function (or probability distribution function, PDF) and the effective particle anisotropy. The authors show clearly how fits to both the FC and the ZFC data are far more sensitive to variations in the PDF than fits to m(H), concluding that only simultaneous triple fitting leads to an unambiguous and highly accurate determination of the PDF and the particle anisotropy. The paper is, however, misleading with regard to the accuracy of the common and widespread technique (see, e.g., Refs. 7 to 9 of Ref. 1) of individual m(H) fitting, using a diameter-weighted Langevin function, to determine PDF alone. Namely, in their discussion of Figure 1 in Ref. 1, the authors state that the three calculated m(H) curves, corresponding to log-normal PDFs with mean diameters (Dm) of 2.7, 3.2, and 3.6 nm, “equally well reproduce” the m(H) data, concluding thus that the technique “is not unambiguous for particle size distributions.” In a printed version of the letter it is, indeed, barely possible to detect any differences between these three curves, however, close inspection of the figure (performing a “zoom-in” in the electronic version) reveals that the red curve (Dm = 3.2 nm) is clearly the best fit to the data, i.e., the sum of the squared residuals (the χ2 value) for this curve is clearly less than that for either of the other two. The paper, therefore, misleads the reader into an understanding that individual fitting of m(H) data can provide only a very rough estimate of Dm. We expect that, left to converge, such fitting of the m(H) data in Ref. 1 will give a PDF with a Dm value very close to, if not the same as, the result (3.2 nm) of the triple fit.

In our experience, individual m(H) fitting of data taken at a temperature at least four times that of the ZFC peak exhibited in a magnetic nanogranular system always converges to the same log-normal PDF regardless of the initial parameters defining this function.2 Thus, there appears to be no local minima in this type of fitting, which implies that the method may indeed be considered unambiguous for particle size distributions. Of course, another issue is the accuracy of the PDF determined by this method with respect to the result obtained from a triple fit. It would, therefore, have been pertinent of the authors to present the PDF from individual m(H) fitting so that it could be compared with the (Dm = 3.2 nm) PDF obtained from the triple fit. First, this would have clarified the need or otherwise for triple-fitting in studies in which a determination of the PDF alone is desired. Second, such a comparison would have informed the reader as to whether triple fitting should necessarily be performed simultaneously: if the PDFs were the same then “sequential fitting”—i.e., individual m(H) fitting followed by FC and ZFC fitting with the PDF fixed from the first step—could have been concluded as viable; if the PDFs were different, then a mention by the authors of the comparison of the FC and ZFC fit qualities between simultaneous and sequential fitting would have been highly instructive.

By addressing our comment, Tamion et al. may clarify the reliability and accuracy of the individual m(H) fitting method, extensively used in nanomagnetism.3 Such clarification is particularly pertinent for systems in which the presence of interparticle interactions would prevent the use of the triple fit method and, hence, the magnetic diameter would be sought by individual fitting of m(H) data taken at a sufficiently high temperature. Their response may also provide a useful comparison of the triple fit strategies (simultaneous versus sequential).

1.
A.
Tamion
,
M.
Hillenkamp
,
F.
Tournus
,
E.
Bonet
, and
V.
Dupuis
,
Appl. Phys. Lett.
95
,
062503
(
2009
).
2.
J. A.
De Toro
,
J. A.
González
,
P. S.
Normile
,
P.
Muñiz
,
R.
López Antón
,
J.
Canales-Vázquez
, and
J. M.
Riveiro
,
Phys. Rev. B
85
,
054429
(
2012
).
3.
A. P.
Guimarães
,
Principles of Nanomagnetism
(
Springer
,
New York
,
2009
).