Dear Zaher,

We thank you for communicating the reports of the referees to our
manuscript entitled "New insights for the description of magnetic
correlations as inferred from \muSR". We thank the referees for their
work and would like to resubmit our text for publication. Below we
respond to the referees comments and detail the amendments to the text.

The message of our text is two-fold.

We first recall the reader of shortcomings which are sometimes
encountered in the \muSR literature. It is exact that the original
material for this part was already published; however it was in a sparse
way. In this respect and concerning NiGa2S4, we think that an example of
a \muSR spectrum with a spontaneous muon spin precession and a magnetic
neutron scattering pattern with so broad reflections is not frequent. In
our opinion it is particularly striking for the \muSR community to see
the two plots side by side as in Figs. 3 and 4. The proceedings of a
\muSR conference is definitely the appropriate channel for the
dissemination of such knowledge.

In a second step we present a report of a new model-free method that we
develop for the analysis of zero and longitudinal field \muSR data. This
is a preliminary description of ongoing work. A more detailed and
exhaustive report of the method will be made available at a later stage.

We now comment more specifically on the second referee report.

It is true that we present the method and its application for a specific
example. The numerical values for the parameters are given for this
example. We do not pretend that they are generic to any case. This is
not the scope of this first report on the topic. However we understand
the frustration expressed by the referee. We have therefore extended the
appendix of our text to explain in greater details how the parameters
\epsilon, p and \lambda are determined. This should give enough
information for a reader who would like to adapt the method to his own
need.

As far as N_B is concerned, a small N_B value is preferred to limit the
computing time. In our case the field interval is about 1.8 mT,
corresponding to a precession frequency of 0.25 MHz. Since the long time
(i.e. above 1 \mu s) decay of the spectrum (Fig. 6) is the signature of
small dynamics, the static spectrum associated to the field distribution
that we compute is structureless above about 1 \mu s. Therefore a
distribution sampling at 0.25 MHz in frequency unit is enough. We have
added a small discussion about N_B in our manuscript.

Now about the stability of the algorithm. The stability was checked
essentially by plotting \chi^2 versus the number of iterations. In the
first hundreds of iterations \chi^2 decreases and reaches a convergence
value (a minimum) about which \chi^2 fluctuates when the iterations are
continued. There is however no guarantee that this minimum is local or
global using this algorithm. The same is true for any other algorithm.
There is no algorithm that can guarantee such convergence. Strict
mathematical derivations can be performed only for a particular
algorithm using a specific class of function, but not in the general
case. Still, the RMC algorithm which accepts a fraction of the
iterations which result in a higher \chi^2 helps notably in avoiding
local minima. We have added sentence about the convergence and stability
of our algorithm.

Reference 10 was devoted to the model-free analysis of TF \muSR data in
the high field limit. In this case the relation between the field
distribution and the \muSR time spectrum is linear (a Fourier
transform). In the case of ZF or LF \muSR the relation is highly
non-linear (Eq. 2 of our text). This is a first important difference in
the two works. The second difference is in the method used to find the
most appropriate distribution. In Ref. 10, it seems it is a steepest
descent or Gauss-Newton type algorithm. In our text this is a RMC
algorithm, which to our knowledge, was never used in \muSR. We have
found that it is useful because the conventional Gauss-Newton method
requires several computations of the function at each iteration. When
the function results from a triple integral this is time consuming. RMC
is also useful because, as already noted it helps avoiding local minima.
The aim of our paper is not a claim on introducing the ME method in
\muSR but to encourage the \muSR community to use it also in ZF or LF
\muSR together with the RMC algorithm.

In summary we have addressed the referee comments with an extension of
the appendix to our text. We believe that our manuscript is now suitable
for publication in the proceedings of this conference.

Yours sincerely 
P. Dalmas de Reotier on behalf of the authors.