[Wien] magnetic susceptibility for a ferromagnetic metal or for a ferromagnetic semiconductor

Fri Jul 21 14:50:49 CEST 2017

Note that the internal field in a metal (or an insulator) is not 
homogeneous. This is because of the inhomogeneous distribution of 
electrons. You don't have a homogeneous distribution of induced magnetic 
moments, and with that the susceptibility also is inhomogenous. chi is 
chi(r), a function of where in the material you do your measurement.

The property of metals calculated with very impressive accuracy by 
Laskowski and Blaha and their NMR module of Wien2k is this LOCAL 
susceptibility at the position of the nuclei, chi(r=r_atom1), ... 
chi(r=r_atomn). This is what you measure in nuclear magnetic resonance, 
NMR, hence the name of the module.

I guess the 'molar magnetic susceptibility' you want to calculate is 
what you get if you put the material in a (perhaps SQUID-) magnetometer: 
The average of chi(r) over the whole sample volume.

 From Peter Blahas comments here I take it that one could calculate this 
average on basis of the results from the NMR module: The spin and 
current distributions are there. My guess is that it will be not as 
trivial as it might look at first sight. For example I seem to recall 
that he mentioned that this is difficult to converge - at least in 
normal metals its a small effect, after all. This is not meant to 
discourage trying, just expect problems.

The NMR module is, however, for 'normal' metals. My warning was about 
high expectations in calculating the macroscopic, homogeneous 
susceptibility of ferromagnets (or other magnetically oŕdered 
materials). Wien2k gives invaluable information about the size of local 
magnetic moments, their exchange energies, moments of itinerant 
electrons in a band structure, ... with the caveats mentioned earlier 
even on the influence of a magnetic field. However, the susceptibility 
is about how the applied field couples the ground state determined by 
DFT to any low lying excited states - and especially in magnetically 
ordered systems these excited states might well be beyond the scope of 
DFT.

---
Dr. Martin Pieper
Karl-Franzens University
Institute of Physics
Universitätsplatz 5
A-8010 Graz
Austria
Tel.: +43-(0)316-380-8564

Am 20.07.2017 18:12, schrieb karima Physique:
> Thank you very much for your detailed answer
> 
> What I understood from what you wrote is that the DFT does not
> accurately estimate the magnetic susceptibility. honestly what is
> encouraged me to take an interest in this property is the paper of
> Prof. Robert Laskowski and Prof Peter Blaha  (doi:
> 10.1021/acs.jpcc.5b05947 [3]) where they compared their results for
> many metals and found values very similar to the experimental ones.
> 
> Now I do not know is what the estimate of molar magnetic
> susceptibility is possible with wien2k or its estimate is not always
> accurate.
> 
> 2017-07-20 16:54 GMT+02:00 pieper <pieper at ifp.tuwien.ac.at>:
> 
>> From what I have understood from userguide and Prof P Blaha's
>> replies;
>> For semiconductor and insulator; there is the orbital part of the
>> magnetic susceptibility only
>> but for the metals there is also the spin part
> 
>  No! This is not correct. Let me expand a little on my view of this
> topic in the hope to clarify the problem at least somewhat:
> 
> In a nutshell, you want Wien2k to find the state minimizing the total
> energy of some solid because you suspect that this is the state whose
> properties you observe in some experiment, and someone told you that
> DFT is the method of choice to do the search.
> 
> Magnetic moments contribute M*B to that energy with M and B being
> vectors in a scalar product. In a first approximation two
> contributions from electrons to M can be considered separately, namely
> the spin moment, and the moment from an orbital momentum (or the
> current associated with a non-zero orbital momentum). Both parts
> contribute to the energy in the field. That is why Peter Blahas very
> first statement was:
> 
> A magnetic field influences the spin and orbital degrees of freedom.
> 
> It always does. Both contributions to M. No matter wether you have an
> insulator or a metal. The influence on specific properties you are
> interested in may be too small to bother, but somewhere else it will
> show up.
> 
> There are different ways to tell Wien2k where to look for the state
> with minimum energy in an applied magnetic field (or electric field).
> This is where symmetry enters stage: Wien2k searches the state with
> lowest energy in the subspace compatible with the symmetries specified
> by the input files. The symmetry of the crystal structure is in the
> struct file. Concerning magnetic moments you can tell Wien2k to
> 
> - consider only states that are symmetric with respect to spin, i.e.
> do a non-spin-polarized calculation. Doesn't make sense if you are
> interested in the effect of a magnetic field or want to model
> ferromagnets, but for the majority of materials and properties it's
> perfect to save time and calculate just spin +1/2, then carry the
> result over to spin -1/2.
> 
> - take into account the two spin channels separately, i.e. do a
> spin-polarized calculation, and introduce B as 'orbital potential' in
> the program orb. Note that a field you put into .inorb acts on the
> electrons in the single atomic shell you specify, and only for the
> part within the muffin-tin radius. Everything else is indirectly
> adjusted according to interactions. I am (of course) with Peter Blaha:
> One can expect very reasonable estimates for field induced moments at
> the given shell, at least if the field induced polarization of
> electrons not affected by .inorb is small. The option also shows a
> Zeeman splitting of spin-up and -down bands due to the interactions,
> but I expect that depending on the case this can rapidly turn into a
> paedagogical example rather than an estimate of the spin
> susceptibility.
> 
> - take into account the fact that the energy contribution M*B quite
> possibly reduced symmetry. M as well as B are vectors, after all, and
> transform as such under symmetry operations. You can switch on
> spin-orbit interaction to tell Wien2k about this. (Be aware that
> Wien2k always assumes that M and B are colinear). As Gerhard Fecher
> pointed out, a reduced symmetry in a magnetic field is NOT taken into
> account in the orb program. With only the orb option active Wien2k may
> search the needle (the energy minimum) in a completely wrong haystack
> (subspace).
> 
> - do a calculation of the linear response of the all-electron wave
> function (representing spins AND orbital moments) to an applied field.
> As I understand it this is what the NMR module does. However, it
> calculates only the local response at the nuclei, not the integrated
> macroscopic susceptibility.
> 
> Note that all this does not represent anything like the macroscopic
> susceptibility you will detect with a ferromagnetic (or any other
> magnetically ordered) material in your magnetometer. The
> susceptibility in these cases even at zero Kelvin (where DFT arguably
> applies) is dominated by things the spins can and will do, but Wien2k
> is completely unaware of (magnons, domain walls ...).
> 
> Finally, don't take the UG or this mailing list as a substitute for a
> textbook. That is not their intention. Follow the advice of Prof.
> Fecher and read up on the subject of magnetism in solids. Perhaps
> start with something on solid state physics in general, not a
> specialized treatment of magnetism. Personally I like the introduction
> to Solid State Physics by Ashcroft and Mermin.
> 
> Good luck
> 
> ---
> Dr. Martin Pieper
> Karl-Franzens University
> Institute of Physics
> Universitätsplatz 5
> A-8010 Graz
> Austria
> Tel.: +43-(0)316-380-8564 [4]
> 
> Am 19.07.2017 16:02, schrieb karima Physique:
> 
>> From what I have understood from userguide and Prof P Blaha's
>> replies;
>> For semiconductor and insulator; there is the orbital part of the
>> magnetic susceptibility only but for the metals there is also the
>> spin
>> part and I ask Prof. P Blaha and Prof Gerhard Fecher  to confirm
>> this
>> answer or to correct it.
>> 
>> 2017-07-19 13:34 GMT+02:00 Wien2k User <wien2k.user at gmail.com>:
>> 
>>> I did not underestimate his answer and the proof I thanked him and
>>> I
>>> apologize if I did not convey my message well
>>> 
>>> 2017-07-19 12:48 GMT+02:00 Wien2k User <wien2k.user at gmail.com>:
>>> 
>>> Dear Fecher, Gerhard
>>> 
>>> You can answer me directly instead of asking me all these
>>> questions
>>> otherwise I thank you for your answer and I will look for this
>>> book
>>> to read it and in the meantime I will wait for the answers of the
>>> users and prof P. Blaha that I much prefer.
>>> 
>>> 2017-07-19 3:47 GMT+02:00 Wien2k User <wien2k.user at gmail.com>:
>>> 
>>> dear wien2k user
>>> 
>>> From the userguide we find how to calculate the magnetic
>>> susceptibility for an insulator or a paramagnetic metal but how to
>>> calculate the magnetic susceptibility for a ferromagnetic metal or
>>> for a ferromagnetic semiconductor?
>> 
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