Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Abderrahmane Reggad]

Thanks again Mr Juan Manuel for the rich information


Would you tell me to what extent this information is just:

*The character of the unit cell distortion is determined by the orientation
of the easy magnetization direction (EMD) of the compounds for binary RCo2
[6]. A close correlation between the EMD and **the symmetry of the
distorted Laves phase was observed,* i.e.* a rhombohedral distortion
corresponds to the EMD of [1 1 1] of the pseudo-cubic structure, a
tetragonal distortion to the EMD of [1 0 0] and an orthorhombic distortion
to the EMD of [1 1 0].*

*Best regards*


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Mr: A.Reggad
Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
Algerie
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Abderrahmane Reggad]

Thanks again Pr Staphan for the procedure and the article. Unfortunately I
have no idea about the Spin Density Wave and I have to learn more about it.

Best regards

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Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
Algerie
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Juan Manuel Perez Mato]

In order to know the symmetry of a structure you do not have to look at the 
unit cell, but to the symmetry group of the structure. You can have a triclinic 
structure with a cubic unit cell. Just look at the symmetry group that is 
indicated in the database, and you will see that its point-group is monoclinic.

The monoclinic magnetic structure of NiO in the database comes from an 
experimental report where any deviation of the positional structure  and 
lattice from the parent cubic was considered negligible. As in general the 
magnetic induced structural distortions are very weak one has to make a 
specific effort to detect them and to characterize them experimentally (and I 
suppose also in calculations as explained by Stefaan Cottenier). A rombohedral 
strain is just a less general strain than a monoclinic one. If the strain is 
very weak, a first appoximation to it can be a rombohedral strain, which has 
only one free parameter to determine, instead of the three that requires the 
monoclinic strain.

best regards,

Manuel


> El 10/6/2016, a las 12:48, Abderrahmane Reggad  escribió:
> 
> 
> Thanks Mr Khan Manuel for your contribution to enrich the subject of 
> geometrical frustration and magnetism .
> 
> After reading your contribution, I made the following remarks:
> 
> * you have said:In the case of NiO the magnetic order reduces the symmetry to 
> monoclinic, but what we know all is that the magnetic order reduces the 
> symmetry in NiO from cubic to rhombohedral.
> 
> * From theMAGNDATA database, It's mentionned that the magnetic unit cell is 
> cubic 
> 
> Lattice parameters of the magnetic unit cell:
> 8.3500 8.3500 8.3500 90. 90. 90.
> 
> Whould you explain that 
> 
> Best regards
> Mr: A.Reggad   
> Laboratoire de Génie Physique
> Université Ibn Khaldoun - Tiaret
> Algerie
> 
> 
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Fac. Ciencia y Tecnologia,
Universidad del Pais Vasco, UPV
48080 BILBAO,
Spain

tel. +34 946012473
fax. +34 946013500
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Stefaan Cottenier]

Now , I understand the origins of the tetragonal and the orthorombic
distortions for the cubic structure of Chromium Cr.

I know how to add the spin-orbit coupling in the wien2k code to get the
tertragonal structure , but I don't know how to take  the spin-density wave
 in account .

Would you explain to me how to do that



We did that long ago:

J. Phys.: Condens. Matter 14 (2002) 3275–3283
(http://stacks.iop.org/JPhysCM/14/3275)

It boils down to preparing a supercell in which one period of the spin 
density wave fits (in this case a 1x1x21 supercell), and preparing in 
case.inst antiferromagnetic moments with a cosine profile as starting 
situation.


In those calculations, the lattice parameters were constrained to 
(multiples of) the cubic values, as the effect of the spin-density wave 
on the energy was much larger then the effect of the induced tetragonal 
symmetry.


Stefaan
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Abderrahmane Reggad]

Thanks again Pr Stephan for the rich information

Now , I understand the origins of the tetragonal and the orthorombic
distortions for the cubic structure of Chromium Cr.

I know how to add the spin-orbit coupling in the wien2k code to get the
tertragonal structure , but I don't know how to take  the spin-density wave
 in account .

Would you explain to me how to do that

 the little thing will be fruitfull

Best regards
Mr: A.Reggad
Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
Algerie
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Stefaan Cottenier]

According to what your are saying , the real magnetic structures for
Chromide is tetragonal and orthorhombic and not cubic as it's mentionned
in the userguide.

I think the cubic magnetic structure fo Cr is given just to simply the
calculation for the beginners of the antiferromagnetic calculation.


The deviation from cubic symmetry is very, very small, and for most 
purposes it is perfectly fine to treat Cr as cubic.


Moreover, spin-orbit coupling is needed to allow the magnetic moments to 
break the cubic symmetry to tetragonal. Spin-orbit coupling is a very 
small effect for a light element as Cr. And in order to get the 
reduction to orthorhombic symmetry, the spin-density wave in Cr is must 
be taken into account (its wave vector is transversal to the magnetic 
moments between 123 K and 311 K, whence the orthorhombic symmetry -- it 
is parallel to the magnetic moments between 0 K and 123 K, that's why a 
tetragonal symmetry is possible).


When Cr is approximated as an antiferromagnetic crystal without 
spin-density wave and without spin-orbit coupling, its ground state is 
exactly cubic.


Stefaan
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Abderrahmane Reggad]

Thank you Pr Stefaan Cottenier for your contribution

According to what your are saying , the real magnetic structures for
Chromide is tetragonal and orthorhombic and not cubic as it's mentionned in
the userguide.

I think the cubic magnetic structure fo Cr is given just to simply the
calculation for the beginners of the antiferromagnetic calculation.

Best regards

-- 
Mr: A.Reggad
Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
Algerie
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Abderrahmane Reggad]

Thanks Mr Khan Manuel for your contribution to enrich the subject of
geometrical frustration and magnetism .

After reading your contribution, I made the following remarks:

* you have said:In the case of NiO the magnetic order reduces the symmetry
to monoclinic, but what we know all is that the magnetic order reduces the
symmetry in NiO from cubic to rhombohedral.

* From theMAGNDATA database, It's mentionned that the magnetic unit cell is
cubic

*Lattice parameters of the magnetic unit cell:*
8.3500 8.3500 8.3500 90. 90. 90.

Whould you explain that

Best regards
Mr: A.Reggad
Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
Algerie
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Stefaan Cottenier]

In general, any magnetic ordering breaks the symmetry of the system, and
structural distortions compatible with the new symmetry can happen due
to magneto-structural coupling. Often this coupling is too weak to be
detected, but in other cases like NiO is strong enough.


And this is indeed what happens for bcc Cr (where the initial question 
was about). Quoting from pages 173-174 of "Phase diagrams of the 
elements" (David A. Young):


"At room pressure and temperature, Cr is bcc. This structure is modified 
very slightly by two first order magnetic phase transitions. From 0 to 
123 K, Cr is antiferromagnetic with a small tetragonal distortion of the 
bcc lattice. From 123 K to 311 K, Cr is antiferromagnetic with as small 
orthorhombic distortion of the bcc lattice."


The original experiments can be found in 
http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.23.979


Stefaan


--
Stefaan Cottenier
Center for Molecular Modeling (CMM) &
Department of Materials Science and Engineering (DMSE)
Ghent University
Tech Lane Ghent Science Park – Campus A
building 903
BE-9052 Zwijnaarde
Belgium

http://molmod.ugent.be
http://www.ugent.be/ea/dmse/en
email: stefaan.cotten...@ugent.be

my conference talks on Youtube: http://goo.gl/P2b1Hs
for China: http://i.youku.com/cottenierlectures
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Abderrahmane Reggad]

Thanks again and I have read that the lifting of the Geometrical
Frustration lead to Ferrimagnetism.

Best regards
-- 
Mr: A.Reggad
Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
Algerie
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Juan Manuel Perez Mato]

This discussion may be very misleading. The concept of frustation is very 
popular, but whatever geometrical frustation may exist in a fcc lattice, the 
magnetic structure of NiO is perfectly collinear (see for instance in the 
MAGNDATA database of the Bilbao crystallographic server: 
http://webbdcrista1.ehu.es/magndata/index.php?this_label=1.6 
) , and each 
triangular plane of spins perpendicular to the <1,1,1>  has NO frustration, as 
the couplings within the planes are FM . Therefore the small structural 
structural strain can not be caused to get rid of the frustration.

In general, any magnetic ordering breaks the symmetry of the system, and 
structural distortions compatible with the new symmetry can happen due to 
magneto-structural coupling. Often this coupling is too weak to be detected, 
but in other cases like NiO is strong enough. In the case of NiO the magnetic 
order reduces the symmetry to monoclinic, and the observed structural 
distortion corresponds to this symmetry break.

best regards,

Manuel

> El 10/6/2016, a las 0:46, delamora  escribió:
> 
> No, because in NaCl you do not have magnetic moments that want to find order, 
> so there is no frustration
> In NiO the distortion is a way out of this frustration
> De: Wien  > en nombre de Abderrahmane 
> Reggad >
> Enviado: jueves, 9 de junio de 2016 05:26:15 p. m.
> Para: wien@zeus.theochem.tuwien.ac.at 
> Asunto: Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic
>  
> Thanks Dr Delamora for your reply 
> 
> Now I inderstand that and according to this raison "geometrical frustration" 
> , is there any structural distortion in the planes
>  (100) and (110) for the NaCl structure.
> 
> Best regards
> -- 
> Mr: A.Reggad   
> Laboratoire de Génie Physique
> Université Ibn Khaldoun - Tiaret
> Algerie
> 
> 
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**
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Fac. Ciencia y Tecnologia,
Universidad del Pais Vasco, UPV
48080 BILBAO,
Spain

tel. +34 946012473
fax. +34 946013500
***

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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[delamora]

I want to say that the distortion does not completely solve the frustration in 
NiO

The geometric frustration in magnetism is vast subject

Cheers

Pablo de la Mora



De: Wien  en nombre de Abderrahmane 
Reggad 
Enviado: jueves, 9 de junio de 2016 06:10:01 p. m.
Para: wien@zeus.theochem.tuwien.ac.at
Asunto: Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic


Thanks again Dr Delamora for your explanation

Best regards
--
Mr: A.Reggad
Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
Algerie


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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Abderrahmane Reggad]

Thanks again Dr Delamora for your explanation

Best regards
-- 
Mr: A.Reggad
Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
Algerie
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[delamora]

No, because in NaCl you do not have magnetic moments that want to find order, 
so there is no frustration

In NiO the distortion is a way out of this frustration


De: Wien  en nombre de Abderrahmane 
Reggad 
Enviado: jueves, 9 de junio de 2016 05:26:15 p. m.
Para: wien@zeus.theochem.tuwien.ac.at
Asunto: Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

Thanks Dr Delamora for your reply

Now I inderstand that and according to this raison "geometrical frustration" , 
is there any structural distortion in the planes (100) and (110) for the NaCl 
structure.

Best regards
--
Mr: A.Reggad
Laboratoire de G?nie Physique
Universit? Ibn Khaldoun - Tiaret
Algerie


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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[Abderrahmane Reggad]

Thanks Dr Delamora for your reply

Now I inderstand that and according to this raison "geometrical
frustration" , is there any structural distortion in the planes (100) and
(110) for the NaCl structure.

Best regards
-- 
Mr: A.Reggad
Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
Algerie
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Re: [Wien] Why the antiferromagnetic structure of Cr is still cubic

[delamora]

In NiO the Ni makes an FCC structure, you cannot have an antiferromagnetic 
arrangement in a triangular lattice (for example in 1,1,1 planes), even less in 
the FCC, which is triangular in many planes, so there is what is called 
"geometrical frustration"

On the other hand, in Cr you have the "Cr up" and "Cr dn" alternated and you 
can have a clear antiferromagnetic arrangement

Pablo

De: Wien  en nombre de Abderrahmane 
Reggad 
Enviado: miércoles, 8 de junio de 2016 05:43 a. m.
Para: wien@zeus.theochem.tuwien.ac.at
Asunto: [Wien] Why the antiferromagnetic structure of Cr is still cubic


Dear wien2k users

I have read that the antiferromagnetic ordering is accompanied with a little 
structural distortion as in the case of NiO. This latter is characterized by a 
distortion from NaCl to rhomboherdral structure; but for the chromide Cr the 
structure is still cubic when there is a magnetic transition from paramagnetic 
to antiferromagnetic state.

Best regards
--
Mr: A.Reggad
Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
Algerie


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