Landau's theory of second-order phase transitions and its application to ferromagnetism

Cracknell, A. P.; Lorenc, J.; Przystawa, J.

doi:10.1088/0022-3719/9/9/015

Cited by 29 publications

(13 citation statements)

References 19 publications

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“…In view of the wrong assignment of the nuclear structures, the proposed models for the magnetic structures are questionable. The magnetic symmetry group of the germanide in the magnetically ordered state should be a subgroup of the magnetic group in the paramagnetic regime [41,42].…”

Section: Discussionmentioning

confidence: 99%

Polymorphism in the Germanides REPdGe with the Heavy Rare Earth Elements

Rodewald

Heying

Hoffmann

et al. 2009

Zeitschrift Für Naturforschung B

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The structures of the equiatomic germanides REPdGe with the heavy rare earth elements have been reinvestigated with respect to palladium-germanium ordering. The samples were prepared by arc-melting of the elements followed by annealing procedures in sealed silica ampoules at different temperatures. The structures of YPdGe, HT-TbPdGe, LT-DyPdGe, HT-DyPdGe, LT-HoPdGe, HT-HoPdGe, ErPdGe, and TmPdGe, and of the new germanide LuPdGe, were refined from single crystal diffractometer data. LT-DyPdGe and LT-HoPdGe crystallize with the YPdSi-type structure, space group Pmmn. The other germanides crystallize with the non-centrosymmetric YbAuSn structure, space group Imm2. All structures are orthorhombically-distorted superstructure variants of AlB 2 , and they show strong intralayer Pd-Ge bonding within the ordered Pd 3 Ge 3 hexagons. There is weak Pd-Ge and Pd-Pd interlayer bonding. The crystal chemical relationship between the different superstructures is discussed.

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Section: Discussionmentioning

confidence: 99%

Polymorphism in the Germanides REPdGe with the Heavy Rare Earth Elements

Rodewald

Heying

Hoffmann

et al. 2009

Zeitschrift Für Naturforschung B

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“…We incorporate these aspects in a theoretical model based on the phenomenological Landau theory of phase transitions [18,19,20] which permits an analysis of the temperature dependence of the elastic moduli in the presence of ferromagnetic ordering.…”

Section: Resultsmentioning

confidence: 99%

“…Instead, a lattice stiffening is observed below T c , similar to the temperature dependence of the elastic moduli of the ferromagnetic Mott insulator YTiO 3 [17]. The classical Landau theory [18,19,20] is utilized to model the thermodynamics of this second order magnetic phase transition. a parallelepiped with all faces perpendicular on the tetragonal crystal axes), which is essential to obtain quantitative values of the single crystalline moduli.…”

Section: Introductionmentioning

confidence: 99%

Elastic properties of the Zintl ferromagnet Yb14MnSb11

et al. 2012

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We report measurements of the elastic moduli as a function of temperature (5-300) K and magnetic field (0-2 T) for the Zintl ferromagnet Yb 14 MnSb 11 , which is believed to be a rare example of an under-screened Kondo lattice. The elastic moduli measured below the Curie temperature in this complex ferromagnet exhibit unusual lattice stiffening that is independent of the magnetic field and can be adequately modeled using the Landau theory.

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“…Actually, in the restricted framework of continuous crystalline transitions associated to order parameter dimensions n 3, it has been established by Michel and Morzrymas [4] that the low-symmetry phases indeed correspond to maximal subgroups. However, these authors, as well as Cracknell et al [10] have pointed out that the converse property is not true. For instance in the case of the 3-dimensional vector representation [6] of the m3m point group, the mm2XY group is not stable below a continuous transition though it constitutes a maximal subgroup of m3m.…”

Section: Le Journal De Physiquementioning

confidence: 97%

A counterexample to the « maximal subgroup rule » for continuous crystalline transitions

Tolédano¹,

Tolédano

1980

J. Phys. France

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2014 Nous décrivons, pour la première fois, un exemple théorique qui contredit une conjecture d'Ascher consistant en une règle du sous-groupe maximum, applicable aux changements de symétrie qui se produisent aux transitions cristallines du second ordre. Il s'agit d'un paramètre d'ordre à 4 dimensions qui sous-tend une représentation irréductible du groupe spatial Go = I41. Nous montrons, sur la base d'un développement de Landau au 4e degré, que ce paramètre d'ordre induit des transitions vers deux groupes G1 et G2 tels que G2 ~ G1 ~ Go (G2 non maximal). En revanche, nous n'avons trouvé aucun contre exemple à la conjecture plus précise de Michel qui exprime que la règle du sous-groupe maximum devrait être respectée relativement au groupe d'invariance complet du polynôme de Landau du 4e degré. Ce groupe est en général un supergroupe de Go. Abstract. 2014 We describe for the first time a theoretical example contradicting Ascher's conjecture of a maximal subgroup rule for the symmetry changes at continuous crystalline transitions. The example is that of a 4-dimensional order parameter spanning an irreducible representation of the space-group Go = I41. We show that this order parameter induces transitions towards groups G1 and G2, with G2 ~ G1 ~ G0 (G2 non maximal), on the basis of a Landau free-energy limited to fourth degree terms. By contrast, we have found no counterexample to the more precise conjecture by Michel stating that the maximal subgroup rule should hold with respect to the complete invariance group of the 4th degree Landau polynomial which is, in general, a supergroup of Go.

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Landau's theory of second-order phase transitions and its application to ferromagnetism

Cited by 29 publications

References 19 publications

Polymorphism in the Germanides REPdGe with the Heavy Rare Earth Elements

Polymorphism in the Germanides REPdGe with the Heavy Rare Earth Elements

Elastic properties of the Zintl ferromagnet Yb14MnSb11

A counterexample to the « maximal subgroup rule » for continuous crystalline transitions

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