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Magnetism and Local Molecular Field Louis Néel 3 December 1971, Volume 174, Number 4013 SCIENCE: Local Molecular Field On the other hand, P. Weiss was unable to offer a satisfactory solution to the problem of the origin of the molec- ular field. It was not until 1928 that Heisenberg found a mechanism of inter- Magnetism and actions that gave a satisfactory order of magnitude. From the point of view of Local Molecular Field interest to us, it is important to note only that these were interactions with a veryshort range, predominating between Louis Neel nearest-neigh-bor atoms and negligible beyond the second or third nearest neighbors. Hence, if one considers an alloy con- Downloaded from It has been known for a long time to absolute zero, the substance exposed sisting of two species A and B of atoms that ferromagnetism is due to inter- to the action of its molecular field alone distributed at random, the surroundings actions between atomic magnetic mo- hm = nJ8 acquires a certain spontaneous of the atoms may be vastly different, ments tending to align them parallel to magnetization J8. and the approximation of a single molec- one another despite the thermal agita- In this treatment, the molecular field ular field representing the action of the http://science.sciencemag.org/ tion. In order to obtain a quantitative is considered to be a uniform field inside surroundings for all the sites must be explanation of the experimental facts, the ferromagnetic sample. In addition, very poor. The theoretical problem of Pierre Weiss postulated (1) that a in order to give a more finished character treating such interactions in a rigorous ferromagnet behaved as a pure para- to his theory, P. Weiss had been led to manner is still far from resolved, but, magnet, that is, a paramagnet with distinguish between the energetic mo- while retaining the simplicity of the carriers of independent moments, with lecular field defined on the basis of the theories based on the molecular field, a magnetization given by internal energy U by the relation one can improve them considerably by making use of what I have termed the 1 = f(H/T) (1) Hm aj (4) local molecular field. and that the effect of these interactions Weiss's hypothesis amounts to writing on June 16, 2020 was equivalent to that of an imaginary and the corrective molecular field of that the energy E, of the system of magnetic field h,,,, called the molecular the equation of state hm defined, as we atoms A and B is written in the form field, proportional to the magnetization J have stated above, by E- - n(JA + JB)2 (7) h, = nJ (2) = hin) (5) where JA and JB designate the respec- and adding to the applied field H. If H tive magnetizations of atoms A and is sufficiently low, one thus obtains the Thermodynamic reasoning shows that atoms B. Actually, since this energy is magnetization law called the Curie- these two fields are related as follows: the sum of the contributions of pairs of Weiss law: nearest neighbor atoms A-A, A-B, = - dhm11 Hill mn T dT (6) and B-B, one should rather write J CH T-e (3) This particular approach, very satisfying Ee =1^(IZAAA2 + 2nABJAJB + nlBBJB) (8) with 0 = nC. If 0 is positive, the to the mind, permits one to treat and susceptibility J/H becomes infinite when explain the energetic properties of This amounts to abandoning the notion the temperature drops below the Curie ferromagnetic substances in an elegant of a general molecular field and intro- point 0. From this temperature a down and simple manner. It has the dis- ducing local molecular fields, hA = advantage of forcing one to admit as nAA1A + nABJB and hB = nABJA + Copyright ©) 1971 by the Nobel Foundation. dogma the uniformity of the molecular nBBJB acting on atoms of A and The author is professor of physics at the Uni- species versity of Grenoble, France. This article is the field and everything that follows from it, atoms of species B, respectively. lecture he delivered in Stockholm, Sweden, in in particular, the linear character of the I first developed this approach (2) in 1970, when he received the Nobel Prize in Phys- ics, a prize which he shared with Dr. Hannes thermal variation of the reciprocal 1932 and showed that the susceptibility Alfv6n. Minor corrections and additions have of been made by the author. The article is published susceptibility above the Curie point. X an alloy containing proportions here with the permission of the Nobel Foundation Advances of the theory have certainly P and Q of atoms A and B, with Curie and will also be included in the complete volume of Les Prix Nobel en 1970 as well as in the se- been retarded by this. constants CA and CB, was written as ries Nobel Lectures (in English) published by the Elsevier Publishing Company, Amsterdam and New York. Dr. Alfv6n's lecture appeared in the T(PCA + QCB) - PQC1A CB(sIA + nBB- 2nAB) (9) X - 4 June 1971 issue of Science. T T(PnAA CA + QnBB CB) + PQCA CB(nAA nBB- nAB) 3 DECEMBER 1971 985 _b -Olr -OI K on a- W. I H Fig. 1 (left). Decomposition of a planar lattice into two oppositely magnetized sublattices. Fig. 2 (middle). Motion of an antiparallel array of atomic moments acted upon by a field H. Fig. 3 (right). Thermal variation of the reciprocal suscepti- bility of an array of randomly oriented pairs of antiparallel moments. Instead of being represented by a ments are parallel and pointing in the certain, since this field is due to the straight line, the thermal variation of same direction, can cause this state of action of the neighboring atoms. These the reciprocal susceptibility l/x was ordering. Weiss and his co-workers thermal fluctuations are fluctuations in henceforth represented by a hyperbola. soon noted that the paramagnetic prop- time, but I was thus naturally led to I applied this theory to the interpre- erties of a certain number of salts were become interested in the spatial fluc- tation of the properties of platinum- suitably interpreted by a formula of the tuations and to analyze more closely Downloaded from cobalt alloys and a little later (3) to type of Eq. 3, but with a negative con- the consequences of the elementary iron-cobalt, iron-nickel, and cobalt- stant 0, that is, with a negative molecu- law of magnetic interaction: namely, nickel alloys. lar field. How such a field could pro- the existence of a coupling energy At the time, this interpretation was duce ordering at low temperature between two nearest-neighbor atoms, not received with great approval. The cannot be visualized. equal to w - cos a, where a denotes the existence of Curie-Weiss straight lines On the other hand, the Weiss theory angle of their magnetic moments. http://science.sciencemag.org/ in the [(l/X),T] representation was a was unable to account for the properties dogma so entrenched that when the ex- of paramagnetic metals such as man- periment would give a curve, it was ganese and chromium, which had a Constant Paramagnetism preferred to resolve it into successive susceptibility approximately indepen- straight lines, each corresponding to a dent of temperature and too large to be The constant w may be negative or different magnetic state obeying the attributable to Pauli paramagnetism, positive: negative in the case of ferro- Curie-Weiss law. that is, that of electrons in an energy magnetism and positive in the case band. of the negative molecular field. In the Such was approximately the state of latter case, the recourse to the molecu- Fluctuations of the the question in 1930 when I became lar field, admissible at high temperature on June 16, 2020 Weiss Molecular Field interested in the difference between the when the situations of all the atoms two Curie points, that is, in the fact are identical on the average, is no In the primitive theory of Weiss, the that the Curie point Op deduced from longer admissible at low temperature, molecular field coefficient n and the the Curie-Weiss law, or the paramag- since the atomic magnets must then Curie point 6 both had positive values, netic Curie point, differed from the tend to become grouped in pairs of and one can understand perfectly that ferromagnetic Curie point Of, the tem- atoms with antiparallel moments. this molecular field, which has a finite perature of disappearance of spon- I thus noted (2, p. 64) that in a positive value when all the atomic mo- taneous magnetization, whereas the Weiss theory implies the equality Of = Op. To explain this difference, I used the thermal fluctuations of the mo- lecular field, whose existence appeared *~~~~~~~~~~~~ A B Fig. 4. Variation of the susceptibility of 8 0T an array of antiparallel moments as a func- 0 T tion of the magnetic field and of the direc- Fig. 5. Influence of the magnitude of Fig. 6. Thermal variation of the recipro- tion of alignment of magnetic moments the magnetic field on the susceptibility of cal susceptibility of an antiferromagnetic relative to the crystal lattice. an array of antiparallel moments. substance. 986 SCIENCE, VOL. 174 body-centered cubic lattice composed of two simple cubic interpenetrating sublattices, the stable equilibrium at low temperature corresponded to an orien- tation in a certain direction of the moments of atoms in one of the sub- lattices and to an opposite orientation of the atomic moments of the other suiblattice, as is shown in Fig. 1 in the case of a planar lattice. This array is perturbed (Fig. 2) under the action of a magnetic field and acquires an aver- age induced magnetization per atom given by I p= g2H/6pw (10)C.._X,,' , ' Fig.
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