# Weiss, Pierre

# WEISS, PIERRE

(*b*. Mulhouse, France, 25 March 1865; *d*. Lyons, France, 24 October 1940), *magnetism*.

Weiss’s fame derives from the success of his phenomenological theory of ferromagnetism, which he conceived and developed on the basis of a large body of experimental results, many of them obtained by himself or his students. The theory is founded on the hypothesis of a molecular field proportional to the magnetization and acting on the orientation of each atomic moment like a magnetic field of very high intensity. With his theory he was able to account for the known characteristic properties of ferromagnetic bodies (notably the abrupt disappearance of ferromagnetism above a temperature known as the Curie point) and to discover the properties of spontaneous magnetization and magnetocaloric phenomena. Modern quantum theories of ferromagnetism have substantiated Weiss’s molecular field hypothesis as a first approximation. According to these theories, the molecular field results from exchange forces of electric origin between the electrons, which bear the atomic magnetic moments.

Weiss came from a petit bourgeois Alsatian family. His father, who owned a haberdashery in Mulhouse, remained there when Alsace was annexed by the German Empire following the Franco Prussian War. After attending secondary school in Mulhouse, Weiss went to the Zurich Polytechnikum. At his majority he chose French citizenship. In 1887 he graduated, first in his class, from the Polytechnikum with a degree in mechanical engineering. Wishing to undertake basic research, he attended the Lycée St. Louis in Paris to prepare for the competitive entrance examination for the École Normale Supérieure. Admitted in 1888, he was *agrégé* in physical science in 1893 and remained at the school as an assistant *(préparateur)* until 1895. During this period he became friendly with a number of fellow students who later became famous: the mathematicians Élie Cartan, Émile Borel, and Henri Lebesgue and the physicists Aimé Cotton, Jean Perrin, and Paul Langevin.

In 1895 Weiss was named *maître de conférences* at the University of Rennes and, in 1899, at the University of Lyons. In the meantime he had defended his doctoral dissertation, “Recherches sur l’aimantation de la magnétite cristallisée et de quelques alliages de fer et d’antimoine” (1896). In 1902 he returned as professor to the Zurich Polytechnikum, where, in addition to teaching, he directed the physics laboratory until 1918. His stay there was interrupted for two years, at the beginning of World War I, when he worked in Paris for the Office of Inventions. Helping to create an acoustical method for locating enemy gun emplacements (Cotton-Weiss method). At Zurich. where his colleagues included Einstein. also a professor at the Polytechnikum, and Peter Debye, professor at the University of Zurich, Weiss gradually developed a great laboratory for magnetic research. He endowed it with a remarkable array of equipment and, above all, trained or attracted many distinguished physicists.

In 1919, following the return of Alsace to France, Weiss went to his native province to create and direct a major physics institute at the University of Strasbourg. Under his guidance, and with the aid of several associates drawn from among the best of his former staff, the laboratory soon surpassed even that of Zurich as a center of magnetic research. Among his numerous students during this period, the most outstanding was Louis Néel. While supervising the many projects undertaken at the institute, Weiss continued to do personal research, even after his retirement in 1936. He was elected to the Paris Academy in 1926.

With the evacuation of Strasbourg at the beginning of World War II, Weiss fled to Lyons, where his best friend. Jean Perrin, also had taken refuge. He died of cancer in October 1940.

In 1898 Weiss married Jane Rancès. whose mother was of English origin. Before her death in 1919, they had had one child, Nicole, who in 1936 married Henri Cartan, son of Élie Cartan and one of the leading mathematicians of his generation. In 1922 Weiss married Marthe Klein. who taught physics in a Paris *lycée*.

Weiss was thin and rather tall. Distinguished looking and extremely courteous, he wore a pincenez and wing collar that gave him an air of elegance. His hair and large moustache became completely white when he was still quite young.

Weiss’s scientific works, which deal almost exclusively with magnetism, are characterized by great unity. From the time he was an engineering student, Weiss was interested in the complex phenomena of ferromagnetism, and it was to them that he devoted his initial research. He was influenced in this choice by the theoretical studies of Alfred Ewing and Pierre Curie’s “Les propriétés magnétiques des corps à diverses températures” (1895). At first he investigated magnetite and pyrrhotite, hoping that their large natural ferromagneitc monocrystals would enable him to discover the fundamental laws of magnetization. In the case of magnetite (1894-1896), he discovered only that it does not behave as an isotropic medium, even though it is crystallized in the cubic system.

The difficult study of pyrrhotite, the crystals of which are hexagonal prisms, proved much more rewarding (1896-1905). First he discovered that whatever the strength and direction of the magnetic field, the resulting magnetization remains, to a very good approximation, directed in the plane perpendicular to the axis of the crystalline prism. He then found that in this plane there is a direction of easy magnetization, in which saturation is reached in fields of twenty or thirty oersteds, and, perpendicularly, a direction of difficult magnetization, in which saturation has the same value but is reached only in fields exceeding 10,000 oersteds. Finally,m he showed that the magnetization produced by an arbitrary field can be determined by vectorially subtracting from this field a “structural field” directed along the axis of difficult magnetization and proportional to the component of the magnetization along that axis. The resulting field assumes the direction of the magnetization, and its strength is linked to that of the magnetization by a relation that is independent of that direction.

In 1905 Paul Langevin published a theory of the paramagnetism of dilute substances. In Langevin’s view, one may neglect the interactions between the magnetic moments μ that are assumed to be borne by each molecule of such substances. In the case of weak fields, the theory led to the Curie law, which states that the magnetization is proportional to the magnetic field *H* and to the reciprocal of the absolute temperature *T.* For very strong fields, or at very low temperatures, however, the law predicts that the magnetization **I** will tend toward a limit **I** _{0}. According to the theory, this saturation corresponds to tehthesituation in which all the molecular moments are oriented in the direction of the field, despite the thermal agitation tending to vary their directions. Using classical statistical mechanics. Langevin obtained a formula giving the magnetization as a function of the ratio *HǀT*:

(1)

In order to develop Langevin’s ideas, Weiss broadened the concept of structural fields proportional to the magnetization, which he had previously introduced to account for the magnetic anisotropism of pyrrhotite. Langevin’s theory led Weiss to conclude that the characteristic properties of the ferromagnetic metals, of which the microcrystalline structure is macroscopically isotropic, result from a global action of the magnetically polarized milieu on each elementary magnetic moment. This orienting action was to be considered equal to that of a magnetic field *H*_{m}, called molecular field, proportional to the magnetization *(H*_{m}= *NI*). According to Weiss, in the presence of an external field H producing a magnetization I, each atomic moment would be subjected to the total field *H + H*_{m}; and the mean orientation of these moments, which creates the magnetization I, should be given by Langevin’s formula, if *H* is replaced by *H + H*_{m}= *H + NI*. The result is

(2)

This is the fundamental formula of ferromagnetism in the theory based on the hypothesis of the molecular field. It remains valid when the Langevin function *f* is replaced by functions arising from the application of quantum statistical mechanics to those moments *M* that can assume only quantized orientations with respect to this field.

The first consequence of Weiss’s formula is that when the temperature T is lower than a certain temperature Θ, a zero magnetization is unstable in the presence of a zero field. In such a case the result will be the appearance of a spontaneous magnetization I_{s} determined by the implicit relation

(3)

This spontaneous magnetization. equal to *I*_{o} at very low temperatures. at first decreases slowly as the temperature rises, then very rapidly, and finally disappears altogether at the instant that the temperature reaches the critical level of Θ = α μ *NI*_{0}/*k*(α being the slope. at the roigin. of the curve representing the function *f*: accordingly. it will be 1/3 for the Langevin faunction. or 1 for the quantum function *f*(a)=tha. relative to the magnetic moment associated with the electron spin ½).

The predicted spontaneous magnetization, however, generally is not apparent: most ferromagnetic metals have a zero magnetization in a zero field. The explanation must be that the variously oriented spontaneous magnetizations cancel each other in very small domains (known as Weiss domains, the existence of which was demonstrated much later). A very strong exterior field is required to render parallel the spontaneous magnetizations of such domains. Further, the saturated macroscopic magnetization at a given temperature differs very little from the spontaneous magnetization, so that the latter quantity can be determined from the former. When the temperature is higher than the temperature Θ, which is that of the Curie point, the spontaneous magnetization is zero. In this case the exterior field *H* induces a very small magnetization, which according to the general formula (2) assumes the value

(4)

The material under examination should then behave like a paramagnetic substance, with a magnetic susceptibility proportional to the reciprocal of the excess of the temperature over that of the Curie point. This relation, known as the Curie-weiss law, is very well established by experiment. It can even be applied to many more or less concentrated paramagnetic substances with very low Curie temperatures, which are often negative (negative molecular field).

Applying the principles of thermodynamics to ferromagnetic substances, Weiss showed in 1908 that the existence of the spontaneous magnetization should add to the ordinary specific heat a magnetic specific heat proportional to the derivative with respect to the temperature of the square of this spontaneous magnetization. This quantity, therefore, should be zero at absolute zero and increase with the temperature, at first slowly and then more and more quickly up to the Curie point, where it should suddenly vanish. Measurements made on nickel gave quantitative confirmation of this prediction and highlighted, in particular, the discontinuity of the specific heat at the Curie point. In 1918 Weiss also discovered the magnetocaloric effects and showed how thermodynamics can be used to calculate the temperature variation of a magnetic substance placed in a field the intensity of which is altered adiabatically.

The absolute saturation *I*_{o} of the magnetization, deduced from the limit toward which the experimental saturation tends at very low temperatures, yields in a very direct manner the value of the atomic moments μ. Measurements on iron and nickel gave values for their atomic moments the ratio of which was almost exactly that of the whole numbers five and three. This finding led Weiss to postulate in 1911 that the moments of the various magnetic atoms are whole multiples of an elementary moment that he called the magneton. Many other measurements of other ferromagnetic substances–and, through the intermediary of Langevin’s theory, of paramagnetic substances–seemed to verify this hypothesis. Several of his contemporaries immediately suggested that his result might well be explained as a quantum effect due to a restriction on the orbital energy of electrons. But Weiss’s experimental magneton was found to be approximately equal to one-fifth of the Bohr magneton, which was deduced several years later from the quantification of the electron orbits. Subsequent research in quantum mechanics, however, has provided no grounds for thinking that all atomic moments are whole multiples of the Bohr magneton or of one-fifth of this quantity. It appears that the integral values found by Weiss arose, in general, from an insufficiently founded interpretation of indirect and difficult measurements.

## BIBLIOGRAPHY

Weiss’s major book is *Le magnétisme* (Paris, 1926), written with G. Foëx.

His earlier articles include “Recherches sur I’aimantation de la magnetite cristallisee et de quelques alliages de fer et d’antimoine,” in *Ėclairage électrique*, **7** (1896), 487–508, and **8** (1896), 56–68, 105–110, 248–254, his dissertation: “Aimantation de la magnétite cristalliseée,” in *Journal de physique*, 3rd ser., **5** (1896), 435–453: “Un nouvel électro-aimant de laboratoire donnant un champ de 30.000 unités,” in Éclairage électique, **15** (188), 481–487: “Sur I’aimantation plane de la pyrrhotine,” in *Journal de Physique*, 3rd sec., **8** (189), 542–544; “Un nouveau système d’ampèremètres et de voltemètres indépendants de leur aimant permanent,” in *Comptes rendus…de I’ Académie des sciences*, **132** (1901), 957; “Un nouveau fréquence-mètre,” in *Archives des sciences physiques et naturelles,*, **18** (1904), 241; “Le travaid d’aimantation des cristaux,” in *journal de physique*, 4th ser., **3** (1904). 194–202: “Propriétés magnétiques de la pyrrhotine,” *ibid*., **4** (1905), 469–508, 829–846; “Variation thermique de I’aimantation de la pyrrhotine,” *ibid.,* 847–873, written with J. Kunz: “La variation du ferromagnétisme avec la température,” in *Comptes rendus …de I’Académie des sciences*, **143** (1906), 1136; and sur la théorie des propriétés magnétiques du fer au delà du point de transformation,” *ibid.,***144** (1906), 25.

Additional articles ar “L’hypothése du champ moléculaire et la propriété ferrmagnétique,” in *Journal de physique*, 4th ser., **6** (1907), 661–690; “Sur la biréfringence des liquides organiques,” in *Comptes rendus…de I’Académie des sciences*. **145** (1907), 870, written with A. Cotton and H. Mouton: “L’intensité d’aimantation à satutation du fer et du nickel,” *ibid.,* 1155: “Électo-aimant de grande puissance,” in *Journal de physique*, 4th ser., **6** (1907), 353–368: “Mesure du phenomene de Zeeman pour les trois raies bleues du Zinu,” *ibid.,* 429–445, written with A. Cotton: “Hystéreèse dans les champs tournants,” *ibid.,* 4th ser., **7** (1908), 5–27, written with V. Planer; “Chaleur speécifique et champ moleculaire des substances ferromagnétiques,” *ibid*., 249–264, written with P. N. Beck; “Sur le rapport de la charge à la masse des électrons,” in *comptes rendus…de I’Académie des sciences*, **147** (1908), 968, written with A. Cotton: “Measure de I’ intensité d’aimantaiton à saturation en valeur absole,” in *Journal de physique*, 4the ser., **9** (110), 373–397; and “Recherches sur I’aimantation aux très basses températures,” *ibid.,* 555–584, written with H. Kamerlingh Onnes.

Also see “Sur I’aimantation du nickel, du cobalt et des alliages nicjel-cobalt,” in *Comptes rendus…de I’Académie des sciences*, **153** (1911). 941, written with O. Bloch; “Étude de I’aimantation des corps ferromangnétiques au-dessus du point de Curie,” , in *Journal de physique*, 5th ser., **1** (111), 274–287, 744–753, 805–814, written with G. Foëx: “Sur la rationalité des rapports des moments magnetiques moléculares et le magnéton,” *ibid.,* 900–912, 965–988: “Sur I’aimantation de I’eau et de I’oxygène,” in *Comptes rendus…de I’Académie des sciences*, **155** (1912), 1234, written with A. Piccard; “Magnetic Properties of Alloys,” in *Transactions of the Faraday Society,***8** (1912), 149–156: “L’aimantation des cristaux et le champ moléculaire,” in *Comptes rendus…de l’Académie des sciences*, **156** (1913), 1836-1837: “Sur les champs magnétiques obtenus avec un électro-aimant muni de pièces polaires en ferrocobalt.” *ibid.*, 1970-1972: “Le spectrographe à prismes de I’École polytechnique de Zurich,” in *Archives des sceinces physiques et naturelles*, **35** (113), 5, written with R. Fortrat: and “Sur la nature du champ moléculaire,” in *Annales de physique*, 9th ser., **1** (1914), 134–162.

Weiss’s later papers include “Ferromagnétisme et équation des fluides,” in *Journal de physique*, 5th ser., **7** (1917), 129–144; “Calorimétrie des substances ferromagnétiques,” in *Archives des sciences physiques et naturelles*, **42** (1917), 378, and **43** (1917), 22, 113, 199, written with A. Piccard and A. Carrard; “Le phenonmene magnétocalorique,” in *Journal de physique*, 5th ser., **7** (1917), 103–109. written with A. Piccard: “Sur un nouveau phénomène magnétocalorique,” in *Comptes rendus …de I’Académie des science*. **166** (1918), 352, written with A. Piccard: “sur les coefficients d’aimantation de I’oxygène, de I’oxyde azotique et la Théorie du magnéton,” in *Comptes rendus…de I’Académie des sciences*. **167** (1918), 484–487, written with E. Bauer and A. Piccard: “Sur le moment atomique de I’oxygène,” in *journal de physique*, 6th ser., **4** (1923), 153–157; “Les moments atomiques,” *ibid.,***5** (1924), 129–152: “Aimantation et phénomène magnétocalorique du nickel,” in *Annales de physique*. 10th ser., **5** (1926), 153–213: “Sur les moments atomiques,” in *Comptes rendus…de I’Acdémie des sciences*, **187** (1928), 744, written with G. Foëx: “La saturation absolue des ferromagnétiques et les lois d’approche en fonction du champ et de la température,” in *Annales de physique*, 10th ser., **12** (1929), 279–374, written with R. Forrer: and “La constante du champ moléculaire. Équation d’état magnétique et calorimétrique,” in *Journal de physique*, 7th ser., **1** (1930), 163–175.

Some of his papers appeared in works issued by the Solvay Council: “Les actions mutuelles des molécules aimantées,” in *Atomes et électrons* (Paris, 1923), 158–163; “Équation d’état des ferromagnétiques,” in *Le magnétisme*(Paris,1932), 281–323; “L’anomalie de volume des ferromagnétiques,” *ibid.*, 325–345; and “Les phenomenes gyromagnétiques,” *ibid,*, 347–379.

On his life and work, see Albert Perrier, “In memoriam (Pierre Weiss),” in *Actes de la Société helvétique des sciences naturelles*, **121** (1941), 422–433, with bibliography; and G. Foex, “L’oeuvre scientifique de pierre Weiss,” in *Annales de physique*. 11th ser., **20** (1945), 111–130.

Francis Perrin

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**Weiss, Pierre**