Physics. — "Magnetic properties of cubic lattices." ]iy Prof. L. S. 

 Ornstein and Dr. F. Zkrnike. (Commiiiicated bj Piof. H. A. 



LORENTZ.) 



(^Communicated in the meeting of September 29, 1918). 



The well-known model of Ewing has been treated more in detail 

 by different scientists. A few have (aken the very nnsatisfactory 

 standpoint, that elementary magnets are distribnted al random in 

 space'). More in accordance with reality is the supposition, from 

 which W. Peddik "), and later on also Honda and Okuba ') have 

 started, that the magnetic particles are arranged in a cubic lattice. 

 The reasonings however show two important fallacies. 



In the first place they neglected the demagnetising force in a sphere; 

 accordingly they think that dipoles cannot yield a result, which 

 made Ihem unnecessarily consider magnets of finite length. In (he 

 second place they considered only those rotations at the research of 

 stability, in which the magnetic axes of all particles ai-e moved 

 in mutual parallelism. 



As will be shown hereafter, the consequence of this unfounded 

 limitation in the freedom of motion of the particles is that the 

 stability becomes much greater than is in reality the case. 



If we sweep this limitation, we find that the arrangement of 

 magnedc atoms in a cubic lattice is unstable without exterior field. 

 A body of such a structure, can therefore possess no coërcitive 

 force. 



§ 1. We consider a cubic lattice with edge d. In the corners of 

 the lattices we imagine dipoles possessing the sdengdi p, and which 

 can rotate freel}'. Be those dipoles directed all parallel (o an edge 

 of the lattice by a strong ex(erior field H. Now we put the question 

 how far the exterior of the field must be weakened (o reach the 

 limit of stability. If the system without exterior field is stable the 

 intensity H>, at which this is the case, will be negative. 



The magnetic properties of the la((ice considered will consequently 



1) Gans u. Hertz, Zeitsch. fur Matlieraatik und Physik. 

 ') Edinburgh Proc. 195 and 7. 

 5) Phys. Review, X, 1917, p. 705. 



59* 



