© Kuznetsov Y. N

Contact to the author: kun3461@yandex.ru

Spin ice are called crystals (for example – titanate disprosium), in which ordered configuration of spins is formed at temperature close to absolute zero. Vectors of spins in junction points are arranged in the form of cross-shaped combination from two pairs. In one pair vectors are directed towards center, in other – from center.

And magnetic moments, concomitant to spins, are oriented similarly (Fig.1). Their overlapping rotor magnetic fields with closed lines of force are mutually compensated up to total stress, close to zero. One pair of magnetic moments comes out of cross-shaped combination in some junction points under action of thermal motion. Then remaining pair (Fig.2) approves itself as source of potential magnetic field (PMF) with open lines of force [1, 2, 3].

There are a number of explanations to observed effect in spin ice. In subsequent statement transition from rotor property of magnetic field to potential one will be considered from the point of view of realization in the nature of two types of vector cause.

According to facts, the cause may be both unidirectional, described by vector (first-rank tensor with uniaxial rotary symmetry), and central-symmetric, described by scalar (null tensor with biaxial rotary symmetry).

Characteristic feature of central-symmetric configuration of causal vectors is null-vector result of their geometrical summing-up. Mathematics and physics integrated in vectors are complied with different rules. Null-vector result is correct from mathematical point of view. Physical interpretation of casual vectors is subjected to principles of conservation.

Let us give examples. In the first example (Fig. 3) mechanical force effecting unidirectionally on the body, enters by vector the second law of Newton. It effects in acceleration on the body, inertial property of which resists change of velocity. During transition to central-symmetric effect (Fig. 4), mechanical forces _squeeze (stretch) body. According to scalar Hook’s law, other its property of body resists to deformation – its elasticity.

ω_Н = ω_Н1 + ω_Н2 + ω_Н12 , (1)   ω_Н12 = 0, (2)     ω_Н = ω_Н1 + ω_{Н2 .} (3)

Since there are no axially-symmetrical currents of rotor magnetic field in common line, currents are not interacting magnetically between each other. Cross member is equal to zero at absence of potential energy of magnetic interaction (2). Hence, all magnetic energy of current fields (3) is retained. We have the following principle conclusion. Null-vector result of geometrical summing up of field vectors is indicative of only mutual compensation of property of rotor character of lines of force, but not lines of force proper. Potentially magnetic property, characterized by open condition of lines of force, is inevitably (and without alternative) manifested within preserving magnetic energy with common field. This theoretical conclusion is confirmed experimentally [4], [5].

Similar transition of magnetic properties is traced in spin ice.

Unidirectional vector source in the form of single magnetic moment with uniaxial symmetry (Fig.9) forms rotor magnetic field of similar symmetry.

Axially-symmetric pair of counter-directed magnetic moments (Fig.10) possesses bi-axial symmetry. As it follows from results of experiments, magnetic field formed by this pair possesses the same symmetry. Therefore, one can speak of scalar magnetic pseudo-charge and its PMF.

Pseudo-charge, vectors of magnetic moment of which are directed outside is supposed to consider a positive factor.

Vector potential of magnetic field is decisive in Schrodinger equation for wave function of charged particle, moving in rotor magnetic field. Substitution of scalar magnetic potential (|A|) in quantum-mechanical equation instead of null-vector result (∑A=0), received during geometrical summing up of vector potentials, theoretically corresponds to detection of longitudinal magnetic force.

Let us consider concrete examples of null-vector field situations in macrocosm, formed in space near countercurrents in twin wire.

First, let us make ordinary coil from twin wire (Photo1, Fig.11). When connecting to source of stationary current, coaxial circular countercurrents are arranged one above another, which is equivalent to sequence of null-vector magnetic moments. Mutual repulsion is taking place inside twin wires and in areas of contact of wires between countercurrents (designated by different colors). Potential energy of interaction of currents is added to magnetic energy of current field. But total magnetic energy is primarily concentrated in inter-current region. There is practically no magnetic energy in null-vector region. Therefore, potential magnetic field can not be formed there. The experiment has confirmed this. Test tube with reference water was located inside winding with circular countercurrents. Ink testing (details in [5]) did not reveal change of water structure. It was simultaneously confirmed that stationary electric field of excessive charges does not exert appreciable effect on water structure. The same is observed in electric field Е ≈10 ⁴ В.

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