Classification of small (0,1)(0,1) matrices

Denote by $A_n$ the set of square $(0,1)$ matrices of order $n$. The set $A_n$, $n\le8$, is partitioned into row/column permutation equivalence classes enabling derivation of various facts by simple counting. For example, the number of regular $(0,1)$ matrices of order 8 is 10160459763342013440. Let $D_n$, $S_n$ denote the set of absolute determinant values and Smith normal forms of matrices from $A_n$. Denote by $a_n$ the smallest integer not in $D_n$. The sets $\mathcal{D}_9$ and $\mathcal{S}_9$ are obtained; especially, $a_9=103$. The lower bounds for $a_n$, $10\le n\le 19$, (exceeding the known lower bound $a_n\ge 2f_{n-1}$, where $f_n$ is $n$th Fibonacci number) are obtained. Row/permutation equivalence classes of $A_n$ correspond to bipartite graphs with $n$ black and $n$ white vertices, and so the other applications of the classification are possible.Comment: 45 pages. submitted to LA

Low temperature magnetic transition in RuSr2EuCeCu2O10 ruthenocuprate

A new magnetic transition in the ruthenocuprate parent compound RuSr2EuCeCu2O10 has been observed below 10 K. It shows up only as a kink in the imaginary part of the ac susceptibility and exhibits a pronounced frequency dependence. At the same time, the real part of the ac susceptibility and the dc magnetization study show very little change in the same temperature window suggesting only a minor fraction of the material to be involved in the transition. Frequency dependence shows excellent agreement with the predictions of the Arrhenius law known to describe well the dynamics of the superparamagnetic particles. The same type of the investigation on the RuSr2Eu1.1Ce0.9Cu2O10 composition showed no evidence of the similar transition, which points to a possible intrinsic behavior.Comment: to be published in Physica

Two component butterfly hysteresis in Ru1222 ruthenocuprate

We report detailed studies of the ac susceptibility butterfly hysteresis on the Ru1222 ruthenocuprate compounds. Two separate contributions to these hysteresis have been identified and studied. One contribution is ferromagnetic-like and is characterized by the coercive field maximum. Another contribution, represented by the so called inverted maximum, is related to the unusual inverted loops, unique feature of Ru1222 butterfly hysteresis. The different nature of the two identified magnetic contributions is proved by the different temperature dependences involved. By lowering the temperature the inverted peak gradually disappears while the coercive field slowly raises. If the maximum dc field for the hysteresis is increased, the size of the inverted part of the butterfly hysteresis monotonously grows while the position of the peak saturates. In reaching saturation exponential field dependence has been demonstrated to take place. At T = 78 K the saturation field is 42 Oe.Comment: 5 pages, 5 figure