Grothendieck rings of o-minimal expansions of ordered abelian groups

We will calculate completely the Grothendieck rings, in the sense of first order logic, of o-minimal expansions of ordered abelian groups by introducing the notion of the bounded Euler characteristic.Comment: to appear J. Algebr

NMR evidence for the persistence of spin-superlattice above the 1/8 magnetization plateau in SrCu2(BO3)2

We present 11B NMR studies of the 2D frustrated dimer spin system SrCu2(BO3)2 in the field range 27-31 T covering the upper phase boundary of the 1/8 magnetization plateau, identified at 28.4 T. Our data provide a clear evidence that above 28.4 T the spin-superlattice of the 1/8 plateau is modified but does not melt even though the magnetization increases. Although this is precisely what is expected for a supersolid phase, the microscopic nature of this new phase is much more complex. We discuss the field-temperature phase diagram on the basis of our NMR data.Comment: 5 pages, 4 figures, published versio

Magnetic frustration in a stoichiometric spin-chain compound, Ca3_3CoIrO6_6

The temperature dependent ac and dc magnetization and heat capacity data of Ca$_3$CoIrO$_6$, a spin-chain compound crystallizing in a K$_4$CdCl$_6$-derived rhombohedral structure, show the features due to magnetic ordering of a frustrated-type below about 30 K, however without exhibiting the signatures of the so-called "partially disordered antiferromagnetic structure" encountered in the isostructural compounds, Ca$_3$Co$_2$O$_6$ and Ca$_3$CoRhO$_6$. This class of compounds thus provides a variety for probing the consequences of magnetic frustration due to topological reasons in stoichiometric spin-chain materials, presumably arising from subtle differences in the interchain and intrachain magnetic coupling strengths. This compound presents additional interesting situations in the sense that, ac susceptibility exhibits a large frequency dependence in the vicinity of 30 K uncharacteristic of conventional spin-glasses, with this frustrated magnetic state being robust to the application of external magnetic fields.Comment: Physical Review (Rapid Communications), in pres

Strong damping of phononic heat current by magnetic excitations in SrCu_2(BO_3)_2

Measurements of the thermal conductivity as a function of temperature and magnetic field in the 2D dimer spin system SrCu$_2$(BO$_3$)$_2$ are presented. In zero magnetic field the thermal conductivity along and perpendicular to the magnetic planes shows a pronounced double-peak structure as a function of temperature. The low-temperature maximum is drastically suppressed with increasing magnetic field. Our quantitative analysis reveals that the heat current is due to phonons and that the double-peak structure arises from pronounced resonant scattering of phonons by magnetic excitations.Comment: a bit more than 4 pages, 2 figures included; minor changes to improve the clarity of the presentatio

Collective Singlet Excitations and Evolution of Raman Spectral Weights in the 2D Spin Dimer Compound SrCu2(BO3)2

We present a Raman light scattering study of the two-dimensional quantum spin system SrCu2(BO3)2 and show that the magnetic excitation spectrum has a rich structure, including several well-defined bound state modes at low temperature, and a scattering continuum and quasielastic light scattering contributions at high temperature. The key to the understanding of the unique features of SrCu2(BO3)2 is the presence of strong interactions between well-localized triplet excitations in the network of orthogonal spin dimers realized in this compound. Based on our analysis of the Heisenberg model relevant for this material, we argue that the collective excitations involving two and three-particle singlet bound states have large binding energies and are observed as well-defined peaks in the Raman spectrum.Comment: 5 pages, 2 figures. Revised version, to appear in Phys. Rev. Lett. (2000

Heat transport in SrCu_2(BO_3)_2 and CuGeO_3

In the low dimensional spin systems $SrCu_2(BO_3)_2$ and $CuGeO_3$ the thermal conductivities along different crystal directions show pronounced double-peak structures and strongly depend on magnetic fields. For $SrCu_2(BO_3)_2$ the experimental data can be described by a purely phononic heat current and resonant scattering of phonons by magnetic excitations. A similar effect seems to be important in $CuGeO_3$, too but, in addition, a magnetic contribution to the heat transport may be present.Comment: 4 pages, 2 figures; appears in the proceedings of the SCES2001 (Physica B

Long range magnetic ordering in a spin-chain compound, Ca3_3CuMnO6_6, with multiple bond distances

The results of ac and dc magnetization and heat capacity measurements as a function of temperature (T = 1.8 to 300 K) are reported for a quasi-one-dimensional compound, Ca$_3$CuMnO$_6$, crystallizing in a triclinically distorted K$_4$CdCl$_6$-type structure. The results reveal that this compound undergoes antiferromagnetic ordering close to 5.5 K. In addition, there is another magnetic transition below 3.6 K. Existence of two long-range magnetic transitions is uncommon among quasi-one-dimensional systems. It is interesting to note that both the magnetic transitions are of long-range type, instead of spin-glass type, in spite of the fact that the Cu-O and Mn-O bond distances are multiplied due to this crystallographic distortion. In view of this, this compound could serve as a nice example for studying "order-in-disorder" phenomena.Comment: Physical Review (in press