For a class of frustrated spin lattices including the kagomé lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the kagomé lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.In frustrated quantum spin lattices the competition of quantum and frustration effects promises rich physics. A reliable description of such systems often constitutes a challenge for theory. A famous example is the kagomé lattice antiferromagnet. In spite of extensive studies during the last decade its ground state properties are not fully understood yet. Classically it has infinite continuous degeneracies. In the quantum case (s=1/2), the system is likely to be a spin liquid with a gap for magnetic excitations and a huge number of singlet states below the first triplet state (see [1,2,3] and references therein).In this Letter we will focus on the zero-temperature magnetic behavior of highly frustrated lattices, in particular for high magnetic fields. One aspect is given by the observation of nontrivial magnetic plateaus in frustrated two dimensional (2D) quantum antiferromagnets like SrCu 2 (BO 3 ) [4,5], which has stimulated theoretical interest (see e.g. [6]). Also the kagomé lattice has a plateau at one third (m = 1/3) of the saturation magnetization [7,8]. Since this plateau can be found also in the Ising model and in the classical Heisenberg model with additional thermal fluctuations [9] it can be considered to be of classical origin. However, the structure of the ground state in the classical model is highly non-trivial at m = 1/3 [10] and has not been clarified yet for the quantum model.Another aspect is given by unusual jumps seen in magnetization curves. Such jumps can arise for different reasons. One possibility is a first-order transition between different ground states like the spin flop transition in classical magnets or in strongly anisotropic quantum chains [11]. Here we discuss another possibility, namely a macroscopically large degeneracy in the exact ground states of the full quantum system for a certain value of the applied field. We argue that this is a general phenomenon in highly frustrated systems. This is remarkable in so far as one can exactly write down ground states at a finite density of magnons in a strongly correlated system which is neither integrable, nor has any apparent non-trivial conservation laws. Such jumps represent a genuine macroscopic quantum effect which is also of possible experimental relevance since it occurs in many wellknown models like the kagomé lattice. This jump occurs just below saturation and should be observable in...

For many spin systems with constant isotropic antiferromagnetic nextneighbour Heisenberg coupling the minimal energies E min (S) form a rotational band, i. e. depend approximately quadratically on the total spin quantum number S, a property which is also known as Landé interval rule. However, we find that for certain coupling topologies, including recently synthesised icosidodecahedral structures this rule is violated for high total spins. Instead the minimal energies are a linear function of total spin. This anomaly results in a corresponding jump of the magnetisation curve which otherwise would be a regular staircase.

For a class of frustrated spin lattices including e.g. the 1D sawtooth chain, the 2D kagomé and checkerboard, as well as the 3D pyrochlore lattices we construct exact product eigenstates consisting of several independent, localized one-magnon states in a ferromagnetic background. Important geometrical elements of the relevant lattices are triangles being attached to polygons or lines. Then the magnons can be trapped on these polygons/lines. If the concentration of localized magnons is small they can be distributed randomly over the lattice. Increasing the number of localized magnons their distribution over the lattice becomes more and more regular and finally the magnons condensate in a crystal-like state.The physical relevance of these eigenstates emerges in high magnetic fields where they become groundstates of the system. As a result a macroscopic magnetization jump appears in the zero-temperature magnetization curve just below the saturation field. The height of the jump decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

We present the high-temperature expansion (HTE) up to 10th order of the specific heat C and the uniform susceptibility χ for Heisenberg models with arbitrary exchange patterns and arbitrary spin quantum number s. We encode the algorithm in a C++ program which allows to get explicitly the HTE series for concrete Heisenberg models. We apply our algorithm to pyrochlore ferromagnets and kagome antiferromagnets using several Padé approximants for the HTE series. For the pyrochlore ferromagnet we use the HTE data for χ to estimate the Curie temperature Tc as a function of the spin quantum number s. We find that Tc is smaller than that for the simple cubic lattice, although both lattices have the same coordination number. For the kagome antiferromagnet the influence of the spin quantum number s on the susceptibility as a function of renormalized temperature T /s(s + 1) is rather weak for temperatures down to T /s(s + 1) ∼ 0.3. On the other hand, the specific heat as a function of T /s(s + 1) noticeably depends on s. The characteristic maximum in C(T ) is monotonously shifted to lower values of T /s(s + 1) when increasing s.

The observation of hysteresis effects in single molecule magnets like Mn12-acetate has initiated ideas of future applications in storage technology. The appearance of a hysteresis loop in such compounds is an outcome of their magnetic anisotropy. In this Letter we report that magnetic hysteresis occurs in a spin system without any anisotropy, specifically, where spins mounted on the vertices of an icosahedron are coupled by antiferromagnetic isotropic nearest-neighbor Heisenberg interaction giving rise to geometric frustration. At T = 0 this system undergoes a first order metamagnetic phase transition at a critical field Bc between two distinct families of ground state configurations. The metastable phase of the system is characterized by a temperature and field dependent survival probability distribution.