Neel temperature and reentrant H-T phase diagram of quasi-2D frustrated magnets

In quasi-2D quantum magnets the ratio of Neel temperature $T_text N$ to Curie-Weiss temperature $Theta_text{CW}$ is frequently used as an empirical criterion to judge the strength of frustration. In this work we investigate how these quantities are related in the canonical quasi-2D frustrated square or triangular $J_1$-$J_2$ model. Using the self-consistent Tyablikov approach for calculating $T_text N$ we show their dependence on the frustration control parameter $J_2/J_1$ in the whole Neel and columnar antiferromagnetic phase region. We also discuss approximate analytical results. In addition the field dependence of $T_text N(H)$ and the associated possible reentrance behavior of the ordered moment due to quantum fluctuations is investigated. These results are directly applicable to a class of quasi-2D oxovanadate antiferromagnets. We give clear criteria to judge under which conditions the empirical frustration ratio $f=Theta_text{CW}/T_text N$ may be used as measure of frustration strength in the quasi-2D quantum magnets.

Frustrated two dimensional quantum magnets

We overview physical effects of exchange frustration and quantum spin fluctuations in (quasi-) two dimensional (2D) quantum magnets ($S=1/2$) with square, rectangular and triangular structure. Our discussion is based on the $J_1$-$J_2$ type frustrated exchange model and its generalizations. These models are closely related and allow to tune between different phases, magnetically ordered as well as more exotic nonmagnetic quantum phases by changing only one or two control parameters. We survey ground state properties like magnetization, saturation fields, ordered moment and structure factor in the full phase diagram as obtained from numerical exact diagonalization computations and analytical linear spin wave theory. We also review finite temperature properties like susceptibility, specific heat and magnetocaloric effect using the finite temperature Lanczos method. This method is powerful to determine the exchange parameters and g-factors from experimental results. We focus mostly on the observable physical frustration effects in magnetic phases where plenty of quasi-2D material examples exist to identify the influence of quantum fluctuations on magnetism.

Momentum space imaging of the FFLO state

In a magnetic field superconductors (SC) with small orbital effect exhibit the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase above the Pauli limiting field. It is characterized by Cooper pairs with finite center of mass momentum and is stabilized by the gain in Zeeman energy of depaired electrons in the imbalanced Fermi gas. The ground state is a coherent superposition of paired and depaired states. This concept, although central to the FFLO state lacks a direct experimental confirmation. We propose that STM quasiparticle interference (QPI) can give a direct momentum space image of the depaired states in the FFLO wave function. For a proof of principle we investigate a 2D single orbital tight binding model with a SC s-wave order parameter. Using the equilibrium values of pair momentum and SC gap we calculate the spectral function of quasiparticles and associated QPI spectrum as function of magnetic field. We show that the characteristic depaired Fermi surface parts appear as a fingerprint in the QPI spectrum of the FFLO phase and we demonstrate its evolution with field strength. Its observation in STM experiments would constitute a direct proof for FFLO ground state wave function.

Thermodynamics of anisotropic triangular magnets with ferro- and antiferromagnetic exchange

We investigate thermodynamic properties like specific heat $c_{V}$ and susceptibility $chi$ in anisotropic $J_1$-$J_2$ triangular quantum spin systems ($S=1/2$). As a universal tool we apply the finite temperature Lanczos method (FTLM) based on exact diagonalization of finite clusters with periodic boundary conditions. We use clusters up to $N=28$ sites where the thermodynamic limit behavior is already stably reproduced. As a reference we also present the full diagonalization of a small eight-site cluster. After introducing model and method we discuss our main results on $c_V(T)$ and $chi(T)$. We show the variation of peak position and peak height of these quantities as function of control parameter $J_2/J_1$. We demonstrate that maximum peak positions and heights in Neel phase and spiral phases are strongly asymmetric, much more than in the square lattice $J_1$-$J_2$ model. Our results also suggest a tendency to a second side maximum or shoulder formation at lower temperature for certain ranges of the control parameter. We finally explicitly determine the exchange model of the prominent triangular magnets Cs$_2$CuCl$_4$ and Cs$_{2}$CuBr$_{4}$ from our FTLM results.

Triplet Cooper Pair Formation by Anomalous Spin Fluctuations in Non-centrosymmetric Superconductors

A microscopic theory for the spin triplet Cooper pairing in non-centrosymmetric superconductors like CePt_3Si and CeTSi_3 (T=Rh, Ir) is presented. The lack of inversion symmetry leads to new anomalous spin fluctuations which stabilize the triplet part in addition to the singlet part originating from the centrosymmetric spin fluctuations. It is shown that both parts have similar nontrivial momentum dependence of A_1 type. Therefore the mixed singlet-triplet gap function has accidental line nodes on both Fermi surface sheets which are stable as function of temperature. This gap function explains the salient features of CePt_3Si and CeTSi_3 superconductors.

Local density of states in disordered graphene

We study two lattice models, the honeycomb lattice (HCL) and a special square lattice (SQL), both reducing to the Dirac equation in the continuum limit. In the presence of disorder (gaussian potential disorder and random vector potential), we investigate the behaviour of the density of states (DOS) numerically and analytically. While an upper bound can be derived for the DOS on the SQL at the Dirac point, which is also confirmed by numerical calculations, no such upper limit exists for the HCL in the presence of random vector potential. A careful investigation of the lowest eigenvalues indeed indicate, that the DOS can possibly be divergent at the Dirac point on the HCL. In spite of sharing a common continuum limit, these lattice models exhibit different behaviour.

Theory of induced quadrupolar order in tetragonal YbRu_{2}Ge_{2}

The tetragonal compound YbRu$_{2}$Ge$_{2}$ exhibits a non-magnetic transition at $T_0$=10.2K and a magnetic transition at $T_1$=6.5K in zero magnetic field. We present a model for this material based on a quasi-quartet of Yb$^{3+}$ crystalline electric field (CEF) states and discuss its mean field solution. Taking into account the broadening of the specific heat jump at $T_0$ for magnetic field perpendicular to [001] and the decrease of $T_0$ with magnetic field parallel to [001], it is shown that ferro-quadrupole order of either O$_{2}^{2}$ or O$_{rm xy}$ - type are prime candidates for the non-magnetic transition. Considering the matrix element of these quadrupole moments, we show that the lower CEF states of the level scheme consist of a $Gamma_{6}$ and a $Gamma_{7}$ doublet. This leads to induced type of O$_{2}^{2}$ and O$_{rm xy}$ quadrupolar order parameters. The quadrupolar order introduces exchange anisotropy for planar magnetic moments. This causes a spin flop transition at low fields perpendicular [001] which explains the observed metamagnetism. We also obtain a good explanation for the temperature dependence of magnetic susceptibility and specific heat for fields both parallel and perpendicular to the [001] direction.

Reentrant Kondo effect in Landau quantized graphene

We have studied the interplay of an Anderson impurity in Landau quantized graphene, with special emphasis on the influence of the chemical potential. Within the slave-boson mean-field theory, we found reentrant Kondo behaviour by varying the chemical potential or gate voltage. Between Landau levels, the density of states is suppressed, and by changing the graphenes Fermi energy, we cross from metallic to semiconducting regions. Hence, the corresponding Kondo behaviour is also influenced. The f-level spectral function reveals both the presence of Landau levels in the conduction band and the Kondo resonance.