Session K23: Quantum Magnets: BEC and 2D

Thermodynamic and Magnetostriction Measuremetns of the Bose-Einstein Condensate NiCl$_{2}$-4SC(NH$_{2})_{2}$

We investigate Bose-Einstein condensation (BEC) of magnons in the organic magnet NiCl$_{2}$-4SC(NH$_{2})_{2}$ (DTN). For magnetic fields applied along the tetragonal c-axis, the antiferromagnetically (AFM) ordered Ni spins can be recharacterized as a system of effective bosons with a hard-core repulsive interaction where the AFM transition corresponds to BEC. New, detailed data of the field-temperature phase diagram of DTN have been taken by means of thermodynamic measurements to dilution fridge temperatures. The magnetic field-temperature quantum phase transition line H$_{c}$-H$_{c1} \quad \sim $ T$^{\alpha }$ approaches a power law at low temperatures, with an exponent $\alpha $ at the quantum critical point that is consistent with the BEC theory prediction of $\alpha $ = 3/2. In addition, new magnetostriction data at dilution refrigerator temperatures will be presented. In the AFM ordering regime, field-induced 2$^{nd}$ order changes in the lattice parameters create field-dependent AFM and spin-orbit coupling parameters, which can in turn distort the phase diagram at high fields.   

High Magnetic Field Susceptibility Measurements for BaCuSi$_2$O$_6$

We have measured the change in magnetic susceptibility of the spin gap system BaCuSi$_2$O$_6$ at high magnetic fields (33T) utilizing the change in the resonant frequency of a tunnel diode oscillator (TDO). At temperatures below T$\sim$3K, measurements reveal the presence of a critical field H$_{c1}$, characterized by a jump in magnetic susceptibility. The evolution of H$_{c1}$ with temperature is in good agreement with the previous magnetization and specific heat measurements and with the theoretical predictions for the realization of Bose-Einstein condensate by the spin system of Cu$^{2+}$ dimers. This technique provides the opportunity for future investigation of this material at high pressures.   

Dimensional reduction at the BEC quantum critical point in BaCuSi$_{2}$O$_{6}$.

We present results on the magnetic spin dimer system BaCuSi$_{2}$O$_{6}$, which can be tuned across a Bose-Einstein condensation (BEC) quantum critical point (QCP) to an ordered BEC of spins by applying an external magnetic field. Experimental results reveal a continuous crossover in critical scaling behaviour near the QCP from 3d to 2d BEC universality, indicating that dimensionality itself is an emergent property at the QCP of this particle density-tuneable BEC. Geometrical frustration leading to inter-layer decoupling is identified as the mechanism responsible for this unique manifestation of a lower dimensional QCP in the 3d BaCuSi$_{2}$O$_{6}$ spin system. While the theoretical concept of dimensional reduction has been extensively discussed in many different contexts as a route to low dimensionality in bulk materials, this is the first experimental realisation of dimensionally reduced criticality.   

Field-Induced Quantum Criticality in a Two-Dimensional Antiferromagnet

We describe neutron scattering measurements on the two-dimensional spin gap antiferromagnet piperanzium hexachlorodicuprate (PHCC) in the vicinity of quantum critical point at which the spin gap is closed by an applied magnetic field. We measure the energy and damping of the propagating $S_z=1$ mode above the spin gap; both quantities become strongly temperature dependent at the critical field. The temperature dependence of the mode energy is successfully described by a self-consistent Hartree-Fock theory of interacting spin excitations.   

Magnon decay in gapped quantum spin systems

In the O(3) $\sigma$-model description of gapped spin systems, $S=1$ magnons can only decay into {\em three\/} lower energy magnons. We argue that the symmetry of the quantum spin Hamiltonian often allows decay into {\em two\/} magnons, and compute this decay rate in model systems. For a realistic model describing two-dimensional spin dimer material $\rm (C_{4}H_{12}N_{2})Cu_{2}Cl_{6}$ (known as PHCC), we compare our results for the momentum-dependent magnon linewidth with recent measurements by Stone {\em et al.} (e-print cond-mat/0511266) and extract new information on the exchange coupling pattern in this material. For $S=1$ Haldane chains, we show that two-magnon decay is allowed in the full lattice description, even though it cannot be induced by any allowed term written in powers and gradients of the $\sigma$-model field. We present estimates for the behavior of the magnon linewidth in Haldane gap chains and discuss relation to the recent experimental work.   

Impurity induced Knight shifts in 2D antiferromagnets

The local response to a uniform field around vacancies in the two-dimensional (2D) spin-1/2 Heisenberg antiferromagnet is determined by numerical quantum Monte Carlo simulations as a function of temperature. It is possible to separate the Knight shifts into uniform and staggered contributions on the lattice which are analyzed and understood in detail. The contributions show interesting long and short range behavior that may be of relevance in NMR and susceptibility measurements. For more than one impurity remarkable non-linear enhancement and cancellation effects take place. We predict that the Curie impurity susceptibility will be observable for a random impurity concentration even in the thermodynamic limit.   

Variational ground states of 2D antiferromagnets in the valence-bond basis

We use a variational method to study two-dimensional \(S=\frac {1}{2} \) Heisenberg antiferromagnets in the valence bond basis. The wave function is of the form \[ \mid \psi \rangle =\prod h(x_{ij},y_{ij})(i,j),\] where \((i,j)\) represents a singlet formed by the spins at sites $i$ and $j$; \[ (i,j)=\frac{1}{\sqrt{2}}(\uparrow_i \downarrow_j - \downarrow_i\uparrow_j), \] and \(h(x_{ij},y_{ij}) \) is the amplitude corresponding to a bond coneenting two spins with seperation \( (x_{ij},y_{ij}) \). The form \( h \sim \frac{1}{r^p} \), where $r$ is the distance, was studied prevously. The best variational energy was obtained for $p = 4$. Now we optimize all \(h(x,y)\)by combining a standard Newton method and a conjugate gradient method. For systems with up to $16\times 16$ spins, the energy of the optimized wave function deviates by less than 0.1\% from the exact ground state energy. The spin-spin correlations are also very well reproduced. The exponent $p=3$ in agreement with recent Monte Carlo simulations. We also investigates this class of wave functions for a quantum-critical bilayer model.   

Dynamics of $S=1/2$ Antiferromagnetic clusters

A site diluted 2-d Quantum Heisenberg Antiferromagnet undergoes a Neel to disordered phase transition at the classical percolation density $p^{*}$, since the sublattice magnetization $m$ has a nonvalishing value on the percolating cluster. Although this implies that some of the exponents of the transition are equal to those of classical percolation, exponents involving dynamics are non-classical. We investigate the quantum dynamics of diluted systems at the percolation point by Lanczos diagonalization, generating histograms of the singlet to triplet excitation gap $\Delta$ for clusters of different size $N$. We investigate the finite-size scaling of the average and typical $\Delta$, to determine the dynamic exponent $z$. In a clean d-dimensional system with Neel order, $\Delta$ scales as $1/L^z$ with $z=d$, which arises from the quantum rotor states when the rotational symmetry has not been broken. As a direct generalization, it has been proposed that $z=D_{\rm f}$ holds for the percolating clusters, where $D_{\rm f}$ is the fractal dimensionality; $D_{\rm f} = 91/48$. This has not been confirmed numerically, however, and there remains the possibility that there could be other excitations of the clusters leading to $z > D_{\rm f}$. In addition to the Lanczos calculations, we also investigate the the distribution of the stagged susceptibility $\chi(\pi,\pi)$ and the stagged structure factor $S(\pi,\pi)$, which give information on the quantum dynamics through sum rules.   

Variational Study of the Two-dimensional Hubbard Model at half-filling

The ground-state properties of the half-filled two-dimensional Hubbard model is systematically investigated by the variational wave function with d-wave supercondcting and anti-ferromagnetic correlations. The enhanced pairing correlation observed in the previous Gutzwiller approximation is found to be strongly suppressed by the doublon-holon and anti-ferromagnetic correlations. In order to check this result, power-Lanczos method is employed to improve the variational wave function. It is found that that pairing is not stable against anti-ferromagnetic long-range order. Possible models for the theory Gossamer superconductivity will be discussed in this paper.   

Investigations of the 2D Isinglike magnet, $ZnMn_2O_4$

$ZnMn_2O_4$ crystallizes at high temperatures in the spinel structure. At lower temperatures, it undergoes a Jahn Teller distortion which lowers its symmetry to tetragonal. At lower temperatures ($T_N \sim 60 $K), the system orders magnetically. Fits to the order parameter, line shape of powder diffraction peaks, and the direct observation of rods of scattering in single crystal diffraction experiments show the system to be two dimensional. This is likely due to an interplay of orbital ordering and frustration. In this talk, I present the results of recent neutron diffraction experiments performed on this compound and discuss the nature of the magnetism.   

Novel magnetic structure of one monolayer Fe on Ir(111)

Due to the interplay between symmetry, nearest-neighbor spacing, and hybridization with the substrate surprising magnetic ground-states can occur for monolayer films such as the two-dimensional antiferromagnetism of Fe on W(001) [1]. Much more complex magnetic structures have been predicted for monolayer thick films of an antiferromagnet on a triangular lattice given e.g. by an (111) fcc surface. To our knowledge, however, there is no experimental proof.\\ Here, we report a novel, nanometer scale magnetic structure for one monolayer Fe on Ir(111). Based on the observed contrast in spin-polarized scanning tunneling microscopy (SP-STM) measurements a giant magnetic unit cell consisting of 15 Fe atoms is suggested. Our first-principles calculations show that the proposed magnetic state is indeed more favorable than all possible magnetic solutions describable by the classical Heisenberg model including interactions between neighbors of arbitrary distance. We find that the $3d-5d$ hybridization between the Fe~ML and the Ir substrate plays a key role for the unusual magnetic behavior.\\ \protect{[1]} A.Kubetzka {\sl et al.}, Phys.\ Rev.\ Lett.\ {\bf 94}, 087204 (2005).   

Magnetic order and lattice anomalies in the J$_1$-J$_2$ model system VOMoO$_4$

High resolution x-ray and neutron powder diffraction measurements were performed on polycrystalline VOMoO$_4$. Below $\simeq 40$ K the system orders in a simple N\'eel antiferromagnetic state (propagation vector $\vec{k}=0$), indicating a dominant role of the nearest-neighbor interactions. The order is three dimensional but the reduced saturated magnetic moment $m$ of 0.41 (1) $\mu_B/V^{4+}$ at 2 K indicates strongly 2D character and enhanced quantum fluctuations. On cooling, there is no evidence of a reduction of the crystal symmetry. However, neutron diffraction indicates an anomalous evolution of the lattice parameters, which can be related to the onset of magnetic correlations.   

Field-induced thermal transport in low-dimensional antiferromagnets

Recent thermal transport experiments in a number of low-dimensional antiferromagnets such as K$_2$V$_3$O$_8$, Nd$_2$CuO$_4$, Pr$_2$CuO$_4$, TlCuCl$_3$ and others have shown that the low-temperature thermal conductivity can be strongly increased by a modest magnetic field. It was suggested that this effect could be due to the field-induced heat transport by spin excitations. We show that in most of the reported cases the observed enhancement of the thermal conductivity is not of spin, but of phononic nature. That is, the increase in the thermal conductivity occurs because of the decrease of the scattering of phonons on spin excitations. This decrease is due to the field-induced gaps in the spin-excitation spectra. Our calculations reproduce quantitatively all characteristic field-dependencies observed in experiments such as increase of the thermal conductivity and its saturation in higher fields. A number of suggestions for future experiments is made.   

Magnetic Properties of a Novel Fe(II) \textit{meso}-tetra(4-pyridyl)porphyrin Network

Magnetic properties of Fe(II) \textit{meso}-tetra(4-pyridyl)porphyrin [Fe(TpyP)], a newly discovered metalloporphyrin network, were investigated using magnetic susceptibility $M(T)$/$H$, isothermal magnetization $M(H)$, and heat capacity $C(T)$ measurements. The crystal structure of Fe(TpyP) at room temperature is orthorhombic with a space group \textit{Cmca} (No. 64). And this network gives rise to an unprecedented two-dimensional paddle-wheel-like pattern (a 4$^{4}$ topology). The results of $M(T)$/$H$ on powder samples of Fe(TpyP) show that the effective moment \textit{$\mu $}$_{eff}$ of Fe$^{2+}$ is 5.52 \textit{$\mu $}$_{B}$ at 340 K, close to the expected value for a high spin Fe$^{2+}$ ($S$ = 2) ion. \textit{$\mu $}$_{eff}$ increases to 5.90 \textit{$\mu $}$_{B}$ as $T$ decreases to the range of 170 K $< \quad T \quad <$ 220 K, and then decreases monotonically as $T$ decreases further. The behavior of \textit{$\mu $}$_{eff}$ in the high temperature region may be attributed to a positive Fe$^{2+}$-Fe$^{2+}$ coupling. The low field ($H \quad \le $ 4 kG) $M(T)$/$H$ data reveal an anomalous behavior of this compound in the low temperature region which seems spin-glass-like. A small hysteresis was observed in $M(H)$ measured at 2 K. No anomaly was seen in the $C(T)$ data from 1.6 to 25 K.   

Signatures of one-dimensional localization of magnetically quantized carriers in graphite: power-law hopping mechanism.

We present results of a transport study on highly oriented pyrolytic graphite (HOPG) in ultra-quantum limit magnetic fields (B$>$8T) applied along the c-axis (z direction). For temperatures in the range 2K$ [Preview Abstract]