Session N15: Focus Session: Frustration in 1D and Spinels

Block versus Stripy Antiferromagnetism in the Fe-Based Spin-Ladder Materials (Ba,K)Fe$_2$Se$_3$

We present a theoretical study of the novel magnetism in the insulating two-leg spin-ladder material Ba$_{1-x}$K$_x$Fe$_2$Se$_3$, which exhibits a spontaneous formation of block and stripy antiferromagnetic spin orders in the Ba and K end members, respectively, and spin glass behavior in between. The bare spin susceptibility calculated with the first-principles electronic structure is found to remain qualitatively unchanged upon hole doping (substitution of K for Ba), ruling out the simple scenario of Fermi surface nesting. We show that these doping-dependent spin orders can be explained by use of a model of coexisting itinerant and localized electronic states on the Fe atoms, which are coupled by Hund's rule coupling. Our results reveal a strong spin frustration coming from the competing antiferromagnetic superexchange and ferromagnetic double-exchange interactions in this system, and unify its magnetism with that of the iron-based superconductors [1,2]. Work supported by DOE DE-AC02-98CH10886. [1] W.-G. Yin, C.-C. Lee, and W. Ku, Phys. Rev. Lett. \textbf{105}, 107004 (2010). [2] W.-G. Yin, C.-H. Lin, and W. Ku, Phys. Rev. B \textbf{86}, 081106(R) (2012).   

Optical Reflection Study of Low-Dimensional Quantum Magnets

We performed a linear optical reflection analysis of a low-dimensional, frustrated quantum magnet. Strongly-correlated low-dimensional systems are important for understanding spin-excitations, which form an important class of low-energy phenomena. Of particular interest are how these spin excitations arise and are then tuned by the environment (e.g. temperature, applied magnetic field). The temperature dependence of the reflection spectra from 215 K down to 4 K was measured. Magnetic field dependence of the reflection spectra from 0 T to 35 T was also measured. We will discuss the behavior of the reflection edge with temperature and magnetic field and its correlation with spin excitations.   

Non-Fermi liquid $d$-wave metal phase of strongly interacting electrons on the two-leg ladder

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau's Fermi liquid theory is of central importance to many outstanding problems in condensed matter physics. Perhaps the most important such pursuit is a microscopic characterization of the cuprates, where the so-called ``strange metal'' behavior above $T_c$ near optimal doping is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of such a strange metal quantum phase could possibly shed new light on the interesting low-temperature behavior in the pseudogap and on the $d$-wave superconductor itself. Here, we present a theory for a specific example of a strange metal, which we term the ``$d$-wave metal.'' Using variational wave functions, gauge theoretic arguments, and ultimately large-scale DMRG calculations, we establish compelling evidence that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian: the venerable $t$-$J$ model supplemented with a frustrated electron ring-exchange term, which we study extensively here on the two-leg ladder. These findings constitute one of the first explicit examples of a non-Fermi liquid metal existing as the ground state of a realistic model.   

Moving toward two dimensions in a $t$-$J$-$K$ model with frustrating ring exchange: the quest to stabilize a non-Fermi liquid $d$-wave metal phase

Recent work (arXiv:1207.6608) has established compelling evidence, on the two-leg ladder, for the existence of a non-Fermi liquid strange metal phase as the ground state of a realistic model Hamiltonian---the $t$-$J$ model supplemented with a frustrating ring-exchange term. Here we present our findings, guided by VMC and DMRG calculations, as we move toward two dimensions in an attempt to fully characterize the phase diagram and to stabilize this ``$d$-wave metal'' phase beyond the two-leg ladder. Ultimately, we are motivated by a desire to understand the strange metal phase in the cuprates, and to determine whether the superconductor and pseudo-gap regimes can potentially be understood as instabilities of the $d$-wave metal phase resulting from this (or a similar) model Hamiltonian.   

Nontrivial ferrimagnetism on the low-dimensional quantum spin systems with frustration

In low-dimensional quantum spin systems with frustration, nontrivial magnetisms often occur due to strong quantum fluctuation. Ferrimagnetism in non-frustrated systems is well-known to occur from the mechanism based on the Marshall-Lieb-Mattis theorem. This type of ferrimagnetism is called ``Lieb-Mattis (LM) type.'' Recently, the occurrence of nontrivial ferrimagnetism has been reported in some one-dimensional Heisenberg spin systems with frustration, in which the continuous change of spontaneous magnetization and the incommensurate modulation in local magnetization are observed. This type is called ``non-Lieb-Mattis (NLM) type.'' In this study, we tackle a problem whether the NLM ferrimagnetism occurs or not in higher dimensional systems. We investigate the S$=$1/2 Heisenberg models on the spatially anisotropic two-dimensional (2D) kagome lattice and on the quasi-one-dimensional (Q1D) kagome strip lattices by the numerical diagonalization and density matrix renormalization group methods. The Q1D models share the same structure in their inner part with the spatially anisotropic 2D kagome lattice; we examine two cases with respect to strip width. We will discuss the relationship between the ground-state properties of the Q1D lattices and those of the 2D lattice.   

Theory of the NMR $1/T_1$ relaxation rate in a quantum spin nematic

Recently, it has been proposed that the material LiCuVO$_4$ may realise quantum spin-nematic order when a magnetic field close to saturation is applied [1,2]. Potentially, a bond-centred, 2-sublattice antiferroquadrupole spin-nematic state is stable at low temperature. However, the experimental evidence for this state remains inconclusive. Building on previous work [3], we develop a detailed theory of the NMR $1/T_1$ relaxation rate in spin-nematic states, and apply this to the specific case of LiCuVO$_4$. We show that $1/T_1$ in the proposed spin-nematic state has qualitatively different features to conventionally ordered magnets, and propose this as an unambiguous test of spin-nematic order.\\[4pt] [1] L.E. Svistov et al., JETP Letters {\bf 93}, 21 (2010).\\[0pt] [2] M.E. Zhitomirsky and H. Tsunetsugu, EPL {\bf 92}, 37001 (2010).\\[0pt] [3] A. Smerald and N. Shannon, Phys. Rev. B {\bf 84}, 184437 (2011).   

Double Magnetic Field-induced Phase Transitions in the Spin-1/2 Alternating Chain System AgVOAsO$_{4}$

The new spin-1/2 compound AgVOAsO4 shows one-dimensional magnetic behavior and a spin gap of about 14 K. The crystal structure of AgVOAsO4 is rather complex with alternating spin chains aligned along the [110] and [110] direction. The experimental magnetic susceptibility yields values of 40 K and 26 K for J1 and J1$'$, respectively. The magnetization curve taken at 1.5 K cannot be fully described by only two coupling constants, which points to sizable inter chain coupling. Furthermore, the magnetization shows the closing of the spin gap at Hc1 =10.5 T and a saturation at Hc2=48.5 T. In the talk, we report the magnetic field - temperature (H-T) phase diagram of AgVOAsO4 measured by specific heat and magnetization experiments. The specific heat taken in high DC fields up to 28 T reveals a distinct double anomaly around 4 K and 2 K. Magnetization experiments follow this double structure down to mk temperatures and reveal a variety of anomalies close to the critical field Hc1 in AgVOAsO4.   

Order and excitations near quantum criticality in quasi-1D S$=$1/2 easy-plane antiferromagnet Cs2CoCl4

We explore the magnetic order and spin dynamics in the quasi-one-dimensional spin-1/2 easy-plane anisotropy antiferromagnet Cs2CoCl4 in a magnetic field applied close to the easy-plane which drives a transition from spontaneous long-range magnetic order to a gapped quantum paramagnet. The commensurate antiferromagnetic order observed at low fields is stable over a wide field range but is replaced by an incommensurate magnetic order (spin density wave) just below the transition to paramagnetic. The main result is the observation of the new incommensurate magnetic phase which was not seen experimentally prior to this work and was also not predicted theoretically. Deep in the paramagnetic phase the excitations are sharp, gapped magnons with minima at the incommensurate wavevectors of the magnetic order below BC $=$ 2.36(2) T and the dispersion relations give values for the intra- and inter-chain couplings. In addition to one magnon excitations at high energies we also observe weak magnetic continuum scattering, which becomes stronger upon approaching the critical field from above and is attributed to multi-magnon transverse field scattering processes.   

Phase diagram of frustrated ladder and 2D antiferromagnets

We investigate the low energy properties of the frustrated two leg diagonal ladder exhibiting both intra- and inter-chain frustration. The renormalization group is used to obtain the phase diagram while varying the microscopic lattice parameters. We particularly emphasize the role of the in-chain marginal operators, which is tuned by the in-chain frustration and can promote a dimer phase in the system. Finally, the physics of the quasi one dimensional diagonal ladder is incorporated into a two dimensional square lattice since the former is used as the primary structure to build up the square lattice. Within the validity of our method, the classical phases---a N\'{e}el antiferromagnet and a collinear antiferromagnet---are predicted. The results are compared to numerical DMRG calculations.   

Quantum criticality and fractional charge excitations in itinerant ice-rule systems

``Ice rule'' is a configurational constraint on Ising-type variables defined on tetrahedron-based lattices, such as a pyrochlore lattice, so that two out of the four sites on a tetrahedron are in the opposite state to the other two. This concept plays an important role in many systems, such as water ice I$_h$, magnetite Fe$_3$O$_4$, and spin ice materials Ho(Dy)$_2$Ti$_2$O$_7$. Under the ice-rule constraint, the ground state is disordered and retains macroscopic degeneracy. Nevertheless, the ice-rule configuration is not completely random but has a peculiar spatial structure with quasi-long-range correlation. It is interesting to ask how itinerant electrons change their properties by coupling to this anomalous spatial structure. To answer this problem, we adopt an extended Falicov-Kimball model as a minimal model, in which itinerant electrons interact with localized charge degrees of freedom under the ice rule. We exactly solve this model on a loop-less variant of the tetrahedron-based lattices, a tetrahedron Husimi cactus and clarify the ground-state phase diagram. The exact solution reveals a quantum critical point separating two insulating phases, where a novel non-Fermi-liquid behavior emerges. We also discuss the nature of fractional excitations breaking the ice-rule manifold.   

Doped Mott insulators in (111) bilayers of perovskite transition-metal oxides with the strong spin-orbit coupling

We study the electronic properties of Mott insulators realized in bilayers of perovskite transition-metal oxides grown along the [111] crystallographic axis. The low-energy effective Hamiltonians for such Mott insulators are derived in the presence of the strong spin-orbit coupling. These models are characterized by the antiferromagnetic Kitaev interaction and the antiferromagnetic or ferromagnetic Heisenberg interaction depending on the $d$ orbital occupancy. From exact diagonalization analyses on finite clusters, Kitaev spin liquid phases are shown to be confined in narrow parameter regimes. Slave-boson mean-field analyses indicate the possibility of non-trivial superconducting states induced by carrier doping into the Mott-insulating parent systems. We also discuss the possible experimental realization of these systems in $4d$ and $5d$ transition-metal oxides.   

$^{27}$Al-NMR Study of the Spinel Compound CoAl$_{2}$O$_{4}$

CoAl$_{2}$O$_{4}$, a geometrically frustrated magnet, is believed to be located in the vicinity of a quantum melting point of the AFM ordered state. In CoAl$_{2}$O$_{4}$, magnetic frustration originates from Co$^{2+}(S =$ 3/2) spins on the tetrahedral A-site via non-magnetic Al ions occupying the octahedral B-site. To study the magnetic properties of CoAl$_{2}$O$_{4}$ from a microscopic point of view, we have carried out $^{27}$Al-NMR measurements using a well-characterized powder sample of CoAl$_{2}$O$_{4}$. The temperature dependence of the magnetic susceptibility $\chi $ shows a broad peak around 15 K and does not show any difference in zero-field-cooled and field-cooled measurements. $^{27}$Al-NMR spectra at 9.3 MHz ($H =$ 0.84 T) show seven peaks characterized by quadrupolar splitting with $\nu_{\mathrm{Q}}=$ 0.55 MHz at temperatures above 10 K. Below 10 K, the spectrum broadens suddenly. We also observe a peak of 1/$T_{1}$ of $^{27}$Al at 10 K. These NMR results clearly indicate magnetic ordering at 10 K, although $\chi $ does not exhibit any signature of long-range magnetic ordering.   

What controls the sign of exchange-induced phonon splitting in ACr$_2$O$_4$ spinels?

The interplay of spin and lattice degrees of freedom can lead to a variety of fundamentally and technologically interesting phenomena. In ACr$_{2}$O$_{4}$ spinels, it has been well established that antiferromagnetic order alone can lower the symmetry of a crystal resulting in a splitting of degenerate phonon frequencies without any structural distortion. A simple model based on nearest neighbor exchange striction has been proposed and confirmed by a novel first-principles approach. Recently however it has been suggested that magnetically induced phonon splitting is universally controlled by the nondominant exchange interaction. In this talk we present our recent first principles study of magnetically induced phonon anisotropy in ACr$_{2}$O$_{4}$ (A$=$Mg, Zn, Cd, Hg) spinels. We demonstrate that the different spin ordering patterns observed in the different spinel compounds can lead to an opposite sign of phonon splitting. This naturally explains the difference in sign experimentally observed for ZnCr$_{2}$O$_{4}$ compared with CdCr$_{2}$O$_{4}$, which have very different magnetic ground states. Additionally, we show that the \textit{ab initio }values for the phonon frequencies can be very well fitted to the previously proposed spin-phonon coupling model including only the nearest neighbor exchange interaction.   

Competing Jahn-Teller and spin Jahn-Teller ordering in $A$Cr$_2$O$_4$ spinels

Magnetic ordering is strongly linked to structural distortions in the frustrated antiferromagnets ZnCr$_2$O$_4$ and MgCr$_2$O$_4$. These systems undergo spin Jahn-Teller distortions at the onset of magnetic order. The addition of magnetic $A$ site cations in $A$Cr$_2$O$_4$ spinels can relieve frustration. High-resolution variable-temperature synchrotron powder X-ray diffraction, detailed magnetic studies, and heat capacity measurements show that dilute amounts of Jahn-Teller active Cu$^{2+}$ or Co$^{2+}$ on the $A$ sites of these spinels have different effects on structure but similar effects on magnetism. Partial replacement of $A$ by Cu$^{2+}$ generates Jahn-Teller distortions at temperatures above the endmember Neel temperatures, yet spin interactions remain frustrated to $\sim$ 12 K. This contrasts with Co$^{2+}$ substitution which also maintains frustration, but results in a suppression of spin Jahn-Teller ordering in ZnCr$_2$O$_4$. We report decoupled Jahn-Teller and spin Jahn-Teller ordering in the canonical frustrated systems ZnCr$_2$O$_4$ and MgCr$_2$O$_4$ that is tunable by varying the identity of the magnetic $A$ site substituent.   

Volume Sensitivity and Effect of Fluctuations on the Frustrated Magnetism in YMn$_2$

Cubic Laves phase (C15) YMn$_2$ with its highly frustrated pyrochlore type sublattice of Mn sites, is one of a small but growing class of ordered magnets that lie close to a quantum critical point at stoichiometry. Its ground state displays long-spiral helical magnetic order that is highly sensitive to volume, disappearing due the substitution of 3\% Sc for the larger Y atom (chemical pressure), or by application of just 0.4 GPa pressure. The large change of volume (5\%) upon ordering (T$_N$ = 100 K) argues for itinerant magnetism, and in recent years there have been developments in modeling magnetic fluctuations in itinerant magnets near the ordering point. We extend earlier results of Terao and Yamada on the first principles based energetics versus volume, and quantify the sensitivity of the magnetic state to pressure. The effects of fluctuations within an itinerant picture will be discussed.