Session C15: Focus Session: New Frustrated Models: Theory & Materials

Emergent critical phase and Ricci flow in a 2D frustrated Heisenberg model

We introduce a two-dimensional frustrated Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices [1]. Classically the two sublattices decouple, and ``order from disorder'' drives them into a coplanar state. Applying Friedan's geometric approach to nonlinear sigma models, we obtain the scaling of the spin-stiffnesses governed by the Ricci flow of a 4D metric tensor. At low temperatures, the relative phase between the spins on the two sublattices is described by a six-state clock model with an emergent critical phase and two Berezinskii-Kosterlitz-Thouless (BKT) phase transitions.\\[4pt] [1] Peter P. Orth, Premala Chandra, Piers Coleman, and J\"org Schmalian, arXiv:1206.5740v1 (2012) (accepted for Phys. Rev. Lett.)   

Pentagonal Spin Ice

We study a novel version of spin ice in the Pentagonal lattice from a theoretical perspective. The coexistence of even (z=4) and odd (z=3) coordinated vertices in this network gives rise to a mixed spin ice phase where the honeycomb spin ice rule is realized at the z=3 sites and the usual spin ice with no magnetic charge occurs at the z=4 vertices. As the system cools down a phase with charge order precludes the spin ordered stage. Magnetic excitations that violate ice-rule at the z=4 vertices behave as emergent monopoles whose interaction with the background charges from z=3 sites exhibits novel dynamics.   

Thermodynamics of Ising Spins on the Star Lattice

There is a new class of two-dimensional magnetic materials polymeric iron (III) acetate fabricated recently in which Fe ions form a star lattice. We study the thermodynamics of Ising spins on the star lattice with exact analytic method and Monte Carlo simulations. Mapping the star lattice to the honeycomb lattice, we obtain the partition function for the system with asymmetric interactions. The free energy, internal energy, specific heat, entropy and susceptibility are presented, which can be used to determine the sign of the interactions in the real materials. Moreover, we find the rich phase diagrams of the system as a function of interactions, temperature and external magnetic field. For frustrated interactions without external field, the ground state is disordered (spin liquid) with residual entropy 1.522 . . . per unit cell. When a weak field is applied, the system enters a ferrimagnetic phase with residual entropy ln4 per unit cell. The arXiv version of this work is arXiv:1210.1675.   

Field-induced multiple-Q phases in a frustrated quantum magnet

We study a frustrated hard-core boson model inspired by recent experiments on the field-induced quantum phase transition in the S$=$1 dimer antiferromagnet Ba$_{3}$Mn$_{2}$O$_{8}$ for a magnetic field H parallel to the c axis. We calculate the effective interactions in the low-density limit by adding the ladder diagrams and determine the ground state phase diagram near the quantum critical point. The phase diagram is very rich and includes different multiple-\textbf{Q} Bose-Einstein condensates (BECs) that combine the six degenerate incommensurate lowest-energy modes $\pm$ \textbf{Q}$_{n}$ (1$\le n\le $3) at the quantum critical point. The multiple-\textbf{Q} states include a lattice of magnetic vortices that emerges out of frustration between the boson-boson interactions.   

Spin-Density-Wave Order and Slow Dynamics in Ca$_{3}$Co$_{2}$O$_{6}$

We study a frustrated quantum Ising model relevant for Ca$_{3}$Co$_{2}$O$_{6\, }$that comprises a triangular lattice of weakly coupled ferromagnetic chains$_{\, }$[Y. Kamiya and C. D. Batista, PRL \textbf{109}, 067204 (2012)]. Our quantum Monte Carlo simulation shows that the chains become ferromagnetic and form a three-sublattice ``up-up-down'' structure in the lowest temperature regime $T\le T_{CI}$ due to a quantum effect. In contrast, long-wavelength spin-density-wave (SDW) modulations along the chains are stabilized for $T_{CI}$\textless $T$\textless $T_{c}$ in agreement with recent experiments. We also discuss a simple mean-field theory revealing quasi-continuous change of the modulation periodicity as a function of $T$ and implying the existence of metastable states in the SDW phase, which explains the slow low-temperature dynamics that has been observed in Ca$_{3}$Co$_{2}$O$_{6}$. The closely related multiferroic materials Ca$_{3}$CoMnO$_{6}$ and Lu$_{2}$CoMnO$_{6\, }$will also be discussed.   

Elastic and inelastic neutron scattering studies on Sr$_{2}$FeSi$_{2}$O$_{7}$

Evolution of static and dynamic spin correlations in a new multiferroics material Sr$_{2}$FeSi$_{2}$O$_{7}$ under an external magnetic field was investigated by elastic and inelastic neutron scattering techniques. An external magnetic field up to $B = $ 14 Tesla induces four different magnetic and ferroelectric phases in Sr$_{2}$FeSi$_{2}$O$_{7}$. The static magneto-electric coupling can be understood as the p-d hybridization proposed for a related material Ba$_{2}$CoGe$_{2}$O$_{7}$. By analyzing the neutron scattering data obtained from a single crystal of Sr$_{2}$FeSi$_{2}$O$_{7}$ under magnetic field, we have determined the spin structure and the effective spin Hamiltonian in this material. The spin structure and spin wave excitations show interesting changes as upon ramping up the system enters the field-induced phases for $B$ \textgreater\ 6.5 Tesla, which will also be discussed.   

Spin-lattice coupling and novel magnetic properties in the triangular lattice antiferromagnet Ag$_2$CrO$_2$

Spin-lattice coupling plays an important role in selecting the ground state in the geometrically frustrated magnets, since a small amount of structural distortion is sufficient to lift the ground state degeneracy and stabilize a long-range magnetic order. Ag$_2$CrO$_2$ consists of insulating triangular lattice planes of CrO$_2$ (Cr$^{3+}$ ion with $S$=3/2), which are separated by the metallic Ag$_2$ layers. Interestingly, the electric transport in the Ag$_2$ layer is strongly affected by the magnetism in the CrO$_2$ layer. We performed neutron diffraction experiments on this material and found that a partially disordered state with 5 sublattices abruptly appears at $T\rm_N$=24 K, accompanied by a structural distortion [1]. The spin-lattice coupling stabilizes the anomalous state, which is expected to appear only in limited ranges of further-neighbor interactions and temperature. The nonnegligible further-neighbor interactions suggest the existence of the RKKY interaction mediated by the conduction electrons. We have recently performed inelastic neutron scattering experiments and found anomalous magnetic excitations, which cannot be explained simply by the linear spin-wave theory. \\[4pt] [1] M. Matsuda {\it et al.}, Phys. Rev. B 85, 144407 (2012).   

The Dugganites: A new, frustrated, and potentially multiferroic class of compounds that exhibit rich magnetic behavior

Ba$_{\mathrm{3}}$NbFe$_{\mathrm{3}}$Si$_{\mathrm{2}}$O$_{\mathrm{14}}$ is a multiferroic langasite (s.g. $P$321) wherein the Fe$^{\mathrm{3+}}$ atoms (S$=$5/2) occupy isolated trimers that stack along the $c$-axis. The spins uniquely order below T$_{\mathrm{N}}=$26 K, where single domain helicity simultaneously exists with triangular chirality. Preparations of other langasites of this type are possible, so long as Fe$^{\mathrm{3+}}$ remains in the trimer site leaving the magnetism relatively unchanged. This is because Fe$^{\mathrm{3+}}$ occupies a tetrahedral site, where most other transition metal ions prefer the octahedral site occupied by Nb$^{\mathrm{5+}}$. Building on previous research, we have circumvented this problem by replacing Nb$^{\mathrm{5+}}$ with Te$^{\mathrm{6+}}$, which is found exclusively in octahedral coordination. Isostructural compounds Pb$_{\mathrm{3}}$TeCo$_{\mathrm{3}}$A$_{\mathrm{2}}$O$_{\mathrm{14}}$ (A$=$V$^{\mathrm{5+}}$, P$^{\mathrm{5+}})$ and Pb$_{\mathrm{3}}$TeMn$_{\mathrm{3}}$P$_{\mathrm{2}}$O$_{\mathrm{14}}$ (where the only magnetic ions are Co$^{\mathrm{2+}}$ and Mn$^{\mathrm{2+}}$ respectively) have been prepared and studied. Despite being isostructural to Ba$_{\mathrm{3}}$NbFe$_{\mathrm{3}}$Si$_{\mathrm{2}}$O$_{\mathrm{14}}$, the dugganites exhibit a rich variety of magnetic behavior, including evidence for multi-k magnetic structural arrangements, long-range coexistence of static and dynamic spins, and spin-spin interactions that potentially exist over 150 unit cells. In at least one dugganite, magnetoelectric coupling was observed at T$_{\mathrm{N}}$ entertaining the possibility that these compounds may also be multiferroic.   

Magnetic structure and excitations in BaV$_{10}$O$_{15}$

Recently, new type of frustrated magnets, BaV$_{10}$O$_{15}$ and SrV$_{10}$O$_{15}$, were found to exhibit interesting physics due to the magnetic V$^{2.8+}$ ions with mixed valence. Using elastic and inelastic neutron scattering measurements we have examined the magnetic structure and excitations of BaV$_{10}$O$_{15}$. Magnetic excitations show highly dispersive two modes along c axis. Furthermore, two excitations are dispersionless along the a-axis. And very interestingly, along the b-axis one excitation is dispersionless while the other is strongly dispersive. Magnetic ground state of BaV$_{10}$O$_{15}$ was studied using neutron powder diffraction data, which order below 45 K with magnetic wave vector Q$_{\mathrm{m}}=$(1/2 0 0). Here we present the possible magnetic structures of BaV$_{10}$O$_{15}$ using representation analysis, which can explain both the magnetic diffraction data and the basic features of the magnetic excitations observed in different directions. Linear spinwave calculations were also performed to shed light in understanding an effective spin hamiltonian for this system.   

Microscopic modeling of the 3D quantum magnet Cu$_2$OSeO$_3$

Unlike most undoped cuprates, the $S=1/2$ Heisenberg magnet Cu$_2$OSeO$_3$ exhibits a ferrimagnetic ground state and sizable magnetoelectric coupling. Recent experiments reported magnetic-field-induced emergence of skyrmions in this material. Based on extensive DFT band structure calculations we evaluate the microscopic magnetic model, including isotropic (Heisenberg) and anisotropic (Dzyaloshinskii-Moriya) terms. We extract five relevant couplings that form a complex, but non-frustrated spin model which can be described as a pyrochlore lattice of magnetic tetrahedra. A peculiar feature of this lattice is the alternation of ``strong'' (the constituent spins are strongly coupled) and ``weak'' tetrahedra. Profiting from a separation of the energy scales we develop an effective model, treating strong tetrahedra either as a classical $S=1$ object or as a coherent quantum superposition of classical states. For the latter case, we find an excellent agreement with the quantum Monte Carlo simulations of the full model and the experimental magnetization and neutron diffraction data. Quite surprising for a 3D model we find distinct manifestations of quantum fluctuations. The developed effective model can be further used to model the field-induced behavior including the formation of skyrmions.   

Frustration by competing interactions in the highly-distorted double perovskites La$_2$NaRuO$_6$ and La$_2$NaOsO$_6$

The usual classical behavior of S = 3/2, B-site ordered double perovskites results in simple, commensurate magnetic ground states. In contrast, heat capacity and neutron powder diffraction measurements for the S = 3/2 systems La$_2$NaB'O$_6$ (B' = Ru, Os) reveal an incommensurate magnetic ground state for La$_2$NaRuO$_6$ and a drastically suppressed ordered moment for La$_2$NaOsO$_6$. This behavior is attributed to the large monoclinic structural distortions of these double perovskites. The distortions have the effect of weakening the nearest neighbor superexchange interactions, presumably to an energy scale that is comparable to the next nearest neighbor superexchange. The exotic ground states in these materials can then arise from a competition between these two types of antiferromagnetic interactions, providing a novel mechanism for achieving frustration in the double perovskite family. Work at ORNL is supported by the Division of Scientific User Facilities and the Materials Science and Engineering Division, DOE Basic Energy Sciences. Work at the University of South Carolina is supported by the Heterogeneous Functional Materials Research Center, funded by DOE under award number de-sc0001061.   

Magnetostriction and magnetic texture to 100.75 Tesla in frustrated SrCu$_2$(BO$_3$)$_2$

SrCu$_2$(BO$_3$)$_2$, a spin-1/2 Heisenberg antiferromagnet in the archetypical Shastry-Sutherland lattice, exhibits a rich spectrum of magnetization plateaus and stripe-like magnetic textures in applied fields. The structure of these plateaus is still highly controversial due to the intrinsic complexity associated with frustration and competing length scales. We discover magnetic textures in SrCu$_2$(BO$_3$)$_2$ via FBG-optical fiber based magnetostriction and magnetocaloric measurements in fields up to 100.75 T. In addition to observing low-field fine structure with unprecedented resolution, the data also reveal lattice responses at 73.6 T and at 82 T that we attribute, using a controlled density matrix renormalization group approach, to a unanticipated 2/5 plateau and to the long-predicted 1/2 plateau. Research supported by NSF, State of Florida and the US DOE Basic Energy Science project ``Science at 100T.'' ref: M. Jaime et al., {\it PNAS} {\bf 109}, 120404 (2012).   

Antiferromagnetism, structural instability and frustration in intermetallic AFe$_4$X$_2$ systems

Magnetic systems with reduced dimensionality or frustration attract strong interest because these features lead to an increase of quantum fluctuations and often result in unusual properties. Here, we present a detailed study of the magnetic, thermodynamic, and structural properties of the intermetallic $A$Fe$_4$X$_2$ compounds ($A$=Sc,Y,Lu,Zr; X=Si,Ge) crystallizing in the ZrFe$_4$Si$_2$ structure type. Our results evidence that these compounds cover the whole regime from frustrated AFM order up to an AFM quantum critical point. Susceptibility $\chi$(T), specific heat, resistivity, and T-dependent XRD measurements were performed on polycrystalline samples. In all compounds we observed a Curie-Weiss behavior in $\chi$(T) at high T indicating a paramagnetic moment of about 3$\mu_B$/Fe. Magnetic and structural transitions as previously reported for YFe$_4$Ge$_2$ occur in all compounds with trivalent $A$. However, transition temperatures, nature of the transition as well as the relation between structural and magnetic transitions change significantly with the A element. Low $T_N$'s and large $\theta_{CW}/T_N$ ratios confirm the relevance of frustration. The results are analyzed and discussed with respect to electronic, structural and magnetic instabilities applying DFT calculations.