Session V13: Focus Session: Geometrical Frustration

Field-induced spin-solid phases in the spin liquids Tb$_{2}$Ti$_{2}$O$_{7}$ and Nd$_{3}$Ga$_{5}$SiO$_{14}$

Here we report thermodynamic and magnetization measurements at zero and high fields in the pyrochlore Tb$_{2}$Ti$_{2}$O$_{7}$ and in the Kagome lattice Nd$_{3}$Ga$_{5}$SiO$_{14}$. In both compounds, previous neutron scattering studies did not reveal any form of magnetic ordering down to the lowest temperatures and have proposed these materials to display a spin-liquid ground state [1]. Here we show that heat capacity normalized by temperature down to $\sim $ 350 mK confirms the absence of ordering. Furthermore, magnetization as a function of field at the lowest temperatures reveal the existence of an intermediary phase protruded between the zero field spin-liquid and the high-field spin-polarized state. In the case Nd$_{3}$Ga$_{5}$SiO$_{14 }$it leads to a 1/2 magnetization plateau for fields along the inter-planar direction, similar to the one recently reported in the pyrochlore compound CdCr$_{2}$O$_{4}$ [2]. But for fields along the planes it displays a 1/3 plateau followed by a metamagnetic transition towards a value closer to 4/5. [1] J. S. Gardner et al. Phys. Rev. Lett. 82, 1012 (1999)~; J. Robert et al., ibid 96\textbf{, }197205 (2006) [2] H. Ueda, Phys. Rev. Lett. 94, 047202 (2005).   

Freezing the 2D distorted kagome spin liquid Nd$_3$Ga$_5$SiO$_{14}$

The distorted kagome system Nd$_3$Ga$_5$SiO$_{14}$ has been investigated with neutron scattering down to 0.046 K with no evidence of magnetic long-ranged order of the Nd$^{3+}$ moments in zero field. Substantial diffuse scattering is observed which is consistent with previous measurements of nearest neighbor correlations between the fluctuating spins. Upon the application of a magnetic field in the c-direction, the diffuse scattering is reduced in intensity while magnetic Bragg peaks grow in intensity to saturate by 1 T. The net moment along the c-axis is 1.5(1) $\mu_{B}$, only 1/2 of the value of the full moment of 3.2 $\mu_{B}$ per Nd spin, consistent with a 1/2 magnetization plateau in the DC susceptibility. A phase diagram is constructed to denote the boundary between a 2D spin liquid and spin solid phase.   

Geometric Frustration and Chemical Tuning of Magnetic Order in the Kagome Lattice System YBaCo$_{4}$O$_{7+x}$

Transition metal oxides containing a Kagome lattice motif of magnetic ions form the basis for exploring geometric frustration and exotic magnetic ground states. Examples of such systems include pyrochlores, spinels, SrCr$_{9p}$Ga$_{12-9}$pO$_{19}$ (SCGO) and jarosite minerals. Joining this class of Kagome lattice antiferromagnets is the recently reported YBaCo$_{4}$O$_{7+x}$ (Y-114), a member of the more general R-114 which can be prepared with small rare-earth ions. The structure is comprised of Kagome layers of CoO$_{4}$ tetrahedra linked in the c direction by a triangular layer of CoO$_{4}$ tetrahedra. We show that appropriate control of oxygen stoichiometry so that x=0.0 yields a long-range antiferromagnet with a unique spin arrangement that seeks to satisfy the 120$^{o}$ ground state of the Kagome net in the a-b plane with a strong collinear interaction along the c-axis. This AFM ground state results because of a structural phase transition that breaks the 6-fold symmetry of the Kagome layers. We also discuss chemical approaches whose objective is to preserve the Kagome symmetry to lowest temperatures with concomitant geometric frustration.   

Magnetic Phase Diagram of Co$_{3}$V$_{2}$O$_{8}$

Kagom\'{e}-staircase lattice structures like Ni$_{3}$V$_{2}$O$_{8}$ and Co$_{3}$V$_{2}$O$_{8}$ have recently attracted attention because of their complex magnetic phase diagrams and the magnetically induced ferroelectric (FE) phase observed in Ni$_{3}$V$_{2}$O$_{8}$. Co$_{3}$V$_{2}$O$_{8}$ at zero magnetic field exhibits five subsequent magnetic phase transition in a narrow temperature range. It has an incommensurate antiferromagnetic phase below T$_{N}$=11.4 K and weak ferromagnetic behavior along the a-axis at T$_{C}$=6.2 K. Along with three other phase transitions in between; T$_{1}$=8.9 K, T$_{2}$=7.0 K and T$_{3}$=6.9 K, the evolution of these five phase transitions under magnetic field, phase boundaries, is traced through magnetic susceptibility and dielectric constant anomalies. We resolve the complete magnetic phase diagram of Co$_{3}$V$_{2}$O$_{8}$ with the magnetic field applied along the principal crystallographic orientations.   

Field dependence of the magnetic order in Co$_3$V$_2$O$_8$

Co$_{3}$V$_{2}$O$_{8}$ (CVO) has a geometrically frustrated magnetic lattice, a Kagom$\acute{e}$ staircase. In zero field [1], CVO initially orders magnetically at 11.3 K into an incommensurate phase, with wave vector $k$ = (0,$\delta$,0) with $\delta$ = 0.55. $\delta$ decreases monotonically with decreasing temperature. It locks into a commensurate antiferromagnetic value of $\frac{1}{2}$ and $\frac{1}{3}$ before the ferromagnetic ground state ($\delta~=~0$) is revealed at 6.2 K. The spin direction for all spins is along the $a$ axis. A theory based on a minimal Ising model with competing exchange interactions can explain the basic features of the magnetic ordering. The application of magnetic field along the $a$ axis strongly affects all of the phases. In particular, the ferromagnetic state is suppressed in favor of the $\delta=0.5$ antiferromagnetic state. [1] Y. Chen, J. W. Lynn, Q. Huang, F. M. Woodward, T. Yildirim, G. Lawes, A. P. Ramirez, N. Rogado, R. J. Cava, A. Aharony, O. Entin-Wohlman, and A. B. Harris, Phys. Rev. B 74, 014430 (2006).   

High-Energy Magneto-Dielectric Effect in Co$_{3}$V$_{2}$O$_{8}$.

We investigate the optical and magneto-optical properties of the Kagom\'{e} staircase compound Co$_{3}$V$_{2}$O$_{8}$ in order to explore mechanistic aspects of the high-energy magneto-dielectric effect. Co$_{3}$V$_{2}$O$_{8}$ displays a much smaller dielectric contrast compared to quasi-isostructural Ni$_{3}$V$_{2}$O$_{8}$, a result that we attribute to a high-temperature local structural distortion in Co$_{3}$V$_{2}$O$_{8}$ along the cross-tie direction. Such a distortion prevents the low temperature magnetic transitions from having a strongly coupled lattice component. This proposition is supported by vibrational studies.   

A Microscopic Model of Magnetoelectric Interactions in Ni3V2O8

We develop a microscopic magnetoelectric coupling in Ni$_3$V$_2 $O$_8$ (NVO) which gives rise to the trilinear phenomenological coupling used previously to explain the phase transition in which magnetic and ferroelectric order parameters appear simultaneously. Using combined neutron scattering measurements and first-principles calculations of the phonons in NVO, we determine eleven phonons which can induce the observed spontaneous polarization. Among these eleven phonons, we find that a few of them can actually induce a significant dipole moment. Using the calculated atomic charges, we find that the required distortion to induce the observed dipole moment is very small ($\sim$0.001 {\AA}) and therefore it would be very difficult to observe the distortion by neutron-powder diffraction. Finally, we identify the derivatives of the exchange tensor with respect to atomic displacements which are needed for a microscopic model of a spin-phonon coupling in NVO and which we hope to obtain from a fundamental quantum calculation such as LDA+U.   

Synthesis and characterization of thin film Ni$_3$V$_2$O$_8$

We have prepared thin films of multiferroic Ni$_3$V$_2$O$_8$ using sputter deposition and spin coating techniques. Raman spectroscopy and XRD confirm that the as-deposited films are amorphous, single-phase Ni$_3$V$_2 $O$_8$. These films develop increasing crystalline order on annealing at 900 $^ {\circ}$C, although they remain polycrystalline. These thin film Ni$_3$V$_2$O$_8$ samples develop a net magnetization below T=4 K; this temperature is consistent with the transition to a canted antiferromagnetic state in bulk samples. We observe an anomaly in the dielectric constant coincident with this magnetic transition. Despite being able to apply an electric field of over 6 MV/m to these samples, we are unable to observe any voltage-induced shift in this anomaly. We will discuss the implications of these results for future studies on thin film multiferroics.   

Thermal expansion and pressure effect in the Kagome-staircase compound Ni$_{3}$V$_{2}$O$_{8}$

Ni$_{3}$V$_{2}$O$_{8}$ has attracted attention because of the ferroelectricity (FE) induced by a helical magnetic order. Strong spin-lattice interaction is necessary to explain the ionic displacements leading to FE. To reveal the signature of lattice strain associated with the ferroelectric transitions we have conducted high-resolution thermal expansion measurements along the $a$, $b, c $axes. The strongest lattice anomalies are observed at the low-temperature (3.9 K) lock-in transition from the incommensurate helical magnetic modulation into a commensurate magnetic structure. The stability of the FE with respect to lattice strain as induced by hydrostatic pressure was investigated by measuring the dielectric constant and the ferroelectric polarization under pressures up to 2 GPa. The pressure-temperature phase diagram of Ni$_{3}$V$_{2}$O$_{8}$ is determined. The low-temperature commensurate phase in Ni$_{3}$V$_{2}$O$_{8}$ is stabilized under pressure and the ferroelectricity is completely suppressed above a critical pressure of 1.64 GPa.   

Optical Properties and Magnetic Field-Induced Phase Transitions in the Ferroelectric State of Ni$_3$V$_2$O$_8$

We present a combination of optical spectra, first principles calculations, and magneto-optical measurements to elucidate the electronic structure and to study the phase diagram of Ni$_3$V$_2$O$_8$. We find a remarkable interplay of magnetic field and optical properties that reveals additional high magnetic field phases and an unexpected electronic structure which we associate with the strong magneto-dielectric couplings in this material over a wide energy range. Specifically, we observed several prominent magneto-dielectric effects that derive from changes in crystal field environment around Ni spine and cross-tie centers. This effect is consistent with a field-induced modification of local structure. We find Ni$_3$V$_2$O$_8$ to be an intermediate gap, local moment band insulator. This electronic structure is particularly favorable for magneto-dielectric couplings, because the material is not subject to the spin charge separation characteristic of strongly correlated large gap Mott insulators, while at the same time remaining a magnetic insulator independent of the particular spin order and temperature.   

Magnetodielectric coupling in Mn$_3$O$_4$ and MnCr$_2$O$_4$

We have investigated the temperature and magnetic field dependent dielectric constants of the ferrimagnetic insulators Mn$_3$O$_4$ and MnCr$_2$O$_4$. We have also measured the heat capacity and AC magnetic susceptibility through the multiple spin ordering transitions in these materials. At the zero field T = 42 K and T = 35 K magnetic transitions in Mn$_3$O$_4$ we observed sharp drops in the dielectric constant. In an applied field of 5 kOe, Mn$_3$O$_4$ shows a positive shift in dielectric constant at the intermediate T = 40 K transition in addition to the features observed at zero field. MnCr$_2$O$_4$ also shows features in the dielectric constant at the magnetic transitions at T = 40 K and T = 20 K, though these shifts were approximately 100 times smaller than those observed in Mn$_3$O$_4$. These results will be discussed in the framework of models for coupling the dielectric constant to non-colinear long-range magnetic order.   

Ab-intitio studies of electronic properties of chalcogenide spinels.

CuCr$_{2}$Se$_{4}$ is a normal chalcogenide spinel which exhibits ferromagnetic properties including a relatively high Curie temperature of 450 K [1] which makes it a promising candidate for use in spintronics devices. Another chalcogenide spinel of enhanced interest for spintronics is CdCr$_{2}$Se$_{4}$ which seems to be a promising ferromagnetic semiconductor for electrical spin injection into III-V device heterostructures [2]. We report first principles calculations of the electronic structure of substoichiometric CuCr$_{2}$Se$_{4-x}$ and Cu$_{x}$Cd$_{1-x}$CrSe$_{4}$ spinels. The calculations were performed using the Vienna ab-initio simulation program (VASP) within the Generalized Gradient Approximation (GGA) of Density Functional Theory (DFT). Our calculations indicate that both Se deficient CuCr$_{2}$Se$_{4-x}$ as well as Cu$_{x}$Cd$_{1-x}$CrSe$_{4}$ show half-metallic behavior over a wide range of $x $with a gap around the Fermi level in the minority density of states. [1] F.K. Lotgering, Solid State Commun. 2 (1964) 55 [2] G. Kioseoglou et al., Nature Materials 3 (2004) 799   

Magnetic anisotropy and geometrical frustration in the Ising spin-chain system Sr$_{5}$Rh$_{4}$O$_{12}$

A structural and thermodynamic study of the newly synthesized single crystal Sr$_{5}$Rh$_{4}$O$_{12}$ is reported. Sr$_{5}$Rh$_{4}$O$_{12}$ consists of a triangular lattice of spin chains running along the c-axis. It is antiferromagnetically ordered below 23 K with the intrachain and interchain coupling being ferromagnetic (FM) and antiferromagnetic (AFM), respectively. There is strong evidence for an Ising character in the interaction and geometrical frustration that causes incomplete long-range AFM order. The isothermal magnetization exhibits two step-like transitions leading to a ferrimagnetic state at 2.4 T and a FM state at 4.8 T, respectively. Sr$_{5}$Rh$_{4}$O$_{12}$ is a unique frustrated spin-chain system ever found in 4d and 5d based materials without a presence of an incomplete 3d-electron shell.   

Antiferromagnetism and geometrical frustration in one-dimensional Ca$_{5}$Ir$_{3}$O$_{12}$ and Ca$_{4}$IrO$_{6}$ single crystals

We report a structural, thermodynamic and transport study of the newly synthesized single crystal Ca$_{5}$Ir$_{3}$O$_{12}$ and Ca$_{4}$IrO$_{6}$. Both materials consist of a triangular lattice of spin chains running along the c-axis. Ca$_{5}$Ir$_{3}$O$_{12 }$and Ca$_{4}$IrO$_{6}$ are antiferromagnetically ordered below 7.8 K and 12 K, respectively. The study reveals an unusually large ratio of the Curie-Weiss temperature to the Neel temperature ($>$36 for Ca$_{5}$Ir$_{3}$O$_{12})$ and a small entropy removal associated with the magnetic phase transition. In addition, the magnetic susceptibility and heat capacity show that the phase transition is essentially insensitive to the application of the magnetic field. All results suggest the presence of the geometrical frustration that causes incomplete long-range antiferromagnetic order. The results will be presented and discussed along with comparisons drawn with other related systems.   

Configurational Electronic Entropy and the Phase Diagram of Mixed-Valence Oxides: The Case of Li$_x$FePO$_4$

We demonstrate that configurational electronic entropy, previously neglected, in {\it ab initio} thermodynamics of materials can qualitatively modify the finite-temperature phase stability of mixed-valence oxides. While transformations from low-T ordered or immiscible states are almost always driven by configurational disorder (i.e.\ random occupation of lattice sites by multiple species), in FePO$_4$--LiFePO$_4$ the formation of a solid solution is almost entirely driven by electronic, rather than ionic configurational entropy. We argue that such an electronic entropic mechanism, rather than an ionic one, may be relevant to most other mixed-valence systems. Details in Phys. Rev. Lett. {\bf 97}, 155704 (2006)