Session S19: Cooperative Phenomena: Spin-Orbit Coupling and Antiferromagnetism

Electron correlation, spin-orbit coupling, intersite effects and the metal-insulator transition in pyrochlore iridates

We perform density functional theory (DFT) plus single-site and cluster dynamical mean-field theory (DMFT/CDMFT) calculations to study the metal-insulator transition in the pyrochlore iridates $Lu_2Ir_2O_7$, $Y_2Ir_2O_7$ and $Eu_2Ir_2O_7$. The calculations include spin-orbit coupling. Single-site DMFT calculations indicate that the Lu compound is much more insulating than the Y or Eu materials but predict that the critical interaction strength is almost exactly the same for the Eu and Y compounds, although experimentally the metal-insulator transition temperatures are quite different. We further carry out the cluster DMFT (CDMFT) and observe much larger differences, consistent with experiments, demonstrating the crucial role played by spatial correlations.   

Magnetization and transport properties of single RPd${_2}$P${_2}$ (R=Y, La-Nd, Sm-Ho, Yb)

Single crystals of RPd${_2}$P${_2}$ (R=Y, La-Nd, Sm-Ho, Yb) were grown using a self-flux method and were characterized by room-temperature powder X-ray diffraction, anisotropic temperature and field dependent magnetization and temperature dependent in-plane resistivity. Anisotropic magnetic properties, arising mostly from crystal electric field (CEF) effects, were observed for most magnetic rare earths. The experimentally estimated CEF parameters B$^2_0$ were calculated from the anisotropic paramagnetic $\theta_{ab} $ and $ \theta_{c} $values. Ordering temperatures, as well as the polycrystalline averaged paramagnetic Curie-Weiss temperature, $\theta_{ave}$, were extracted from magnetization and resistivity measurements.   

Dynamic scaling invariance at low temperatures

Using thermodynamic arguments we prove that the conventional consequences of the dynamic scale hypothesis change their character in the limit as the critical temperature $T_{c}$ approaches zero. In particularly, for liquid helium-4, the critical exponent $\alpha $ associated with the heat capacity ($\alpha $ \textless 0) and other exponents related by the following new relation \begin{equation} \label{eq1} \nu (z-1)=(1+S_{I} -\alpha )/6\,\,,\,\,\,\,T_{C} =T_{\lambda } \ge 0\,\,, \end{equation} \begin{equation} \label{eq2} S_{I} =\left( {\frac{T_{C} }{T }} \right)^{n}\,,\,\,\,\,\,\,T\ge T_{C} \quad , \end{equation} where $n$ is a positive constant [1] and $z$ is the dynamic critical exponent, $\nu $ -- the critical exponent of the correlation length. It is important that now the exponent $z$ depends on $T$ and $T_{\lambda } $. If $T_{\lambda } \quad =$0 and $T$\textgreater 0, then the $S_{I} $-function [1] is zero and Eq. (\ref{eq1}) becomes \begin{equation} \label{eq3} \nu (z-1)=(1-\alpha )/6\,\,,\,\,\,\,T_{C} =0,\,\,\,(T>0,\,\,\,\alpha <0)\,\,. \end{equation} Eq. (\ref{eq3}) can be applied, for example, to a mixture of liquid $He^{3}$ and $He^{4}$. The results are valid for multi-component order parameter. 1.~Udodov V. Violating of the Essam-Fisher and Rushbrooke Relationships at Low Temperatures// World Journal of Condensed Matter Physics. --- 2015. --- Ò.5. --- ¹2. --- Ñ. 55-59. \underline {http://dx.doi.org/10.4236/wjcmp.2015.52008}.   

Application of Novel Molecular Field Theory to Helical Antiferromagnetic Ordering in ${\rm\bf EuCo_2P_2}^\ast$

A formulation of Weiss molecular field theory (MFT) was recently advanced for antiferromagnetic (AFM) systems of identical crystallographically-equivalent local moments interacting by Heisenberg exchange that does not utilize the concept of magnetic sublattices.$^1$ This formulation has the attractive feature that the magnetic and thermal properties in magnetic fields $H\to0$ depend only on the interactions of a representative spin with its neighbors, and thus allows the properties of collinear and coplanar noncollinear AFM structures to be understood and modeled on the same footing. Neutron diffraction measurements showed that ${\rm EuCo_2P_2}$ with the bct ${\rm ThCr_2Si_2}$-type structure undergoes an AFM transition to a coplanar noncollinear $c$-axis helical AFM structure below the ordering temperature $T_{\rm N} = 66.5$ K.$^2$ Here we report the properties and apply our MFT to model the anisotropic magnetic susceptibility of single-crystal ${\rm EuCo_2P_2}$ below $T_{\rm N}$. \\ 1. D. C. Johnston, PRL {\bf 109}, 077201 (2012); PRB {\bf 91}, 064427 (2015).\\ 2. M. Reehuis et al., J. Phys. Chem. Solids {\bf 53}, 687 (1992). \\ $^\ast$Research supported by U.S. Department of Energy, Division of Materials Science and Engineering, under Contract No.~DE-AC02-07CH11358.   

Investigation of Quantum Phase Transitions of Spin-3/2 AKLT Systems On the Hexagonal Lattice via the Tensor-Network Method

The spin-3/2 Affleck-Kennedy-Lieb-Tasaki (AKLT) state on the hexagonal lattice is an example of valence-bond solid state (VBS), which is recently shown to provide resource for quantum computation and is also a nontrivial symmetry protected topologically ordered state if the translation invariance is imposed in addition to the rotation symmetry. Niggemann et al. previously studied a deformation of the AKLT model and derived a one-parameter family of ground states (parametrized by $a$) that are deformed from the AKLT point ($a=\sqrt{3}$). By mapping to a free-fermion eight-vertex model, they identified a VBS to N\'eel transition at $a_{c2}\approx 2.5425$. We employ the tensor-network method to directly compute the N\'eel order parameter and obtain results that agree with theirs. We also study the regime where the deformation parameter $a$ decreases close to zero. We find that there is a transition at $a_{c1}\approx 0.58$ to an XY phase, which is characterized by algebraically decaying correlations, rotation invariance of spins in the x-y plane and the induced magnetization being aligned with the direction of the extend field.   

Inelastic neutron scattering study and magnetic excitations on the low-dimensional antiferromagnet $\alpha-$Cu$_{2}$V$_{2}$O$_{7}$

Magnetic excitations of the low-dimensional antiferromagnet $\alpha-$Cu$_{2}$V$_{2}$O$_{7}$ have been investigated using inelastic neutron scattering. The study reveals unusual commensurate splitting of magnetic excitation branches centered at a wave vector (0, $\pm \delta$, 0) with $\delta$ = 0.25 away from a magnetic zone center, where a magnetic Bragg peak is observed. The energy gap of 0.75 meV at (0, $\pm \delta$, 0) was found to decrease as a function of temperature and the magnetic excitations become diffusive and disappear above 35 K coincident with T$_N$ = 33.4 K. A recent experiment at the Multi Axis Crystal Spectrometer, MACS, to map the excitations over a large momentum space clearly shows the splitting of the dispersion at most of the allowed magnetic reflections. This commensurate splitting of the spin-wave-type excitations without the magnetic Bragg reflections at the same commensurate wave vectors has not yet been previously observed and remains unexplained. In the presentation, the experimental data will be shown and the possible explanation will also be discussed.   

Tunable Collective Modes in the Dilute Ising Magnet LiHo${}_{0.045}$Y${}_{0.955}$F${}_4$

Collections of quantum mechanical spins with dipolar interactions exhibit a complex set of states and excitations due to the long range and alternating sign of the dipolar potential. We use nonlinear ac magnetic susceptibility on the dilute dipole Ising magnet LiHo${}_{0.045}$Y${}_{0.955}$F${}_4$ to study the behavior of coupled clusters of spins. Pump-probe spectroscopy excites Fano resonance behavior between coherent, isolated spin clusters and a background spin bath. The evolution of these clusters exhibits universal behavior as a function of several different tuning parameters such as static transverse field, ac pump field, and thermal connectivity to a heat reservoir. We discuss our results within the framework of many-body localization.   

Physical properties of $R$Mg$_{2}$Cu$_{9}$ ($R$ = Y, Ce-Nd, Gd-Dy)

$R$Mg$_{2}$Cu$_{9}$ is a family of hexagonal compounds with a single rare earth site that has a $\bar{6}$m2 local symmetry. In this talk, magnetic, electric transport and specific heat data measured on single crystals of $R$Mg$_{2}$Cu$_{9}$ synthesized using Ta crucible will be presented and discussed. Due to a strong CEF effect, all local moment bearing members (except for isotropic GdMg$_{2}$Cu$_{9}$) in the present study show a higher magnetic susceptibility when external field is applied along the ab-plane than along the c-axis. For $R$ = Ce, Nd, Gd-Dy, the compounds order antiferromagnetically above 2 K. The ordering temperature deviates from de Gennes scaling with GdMg$_{2}$Cu$_{9}$ ordering at a lower temperature than TbMg$_{2}$Cu$_{9}$. PrMg$_{2}$Cu$_{9}$ does not order magnetically down to 2 K and might have a singlet ground state. This series of compounds offer an opportunity to study in-plane anisotropy of rare earth in a hexagonal CEF configuration, following our previous work on in-plane 4-state clock model in a tetragonal system, for example: HoNi$_{2}$B$_{2}$C (P.C. Canfield et al. PRB 55, 970) and DyAgSb$_{2}$ (K.D. Myers et al. PRB 59, 1121).   

Multiplicative logarithmic corrections to quantum criticality in three-dimensional dimerized antiferromagnets

We investigate the quantum phase transition in an S=1/2 dimerized Heisenberg antiferromagnet in three spatial dimensions. By means of quantum Monte Carlo simulations and finite-size scaling analyses, we get high-precision results for the quantum critical properties at the transition from the magnetically disordered dimer-singlet phase to the ordered Neel phase. This transition breaks O(N) symmetry with N=3 in D=3+1 dimensions. This is the upper critical dimension, where multiplicative logarithmic corrections to the leading mean-field critical properties are expected; we extract these corrections, establishing their precise forms for both the zero-temperature staggered magnetization, $m_s$, and the Neel temperature, $T_N$. We present a scaling ansatz for $T_N$, including logarithmic corrections, which agrees with our data and indicates exact linearity with $m_s$, implying a complete decoupling of quantum and thermal fluctuation effects close to the quantum critical point. These logarithmic scaling forms have not previously identified or verified by unbiased numerical methods and we discuss their relevance to experimental studies of dimerized quantum antiferromagnets such as TlCuCl$_3$. Ref.: arXiv:1506.06073   

Magnon-induced nonanalyticities in thermodynamic and transport properties of quantum ferromagnets

Soft modes and their effects on thermodynamic and transport properties are of great interest. An example of a nonanalyticity induced by Goldstone modes is the divergence of the longitudinal susceptibility, $\chi _{\mathrm{L}}(k) \sim 1/k^{4-d}$, in a classical isotropic Heisenberg ferromagnet in $2 [Preview Abstract]

\textbf{Magnetic phase transitions and magnetization reversal in MnRuP}

The ternary phosphide MnRuP is an incommensurate antiferromagnetic metal crystallizing in the non-centrosymmetric Fe$_{2}$P-type crystal structure. Below the Neel transition at 250 K, MnRuP exhibits hysteretic anomalies in resistivity and magnetic susceptibility curves as the propagation vectors of the spiral spin structure change discontinuously across T$_{1}=$ 180 K and T$_{2}=$ 100 K. Temperature-dependent X-ray diffraction data indicate that the first-order spin reorientation occurs in the absence of a structural transition. A strong magnetization reversal (MR) effect is observed upon cooling the system through T$_{N}$ in moderate dc magnetic fields. Positive magnetization is recovered on further cooling through T$_{1}$ and maintained in subsequent warming curves. The field dependence and training of the MR effect in MnRuP will be discussed in terms of the underlying magnetic structures and compared to anomalous MR observed in vanadate systems.   

\textbf{ARPES study of the Kitaev Candidate RuCl}$_{\mathbf{3\, }}$

RuCl$_{3}$ has been identified as a spin-orbital-assisted Mott insulator with possible Kitaev magnetic orders at low temperature by X-ray absorption, susceptibility, specific heat and Raman scattering[1-3]. Here we report high resolution ARPES spectroscopy measurements on single crystal RuCl$_{3}$, and compare it with DFT calculations with and without magnetic order. Furthermore, the possible spin-orbital-assisted Mott transition is investigated through electron doping. [1] K.W.Plumb et al., Phys. Rev. B, 90, 041112 (2014). [2] J.A.Sears et al., Phys. Rev. B, 94, 144420 (2015). [3] L. J. Sandilands et al. Phys. Rev. Lett. 114, 147201 (2015).   

Lifshitz-type metal-to-insulator transition via strong relativistic renormalization in NaOsO$_3$

Using \emph{ab initio} band structure methods in the framework of density functional theory (DFT), we study the mechanism responsible for the metal-to-insulator transition (MIT) in the 5$d$ oxide NaOsO$_3$ and reinterpret its previously proposed Slater nature. We show that spin-orbit coupling (SOC) causes a strong relativistic renormalization of the electronic correlation that moves the system to a weakly interacting itinerant limit, where the physics of itinerant magnetism prevails. This is the opposite effect as compared to the widely studied iridates, where SOC drives the formation of a relativistic Mott state. By mapping the magnetically constrained non-collinear DFT calculation using spin-fluctuation theory, we explain the MIT of the system in connection with the anomalies observed in the experimental resistivity curve. We show that the continuous MIT is associated to the progressive disappearance of electron and hole pockets in the Fermi surface, typical of a Lifshitz-type MIT, and is mediated by spin-fluctuations. We discuss the inconsistencies of a pure Slater interpretation and propose that NaOsO$_3$ should be classify as a magnetically-driven relativistic Lifshitz insulator.   

Spin-texture induced by oxygen vacancies in Strontium perovskites (001) surfaces: A theoretical comparison between SrTiO$_3$ and SrHfO$_3$

The electronic structure of SrTiO$_3$ and SrHfO$_3$ (001) surfaces with oxygen vacancies is studied by means of first-principles calculations. We reveal how oxygen vacancies within the first atomic layer of the SrTiO$_3$ surface (i) induce a large antiferrodistortive motion of the oxygen octahedra at the surface, (ii) drive localized magnetic moments on the Ti--3$d$ orbitals close to the vacancies and (iii) form a two-dimensional electron gas localized within the first layers. The analysis of the spin-texture of this system exhibits a splitting of the energy bands according to the Zeeman interaction, lowering of the Ti--3\emph{d$_{xy}$} level in comparison with \emph{d$_{xz}$} and \emph{d$_{yz}$} and also an in-plane precession of the spins. No Rashba-like splitting for the ground state neither for ab initio molecular dynamics trajectory at 400K is recognized as suggested recently by A. F. Santander-Syro \emph{et al.} \cite{Santander-Syro2014}. Instead, a sizeable Rashba-like splitting is observed when the Ti atom is replaced by a heavier Hf atom with a much larger spin-orbit interaction. However, we observe the disappearance of the magnetism and the surface two-dimensional electron gas when full structural optimization of the SrHfO$_3$ surface is performed. Our results uncove   

Quantum Impurities develop Fractional Local Moments in Spin-Orbit Coupled Systems

Systems with spin-orbit coupling have the potential to realize exotic quantum states which are interesting both from fundamental and technological perspectives. We investigate the new physics that arises when a correlated spin-{\em 1/2} quantum impurity hybridizes with a spin-orbit coupled Fermi system. The intriguing aspect uncovered is that, in contrast to unit local moment in conventional systems, the impurity here develops a {\em fractional local moment} of {\em 2/3}. The concomitant Kondo effect has a high Kondo temperature ($T_K$). Our theory explains these novel features including the origins of the fractional local moment and provides a recipe to use spin-orbit coupling($\lambda$) to enhance Kondo temperature ($T_K \sim \lambda^{4/3}$). These results will be useful in shedding light on a range of experiments, including those of magnetic impurities at oxide interfaces. Our predictions can also be directly tested in cold-atom systems where the spin-orbit coupling can be engendered via a uniform synthetic non-Abelian gauge field. In addition, this work opens up new directions of research in spin-orbit coupled Kondo lattice systems. Reference: arXiv:1509.07328