Session Y16: Magnetic Theory II

Dynamics of Thermal Effects in the Spin-Wave Theory of Quantum Antiferromagnets

The main propose of this work [1] is to study the dynamics of quantum antiferromagnets due to the interaction with a thermal environment. To this end we resort to the spin wave theory which has become by now an standard and reference tool in order to have a good approximate description of quantum antiferromagnetic systems in appropriate dimensions. We derive a master equation that allows us to study non-equilibrium dynamics due to the thermal bosons in the environment, and give closed analytic form for the magnon decay rates. Moreover, we show that these ones turn out to be closely related to form factors, which are experimentally accessible by means of neutron and Raman scattering. Furthermore, we compute the time-evolution of the staggered magnetization showing that, for moderate temperatures, the magnetic order is not spoilt even if the coupling is fully isotropic. As far as we know, this is a fundamental aspect of spin wave theory that has remained unexplored. We expect this presentation may be interesting for a broad audience as it is at the crossroads of strongly correlated systems and the physics of quantum open systems, that is so much rooted in quantum information theory.\\[4pt] [1] A. Rivas and M.A. Martin-Delgado, Ann. Phys. (N.Y.) (in press), and arXiv:1112.315.   

Relevance of Deconfined-Criticality Action in the Light of the J-Q Spin Model

We perform large scale Monte Carlo simulations to study critical flows of 2D spin-1/2 J-Q model and 3D SU(2) symmetric discrete NCCP$^1$ model, a.k.a. deconfined-critical-point (DCP) action. The flows of the J-Q model and the DCP action collapse in a significantly large region of system sizes (up to L$\sim 60-80$), implying that the DCP theory (in general) and the discrete NCCP$^1$ model (in particular) correctly capture mesoscopic physics of the competition between the antiferromagnetic and valence-bond orders in quantum spin systems. At larger sizes we observe significant deviations between the two flows which both demonstrate strong violations of scale invariance. Furthermore, while the Neel state is perfectly space-time symmetric, the competing phase shows significant deviations from this symmetry. Possible scenarios are outlined.   

Condensation transitions in critical spin chains

We show that two well known one-dimensional spin chains, namely the XY spin chain and the transverse field Ising model with only next-nearest neighbor interactions, can be related at their critical points via an exact mapping. For periodic boundary conditions, the two chains only differ by a boundary term, which accounts for the differences in the critical behavior. We argue that the boundary term induces a ``condensation transition,'' which is closely related to condensation transitions between gapped two-dimensional topological phases.   

Oxygen vacancy driven structural and orbital reconstruction on SrTiO$_{3}$ surface and subsurface

The role played by oxygen vacancies in bringing about important structural and electronic changes on oxide surfaces and interfaces have been a subject of intense scientific study. From two-dimensional electronic conductivity to the formation of magnetic states, oxygen vacancies have been suggested to be responsible for introducing a variety of interesting physical effects in bulk oxides and their surfaces. In this work, we employ Density Functional theory to perform first principles calculations of oxygen vacancy defects on SrTiO$_{3}$ surface and subsurface. In a defect free SrTiO$_{3}$ surface, the surface Ti atoms have conduction bands whose lower end comprises of split $t_{2g}$ states (lower lying degenerate $d_{xz}$ and $d_{yz}$ states and the upper lying $d_{xy}$ state). The upper conduction bands consist of split $e_{g}$ states where the $d_{z}^{2}$ orbital is shifted lower in energy with respect to the $d_{{x^2}-{y^2}}$ orbital. In the presence of an oxygen vacancy, orbitals reorder and the Ti $d_{z}^{2}$ orbitals, (which also hybridizes itself with Ti \textit{4s} state and the neighboring oxygen $p$ states) gets pushed down and occupied leading to the formation of a defect state. Formation energies of oxygen vacancies on the surface and subsurface of SrTiO$_{3}$ will be presented and the possibility of vacancy induced magnetic states on SrTiO$_{3}$ surface will be discussed.   

A classification scheme of oxide sulfides to guide the design of new hole-conducting transparent materials

The addition of S to transition metal oxides has been contemplated as a way to overcome the limitations of pure oxides by producing a hybridized O-S band with lighter hole mass and narrower gap. Here, we show that O-S mixing could lead either to a continuous band broadening and an upward shift of the valence bands (``band amalgamation" scenario) or to the formation of S-localized states deep in the band gap of the host oxide above the O band (``band pinning" scenario). We survey the La-based oxide sulfides by first-principles methods and we observe the following types of VBM wavefunction in relation to the coordination of the O and S atoms: (i) O and S segregate into separate molecular units; the VBM is preferentially localized on the S units (e.g., LaOCuS). (ii) O and S segregate into separate molecular units; the VBM is delocalized on both O and S units (e.g., (LaO)$_{2}$SnS$_{3}$). (iii) O and S are spatially mixed in the lattice; the VBM is preferentially localized on S (e.g., LaGaOS$_{2}$). (iv) O and S are spatially mixed in the lattice; the VBM is delocalized on both S and O (e.g., LaCrOS$_{2}$). Thus, selecting the type of anion coordination is a posible route to tune the hole conductivity in oxide sulfides.   

Second Order Effective Theory of Bloch Electrons in Electromagnetic Fields

In the first order effective theory of Bloch electrons in electromagnetic fields, the Berry curvature is introduced to yield an anomalous velocity term, which results in profound modification of the phase space density of states.~ Here we derive the second order single band effective theory, finding that the semiclassical dynamics of physical variables still follows the same structure as before, but with additional field corrections in the Berry curvature and band energy. We also discuss applications of our theory and its extension to multiple band case.   

Efficient simulation of infinite tree tensor network states on the Bethe lattice

We show that the simple update approach proposed by Jiang et al [H.C. Jiang, Z.Y. Weng, and T. Xiang, Phys. Rev. Lett. \textbf{101}, 090603 (2008)] is an efficient and accurate method for determining the infinite tree tensor network states on the Bethe lattice. Ground state properties of the quantum transverse Ising model and the Heisenberg XXZ model on the Bethe lattice are studied. The transverse Ising model is found to undergo a second-order quantum phase transition with a diverging magnetic susceptibility but a finite correlation length which is upper-bounded by $1/\ln(q-1)$ even at the transition point ($q$ is the coordinate number of the Bethe lattice). An intuitive explanation on this peculiar ``critical'' phenomenon is given. The XXZ model on the Bethe lattice undergoes a first-order quantum phase transition at the isotropic point. Furthermore, the simple update scheme is found to be related with the Bethe approximation. Finally, by applying the simple update to various tree tensor clusters, we can obtain rather nice and scalable approximations for two-dimensional lattices.   

A Monte Carlo Approach to Modeling Thermal Decay in Perpendicular Recording Media

A procedure is developed to study the evolution of high anisotropy magnetic recording media due to thermally activated grain reversal [1]. Single-domain grains evolve by passing through a sequence of relatively long-lived metastable states punctuated by abrupt reversals. Solutions to the rate equations are obtained using a stochastic integration procedure that calculates the time between successive reversals. Transition rates are formulated from the Arrhenius-Neel expression in terms of the material parameters, the temperature and the applied field. The method is applied to study the rate dependence of finite temperature MH loops and the thermal degradation of a recorded bit pattern in perpendicular recording media. A significant advantage of the method is its ability to extend simulations over time intervals many orders of magnitude greater than is feasible using standard micromagnetics with relatively modest computational effort.\\ $[1]$ T.J. Fal, J.I. Mercer, M.D. Leblanc, J.P. Whitehead, M.L. Plumer, and J. van Ek, Phys, Rev. B, submitted (2012).   

Numerical simulation of 2D ferromagnetic films with perpendicular magnetic anisotropy using a hexagonal lattice and a long range RKKY interaction potential

A numerical $\varphi^4$ model combined with a RKKY potential was used to simulate 2-D ferromagnetic domains. A small random field component was added to allow for a controlled amount of disorder to be introduced into the system. A hexagonal lattice allows for more realistic domains patterns than a square lattice due to the higher density of lattice sites compared to the conventional square lattice. We find that appropriate regions of parameter space produce realistic domain patterns, major hysteresis loops, and reversal curves. For parameters that produce regions of rapid nucleation and growth we observe reversal curves that can extend outside the major hysteresis loops, due to highly frustrated domain configurations as recently observed by Ref. [1]. We also observe a significant region of exponential dependence of the domain spacing upon the interaction potential. Future work will include increasing the random field contribution to determine if the dependence of the domains and hysteresis loops upon disorder matches experimental systems [2].\\[4pt] [1] J.E. Davies et al., Appl. Phys. Lett. 95, 022505 (2009).\\[0pt] [2] M.S. Pierce, et al., submission to Phys. Rev. B   

Inhomogeneous phases of repulsive fermions in cubic lattices

We present a fully self-consistent mean-field study of the inhomogeneous phases in the three-dimensional Hubbard model as the density deviates from half-filling. As the interaction U increases at fixed density, there is a transition from a uniform Fermi liquid to an inhomogeneous metallic phase characterized by a spin density wave along the [001] direction. Upon further increase of U the system undergoes a discontinuous transition to an insulating phase with a spin density wave along the [111] direction. We determine the evolution of the modulation wavelength of the spin density wave as a function of U and density, and discuss signature in the momentum distribution that are relevant to optical lattice experiments. Crossover from two- to three-dimensions is also studied.   

Theoretical Scanning Probe Images of the (001) Surfaces of MnO and NiO

In the paramagnetic state the ground-state crystal structure of the 3$d$ transition metal oxides (TMOs) MnO and NiO is given by an ideal rock-salt ($rs$) structure. Below their respective N\'eel temperature, however, it is characterized by the formation of an antiferromagentic ordering AFM2 which is acompanied by a rhombohedral distortion along the [111] direction. The intersection of the thermally swichable magnetic ordering AFM2 with the crystal surfaces makes TMO surfaces ideal benchmark materials for the investigation of recent magnetic scanning probe techinques such as spin-polarized scanning tunneling microscopy (SP-STM) and magnetic exchange force microscopy (MExFM). We present a density functional theory (DFT) study of the (001) surfaces of MnO and NiO inculding an on-site interaction $U$. Different theoretical approaches for the description of magnetic scanning probe techniques are employed. the magnetic tip is modelled by a single Fe or 5-Fe-atom pyramid. For NiO, the calculated scanning probe images explain the spin contrast and the corrugation found experimentally. For MnO, the calculated images represent interesting predictions which differ from that of NiO.   

Calculated magnetic structure of mobile defects in Fe

Mobile defects such as dislocations and crowdions respond to gradients of strain, temperature, concentration, and applied field, thereby, determining a material's viability in particular applications. In Fe, defects affect the magnetic state of the surrounding atoms. We discuss the defect-induced changes in magnetic moment magnitude and orientation, magnetic anisotropy and magnetic interactions. These quantities are calculated (density functional theory (DFT)) for defect models ranging in size from a few hundred to a few thousand. Comparisons are made between different DFT methods. The importance of magnetism to the response of defects to gradients is discussed.   

Iron impurities in gold and silver: Comparison of magnetoresistance data to numerical renormalization group calculations exploiting non-Abelian symmetries

We consider iron impurities in the noble metals gold and silver and compare experimental data for the resistivity and decoherence rate to numerical renormalization group results for a fully screened $n$-channel, spin $S=n/2$ Kondo model. Our code exploits non-abelian symmetries, which increases the efficiency by orders of magnitude compared to plain abelian NRG. To be specific, the symmetries used were U(1) for charge conservation, U(1) for spin conservation in the presence of magnetic field and the SU(3) channel symmetry. Compared to previous work [1] on this subject, we show superior numerical data for both quantities at finite temperature and extend our analysis to the resistivity at finite magnetic field. We show that our results are converged and that all examined quantities can be described consistently with a single value of $T_K$. The excellent agreement between experiment and theory for $n=3$ shows that both systems are described by a spin-3/2 three-channel Kondo model. [1] T. Costi et al. Phys. Rev. Lett. \textbf{102}, 056802 (2009).   

Magnetic vortices induced by a moving tip

A two-dimensional easy-plane ferromagnetic substrate interacting with a dipolar tip which is magnetized perpendicular with respect to the easy plane is studied numerically by solving the Landau-Lifshitz Gilbert equation [Europhys.\ Lett.\ \textbf{100}, 27004 (2012)]. Due to the symmetry of the dipolar field of the tip, in addition to the collinear structure a magnetic vortex structure becomes stable. It is robust against excitations caused by the motion of the tip. The moved vortex structure shows an increased energy dissipation compared to the collinear structure. We show that for high excitations the system may perform a transition between the two states. The influence of domain walls, which may also induce this transition, is examined.