Instanton paths for the problem of coherent quantum tunneling in small ferromagnetic particles

It is shown that the problem of instantons in ferromagnetic materials in a large-spin model is reduced to an exactly integrable dynamical system with a finite number of variables. For a rather wide class of models, there exists a continuum of instanton paths that form a one-parameter family of paths with essentially different shapes but with the same value of the Euclidean action. On the basis of the formalism developed, exact instanton solutions are constructed that describe macroscopic quantum tunneling for a small ferromagnetic particle with uniaxial or biaxial quadratic anisotropy in the presence of a magnetic field applied perpendicularly to the easy axis. These solutions are valid for any relations between the anisotropy parameters and for any magnitude of the magnetic field and its direction in the base plane. Based on the solutions obtained, the principles of macroscopic quantum tunneling in high-spin-molecule-type magnetic particles are described. Tunneling regimes of two types are obtained: (1) regimes that are characterized by destructive interference of instanton trajectories and oscillatory dependence of the transition probability on the magnitude of the magnetic field and (2) regimes in which all instantons have the same purely real value of the Euclidean action and there is no destructive interference.     

Topological phase interference effects in resonant quantum tunneling of the Néel vector between nonequivalent magnetic wells in mesoscopic single-domain antiferromagnets

Resonant quantum tunneling of the Néel vector between nonequivalent magnetic wells is investigated theoretically for a nanometer-scale single-domain antiferromagnet with biaxial crystal symmetry in the presence of an external magnetic field applied along the easy anisotropy axis, based on the two-sublattice model. Both the Wentzel-Kramers-Brillouin exponent and the preexponential factors are evaluated in the instanton contribution to the tunneling rate for finite and zero magnetic fields by applying the instanton technique in the spin-coherent-state path-integral representation, respectively. The quantum interference or spin-parity effects induced by the topological phase term in the Euclidean action are discussed in the rate of quantum tunneling of the Néel vector. In the absence of an external applied magnetic field, the effect of destructive phase interference or topological quenching on resonant quantum tunneling of the Néel vector is evident for the half-integer excess spin antiferromagnetic nanoparticle. In the weak field limit, the tunneling rates are found to oscillate with the external applied magnetic field for both integer and half-integer excess spins. We discuss the experimental condition on the applied magnetic field which may allow one to observe the topological quenching effect for nanometer-scale single-domain antiferromagnets with half-integer excess spins. Tunneling behavior in resonant quantum tunneling of the magnetization vector between nonequivalent magnetic wells is also studied for a nanometer-scale single-domain ferromagnet by applying the similar technique, but in the large noncompensation limit. Received 4 June 1999     

Dynamics of the intermediate state and domain walls in an external oscillating magnetic field

We study the dynamics of 90-degree domain walls in the intermediate state of antiferromagnets, the state being realized in a first-order spin-flop transition in an external magnetic field. We show that an additional oscillating external magnetic field leads to a drift in the domain walls and find the dependence of the drift velocity on the amplitude, frequency, and polarization of the oscillating field. Finally, we discuss the possibility of the domain structure drifting as a whole. Zh. éksp. Teor. Fiz. 112, 1374–1385 (October 1997)     

A mean-field theory for strongly disordered non-frustrated antiferromagnets

Motivated by impurity-induced magnetic ordering phenomena in spin-gap materials like TlCuCl₃, we develop a mean-field theory for strongly disordered antiferromagnets, designed to capture the broad distribution of coupling constants in the effective model for the impurity degrees of freedom. Based on our results, we argue that in the presence of random magnetic couplings the conventional first-order spin-flop transition of an anisotropic antiferromagnet is split into two transitions at low temperatures, associated with separate order parameters along and perpendicular to the field axis. We demonstrate the existence of either a bicritcal point or a critical endpoint in the temperature–field phase diagram, with the consequence that signatures of the spin flop are more pronounced at elevated temperature.     

The Mössbauer effect and magnetic phase transitions

The Mössbauer effect provides a direct method for identifying the spin axis in magnetic crystals and observing magnetic phase transitions. The order of the transition may be inferred from the Mössbauer spectrum. Phase changes can occur as a function of temperature (e.g. when the anisotropy fieldB _A changes sign) or as a function of applied magnetic field. In an antiferromagnet a field ?(2B _E B _A)^1/2 along the spin axis whereB _E is the exchange field causes the spin-flop transition which is normally first order (sharp) whereas the transition to the paramagnetic phase which occurs at higher fields?2B _E is second order (continuous). In quasi-one-dimensional crystals Mössbauer spectra show that the spin-flop transition is first order locally but occurs over a range of fields throughout the crystal, so that the first order character is masked in a conventional magnetization measurement. In fields applied at a finite angle>B _A/2B _E to the spin axis the transition becomes second order, i.e. a continuous rotation of the spins occurs. In canted antiferromagnets (or weak ferromagnets) the spin-flop transition is also continuous; in addition a “screw” re-orientation may be induced by fields applied perpendicular to the spin axis and arises from antisymmetric exchange. For crystals with lowT _N the hyperfine field changes when a magnetic field is applied and has a minimum at a phase transition; this may be used to map out the magnetic phase diagram.     

Vortices, tunneling, and deconfinement in bilayer quantum Hall excitonic superfluid

The physics of vortices, instantons, and deconfinement is studied for layered superfluids in connection to bilayer quantum Hall systems at filling fraction nu = 1. We develop an effective gauge theory taking into account both vortices and instantons induced by interlayer tunneling. The renormalization group flow of the gauge charge and the instanton fugacity shows that the coupling of the gauge field to vortex matter produces a continuous transition between the confining phase of free instantons and condensed vortices and a deconfined gapless superfluid where magnetic charges are bound into dipoles. The interlayer tunneling conductance and the layer-imbalance induced inhomogeneous exciton condensate are discussed in connection to experiments.     

Magnetic properties of the intermetallic compound PrAg

The field and temperature dependences of the magnetization of PrAg are found to be those of an antiferromagnet whose Néel point is ～11°K and which undergoes a spin-flop transition at a critical field of ～5 kOe, as confirmed by high-field neutron diffraction measurements. Preliminary comparisons are made with properties calculated from crystal-field theory.     

Magnetoelectric effect in antiferromagnetic crystals

Magnetoelectric experiments provide information on spin configurations, critical indices and microscopic ionic interactions. The basic theory of the magnetoelectric effect in antiferromagnets is rederived in this article and extended to situations in which there is an external magnetic field including the spin-flop phase. It is found that measurements of the magnetoelectric tensor α as a function of field in the antiferromagnetic and spin-flop phases of an antiferromagnet can provide more complete information in all three categories above. Certain higher-order terms are examined and it is found that it is possible to measure the staggered susceptibility directly in magnetoelectric materials. It is shown that a non-zero value of α causes a tetragonal antiferromagnet to be optically biaxial. A pedagogical discussion of the origins of magnetoelectric effects is given in the Appendix.     

Noncommutative Instantons: A New Approach

We discuss instantons on noncommutative four-dimensional Euclidean space. In the commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the trivial field at infinity. However, technically it is more convenient to work on the four-dimensional sphere. We will show that the situation in the noncommutative case is quite similar. One can analyze instantons taking as a starting point the algebra of smooth functions vanishing at infinity, but it is convenient to add a unit element to this algebra (this corresponds to a transition to a sphere at the level of topology). Our approach is more rigorous than previous considerations; it seems that it is also simpler and more transparent. In particular, we obtain the ADHM equations in a very simple way. Received: 30 March 2001 / Accepted: 3 April 2001     

Magneto-optics of antiferromagnets

Antiferromagnetic crystals in which crystallographic sites occupied by magnetic ions from various sublattices are not transnationally equivalent and are not associated with each other by a symmetry center can have magneto-optic properties distinct from the properties of other antiferromagnets. In particular, birefringence and dichroism of linear polarized light can be observed which are directly proportional to the magnetic field strength, as well as magnetic rotation and circular dichroism quadratic in the field strength. Both effect—the linear magneto-optic effect and quadratic magnetic gyration — are sensitive to the crystal magnetic symmetry and to reorientation of the antiferromagnetic vector. Both effects reverse their signs when the directions of the magnetic moments of a sublattice are changed. These properties of new magneto-optic effects can be used to study the time-reversed domain structure of antiferromagnets, to define the symmetry of magnetic ordering and to study the magnetic crystal energy spectra by spectroscopic methods. The results of experimental studies of the linear magneto-optic effect and quadratic magnetic rotation in tetragonal antiferromagnetic fluorides of transition metals, manganese-germanium garnet and other antiferromagnets are reported. Experimental results on the domain structure of high symmetric antiferromagnets, the point magnetic symmetry of non-collinear multisublattice antiferromagnetic garnet MnGeG are discussed.     

Uniaxially anisotropic antiferromagnets in a field on a square lattice

Classical uniaxially anisotropic Heisenberg and XY antiferromagnets in a field along the easy axis on a square lattice are analysed, applying ground state considerations and Monte Carlo techniques. The models are known to display antiferromagnetic and spin-flop phases. In the Heisenberg case, a single-ion anisotropy is added to the XXZ antiferromagnet, enhancing or competing with the uniaxial exchange anisotropy. Its effect on the stability of non-collinear structures of biconical type is studied. In the case of the anisotropic XY antiferromagnet, the transition region between the antiferromagnetic and spin-flop phases is found to be dominated by degenerate bidirectional fluctuations. The phase diagram is observed to resemble closely that of the XXZ antiferromagnet without single-ion anisotropy.     

Low temperature magnetism in the rare-earth perovskite GdScO_3

The magnetic phase diagram of rare-earth perovskite compound, GdScO_3, has been investigated by magnetization and heat capacity. The system undergoes an antiferromagnetic phase transition at T_N= 2.6K, with an easy axis of magnetization along the a axis. The magnetization measurements show that it exists a spin-flop transition around 0.3 T for the applied field along the a axis. The critical magnetic field for the antiferromagnetic-to-paramagnetic transition is near 3.2 T when temperature approaches zero. By scaling susceptibilities, we presume this point(B = 3.2 T, T = 0 K) might be a fieldinduced quantum critical point and the magnetic critical fluctuations can even be felt above TN.     

Interplay of iron and rare-earth magnetic order in rare-earth iron pnictide superconductors under magnetic field

The magnetic properties of iron pnictide superconductors with magnetic rare-earth ions under strong magnetic field are investigated based on the cluster self-consistent field method. Starting from an effective Heisenberg model, we present the evolution of magnetic structures on magnetic field in RFeAsO(R = Ce, Pr, Nd, Sm, Gd, and Tb) and RFe_2As_2(R =Eu) compounds. It is found that spin-flop transition occurs in both rare-earth and iron layers under magnetic field, in good agreement with the experimental results. The interplay between rare-earth and iron spins plays a key role in the magneticfield-driven magnetic phase transition, which suggests that the rare-earth layers can modulate the magnetic behaviors of iron layers. In addition, the factors that affect the critical magnetic field for spin-flop transition are also discussed.     

Effects of interaction on quantum spin Hall insulators

We study the S(z)-conserving quantum spin Hall insulator in the presence of Hubbard U from a field theory point of view. The main findings are the following. (1) For arbitrarily small U the edges possess power-law correlated antiferromagnetic XY local moments. Gapless charge excitations arise from the Goldstone-Wilczek mechanism. (2) Electron tunneling between opposite edges allows vortex instantons to proliferate when K, the XY stiffness constant, satisfies 4πK+(4πK)(-1)<4. When the preceding inequality is violated, the edge modes remain gapless despite the sample width being finite. (3) The phase transition from the topological insulator to the large U antiferromagnetic insulator is triggered by the condensation of magnetic excitons. (4) In the large U antiferromagnetic insulating phase the magnetic vortices carry charges proportional to the square magnitude of the antiferromagnetic order parameter.     

Anomalous magnetic properties near the spin-flop bicritical point in Mn(2)AS(4) (A = Si and Ge)

The magnetic properties of the single crystalline Mn(2)AS(4) (A = Si and Ge) with an olivine structure, which are the uniaxially anisotropic antiferromagnets (the b axis as an easy axis), were investigated. Near the Néel temperature, both compounds exhibit the contrastive magnetic responses along the c axis, namely, the spontaneous weak ferromagnetism in A = Si and the significant enhancement of the differential susceptibility (dM/dH) under the small magnetic field in A = Ge. When A = Ge, we also observed the evolution of dM/dH along the axis at low temperatures. We discuss these phenomena on the basis of the magnetic field-temperature (H-T) phase diagram with the spin-flop bicritical point (H(BP), T(BP). The role of the thermal or quantum fluctuation was stressed.     

La2CuO4在平行CuO2面磁场中的磁转变

本文在平均场近似下,给出一个关于在平行CuO₂面的磁场作用下,La₂CuO₄的磁转变理论。理论给出的临界磁场随温度T的变化,在定性上与实验相符。但是,从本文理论看,不存在多重临界点。简单讨论了理论和实验不符合的原因。 关键词：     

Two-stage spin-flop transitions in the S = 1/2 antiferromagnetic spin chain BaCu(2)Si(2)O(7)

Two-stage spin-flop transitions are observed in the quasi-one-dimensional antiferromagnet BaCu(2)Si(2)O(7). A magnetic field applied along the easy axis induces a spin-flop transition at 2.0 T followed by a second transition at 4.9 T. The magnetic susceptibility indicates the presence of Dzyaloshinskii-Moriya (DM) antisymmetric interactions between the intrachain neighboring spins. We discuss a possible mechanism whereby the geometrical competition between DM and interchain interactions, as discussed for the two-dimensional antiferromagnet La(2)CuO(4), causes the two-stage spin-flop transitions.     

Magnetic properties of stoichiometric iron sulfide single crystals near the alpha transition temperature

The magnetic susceptibility of nearly stoichiometric iron sulfide single crystals grown by normal freezing was measured in the vicinity of the crystallorgraphic transition temperature T_α ～ 155°C. The existence of two anomalies in the χ vs T curve clearly indicated that the spin-flop transition occurs at a much higher temperature (T_s ～ 190°C).     

Magnetic ordering in rare earth iron silicides and germanides of the RFe2X2 type

Rare earth iron silicides and germanides of the RFe₂Si₂ or RFe₂Ge₂ type with R = La, Ce, Pr, Nd, Sm, Gd and Dy were measured for their magnetic susceptibility. The silicides and germanides of Nd and Gd are antiferromagnetically ordered below a Neel point of, respectively, 11 and 7°K for the silicides and 13 and 11 for the germanides. The Nd sublattice under-goes a spin-flop transition which at 4.2°K is at 11 KOe. Although the Fe sublattice is diamagnetic, all the samples showed a weak ferromagnetic ordering below a temperature of about 700°K. The ratio between the dia- and ferromagnetic phases is 94:6 per cent in the silicides and 80:20 in the germanides, as determined by Mössbauer spectroscopy and supported by magnetization measurements.     

SU(2) instantons with boundary jumps and spin tunneling in magnetic molecules

Coherent state path integrals are shown in general to contain instantons with jumps at the boundaries, i.e., boundary points lying outside classical phase space. Inclusion of these instantons is shown to resolve the "missing quench paradox" in the magnetic molecule Fe8, i.e., the fact that the tunneling between the ground Zeeman states of this molecule is quenched at only four magnetic field values, instead of the ten that would be expected from the topological Berry phase between interfering instantons. An approximate formula is found for the location of the four remaining quenches.