Condon Domains Research Articles

Dynamic peculiarities of interphase boundaries and domain walls for non-spin domains

The analysis of magnetization oscillations (de Haas – van Alphen effect; dHvA effect) and features of the Fermi surface shape in three (3D)- and two-dimensional (2D) metals shows that the dynamic phenomena — the dynamics of domain walls and interphase boundaries during diamagnetic phase transitions — are described by a new nonlinear partial differential equation. The equation is a result of the inclusion of the case of multiple extremal cross sections of the Fermi surface in these metals. Our consideration indicates the possibility of the appearance of metastable non-spin domains (Condon domains) and first-order phase transitions to the ordered phase in the regime of dHvA oscillations for the two-frequency case. Sine–Gordon, Klein–Gordon, double sine–Gordon, time-dependent Ginzburg–Landau equations, and the telegraph equation are limiting cases of the derived equation. We show that particular moving kink-soliton solutions of the equation describe traveling wave fronts being moving domain walls and interphase boundaries in the Condon domain phase.

Metastability in the formation of Condon domains

Metastability effects in the formation of Condon non-spin magnetic domains are considered. A possibility for the first-order phase transition occurrence in a three-dimensional electron gas is described in the case of two-frequency de-Haas-van Alphen magnetization oscillations originating from two extremal cross sections of the Fermi surface. The appearance of two additional domains is shown in the metastable region in aluminum. The phase diagram temperature-magnetic field exhibits the presence of second-order and first- order phase transitions in the two-frequency case.

Size effect on quantum magnetic and thermo-magnetic oscillations in the non-spin domain phase

Magnetic and thermo-magnetic (magneto-caloric) oscillations are studied in quantizing magnetic fields in slabs under conditions of the existence of non-spin (Condon) domains. Size effects on the magnetization oscillations in thin samples are calculated in the domain phase. Computations are carried out in the center of the period of the magnetization and temperature oscillations, taking into account the sample size. Phase diagrams, describing diamagnetic phase transitions and formation of Condon domains, are presented in finite size silver and quasi-two-dimensional organic conductors (2D) samples.

The Diamagnetic Phase Transition of Dense Electron Gas: Astrophysical Applications

Neutron stars are ideal astrophysical laboratories for testing theories of the de Haas–van Alphen effect and diamagnetic phase transition which is associated with magnetic domain formation. The “magnetic interaction” between delocalized magnetic moments of electrons (the Shoenberg effect), can result in an effect of the diamagnetic phase transition into domains of alternating magnetization (Condon's domains). Associated with the domain formation are prominent magnetic field oscillation and anisotropic magnetic stress which may be large enough to fracture the crust of magnetar with a super-strong field. Even if the fracture is impossible as in “low-field” magnetar, the depinning phase transition of domain wall (DW) motion driven by low field rate (mainly due to the Hall effect) in the randomly perturbed crust can result in a catastrophically variation of magnetic field. This intermittent motion, similar to the avalanche process, makes the Hall effect be dissipative. These qualitative consequences about magnetized electron gas are consistent with observations of magnetar emission, and especially the threshold critical dynamics of driven DW can partially overcome the difficulties of “low-field” magnetar bursts and the heating mechanism of transient, or “outbursting” magnetar.

Diamagnetic phase transitions in two-dimensional conductors

A theory describing the susceptibility amplitude and the magnetic induction bifurcation near the dHvA driven diamagnetic phase transitions in quasi two-dimensional (2D) organic conductors of the (ET)2X with X=Cu(NCS)2,KHg(SCN)4,I3,AuBr2,IBr2, etc. is presented. We show that there is a drastic increase in the temperature and magnetic field dependence of the susceptibility amplitude on approaching the diamagnetic phase transition point. Near the phase transition point the temperature and magnetic field dependences are fitted by the ones typical of the mean-field phase transition theory. These dependences confirm the long-range character of the magnetic interactions among the conduction electrons leading to diamagnetic phase transitions. We demonstrate that the magnetic induction splitting of nuclear magnetic resonance (NMR) and muon spin-rotation spectroscopy (μSR) lines due to two Condon domains decreases tending to zero on approaching the diamagnetic phase transition. This decrease is fitted by the temperature and magnetic field dependence of the susceptibility characteristic of the mean-field theory of phase transitions. Performing new susceptibility, NMR and μSR experiments will enable to detect diamagnetic phase transitions and Condon domains in quasi 2D metals.

Dynamics of Condon domain walls

A new nonlinear partial differential equation is used for description of the dynamics of domain walls of magnetic domains of the non-spin type (Condon domains). This equation is derived on the basis of the exact expression for the thermodynamic potential density enabling to take into account the oscillating behavior of the magnetization. The inhomogeneity is included in the generalized equation of state. The derived equation is solved analytically. A new shape of the moving domain wall is presented by the new kink solution of the obtained equation. It is shown that the moving domain wall preserves its profile in the wide range of magnetic fields and temperatures far from the diamagnetic phase transition. This shape coincides with the profile of the static domain wall found in our previous article, which was derived based on a new exact equation of state taking into account the oscillating behavior of the magnetization without expansion of the thermodynamic potential density into a power series. The dependence of the domain wall velocity and thickness on the magnetic field strength, temperature, and Dingle temperature is calculated.

Static properties of Condon domains

A new nonlinear differential equation is used for description of the static properties of domain walls of magnetic domains of the non-spin type (Condon domains). This equation is derived on the basis of the exact expression for the thermodynamic potential density, enabling taking into account the oscillating behavior of the magnetization. Inhomogeneity is included in the generalized equation of state. The derived equation is solved analytically. A new shape of the domain wall is presented by the new kink solution of the obtained equation. The width and surface tension of the domain wall is presented as a function of the magnetic field strength, temperature, and Dingle temperature. They exhibit the critical behavior typical of the mean-field theory of second-order phase transitions. The calculated critical exponents are in agreement with nuclear magnetic resonance, muon spin-rotation spectroscopy and Hall probes measurements.

Diamagnetic length scales of the Condon domain phase in Lifschitz–Kosevich–Shoenberg approximation

Equilibrium properties of the non-uniform diamagnetic phase in normal metals (Condon domains) are studied theoretically in the framework of Lifschitz–Kosevich–Shoenberg (LKS) approximation. It is found that characteristic diamagnetic lengths of the phase, e.g. a period of the domain structure and width of interface boundary between domains, as well as specific surface energy of domain wall, are strongly affected by electron correlations and depend on temperature, magnetic field and purity of the sample. The developed theory is in a good agreement with existent experiment data.

Morphology of Condon domain phases in plate-like sample

The morphology of Condon domains in a plate-like sample is studied based on Shoenberg's assumption for the magnetic flux dependence of the diamagnetic moments which account for the instability of a correlated electron gas under the conditions of strong de Haas–van Alphen (dHvA) effect. At every period of the dHvA oscillations the formation of the intrinsic structure of the non-uniform diamagnetic phase is governed by the first order phase transitions which are strongly affected by temperature, magnetic field and impurity content of the sample. The evolution of phase diagram of the diamagnetic phases, e.g. stripe domain structure, periodic bubble lattice and isolated bubbles, are calculated.

High field measurements of the Condon domain phase diagram in silver

Condon domains form when the de Haas-van Alphen (dHvA) amplitude becomes large compared to the dHvA period, i.e. μ0∂M/∂B > 1, where M is the magnetization and B the induction. This equation defines the boundary between the homogeneous magnetization and the Condon domain state. The phase diagram in the (B, T) plane can be predicted using the Lifshitz-Kosevich formula. We present the Condon domain phase diagram for a silver single crystal measured in magnetic fields up to 28 T and temperatures Tdown to 1.3 K. A standard ac method with a pickup coil system is used at low frequency for the measurements of the de Haasvan Alphen (dHvA) e..ect. The transition point from the state of homogeneous magnetization to the inhomogeneous Condon domain state is found as the point where a small irreversibility in the dHvA magnetization arises, as manifested by an extremely nonlinear response in the pickup voltage showing threshold character. The experimental results are in good agreement with theoretical predictions based on the Lifshitz-Kosevich formula.

Temperature and magnetic field dependencies of Condon domain phase in Lifschitz–Kosevich–Shoenberg approximation

The temperature and magnetic field behavior of non-uniform diamagnetic phase of strongly correlated electron gas at the conditions of the dHvA effect is analyzed. It is shown that in the framework of Lifschitz–Kosevich–Shoenberg approximation the magnetic induction splitting, as well as the range of existence of Condon domains, are characterized by strong dependencies on temperature, magnetic field and impurities of the sample.

Magnetic Domain Formation in Itinerant Metamagnets

We examine the effects of long-range dipolar forces on metamagnetic transitions and generalize the theory of Condon domains to the case of an itinerant electron system undergoing a first-order metamagnetic transition. We demonstrate that, within a finite range of the applied field, dipolar interactions induce a spatial modulation of the magnetization in the form of stripes or bubbles. Our findings are consistent with recent observations in the bilayer ruthenate Sr(3)Ru(2)O(7).

Direct Observation of Condon Domains in Silver by Hall Probes

Using a set of micro Hall probes for the detection of the local induction, the inhomogeneous Condon domain structure has been directly observed at the surface of a pure silver single crystal under strong Landau quantization in magnetic fields up to 10 T. The inhomogeneous induction occurs in the theoretically predicted part of the Condon domain phase diagram. Information about size, shape, and orientation of the domains is obtained by analyzing Hall probes placed along and across the long sample axis and by tilting the sample. On a beryllium surface the induction inhomogeneity is almost absent although the expected induction splitting here is at least 10 times higher than in silver.

Non-linear behaviour of diamagnetic moments in Condon domain phase

A model for non-linear behaviour of a magnetization in strong de Haas van Alphen effect is proposed. It describes correctly measured values of the magnetic induction splitting due to Condon domains in silver, beryllium and aluminium. It is shown that the characteristics of magnetization curve in Condon domain phase depend on temperature, magnetic field and Dingle temperature.

Critical phenomena at diamagnetic phase transitions

The critical phenomena near diamagnetic phase transitions and in the domain phase are considered. Possibilities of the soft-mode existence and the static critical effect in susceptibility related to the appearance of Condon domains in aluminium are discussed. The constructed phase diagram and the temperature behaviour of the susceptibility give the value of the phase-transition temperature observed in aluminium. We present the temperature dependence of the magnetisation in each domain being the order parameter of the diamagnetic phase transition and confirming the softening of the orbital magnon-mode in aluminium. Calculations of the spectral density of excitations at diamagnetic phase transitions are made in order to explain the critical growth of the helicon damping observed in aluminium. The temperature dependence of the damping coincides with that measured in aluminium. The calculated magnetic-induction splitting due to Condon domains turns out to be close to that estimated in muon rotation spectroscopy experiment.

Formation of Condon domains as a phase transition

It is shown, for the first time, that approaching the Condon domain phase in temperature from above is accompanied by critical temperature growth of the susceptibility thereby indicating formation of Condon domains, which occurs as a phase transition. The study is based on a recent measurement of the temperature dependence of the susceptibility in silver in magnetic field of 25 T under conditions of the nonlinear de Haas-van Alphen effect. Experimental results for the positive and negative slopes of the magnetization in one de Haas-van Alphen period are in good agreement with results of the calculations presented here. The Curie–Weiss law for the susceptibility is derived for a needle-type specimen. The Curie constant is calculated.

Coherent spin control of matrix isolated molecules by IR+UV laser pulses: quantum simulations for ClF in Ar.

Two coherent sequential IR+UV laser pulses may be used to generate two time-dependent nuclear wave functions in electronic excited triplet and singlet states via single (UV) and two photon (IR+UV) excitation pathways, exploiting spin-orbit coupling and vibrational pre-excitation, respectively. These wave functions evolve from different Franck-Condon domains until they overlap in a domain of bond stretching with efficient intersystem crossing. Here, the coherence of the laser pulses is turned into optimal interferences of the wave packets, yielding the total wave packet at the target place, time, and with dominant target spin. The time resolution of spin control is few femtoseconds. The mechanism is demonstrated by means of quantum model simulations for ClF in an Ar matrix.

Size-dependent effects on the magnetization dynamics of Condon domains

The existence of magnetic domains in nonferromagnetic metals at quantizing magnetic fields is examined under conditions of de Haas\char21{}van Alphen oscillations in the range of strong magnetic fields in thin slabs in a three-dimensional electron gas. Dynamics of Condon domain walls are studied in bulk metals and films at time-varying and time-independent applied magnetic fields. The temperature, magnetic field, purity, and sample size-dependent effects on the width, velocity and mobility of domain walls are calculated. Domain wall resonance and relaxation effects are considered in the three-dimensional electron gas.

Domain State Occurring in the de Haas–van Alphen Effect in Silver

Hysteresis has been observed in de Haas-van Alphen measurements of the Condon domains in silver, and it shows the first-order nature of the transition to the domain state. The hysteresis, and thus the first-order nature, is manifested in a nonlinear effect where a double-valued response of the amplitude with the applied external field is observed.

Magnetic domains in non-ferromagnetic metals: The non-linear de Haas-van Alphen effect

This review is devoted to an exposition of the principles of the physics of magnetic domains in non-ferromagnetic metals and diamagnetic phase transitions, which lead to the formation of the so-called Condon domains during magnetic oscillations in a three-dimensional electron gas. One of the goals of the review is to provide a deeper insight into the nature of this instability of the electron gas in normal metals and improve the understanding of this type of non-spin magnetism. We discuss theoretical aspects of the physics underlying magnetic ordering of conduction electrons in bulk metals and in thin films, and describe the behaviour of the susceptibility, thermal expansion, specific heat, compressibility, sound velocity, magnetic induction bifurcation, the order parameter, domain formation, wetting of domain walls, nucleation and kinetics of diamagnetic phase transitions. In the vicinity of diamagnetic phase transitions the results obtained coincide with those following from the Landau theory of phase t...