Session U33: Focus Session: Theory and Simulations of Magnetism I

Tailoring Magnetism in Bulk Semiconductors and Quantum Dots

Carrier-mediated magnetism in semiconductors shows important and potentially useful differences from their metallic counterparts [1]. For example, in magnetically doped semiconductors the change in carrier density induced by light or bias could be sufficient to turn the ferromagnetism on and off. However, there remain many important challenges to fully understand these materials. Our density functional theory study of Mn- doped II-IV-V$_2$ chalcopyrites [2] reveals that variation of magnetic properties across 64 different materials cannot be explained by the dominant models of ferromagnetism in semiconductors. We observe no qualitative similarity with the suggested Curie temperature scaling with the inverse cube of the lattice constant [3]. In contrast to most of the theoretical studies, we explicitly include the temperature dependence of the carrier density and propose a model which permits analysis of the thermodynamic stability of the competing magnetic states [4]. As an example we analyze the stability of a possible reentrant ferromagnetic semiconductor and discuss the experimental support for this prediction. An increasing temperature leads to an increased carrier density such that the enhanced coupling between magnetic impurities results in the onset of ferromagnetism as temperature is raised. We also use the real space finite-temperature local spin density approximation to examine magnetically doped quantum dots in which the interplay of quantum confinement and strong Coulomb interactions can lead to novel possibilities to tailor magnetism. We reveal that, even at a fixed number of carriers, the gate induced changes in the screening [5] or deviations from isotropic quantum confinement [6] could allow for a reversible control of magnetism and switching between zero and finite magnetization. Such magnetic quantum dots could also provide versatile voltage-control of spin currents and spin filtering. The work done in collaboration with S. C. Erwin (Naval Research Lab), A. G. Petukhov (South Dakota School of Mines and Technology), R. M. Abolfath (SUNY Buffalo) and P. Hawrylak (NRC, Canada). [1] T. Jungwirth et al., Rev. Mod. Phys 78, 1311 (2006); I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004). [2] S. C. Erwin and I. Zutic, Nature Mater. 3, 410 (2004). [3] T. Dietl et al., Science 287, 1019 (2000). [4] A. G. Petukhov, I. Zutic, and S. Erwin, Phys. Rev. Lett. 99, 257202 (2007) [5] R. M. Abolfath, P. Hawrylak, and I. Zutic, Phys. Rev. Lett. 98, 207203 (2007); New J. Phys. 9, 353 (2007). [6] R. M. Abolfath, A. G. Petukhov, and I. Zutic, arXiv:0707.2805.   

Effect of vacancies on ferromagnetism in GaN:Mn dilute magnetic semiconductors from first principles

In spite of considerable interest in ferromagnetism of the dilute magnetic semiconductor GaN:Mn, the nature of ferromagnetism is still quite controversial. Experimental values for the Curie temperature T$_C$ vary widely depending upon the details of the the impurity concentrations. We have performed {\it ab initio} density functional studies of the magnetic interactions in GaN in the presence of nitrogen and gallium vacancies. Previous studies have found the nitrogen vacancy has the lowest formation energy. The nitrogen vacancy releases electrons in the system which changes the Mn $d^4$ state to a half-filled Mn $d^5$ state, so that the antiferromagnetic superexchange becomes dominant. The naive picture of Ga vacancies is the release of holes into the system which should increase ferromagnetism. However, we find an antiferromagnetic interaction for the Ga vacancy as well, in agreement with Mahadevan's work$^2$. This can be attributed to the localized nature of the hole states which do not participate in the transport. This hole localization from the Ga vacancy has been demonstrated using the virtual crystal approximation. Thus, both the nitrogen and gallium vacancy are found to impede ferromagnetism. This work is supported by AFOSR-FA 9550-05-1-0462.   

Effect of magnetic short-range order on spin disorder resistivity.

Spin-disorder resistivity (SDR) of Fe and Ni is studied using the noncollinear density functional theory. The Landauer conductance is averaged over random disorder configurations and fitted to Ohm's law. In the fully disordered state, SDR for Fe is close to the experiment, while for fcc Ni it exceeds the experimental value by a factor of 2.3. This indicates either strong magnetic short-range order (MSRO) or reduced local moment above T$_{C}$ for Ni. The temperature dependence of SDR for Fe was studied using the mean-field approximation and the Monte Carlo method applied to the classical nearest-neighbor Heisenberg model. Both methods gives the same magnetization dependence of SDR that is in excellent agreement with the results for the isotropic s-d model. Further using the Reverse Monte Carlo method we generated disordered spin structures with strong MSRO. We found that resulting SDR is not significantly different than for Monte Carlo and mean-field methods. This result indicates that for Fe MSRO is not very important for SDR.   

First-Principle theory of Longitudinal Spin-Fluctuations at high temperatures for itinerant ferromagnets.

We have developed a framework for calculating parameters of effective magnetic Hamiltonian, which includes transverse as well as longitudinal spin fluctuations (LSF) on equal footing. The method is based on the set of constrained calculations within a Local Spin-Density Approximation and Coherent Potential Approximations. The used effective Hamiltonian is similar to those derived in Moriya-Takahashi theory approximating between local and weak itinerant limits of magnetism. The Curie temperatures, paramagnetic susceptibilities and magnetic specific heat have been calculated for bcc Fe and fcc Ni in good agreement with experiment. The importance of LSF contribution even for qualitatively correct description of magnetism of Ni is demonstrated. The first principles criteria for magnetic moment `itineracy', based on fixed spin moment constrained calculations of a magnetic impurity in the Disordered Local Moment host, is established and applied to various magnetic systems. In particular, the famous Rhodes-Wohlfarth plot has been revisited. It is found that in some cases, like VAu$_{4}$, the magnetic moments have very local character in contrast to their long-standing interpretation as weak itinerant ferromagnets.   

Calculation of diamagnetic susceptibility in Cu, graphite and Bi from band-structure

Since early pioneering work on the orbital diamagnetism of free electrons[1] the problem of calculation of diamagnetic susceptibility has attracted attention in systems such as graphite and bismuth. Recent interest in this problem has been motivated by the unconventional electronic properties of mono- and multilayered graphenes. These materials demonstrate large orbital diamagnetism caused by a specific type of band dispersion: a crossing of two bands, each with linear dispersion near the Fermi level. Significant progress in the theoretical description of orbital diamagnetism of electrons in periodic potentials was achieved by Fukuyama[2], with an exact expression for diamagnetic susceptibility, but with an approximation for band dispersion put in by hand. As an alternate approach, we use band structure obtained from a first-principles calculation (LMTO). The orbital susceptibility was calculated for Cu, as an example of a metal with small orbital diamagnetism, as well as for graphite and Bi, materials with known, large diamagnetic susceptibilities. [1] L. Landau, Z. Physik. {\bf 64}, (1930) 629. [2] H. Fukuyama, Prog. Theor. Phys. {\bf 45}, (1971) 704.   

Magnetic Moment of MnSi

MnSi is a metallic helimagnet below 29 K. Density functional theory predicts that it has a moment of 1.0 $\mu_B$/Mn, which is much larger than the measured value of ~0.4 $\mu_B$/Mn. By adding a Hubbard-U correction, we have found a ground state with a moment consistent with the experimental value. These solutions posess a novel quadrupolar spin ordering. We discuss their behavior under pressure and in a magnetic field.   

Piezomagnetic effect in Mn-based antiperovskites

We predict large piezomagnetic effect in Mn-based antiperovskites. The magnetic ground state is determined to be the non-collinear $^{5g}$ structure, which can be viewed as a sequence of alternating layers of clockwise and counterclockwise triangular spin currents in (111) plane, resulting in the zero total magnetization of the system. We use PAW method (VASP) within PBE generalized gradient approximation. We find that the system develops non-zero magnetization under biaxial strain due to the lowering of the crystal symmetry from cubic to tetragonal. The system exhibits linear magnetization dependence on the applied strain over the moderate range (up to 1{\%}) of the latter. The magnetization under strain appears as a result of the rotation of local magnetic moments (LMM) on Mn atoms in Mn$_{2}$N plane. Besides, the system exhibits biaxial anisotropy under strain. We propose using the observed piezomagnetic effect to build the magnetoelectric perovskite ferroelectric -- antiperovskite piezomagnetic heterostructures. The estimated magnetoelectric coefficient is $\sim $ 2*10$^{-9 }$s/m. Because of the piezomagnetic effect, Mn-based antiperovskites can be used in memory cells with electric control of magnetization. It can be also applicable in spintronics, as the system developes a net polarization of up to 30{\%} under external strain.   

Spin Flip in the Presence of a Complex Absorbing Potential

We examine the impact of a complex absorbing potential on electron transport, both in the continuum and on a lattice. This requires the use of non-Hermitian Hamiltonians; the required formalism is briefly outlined. The lattice formulation allows us to study the interesting problem of an electron interacting with a stationary spin, and the subsequent time evolution of the electron and spin properties as the electron is absorbed after the initial interaction. Remarkably, the properties of the localized spin are affected `at-a-distance' by the interaction of the (now entangled) electron with a complex potential.   

Giant Zeeman electric-dipole resonance in antiferromagnetic conductors.

Essential dependence of the electron g-factor on the quasiparticle momentum is a fundamental and, so far, largely overlooked property of antiferromagnetic conductors. It leads to a number of remarkable phenomena, such as excitation of spin flip transitions by AC *electric* field. Absorption intensity of these transitions exceeds that of the Electron Spin Resonance by some four orders of magnitude. I develop a theory of this phenomenon in a weakly doped antiferromagnetic insulator. The predictions may be relevant for a number of antiferromagnetic conductors, ranging from chromium to electron-and hole-doped cuprates, to organic conductors with spin density wave, and to heavy fermion antiferromagnetic metals.   

Electronic properties and magnetic moments of Mn$_{x}$Si$_{1-x}$ for x $<$ 5{\%}.

Recently, there have been experimental reports about Mn$_{x}$Si$_{1-x}$ alloys. All show great promise for room temperature spintronic applications. We report on theoretical studies of the electronic properties of Mn$_{x}$Si$_{1-x}$ for x $<$ 5{\%}, using first principles density functional methods. For the Mn-doped Si, we consider three configurations of the Mn impurities: nearest neighbor (nn), second nearest neighbor (snn), and a three-atom chain configuration. For the nn and snn configurations, the ferromagnetic and antiferromagnetic phases have been compared. The magnetic moment/unit-cell for the nn and ferromagnetic configurations is smaller than for the ferromagnetic snn and chain configurations. The reason will be given. Supported in part by NSF grant: ESC-0725902.   

Monte Carlo simulation of giant magnetoresistance

Monte Carlo method was used to simulate giant magnetoresistance in solids. A square lattice, composed by Ising spins, was generated by the usual Monte Carlo method, using periodic conditions for the borders. Resistivity was measured considering the number of clusters connected between right and left sides of the lattice, with and without applied magnetic field. The calculation of the number and surface of the connecting clusters was calculated using the Hoshen-Kopelman algorithm [1]. As we developed previously pseudorandom non-periodic numbers [2], which allows that the sizes of the clusters as big as necessary, and the steps near the transition as small as desired. This allowed a detailed study near the percolation region, over and below the magnetic transition. Three dimensional lattices, and models other than Ising for the spin coupling are natural extension of the calculation. [1]J. Hoshen and R. Kopelman, Phys. Rev. B14, 3438 (1976) [2]G.E. Barberis,Physica B 398, 468 (2007)   

Propagators for Hamiltonians with Spin-Orbit Coupling

Quantum mechanical propagators can be used to understand the dynamics of electrons in confined electromagnetic environments. We extend the propagator formalism to include the spin degree of freedom for spin-orbit coupling potentials~in two-dimensional geometries.~The 2x2 spin propagators allow us to follow the evolution in time and space of the spin-components of localized wave packets. We apply the technique to Rashba and Dresselhaus interactions and present graphical displays of the corresponding spin motions.~