Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite-size spin chains with a chiral spin ground state observed on biatomic Fe chains deposited on iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the noncollinear nature of the classical ground state, there is a significant zero-point reduction of the ground-state magnetization of the spin spiral. Second, there is a critical external field from which the ground state changes from chiral spin ground state to collinear ferromagnetic order. The character of the two lowest-energy spin waves changes from edge modes to confined bulk modes over this critical field. Third, in the spin-spiral state, the spin-wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

Province of the Massachusetts-Bay, By His Excellency the Governor, you are by and with advice and consent of His Majesty's Council, ordered and directed to pay unto

Not in Evans or Ford.

Proof theory for lattice-ordered groups

Proof-theoretic methods are developed and exploited to establish properties of the variety of lattice-ordered groups. In particular, a hypersequent calculus with a cut rule is used to provide an alternative syntactic proof of the generation of the variety by the lattice-ordered group of automorphisms of the real number chain. Completeness is also established for an analytic (cut-free) hypersequent calculus using cut elimination and it is proved that the equational theory of the variety is co-NP complete.

To establish a uniform system of bankruptcy : June 15 (calendar day, June 18), 1934 : ordered to be printed.

Caption title.

Finite Markov chains,

Mode of access: Internet.

Acts of parliament and bench table orders of the Inner Temple. Ordered to be printed 3 November, 1893.

Mode of access: Internet.

First ( -fourth) report of the Committee appointed by the Lords of the Treasury, in pursuance of addresses of the House of Commons of the 12th, 14th, and 20th August 1839 : Ordered (by the House of Commons) to be printed ... /

Titles of 3rd and 4th reports headed: "Railway communication."

Uptake of radioisotopes and their transfer through food chains by marine organisms : annual report, 1959-1960 /

"September 1961."

Canonical simplification of finite objects, well quasi-ordered by tree embedding /

"UILU-ENG 79 1727."

Enumerations of ordered trees /

Errata slip inserted.

Generating binary trees lexicographically /

Bibliography: p. 26.

Partially ordered classes of finite automata /

Vita.