Stochastic hyperfine interactions modeling library

Abstract The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A 22 can be neglected. Program summary Program title: SHIML Catalogue identifier: AEIF_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 3 No. of lines in distributed program, including test data, etc.: 8224 No. of bytes in distributed program, including test data, etc.: 312 348 Distribution format: tar.gz Programming language: C Computer: Any Operating system: LINUX, OS X RAM: Varies Classification: 7.4 External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4] Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), Mossbauer effect (ME), muon spin rotation (μSR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When interactions fluctuate at rates comparable to the time scale of a hyperfine method, there is a loss in signal coherence, and spectra are damped. The degree of damping can be used to determine fluctuation rates, provided that theoretical expressions for spectra can be derived for relevant physical models of the fluctuations. SHIML provides routines to help researchers quickly develop code to incorporate stochastic models of fluctuating hyperfine interactions in calculations of hyperfine spectra. Solution method: Calculations are based on the method for modeling stochastic hyperfine interactions for PAC by Winkler and Gerdau [5]. The method is extended to include other hyperfine methods following the work of Dattagupta [6]. The code provides routines for reading model information from text files, allowing researchers to develop new models quickly without the need to modify computer code for each new model to be considered. Restrictions: In the present version of the code, only methods that measure the hyperfine interaction on one probe spin state, such as PAC, μSR, and NMR, are supported. Running time: Varies References: [1] M.O. Zacate, The adjustable parameter package, Technical report 2, CINSAM Grant 2006-R7 (unpublished); available for download at http://tapp.nku.edu/ . [2] L.S. Blackford, et al., ACM Trans. Math. Soft. 28 (2) (2002) 135–151; J. Dongarra, International Journal of High Performance Applications and Supercomputing 16 (1–2) (2002) 1–199; http://www.netlib.org/blas/ . [3] M. Galassi, et al., GNU Scientific Library Reference Manual, third edition (2009); available for download at http://www.gnu.org/software/gsl/ . [4] E. Anderson, et al., LAPACK Users' Guide, third edition, Society for Industrial and Applied Mathematics, Philadelphia, 1999; http://www.netlib.org/lapack/ . [5] H. Winkler, E. Gerdau, Z. Phys. 262 (1973) 363–376. [6] S. Dattagupta, Hyperfine Interactions 11 (1981) 77–126.