Spin tunneling in a swept magnetic field

Europhysics Letters

Volumn 39, Issue 1, 1997, Pages 1-6

  Gunther, L ^a,b  

^a TUFTS UNIVERSITY   (United States)

^b LABORATOIRE DE CRISTALLOGRAPHIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031184748     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i1997-00545-8     Document Type: Article

References (20)

1. FRIEDMAN J., SARACHIK M. P., TEJADA J. and ZIOLO R., Phys. Rev. Lett., 76 (1996) 3830; THOMAS L., LIONTI F., BALLOU R., GATTESCHI D., SESSOLI R. and BARBARA B., Nature, 383 (1996) 145; HERNANDEZ J., ZHANG X. X., LUIS F., BARTOLEMÉ J., TEJADA J. and ZIOLO R., Europhys. Lett., 35 (1996) 301.
2. FRIEDMAN J., SARACHIK M. P., TEJADA J. and ZIOLO R., Phys. Rev. Lett., 76 (1996) 3830; THOMAS L., LIONTI F., BALLOU R., GATTESCHI D., SESSOLI R. and BARBARA B., Nature, 383 (1996) 145; HERNANDEZ J., ZHANG X. X., LUIS F., BARTOLEMÉ J., TEJADA J. and ZIOLO R., Europhys. Lett., 35 (1996) 301.
3. FRIEDMAN J., SARACHIK M. P., TEJADA J. and ZIOLO R., Phys. Rev. Lett., 76 (1996) 3830; THOMAS L., LIONTI F., BALLOU R., GATTESCHI D., SESSOLI R. and BARBARA B., Nature, 383 (1996) 145; HERNANDEZ J., ZHANG X. X., LUIS F., BARTOLEMÉ J., TEJADA J. and ZIOLO R., Europhys. Lett., 35 (1996) 301.
4. GUNTHER L., Physics World, 12 (1990) 28; STAMP P., Nature, 383 (1996) 125; CHUDNOVSKY E. C., Science, 274 (1996) 938.
5. GUNTHER L., Physics World, 12 (1990) 28; STAMP P., Nature, 383 (1996) 125; CHUDNOVSKY E. C., Science, 274 (1996) 938.
6. GUNTHER L., Physics World, 12 (1990) 28; STAMP P., Nature, 383 (1996) 125; CHUDNOVSKY E. C., Science, 274 (1996) 938.
7. GUNTHER L. and BARBARA B. (Editors), Proceedings of the first workshop on Quantum Tunneling of Magnetization - QTM '94 (Kluwer, Dordrecht) 1995.
8. SESSOLI R., GATTESCHI D., CANESCHI A. and NOVAK M., Nature (London), 365 (1993) 141.
9. GATTESCHI D., CANESCHI A., PARDI L. and SESSOLI R., Science, 265 (1995) 1054.
10. VILLAIN J., HARTMANN-BOUTRON F., SESSOLI R. and RETTORI A., Europhys. Lett., 27 (1994) 159.
11. NOVAK M. and SESSOLI R., in Quantum Tunneling of Magnetization (ref. [3]), p. 171.
12. BARBARA B. et al., J. Magn. & Magn. Mater., 140-144 (1995) 1825.
13. POLITI P., RETTORI A., HARTMANN-BOUTRON F. and VILLAIN J., Phys. Rev. Lett., 75 (1995) 537.
14. In actuality, the exponent obtained in the fit was 1.57, which we have replaced by π/2.
15. BOHM D., Quantum Theory, (J. Wiley, New York) 1951, Chapt. 20. (There is a misleading remark therein, connected with the transition from eq. (7) to eq. (11), with no effect on the final results.)
16. The actual problem of spin tunneling involves a more complex Hamiltonian with a (2S + 1) × (2S + 1) matrix, where S is the total spin. We have proved that the relations eqs. (5) and (6) hold generally, close to a crossing that is split by off-diagonal terms, when the Zeeman energies due to the applied longitudinal field, here reflected by h and h′, are small perturbations to the diagonal terms of the Hamiltonian.
17. 2k/m eε/(latin small letter h with stroke) , where e and m axe the electron charge and mass, respectively, k is the wave vector, to be set equal to that at the band edge, and ε is the applied electric field. Our result holds for all sweep rates, while the result for Zener tunneling makes use of a WKB approximation that holds only for small electric fields (corresponding to low sweep rates). (See SMITH R. A., Wave Mechanics of Crystalline Solids (Chapman and Hall, London) 1969.)
18. GARANIN D. A., J. Phys. A, 24 (1991) L61.
19. BARBARA B. and GUNTHER L., J. Magn. & Magn. Mater., 128 (1993) 35.
20. In a preprint received after this paper was first submitted for publication, PROKOF'EV N. V. and STAMP P. C. E. claim that the relaxation time in fixed field is governed by the fluctuating hyperfine fields and the spin-phonon interaction. See also their more comprehensive article on the role of nuclear spins, J. Low Temp. Phys., 104 (1996) 143.