Model for ferromagnetic nanograins with discrete electronic states

Silvia Kleff; Jan von Delft; Mandar M. Deshmukh; D. C. Ralph

doi:10.1103/PhysRevB.64.220401

Rapid Communication
Access by Xinjiang University

Model for ferromagnetic nanograins with discrete electronic states

Silvia Kleff¹, Jan von Delft^1,2, Mandar M. Deshmukh³, and D. C. Ralph³

¹Institut für Theoretische Festkörperphysik, Universität Karlsruhe, 76128 Karlsruhe, Germany
²Physikalisches Institut, Universität Bonn, 53115 Bonn, Germany
³Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853

PDF

Phys. Rev. B 64, 220401(R) – Published 19 November, 2001

DOI: https://doi.org/10.1103/PhysRevB.64.220401

Abstract

We propose a simple phenomenological model for an ultrasmall ferromagnetic grain, formulated in terms of the grain’s discrete energy levels. We compare the model’s predictions with recent measurements of the discrete tunneling spectrum through such a grain. The model can qualitatively account for the observed features if we assume (i) that the anisotropy energy varies among different eigenstates of one grain, and (ii) that nonequilibrium spin accumulation occurs.

References (24)

K.E. Johnson, J. Appl. Phys. 87, 5365 (2000).
S. Sun, C.B. Murray, D. Weller, L. Folks, and A. Moser, Science 287, 1989 (2000).
S. Guéron, M.M. Deshmukh, E.B. Myers, and D.C. Ralph, Phys. Rev. Lett. 83, 4148 (1999).
C.M. Canali and A.H. MacDonald, Phys. Rev. Lett. 85, 5623 (2000).
D. A. Papaconstantopoulos, Handbook of the Band Structure of Elemental Solids (Plenum, NY, 1986).
J. von Delft and D.C. Ralph, Phys. Rep. 345, 61 (2001).
M.M. Deshmukh, S. Kleff, S. Guéron, E. Bonet Orozco, A. Pasupathy, J. von Delft, and D.C. Ralph, Phys. Rev. Lett. (to be published).
D.C. Ralph, C.T. Black, and M. Tinkham, Phys. Rev. Lett. 74, 3241 (1995); ibid.78, 4087 (1997).
D. Davidović and M. Tinkham, Phys. Rev. Lett. 83, 1644 (1999).
We use $d_{σ} = 1 / [N_{a} N_{σ} (ɛ_{F})]$ , where $N_{σ} (ɛ)$ is the spin-dependent bulk density of states per atom (Ref. ). Using bulk values is appropriate for nanoscale grains, since quantum chemical calculations (Ref. ) on Ni clusters have shown that $N_{σ} (ɛ)$ has converged to its bulk shape already for $N_{a}$ as small as 6.
See, e.g., E. Bonet et al., Phys. Rev. Lett. 83, 4188 (1999), and references therein.
To change the ground state spin value by applying a magnetic field requires in general a field of $δ h \sim (d_{maj} + d_{\min} - U) / 2$ , which is generically (but not necessarily) large in nanomagnets $(μ_{0} δ H ≳ 25 T$ for $s_{0} ≲ 1250)$ .
A. Thiaville, Phys. Rev. B 61, 12 221 (2000).
This value is in good agreement with that found recently by Jamet et al. (Ref. ) (our $k_{N}$ corresponds to their $K_{1} {v / s}_{0}$ ≈0.017 meV). The estimate $k_{N} \approx 0.1 meV$ of Ref. is unreliable, since derived from spectral jump sizes. These, however, can change by a factor of ten or more as $δ k_{\pm}$ is varied (cf. Fig. 11). This fact was overlooked in Ref. , since $k_{N}$ fluctuations were not considered there.
G.M. Pastor, J. Dorantes-Dávila, S. Pick, and H. Dreyssé, Phys. Rev. Lett. 75, 326 (1995).
D.C. Douglass, A.J. Cox, J.P. Bucher, and L.A. Bloomfield, Phys. Rev. B 47, 12 874 (1993).
S. Kleff and J. von Delft, cond-mat/0110348 (unpublished).
O. Agam, N.S. Wingreen, B.L. Altshuler, D.C. Ralph, and M. Tinkham, Phys. Rev. Lett. 78, 1956 (1997).
If $| α 〉$ is the spin ${(s}_{0} \mp 1)$ -ground state, we find [using Eq. (2) of Ref. ] that $E_{α}^{N} - E_{G}^{N} = d_{\min / maj} - U / 2 \mp d_{0}$ , whose maximum value is of order $≳ 1 meV$ for $s_{0} ≲ 1000$ .
For GDMR’s Co nanograins, we estimate $Γ_{tun}$ from the conductance to be $Γ_{tun} \approx G d_{\min} {/ e}^{2} \approx 10^{9} s^{- 1}$ , and the rate for spin-conserving electronic relaxation [by Eq. (8) of Ref. ] to be $Γ_{el} \approx 10^{9} s^{- 1}$ . Since in general $Γ_{sf} ≪ Γ_{el},$ we expect that $Γ_{sf} ≪ Γ_{tun}$ for GDMR’s grains.
Previous predictions of spin accumulation always involved ferromagnetic leads; see, e.g., J. Barnaś et al., Phys. Rev. B 62, 12 363 (2000), and references therein.
For simplicity, we have not included the possibility of a nonequilibrium population of either single-particle excitations or spin-wave excitations (i.e., states of the form $| s, m 〉$ , with $m < s)$ in our calculations or in Fig. 22. However, they certainly exist, and if taken into account, would lead to additional resonances in the tunneling spectrum. Note, though, that the threshold spacing expected for transitions involving spin-wave excitations is $k_{N} {/ s}_{0}$ (or $2 | δ k_{\pm} |)$ if $δ k_{\pm} = 0$ (or $\neq 0)$ which is exceedingly small in both cases.
G. Pacchioni and N. Rösch, Acc. Chem. Res. 28, 390 (1995), and references therein.
M. Jamet et al., Phys. Rev. Lett. 86, 4676 (2001).

[c1] K.E. Johnson, J. Appl. Phys. 87, 5365 (2000).

[c2] S. Sun, C.B. Murray, D. Weller, L. Folks, and A. Moser, Science 287, 1989 (2000).

[c3] S. Guéron, M.M. Deshmukh, E.B. Myers, and D.C. Ralph, Phys. Rev. Lett. 83, 4148 (1999).

[c4] C.M. Canali and A.H. MacDonald, Phys. Rev. Lett. 85, 5623 (2000).

[c5] D. A. Papaconstantopoulos, Handbook of the Band Structure of Elemental Solids (Plenum, NY, 1986).

[c6] J. von Delft and D.C. Ralph, Phys. Rep. 345, 61 (2001).

[c7] M.M. Deshmukh, S. Kleff, S. Guéron, E. Bonet Orozco, A. Pasupathy, J. von Delft, and D.C. Ralph, Phys. Rev. Lett. (to be published).

[c8] D.C. Ralph, C.T. Black, and M. Tinkham, Phys. Rev. Lett. 74, 3241 (1995); ibid.78, 4087 (1997).

[c9] D. Davidović and M. Tinkham, Phys. Rev. Lett. 83, 1644 (1999).

[c10] We use $d_{σ} = 1 / [N_{a} N_{σ} (ɛ_{F})]$ , where $N_{σ} (ɛ)$ is the spin-dependent bulk density of states per atom (Ref. ). Using bulk values is appropriate for nanoscale grains, since quantum chemical calculations (Ref. ) on Ni clusters have shown that $N_{σ} (ɛ)$ has converged to its bulk shape already for $N_{a}$ as small as 6.

[c11] See, e.g., E. Bonet et al., Phys. Rev. Lett. 83, 4188 (1999), and references therein.

[c12] To change the ground state spin value by applying a magnetic field requires in general a field of $δ h \sim (d_{maj} + d_{\min} - U) / 2$ , which is generically (but not necessarily) large in nanomagnets $(μ_{0} δ H ≳ 25 T$ for $s_{0} ≲ 1250)$ .

[c13] A. Thiaville, Phys. Rev. B 61, 12 221 (2000).

[c14] This value is in good agreement with that found recently by Jamet et al. (Ref. ) (our $k_{N}$ corresponds to their $K_{1} {v / s}_{0}$ ≈0.017 meV). The estimate $k_{N} \approx 0.1 meV$ of Ref. is unreliable, since derived from spectral jump sizes. These, however, can change by a factor of ten or more as $δ k_{\pm}$ is varied (cf. Fig. 11). This fact was overlooked in Ref. , since $k_{N}$ fluctuations were not considered there.

[c15] G.M. Pastor, J. Dorantes-Dávila, S. Pick, and H. Dreyssé, Phys. Rev. Lett. 75, 326 (1995).

[c16] D.C. Douglass, A.J. Cox, J.P. Bucher, and L.A. Bloomfield, Phys. Rev. B 47, 12 874 (1993).

[c17] S. Kleff and J. von Delft, cond-mat/0110348 (unpublished).

[c18] O. Agam, N.S. Wingreen, B.L. Altshuler, D.C. Ralph, and M. Tinkham, Phys. Rev. Lett. 78, 1956 (1997).

[c19] If $| α 〉$ is the spin ${(s}_{0} \mp 1)$ -ground state, we find [using Eq. (2) of Ref. ] that $E_{α}^{N} - E_{G}^{N} = d_{\min / maj} - U / 2 \mp d_{0}$ , whose maximum value is of order $≳ 1 meV$ for $s_{0} ≲ 1000$ .

[c20] For GDMR’s Co nanograins, we estimate $Γ_{tun}$ from the conductance to be $Γ_{tun} \approx G d_{\min} {/ e}^{2} \approx 10^{9} s^{- 1}$ , and the rate for spin-conserving electronic relaxation [by Eq. (8) of Ref. ] to be $Γ_{el} \approx 10^{9} s^{- 1}$ . Since in general $Γ_{sf} ≪ Γ_{el},$ we expect that $Γ_{sf} ≪ Γ_{tun}$ for GDMR’s grains.

[c21] Previous predictions of spin accumulation always involved ferromagnetic leads; see, e.g., J. Barnaś et al., Phys. Rev. B 62, 12 363 (2000), and references therein.

[c22] For simplicity, we have not included the possibility of a nonequilibrium population of either single-particle excitations or spin-wave excitations (i.e., states of the form $| s, m 〉$ , with $m < s)$ in our calculations or in Fig. 22. However, they certainly exist, and if taken into account, would lead to additional resonances in the tunneling spectrum. Note, though, that the threshold spacing expected for transitions involving spin-wave excitations is $k_{N} {/ s}_{0}$ (or $2 | δ k_{\pm} |)$ if $δ k_{\pm} = 0$ (or $\neq 0)$ which is exceedingly small in both cases.

[c23] G. Pacchioni and N. Rösch, Acc. Chem. Res. 28, 390 (1995), and references therein.

[c24] M. Jamet et al., Phys. Rev. Lett. 86, 4676 (2001).

Physical Review B

Export citation

Export citation

Model for ferromagnetic nanograins with discrete electronic states

Abstract

References (24)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation