Selective measurement of the longitudinal electron spin relaxation time ${T}_{1}$ of ${\mathrm{Ce}}^{3+}$ ions in a YAG lattice: Resonant spin inertia

Selective measurement of the longitudinal electron spin relaxation time $T_{1}$ of ${Ce}^{3 +}$ ions in a YAG lattice: Resonant spin inertia

V. V. Belykh and S. R. Melyakov

Phys. Rev. B 105, 205129 – Published 23 May 2022

Abstract

Electron spin oriented along an external magnetic field is subject to longitudinal spin relaxation with characteristic time $T_{1}$ . The corresponding decay is nonoscillating, so one cannot readily ascribe $T_{1}$ to a certain $g$ factor. This becomes a problem when several electronic states with different $g$ factors are present in the system, e.g., electrons and holes. We solve this problem by optically pumping spin polarization and then selectively depolarizing it using a radio frequency (rf) field. By modulating the rf field amplitude one can observe the retarded modulation of spin polarization which depends on the relation between the modulation period and $T_{1}$ . Using this resonant spin inertia method, we unveil the strong anisotropy of $T_{1}$ for rare-earth ${Ce}^{3 +}$ ions in a YAG crystal at low temperatures and low magnetic fields. We also show that the spread of Larmor frequencies within the electron ensemble in this system is not static, but results from the fluctuations of internal magnetic fields on a timescale much shorter than $T_{1}$ .

Received 22 January 2022
Revised 9 May 2022
Accepted 11 May 2022

DOI:https://doi.org/10.1103/PhysRevB.105.205129

Physics Subject Headings (PhySH)

Faraday effect Optical generation of spin carriers Spin accumulation Spin polarization Spin relaxation

Rare-earth doped crystals

Electron paramagnetic resonance Electron spin resonance Kerr effect Liquid helium cooling Optically detected magnetic resonance Pump-probe spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

V. V. Belykh ^* and S. R. Melyakov

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 119991 Moscow, Russia

^*belykh@lebedev.ru

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 105, Iss. 20 — 15 May 2022

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Scheme of the experiment. (b) Qualitative interpretation of the effect: optical pumping leads to the accumulation of spin polarization along the Larmor frequency $ω_{L}$ , while the rf field resonant with the Larmor frequency unwinds spin polarization from the direction of $ω_{L}$ and suppresses spin accumulation. (c) Faraday rotation signal as a function of the rf field frequency (ODMR spectra) for different values of the magnetic field applied at the angle $θ = 45^{\circ}$ with respect to the sample normal. (d) Magnetic field dependencies of the frequencies corresponding to the two main peaks in the ODMR spectra. Their slopes give $g$ -factor values of 0.9 and 1.9. (e) Faraday rotation signal (shown by color) as a function of the angle of the magnetic field with respect to the sample normal and the rf field frequency. Left axis shows the $g$ -factor values. Dashed lines show calculation results as described in Appendix pp1. $B = 3.5 mT$ . (c)–(e) $T = 5$ K.
Reuse & Permissions
Figure 2
(a) rf field protocols with different modulation frequencies and corresponding calculated spin polarization dynamics. When the rf modulation period becomes smaller than $T_{1}$ , the modulation depth $Δ S$ of the spin polarization is reduced. (b) Calculated spin polarization amplitude $Δ S$ as a function of rf field modulation frequency (spin inertia curve). (c) Faraday rotation signal as a function of the rf field modulation frequency (spin inertia curves) for different laser powers. Red lines show the fits to the experimental data with Eq. (19). (d) Longitudinal spin relaxation rate $1 / T_{1}$ extracted from the spin inertia curves as a function of the laser power. Red line shows the linear fit which is used to extrapolate the dependence to $P = 0$ . (c) and (d) $B = 4 mT$ , $θ = 12^{\circ}$ , $f_{rf} = 80$ MHz, and $T = 5$ K.
Reuse & Permissions
Figure 3
(a) Spin inertia curves for different temperatures. Red lines show the fit to the experimental data with Eq. (19). $B = 4 mT$ , $θ = 12^{\circ}$ , $f_{rf} = 80$ MHz. (b) Summary of the temperature dependencies of $T_{1}$ from this work at $B = 4 mT$ (balls) in the limit of $P = 0$ , from Ref. [24] at $B = 474.4 mT$ (triangles), and $T_{2}$ from Ref. [2] at $B = 3.3 mT$ (crosses) for ${Ce}^{3 +}$ :YAG.
Reuse & Permissions
Figure 4
(a) Magnetic field dependencies of $T_{1}$ for three different $g$ factors and $θ = 20^{\circ}$ . (b) Values of $T_{1}$ , reflected by the sizes of the bubbles, as a function of the magnetic field angle $θ$ and the rf field frequency $f_{rf}$ . Left axis shows the $g$ -factor values. Dotted lines show calculations as described in Appendix pp1. $B = 3.5 mT$ . (a) and (b) $P = 0.5$ mW, $T = 5$ K.
Reuse & Permissions
Figure 5
(a) rf field profile. (b) Schematic representation of the ensemble spin dynamics for frozen Larmor frequencies. (c) Schematic representation of the ensemble spin dynamics for time-fluctuating Larmor frequencies. (d) Frequency dependence of the spin dynamics convolved with sine $[X$ , $sin (2 π f_{m} t)]$ and cosine $[Y$ , $cos (2 π f_{m} t)]$ functions. Dashed and solid lines show calculations for the assumptions of frozen and time-fluctuating $ω_{L}$ . Time-fluctuating $ω_{L}$ results in additional decay of the spin polarization when the rf field is on. The rate of this decay as a function of the Rabi frequency (rf field amplitude) is shown in (e). (d) and (e) $B = 4 mT$ , $θ = 12^{\circ}$ , $f_{rf} = 80$ MHz, $P = 1$ mW, $T = 5$ K.
Reuse & Permissions
Figure 6
(a) Faraday rotation signal normalized to $P$ as a function of the Rabi frequency. $P = 1$ mW, $T = 5$ K. (b) Faraday rotation signal normalized to $P$ as a function of the longitudinal spin relaxation time $T_{1}$ . Full squares correspond to different temperatures. Open circles correspond to different laser powers at $T = 5$ K. (a) and (b) Red lines show the quadratic dependence. $f_{m} = 60 Hz$ , $B = 4 mT$ , $θ = 12^{\circ}$ , $f_{rf} = 80$ MHz.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Selective measurement of the longitudinal electron spin relaxation time $T_{1}$ of ${Ce}^{3 +}$ ions in a YAG lattice: Resonant spin inertia

V. V. Belykh and S. R. Melyakov

Phys. Rev. B 105, 205129 – Published 23 May 2022

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review B

covering condensed matter and materials physics

Selective measurement of the longitudinal electron spin relaxation time T1 of Ce3+ ions in a YAG lattice: Resonant spin inertia

V. V. Belykh and S. R. Melyakov

Phys. Rev. B 105, 205129 – Published 23 May 2022

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Selective measurement of the longitudinal electron spin relaxation time $T_{1}$ of ${Ce}^{3 +}$ ions in a YAG lattice: Resonant spin inertia