Phonon bottleneck in the spin relaxation of dilute magnetic semiconductors: New model for the narrowing of the magnetization steps in pulsed fields

Bindilatti, V.; Vu, T.Q.; Shapira, Y.

doi:10.1016/0038-1098(91)90229-o

Cited by 18 publications

(21 citation statements)

References 12 publications

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“…Our findings could directly bear on other recent works [1,2], concerning the width of the magnetization steps of DMS at high magnetic fields. The strongest interaction between two nearest-neighbor (n.n.)…”

supporting

confidence: 83%

“…[3,5,9]. The relaxation rates observed by us are much faster than observed under phonon bottleneck condition at lower temperatures for other DMS, namely CdMnS and ZnMnS [2]. But particularly the relaxation of n.n.…”

mentioning

confidence: 64%

“…[1] expect a pair SLR rate smaller than 2 x 10 3 s-1 . V. Bindilatti et al show [2] that these magnetization measurements are limited by a phonon bottleneck. However, in our technique based on heating the lattice by radiation pulses, phonons are provided, thus, the phonon system is slightly heated.…”

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confidence: 99%

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The Relaxation of Mn Pairs in CdMnTe at High Magnetic Fields

1991

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The spin-lattice relaxation in CdMnTe at 4.7 K has been measured at high magnetic fields up to 24.5 T. At fields, where the ground state of nearest--neighbor exchange coupled Mn pairs changes due to energy 1eve1 crossing, an increase in the relaxation rate is observed. This is attributed to the change of relaxation of nearest-neighbor Mn pairs. It proves that not only 1arge size Mn clusters are involved in the relaxation as it has been shown previously, but also Mn pairs. It shows as well that the mixing of pair states is quite effective.PACS numbers: 78.20.Ls, 78.47.+p For the first time spin-lattice relaxation (SLR) of Mn pairs in the diluted magnetic semiconductor (DMS) CdMnTe has been observed. Our findings could directly bear on other recent works [1,2], concerning the width of the magnetization steps of DMS at high magnetic fields. The strongest interaction between two nearest-neighbor (n.n.) Mn ions in a DMS is the exchange interaction. The exchange Hamiltonian can be written in the Heisenberg form: Hint = -2JS1 • S2, where J is the n.n. exchange constant and S1 and 52 are the spin operators of two n.n. spins. Taking into account only Zeeman and exchange interactions, and neglecting all other interactions, the eigenenergies of the Mn pair at external magnetic field B are given by where the second term gives the energy of the multiplets with total spin ST and magnetic quantum numbers MS. The first term describes the Zeeman splitting. The energy level scheme of these pairs is shown in the upper part of Fig. 1 (calculated for J/kB = -6.5 K).We studied the SLR in Cd0.99Mn0.01Te at 4.7 K as a function of the external magnetic field up to fields of 24.5 T using a novel technique [3]. Very short, nonresonant radiation pulses are applied on the sample. Weakly absorbed by the lattice,

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confidence: 83%

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confidence: 64%

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The Relaxation of Mn Pairs in CdMnTe at High Magnetic Fields

1991

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“…26,27,28,29,30,31,32,33,34 The extreme case of a sample isolated from the thermal reservoir (adiabatic conditions) was discussed by Wolf long ago, assuming thermal equilibrium within the sample.…”

Section: 22232425mentioning

confidence: 99%

“…40,41 Treatments of this phenomenon in the context of the magnetization process of magnetic clusters led to the development of several IHF models. 27,29,30,31,33,34 The common feature of these models is that the spin and phonon subsystems, within the sample, are very nearly in thermal equilibrium. The spin temperature T s , the phonon temperature, and the sample temperature are the same.…”

Section: Inadequate Heat Flow (Ihf) Modelsmentioning

confidence: 99%

Magnetization steps in a diluted Heisenberg antiferromagnetic chain: Theory and experiments on(CH3)4NMn<

Paduan-Filho

Oliveira²,

Bindilatti³

et al. 2003

Phys. Rev. B

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A theory for the equilibrium low-temperature magnetization M of a diluted Heisenberg antiferromagnetic chain is presented. Only the nearest-neighbor exchange interaction is included, and the distribution of the magnetic ions is assumed to be random. Values of the magnetic fields Bi at the magnetization steps (MST's) from finite chains with 2 to 5 spins (pairs, triplets, quartets, and quintets) are given for chains composed of spins S=5/2. The magnitudes of these MST's as a function of the fraction, x, of cations that are magnetic are given for any S. An expression for the apparent saturation value of M is derived. The magnetization curve, M versus B, is calculated using the exact contributions of finite chains with 1 to 5 spins, and the "rise and ramp approximation" for longer chains. An expression for the low-temperature saturation magnetic field Bs(n) of a finite chain with n spins is given. Some non-equilibrium effects that occur in a rapidly changing B, are also considered. Some of these result from the absence of thermal equilibrium within the sample itself, whereas others are caused by the absence of thermal equilibrium between the sample and its environment (e.g., liquid-helium bath). Specific non-equilibrium models based on earlier treatments of the phonon bottleneck, and of spin flips associated with cross relaxation and with level crossings (anticrossings), are discussed. Magnetization data on powders of TMMC diluted with cadmium [i.e., (CH3)4NMn x Cd1−xCl3, with 0.16 ≤ x ≤ 0.50] were measured at 0.55 K in 18 T superconducting magnets. The field B1 at the first MST from pairs is used to determine the NN exchange constant J. This J/kB changes from −5.9 K to −6.5 K as x increases from 0.16 to 0.50. The magnetization curves obtained in the superconducting magnets are compared with simulations based on the equilibrium theory. A reasonably good agreement is found. Data for the differential susceptibility, dM/dB, were taken in pulsed magnetic fields (7.4 ms duration) up to 50 T. The powder samples were in direct contact with a 1.5 K liquid-helium bath. Non-equilibrium effects, which became more severe as x decreased, were observed. For x=0.50 the non-equilibrium effects are tentatively interpreted using the "Inadequate Heat Flow Scenario," developed earlier in connection with the phonon bottleneck problem. The more severe non-equilibrium effects for x=0.16 and 0.22 are tentatively attributed to cross-relaxation, and to crossings (more accurately, anticrossings) of energy levels, including those of excited states. For x=0.16 (lowest x), no MST's were observed above 20 T, which is attributed to a very slow spin relaxation for pairs, compared to a millisecond. A definitive interpretation of this and some other non-equilibrium effects is still lacking.

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Spin‐lattice relaxation in diluted magnetic semiconductors

Scalbert

1996

Physica Status Solidi (b)

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The contribution of pairs and triads of nearest-neighbor spins to the spin-lattice relaxation of magnetization is evaluated in Mn-based diluted magnetic semiconductors. Modulation of the exchange interaction by lattice vibrations allows transitions in the cluster which change the total magnetization when the Dzyaloshinski-Monya interaction is taken into account. Spin-lattice relaxation rates are calculated for pairs and open triads due to a two-phonon Orbach process. In Cdl_,Mn,Te it is found that the main contribution to relaxation of magnetization comes from triads. For temperatures ranging from 10 to 35 K and for x between 0.002 and 0.02 relaxation of triads can account very well for the observed relaxation rates, if one assumes rapid spin diffusion. Fitting of the experimental data yields an approximate value of a = J/(dJ/dr) M 0.35 A, where J is the nearest-neighbors exchange constant and r the Mn-anion bond length, in good agreement with the expected value for a superexchange interaction.

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Phonon bottleneck in the spin relaxation of dilute magnetic semiconductors: New model for the narrowing of the magnetization steps in pulsed fields

Cited by 18 publications

References 12 publications

The Relaxation of Mn Pairs in CdMnTe at High Magnetic Fields

The Relaxation of Mn Pairs in CdMnTe at High Magnetic Fields

Magnetization steps in a diluted Heisenberg antiferromagnetic chain: Theory and experiments on(CH3)4NMn<

Spin‐lattice relaxation in diluted magnetic semiconductors

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