Temperature dependent magnetization and magnetic phases of conduction-band dilute-magnetic-semiconductor quantum wells with non-step-like density of states

Constantinos Simserides 1,2

1 University of Athens, Physics Department, Solid State Section, Athens, Greece 2 Leibniz Institute for Neurobiology, Special Lab for Non-Invasive Brain Imaging, Magdeburg, Germany

Density of States (DOS)

,i ,i )E(Am

)(n*

22

● the DOS deviates from the famous step-like (B→0) form.

Not only the general shape of the DOS varies , but this effect is also quantitative.

• for any type of interplay between spatial and magnetic confinement

,i x,i

x,ix

*

)k(E

))k(E(dk

mA)(n

222

2

RESULTS AND DISCUSSION

Density of States diverges significantly from ideal step-like 2DEG form

severe changes to physical properties:

• spin-subband populations

• internal energy, U

• free energy, F

• Shannon entropy, S

• magnetization, M

~ parabolic spin subbands

increase B

more flat dispersion

few % DOS increase

A single behavior of

Internal Energy

Free Energy

Entropy

L = 10 nm (spatial confinement dominates)

L = 30 nm(drastic dispersion modification) Spin-subband dispersion and DOS

Spin-subband Populations Internal energyFree Energy Entropy

L = 30 nm

+ Depopulation of higher spin-subband

L = 60 nm(~ spin-down bilayer system)

Spin-subband dispersion and DOS

L = 60 nm Spin-subband Populations Internal EnergyFree Energy Entropy

+ Depopulation of higher spin-subband

Bibliography[1] H. Ohno, J. Magn. Magn. Mater. 272-276, 1 (2004); J. Crystal Growth 251, 285 (2003). [5] S. P. Hong, K. S. Yi, J. J. Quinn, Phys. Rev. B 61, 13745 (2000). [9] H. W. Hölscher, A. Nöthe and Ch. Uihlein, Phys. Rev. B 31, 2379 (1985). [2] M. Syed, G. L. Yang, J. K. Furdyna, et al, Phys. Rev. B 66, 075213 (2002). [6] H. J. Kim and K. S. Yi, Phys. Rev. B 65, 193310 (2002). [10] B. Lee, T. Jungwirth, A. H. MacDonald, Phys. Rev. B 61, 15606 (2000).[3] S. Lee, M. Dobrowolska, J. K. Furdyna, and L. R. Ram-Mohan, Phys. Rev. B 61, 2120 (2000). [7] C. Simserides, Physica E 21, 956 (2004). [11] L. Brey and F. Guinea, Phys. Rev. Lett. 85, 2384 (2000).[4] C. Simserides, J. Comput. Electron. 2, 459 (2003); Phys. Rev. B 69, 113302 (2004). [8] H. Venghaus, Phys. Rev. B 19, 3071 (1979).

Epilogue - Outlook

☺ Magnetization of conduction-band, narrow to wide NMS/DMS/NMS structures with in-plane B.

☺ If strong competition (spatial vs. magnetic) confinement impressive fluctuation of M.

☺ Spin polarization tuned by varying T and B.

♫ In this poster we have approximated ndown(r) – nup(r) by (Ns,down - Ns,up) / L …

♫ A more orderly study of the magnetic phases will be hopefully presented …

Dispersion, Density of States, Free Energy

considerable fluctuation of M(if vigorous competition between spatial and magnetic confinement)

L = 10 nm : almost parabolic dispersion

L = 30 nm : strong competition between spatial and magnetic confinement

L = 60 nm : ~ spin-down bilayer system

Magnetization

Enhanced electron spin-splitting, Uoσ

Low temperatures.

spin-splitting maximum,~ 1/3 of conduction band offset

Higher temperatures.

spin-splitting decreases enhanced contribution of spin-up electrons

Feedback mechanism due to ndown(r) - nup(r).

)(SBJyNm

mgU Sdspc

e

**

o 02

Tk

nnSJSBg

B

updowndspBMn 2

spin-spin exchange interaction between

s- or p- conduction band electrons and

d- electrons of Μn+2 cations

proportional to the cyclotron gap

in-plane

magnetic field

SUMMARYWe study the magnetization and the magnetic phases of

II-VI-based n-doped non-magnetic-semiconductor (NMS) / narrow to wide dilute-magnetic-semiconductor (DMS) /

n-doped NMS quantum wells under in-plane magnetic field.The parallel magnetic field is used as a tool, in order to achieve

non-step-like density of states in these -appropriate for conduction-band spintronics- structures.

conduction band, narrow to wide, DMS QWs

Spin polarization tuned by varying temperature and magnetic field.s

up,sdown,s

N

NN

narrow L = 10 nm, almost parabolic dispersion

Magnetic Phases, Spin Polarization

L = 60 nm, ~ bilayer system

e.g. n-doped DMS ZnSe / Zn1-x-yCdxMnySe / ZnSe QWs