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Interlayer exchange coupling in (Ga,Mn)As ferromagnetic semiconductor multilayer systems

Sanghoon Lee1, , Sunjae Chung1, Hakjoon Lee1, Xinyu Liu2, M. Dobrowolska2 and J. K. Furdyna2

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 Corresponding author: Sanghoon Lee, slee3@korea.ac.kr

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Abstract: This paper describes interlayer exchange coupling (IEC) phenomena in ferromagnetic multilayer structures, focusing on the unique IEC features observed in ferromagnetic semiconductor (Ga,Mn)As-based systems. The dependence of IEC on the structural parameters, such as non-magnetic spacer thickness, number of magnetic layers, and carrier density in the systems has been investigated by using magnetotransport measurements. The samples in the series show both a typical anisotropic magnetoresistance (AMR) and giant magnetoresistance (GMR)-like effects indicating realization of both ferromagnetic (FM) and antiferromagnetic (AFM) IEC in (Ga,Mn)As-based multilayer structures. The results revealed that the presence of carriers in the non-magnetic spacer is an important factor to realize AFM IEC in this system. The studies further reveal that the IEC occurs over a much longer distance than predicted by current theories, strongly suggesting that the IEC in (Ga,Mn)As-based multilayers is a long-range interaction. Due to the long-range nature of IEC in the (Ga,Mn)As-based systems, the next nearest neighbor (NNN) IEC cannot be ignored and results in multi-step transitions during magnetization reversal that correspond to diverse spin configurations in the system. The strength of NNN IEC was experimentally determined by measuring minor loops that correspond to magnetization flips in specific (Ga,Mn)As layer in the multilayer system.

Key words: thin filmcrystalferromagnetic semiconductorinterlayer coupling



[1]
Binasch G, Grünberg P, Saurenbach F, et al. Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange. Phys Rev B, 1989, 39(7), 4828 doi: 10.1103/PhysRevB.39.4828
[2]
Baibich M N, Broto J M, Fert A, et al. Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices. Phys Rev Lett, 1988, 61(21), 2472 doi: 10.1103/PhysRevLett.61.2472
[3]
Parkin S S P, Farrow R F C, Marks R F, et al. Oscillations of interlayer exchange coupling and giant magnetoresistance in (111) oriented permalloy/Au multilayers. Phys Rev Lett, 1994, 73(8), 1190 doi: 10.1103/PhysRevLett.73.1190.2
[4]
Bloemen P J H, van Kesteren H W, Swagten H J M, et al. Oscillatory interlayer exchange coupling in Co/Ru multilayers and bilayers. Phys Rev B, 1994, 50(18), 13505 doi: 10.1103/PhysRevB.50.13505
[5]
Borchers J A, Dura J A, Unguris J, et al. Observation of antiparallel magnetic order in weakly coupled Co/Cu multilayers. Phys Rev Lett, 1999, 82(13), 2796 doi: 10.1103/PhysRevLett.82.2796
[6]
Parkin S S P. Systematic variation of the strength and oscillation period of indirect magnetic exchange coupling through the 3d, 4d, and 5d transition metals. Phys Rev Lett, 1991, 67(25), 3598 doi: 10.1103/PhysRevLett.67.3598
[7]
Parkin S S P, More N, Roche K. Oscillations in exchange coupling and magnetoresistance in metallic superlattice structures: Co/Ru, Co/Cr, and Fe/Cr. Phys Rev Lett, 1990, 64(19), 2304 doi: 10.1103/PhysRevLett.64.2304
[8]
Berger L. Emission of spin waves by a magnetic multilayer traversed by a current. Phys Rev B, 1996, 54(13), 9353 doi: 10.1103/PhysRevB.54.9353
[9]
Miron I M, Garello K, Gaudin G, et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature, 2011, 476, 189 doi: 10.1038/nature10309
[10]
Slonczewski J C. Current-driven excitations of magnetic multilayers. J Magn Magn Mater, 1996, 159, L1 doi: 10.1016/0304-8853(96)00062-5
[11]
Koshihara S, Oiwa A, Hirasawa M, et al. Ferromagnetic order induced by photogenerated carriers in magnetic III–V semiconductor heterostructures of (In, Mn)As/GaSb. Phys Rev Lett, 1997, 78(24), 4617 doi: 10.1103/PhysRevLett.78.4617
[12]
Lee H, Choi S, Lee S, et al. Effect of light illumination on the [100] uniaxial magnetic anisotropy of (Ga,Mn)As film. Solid State Commun, 2014, 192, 27 doi: 10.1016/j.ssc.2014.04.010
[13]
Lee S, Shin D Y, Chung S J, et al. Tunable quaternary states in ferromagnetic semiconductor (Ga,Mn)As single layer for memory devices. Appl Phys Lett, 2007, 90(15), 152113 doi: 10.1063/1.2721144
[14]
Liu X, Sasaki Y, Furdyna J K. Ferromagnetic resonance in Ga1− xMn xAs effects of magnetic anisotropy. Phys Rev B, 2003, 67(20), 205204 doi: 10.1103/PhysRevB.67.205204
[15]
Ohno H, Chiba D, Matsukura F, et al. Electric-field control of ferromagnetism. Nature, 2000, 408(6815), 944 doi: 10.1038/35050040
[16]
Lee H, Lee S, Choi S, et al. Interlayer exchange coupling in MBE-grown (Ga,Mn)As-based multilayer systems. J Cryst Growth, 2017, 477, 188 doi: 10.1016/j.jcrysgro.2017.01.039
[17]
Bac S K, Lee H, Kee S, et al. Effects on magnetic properties of (Ga,Mn)As induced by proximity of topological insulator Bi2Se3. J Electron Mater, 2018, 47(8), 4308 doi: 10.1007/s11664-018-6238-1
[18]
Chang J, Bhoi S, Lee K J, et al. Effects of film thickness and annealing on the magnetic properties of (Ga,Mn)AsP ferromagnetic semiconductor. J Cryst Growth, 2019, 512, 112 doi: 10.1016/j.jcrysgro.2019.01.035
[19]
Yuldashev S U, Im K, Yalishev V S, et al. Effect of additional nonmagnetic acceptor doping on the resistivity peak and the Curie temperature of Ga1− xMn xAs epitaxial layers. Appl Phys Lett, 2003, 82(8), 1206 doi: 10.1063/1.1554482
[20]
Chung S, Lee S, Chung J H, et al. Giant magnetoresistance and long-range antiferromagnetic interlayer exchange coupling in (Ga,Mn)As/GaAs: Be multilayers. Phys Rev B, 2010, 82(5), 054420 doi: 10.1103/PhysRevB.82.054420
[21]
Chung S, Lee S, Yoo T, et al. Determination of interlayer exchange fields acting on individual (Ga,Mn)As layers in (Ga,Mn)As/GaAs multilayers. Jpn J Appl Phys, 2015, 54(3), 033001 doi: 10.7567/JJAP.54.033001
[22]
Lee H, Lee S, Choi S, et al. Antiferromagnetic interlayer exchange coupling in ferromagnetic (Ga,Mn)As/GaAs: Be multilayers. IEEE Trans Magn, 2015, 51(11), 2400604 doi: 10.1109/tmag.2015.2438294
[23]
Leiner J, Lee H, Yoo T, et al. Observation of antiferromagnetic interlayer exchange coupling in a Ga1− xMnxAs/GaAs: Be/Ga1− xMn xAs trilayer structure. Phys Rev B, 2010, 82(19), 195205 doi: 10.1103/PhysRevB.82.195205
[24]
Baxter D V, Ruzmetov D, Scherschligt J, et al. Anisotropic magnetoresistance in Ga1− xMn xAs. Phys Rev B, 2002, 65(21), 212407 doi: 10.1103/PhysRevB.65.212407
[25]
Wang K Y, Edmonds K W, Campion R P, et al. Anisotropic magnetoresistance and magnetic anisotropy in high-quality (Ga,Mn)As films. Phys Rev B, 2005, 72(8), 085201 doi: 10.1103/PhysRevB.72.085201
[26]
Shin D Y, Chung S J, Lee S, et al. Temperature dependence of magnetic anisotropy in ferromagnetic (Ga,Mn)As films: Investigation by the planar Hall effect. Phys Rev B, 2007, 76(3), 035327 doi: 10.1103/PhysRevB.76.035327
[27]
Grünberg P A. Exchange anisotropy, interlayer exchange coupling and GMR in research and application. Sens Actuators A, 2001, 91(1), 153 doi: 10.1016/s0924-4247(01)00513-1
[28]
Giddings A D, Jungwirth T, Gallagher B L. (Ga,Mn)As based superlattices and the search for antiferromagnetic interlayer coupling. Phys Rev B, 2008, 78(16), 165312 doi: 10.1103/PhysRevB.78.165312
[29]
Sankowski P, Kacman P. Interlayer exchange coupling in (Ga,Mn)As-based superlattices. Phys Rev B, 2005, 71(20), 201303 doi: 10.1103/PhysRevB.71.201303
[30]
Szałowski K, Balcerzak T. Antiferromagnetic interlayer coupling in diluted magnetic thin films with RKKY interaction. Phys Rev B, 2009, 79(21), 214430 doi: 10.1103/PhysRevB.79.214430
[31]
Chung J H, Chung S J, Lee S, et al. Carrier-mediated antiferromagnetic interlayer exchange coupling in diluted magnetic semiconductor multilayers Ga1− xMn xAs: GaAs: Be. Phys Rev Lett, 2008, 101(23), 237202 doi: 10.1103/PhysRevLett.101.237202
[32]
Chung J H, Lin J, Furdyna J K, et al. Investigation of weak interlayer exchange coupling in (Ga,Mn)As/GaAs superlattices with insulating nonmagnetic spacers. J Appl Phys, 2011, 110(1), 013912 doi: 10.1063/1.3609080
[33]
Kępa H, Le V K, Brown C M, et al. Probing hole-induced ferromagnetic exchange in magnetic semiconductors by inelastic neutron scattering. Phys Rev Lett, 2003, 91(8), 087205 doi: 10.1103/PhysRevLett.91.087205
[34]
Rhyne J J, Lin J, Furdyna J K, et al. Anomalous antiferromagnetic coupling in [ZnTe¦MnTe] superlattices. J Magn Magn Mater, 1998, 177–181, 1195 doi: 10.1016/S0304-8853(97)00741-5
[35]
Unguris J, Celotta R J, Pierce D T. Observation of two different oscillation periods in the exchange coupling of Fe/Cr/Fe(100). Phys Rev Lett, 1991, 67(1), 140 doi: 10.1103/PhysRevLett.67.140
[36]
Bruno P, Chappert C. Oscillatory coupling between ferromagnetic layers separated by a nonmagnetic metal spacer. Phys Rev Lett, 1991, 67(12), 1602 doi: 10.1103/PhysRevLett.67.1602
[37]
Bruno P, Chappert C. Ruderman-Kittel theory of oscillatory interlayer exchange coupling. Phys Rev B, 1992, 46(1), 261 doi: 10.1103/PhysRevB.46.261
[38]
Yafet Y. Ruderman-Kittel-Kasuya-Yosida range function of a one-dimensional free-electron gas. Phys Rev B, 1987, 36(7), 3948 doi: 10.1103/PhysRevB.36.3948
[39]
Chen B, Xu H, Ma C, et al. All-oxide-based synthetic antiferromagnets exhibiting layer-resolved magnetization reversal. Science, 2017, 357(6347), 191 doi: 10.1126/science.aak9717
[40]
Chung S, Lee S, Yoo T, et al. The critical role of next-nearest-neighbor interlayer interaction in the magnetic behavior of magnetic/non-magnetic multilayers. New J Phys, 2013, 15(12), 123025 doi: 10.1088/1367-2630/15/12/123025
[41]
Eid K F, Stone M B, Ku K C, et al. Exchange biasing of the ferromagnetic semiconductor Ga1− xMn xAs. Appl Phys Lett, 2004, 85(9), 1556 doi: 10.1063/1.1787945
[42]
Yu K M, Walukiewicz W, Wojtowicz T, et al. Effect of film thickness on the incorporation of Mn interstitials in Ga1− xMn xAs. Appl Phys Lett, 2005, 86(4), 042102 doi: 10.1063/1.1855430
[43]
Lee H, Bac S K, Lee S, et al. Experimental determination of next-nearest-neighbor interlayer exchange coupling in ferromagnetic (Ga,Mn)As/GaAs: Be multilayers. Appl Phys Lett, 2015, 107(19), 192403 doi: 10.1063/1.4935597
[44]
Han J H, Lee H W. Interlayer exchange coupling between next nearest neighbor layers. Phys Rev B, 2012, 86(17), 174426 doi: 10.1103/PhysRevB.86.174426
Fig. 1.  (Color online) Magnetoresistance of (Ga,Mn)As/GaAs multilayers measured with magnetic field applied near the [110] direction at T = 30 K. Although the AMR typical for (Ga,Mn)As layers dominates the MR observed in most of the samples, giant magnetorsistance (GMR)-like effect is clearly seen in samples B3 and B4, indicating the presence of AFM IEC in those specimens. The arrows indicate the direction of field scan. (Adapted from Ref. [20])

Fig. 2.  (Color online) Magnetoreistance observed in six (Ga,Mn)As/GaAs multilayers with different structural parameters. Samples C1, D1, and E2 show only anisotropic magnetoresistance (AMR), characteristic of FM IEC between the (Ga,Mn)As layers; Samples C3, D2, and E3 show a GMR-like behavior, indicating the presence of AFM IEC in these samples similar to that seen in the [(Ga,Mn)As/GaAs:Be]10 multilayer discussed in detail in the Fig. 1.

Fig. 3.  (Color online) Summary plot of IEC type for the various (Ga,Mn)As multilayers depending on carrier concentrations and spacer layer thicknesses. Black open squares and red open circles show FM IEC and AFM IEC, respectively. (Adapted from Ref. [16])

Fig. 4.  (Color online) The process of magnetization reversal in the [(Ga,Mn)As/GaAs:Be]10 multilayer system. (a) MR is measured at 35 K as the field is cycled between −100 and 100 Oe. The down- and up-scans, shown by solid (blue) and open (red) circles, respectively, have a completely symmetrical behavior. Two types of fully AFM spin configurations between the (Ga,Mn)As layers, AFM1 and AFM2, can be realized at zero field, as shown schematically by the vertical arrows. Each field scan (down or up) contains a four-step restoring process and a five- step saturation process, with resistance plateaus marked as R1–R4 and S1–S4. (b) The number of pairs with AFM alignment between adjacent (Ga,Mn)As layers in the multilayer is obtained by minimizing the IEC energy given by Eq. (1) during the down-scan of the field. The field is scaled in terms of the NN IEC strength J1. The reversal process determined from calculation using Eq. (1) clearly shows a four-step restoring and a five-step saturation process, similar to that observed in the MR experiment shown in the upper panel. The crossing of the calculated energies for the R3, R4 and FM1 states is shown in the inset. The spin configuration corresponding to each plateau in the field scan is indicated schematically by vertical arrows. (Adapted from Ref. [40])

Fig. 5.  (Color online) Magnetic field dependence of MR and IEC energy during (a) up-scan and (b) down-scan of applied field for samples used in this study. The experimentally measured MR at 23 K and calculated IEC energy for possible spin configurations are plotted in left and right columns of each figure, respectively. (Adapted from Ref. [43])

Fig. 6.  (Color online) Minor MR hysteresis loops obtained during the “restoring” process for our three samples. The minor loops are plotted with red open circles on top of main loops shown by black lines. The magnetization alignments involved in the minor loop of each sample are schematically shown by arrows at corresponding values of MR. The solid vertical lines indicate minor loop shifts HMLS from zero field. (Adapted from Ref. [43])

Table 1.   Description of parameters and structures for the sample series from A to E. (Adapted from Ref. [16])

Sample # of (Ga,Mn)As layers Spacer layer (Ga,Mn)As thickness dm (nm) Spacer layer thickness dnm (nm) Mn composition (%) Carrier concentration p (cm–3) IEC type
A1 10 GaAs 6.9 0.7 3 1.0 × 1020 FM
A2 10 GaAs 6.9 2.3 3 8.9 × 1019 FM
A3 10 GaAs 6.9 3.5 3 7.8 × 1019 FM
A4 10 GaAs 6.9 7.1 3 5.8 × 1019 FM
B1 10 GaAs:Be 6.9 1.2 3 1.2 × 1020 FM
B2 10 GaAs:Be 6.9 2.3 3 1.2 × 1020 FM
B3 10 GaAs:Be 6.9 3.5 3 1.2 × 1020 AFM
B4 10 GaAs:Be 6.9 7.1 3 1.2 × 1020 AFM
C1 2 GaAs:Be 17.2, 8.6 4.3 5 1.4 × 1019 FM
C2 2 GaAs:Be 17.2, 8.6 4.3 5 1.0 × 1020 FM
C3 2 GaAs:Be 17.2, 8.6 4.3 5 2.0 × 1020 AFM
D1 6 GaAs:Be 8.5 4.2 1.2 2.0 × 1019 FM
D2 6 GaAs:Be 8.5 4.2 1.2 1.9 × 1020 AFM
E2 8 GaAs:Be 8 4 3.5 1.1 × 1020 AFM
E3 8 GaAs:Be 8 4 6.5 1.5 × 1019 FM
E4 9 GaAs:Be 8 4 6.5 1.4 × 1019 FM
DownLoad: CSV

Table 2.   Calculated IEC field HIEC and experimentally observed minor loop shifts HMLS. (Adapted from Ref. [43])

Sample IEC field, HIEC HIEC ratio Minor loop shift, HMLS HMLS ratio
2-layer J1Mi 1 2.88 1.00
3-layer 2J1Mi 2 5.94 2.06
5-layer (2J1 + 2J2)Mi 2 + 2(J2/J1) 7.09 2.46
DownLoad: CSV
[1]
Binasch G, Grünberg P, Saurenbach F, et al. Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange. Phys Rev B, 1989, 39(7), 4828 doi: 10.1103/PhysRevB.39.4828
[2]
Baibich M N, Broto J M, Fert A, et al. Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices. Phys Rev Lett, 1988, 61(21), 2472 doi: 10.1103/PhysRevLett.61.2472
[3]
Parkin S S P, Farrow R F C, Marks R F, et al. Oscillations of interlayer exchange coupling and giant magnetoresistance in (111) oriented permalloy/Au multilayers. Phys Rev Lett, 1994, 73(8), 1190 doi: 10.1103/PhysRevLett.73.1190.2
[4]
Bloemen P J H, van Kesteren H W, Swagten H J M, et al. Oscillatory interlayer exchange coupling in Co/Ru multilayers and bilayers. Phys Rev B, 1994, 50(18), 13505 doi: 10.1103/PhysRevB.50.13505
[5]
Borchers J A, Dura J A, Unguris J, et al. Observation of antiparallel magnetic order in weakly coupled Co/Cu multilayers. Phys Rev Lett, 1999, 82(13), 2796 doi: 10.1103/PhysRevLett.82.2796
[6]
Parkin S S P. Systematic variation of the strength and oscillation period of indirect magnetic exchange coupling through the 3d, 4d, and 5d transition metals. Phys Rev Lett, 1991, 67(25), 3598 doi: 10.1103/PhysRevLett.67.3598
[7]
Parkin S S P, More N, Roche K. Oscillations in exchange coupling and magnetoresistance in metallic superlattice structures: Co/Ru, Co/Cr, and Fe/Cr. Phys Rev Lett, 1990, 64(19), 2304 doi: 10.1103/PhysRevLett.64.2304
[8]
Berger L. Emission of spin waves by a magnetic multilayer traversed by a current. Phys Rev B, 1996, 54(13), 9353 doi: 10.1103/PhysRevB.54.9353
[9]
Miron I M, Garello K, Gaudin G, et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature, 2011, 476, 189 doi: 10.1038/nature10309
[10]
Slonczewski J C. Current-driven excitations of magnetic multilayers. J Magn Magn Mater, 1996, 159, L1 doi: 10.1016/0304-8853(96)00062-5
[11]
Koshihara S, Oiwa A, Hirasawa M, et al. Ferromagnetic order induced by photogenerated carriers in magnetic III–V semiconductor heterostructures of (In, Mn)As/GaSb. Phys Rev Lett, 1997, 78(24), 4617 doi: 10.1103/PhysRevLett.78.4617
[12]
Lee H, Choi S, Lee S, et al. Effect of light illumination on the [100] uniaxial magnetic anisotropy of (Ga,Mn)As film. Solid State Commun, 2014, 192, 27 doi: 10.1016/j.ssc.2014.04.010
[13]
Lee S, Shin D Y, Chung S J, et al. Tunable quaternary states in ferromagnetic semiconductor (Ga,Mn)As single layer for memory devices. Appl Phys Lett, 2007, 90(15), 152113 doi: 10.1063/1.2721144
[14]
Liu X, Sasaki Y, Furdyna J K. Ferromagnetic resonance in Ga1− xMn xAs effects of magnetic anisotropy. Phys Rev B, 2003, 67(20), 205204 doi: 10.1103/PhysRevB.67.205204
[15]
Ohno H, Chiba D, Matsukura F, et al. Electric-field control of ferromagnetism. Nature, 2000, 408(6815), 944 doi: 10.1038/35050040
[16]
Lee H, Lee S, Choi S, et al. Interlayer exchange coupling in MBE-grown (Ga,Mn)As-based multilayer systems. J Cryst Growth, 2017, 477, 188 doi: 10.1016/j.jcrysgro.2017.01.039
[17]
Bac S K, Lee H, Kee S, et al. Effects on magnetic properties of (Ga,Mn)As induced by proximity of topological insulator Bi2Se3. J Electron Mater, 2018, 47(8), 4308 doi: 10.1007/s11664-018-6238-1
[18]
Chang J, Bhoi S, Lee K J, et al. Effects of film thickness and annealing on the magnetic properties of (Ga,Mn)AsP ferromagnetic semiconductor. J Cryst Growth, 2019, 512, 112 doi: 10.1016/j.jcrysgro.2019.01.035
[19]
Yuldashev S U, Im K, Yalishev V S, et al. Effect of additional nonmagnetic acceptor doping on the resistivity peak and the Curie temperature of Ga1− xMn xAs epitaxial layers. Appl Phys Lett, 2003, 82(8), 1206 doi: 10.1063/1.1554482
[20]
Chung S, Lee S, Chung J H, et al. Giant magnetoresistance and long-range antiferromagnetic interlayer exchange coupling in (Ga,Mn)As/GaAs: Be multilayers. Phys Rev B, 2010, 82(5), 054420 doi: 10.1103/PhysRevB.82.054420
[21]
Chung S, Lee S, Yoo T, et al. Determination of interlayer exchange fields acting on individual (Ga,Mn)As layers in (Ga,Mn)As/GaAs multilayers. Jpn J Appl Phys, 2015, 54(3), 033001 doi: 10.7567/JJAP.54.033001
[22]
Lee H, Lee S, Choi S, et al. Antiferromagnetic interlayer exchange coupling in ferromagnetic (Ga,Mn)As/GaAs: Be multilayers. IEEE Trans Magn, 2015, 51(11), 2400604 doi: 10.1109/tmag.2015.2438294
[23]
Leiner J, Lee H, Yoo T, et al. Observation of antiferromagnetic interlayer exchange coupling in a Ga1− xMnxAs/GaAs: Be/Ga1− xMn xAs trilayer structure. Phys Rev B, 2010, 82(19), 195205 doi: 10.1103/PhysRevB.82.195205
[24]
Baxter D V, Ruzmetov D, Scherschligt J, et al. Anisotropic magnetoresistance in Ga1− xMn xAs. Phys Rev B, 2002, 65(21), 212407 doi: 10.1103/PhysRevB.65.212407
[25]
Wang K Y, Edmonds K W, Campion R P, et al. Anisotropic magnetoresistance and magnetic anisotropy in high-quality (Ga,Mn)As films. Phys Rev B, 2005, 72(8), 085201 doi: 10.1103/PhysRevB.72.085201
[26]
Shin D Y, Chung S J, Lee S, et al. Temperature dependence of magnetic anisotropy in ferromagnetic (Ga,Mn)As films: Investigation by the planar Hall effect. Phys Rev B, 2007, 76(3), 035327 doi: 10.1103/PhysRevB.76.035327
[27]
Grünberg P A. Exchange anisotropy, interlayer exchange coupling and GMR in research and application. Sens Actuators A, 2001, 91(1), 153 doi: 10.1016/s0924-4247(01)00513-1
[28]
Giddings A D, Jungwirth T, Gallagher B L. (Ga,Mn)As based superlattices and the search for antiferromagnetic interlayer coupling. Phys Rev B, 2008, 78(16), 165312 doi: 10.1103/PhysRevB.78.165312
[29]
Sankowski P, Kacman P. Interlayer exchange coupling in (Ga,Mn)As-based superlattices. Phys Rev B, 2005, 71(20), 201303 doi: 10.1103/PhysRevB.71.201303
[30]
Szałowski K, Balcerzak T. Antiferromagnetic interlayer coupling in diluted magnetic thin films with RKKY interaction. Phys Rev B, 2009, 79(21), 214430 doi: 10.1103/PhysRevB.79.214430
[31]
Chung J H, Chung S J, Lee S, et al. Carrier-mediated antiferromagnetic interlayer exchange coupling in diluted magnetic semiconductor multilayers Ga1− xMn xAs: GaAs: Be. Phys Rev Lett, 2008, 101(23), 237202 doi: 10.1103/PhysRevLett.101.237202
[32]
Chung J H, Lin J, Furdyna J K, et al. Investigation of weak interlayer exchange coupling in (Ga,Mn)As/GaAs superlattices with insulating nonmagnetic spacers. J Appl Phys, 2011, 110(1), 013912 doi: 10.1063/1.3609080
[33]
Kępa H, Le V K, Brown C M, et al. Probing hole-induced ferromagnetic exchange in magnetic semiconductors by inelastic neutron scattering. Phys Rev Lett, 2003, 91(8), 087205 doi: 10.1103/PhysRevLett.91.087205
[34]
Rhyne J J, Lin J, Furdyna J K, et al. Anomalous antiferromagnetic coupling in [ZnTe¦MnTe] superlattices. J Magn Magn Mater, 1998, 177–181, 1195 doi: 10.1016/S0304-8853(97)00741-5
[35]
Unguris J, Celotta R J, Pierce D T. Observation of two different oscillation periods in the exchange coupling of Fe/Cr/Fe(100). Phys Rev Lett, 1991, 67(1), 140 doi: 10.1103/PhysRevLett.67.140
[36]
Bruno P, Chappert C. Oscillatory coupling between ferromagnetic layers separated by a nonmagnetic metal spacer. Phys Rev Lett, 1991, 67(12), 1602 doi: 10.1103/PhysRevLett.67.1602
[37]
Bruno P, Chappert C. Ruderman-Kittel theory of oscillatory interlayer exchange coupling. Phys Rev B, 1992, 46(1), 261 doi: 10.1103/PhysRevB.46.261
[38]
Yafet Y. Ruderman-Kittel-Kasuya-Yosida range function of a one-dimensional free-electron gas. Phys Rev B, 1987, 36(7), 3948 doi: 10.1103/PhysRevB.36.3948
[39]
Chen B, Xu H, Ma C, et al. All-oxide-based synthetic antiferromagnets exhibiting layer-resolved magnetization reversal. Science, 2017, 357(6347), 191 doi: 10.1126/science.aak9717
[40]
Chung S, Lee S, Yoo T, et al. The critical role of next-nearest-neighbor interlayer interaction in the magnetic behavior of magnetic/non-magnetic multilayers. New J Phys, 2013, 15(12), 123025 doi: 10.1088/1367-2630/15/12/123025
[41]
Eid K F, Stone M B, Ku K C, et al. Exchange biasing of the ferromagnetic semiconductor Ga1− xMn xAs. Appl Phys Lett, 2004, 85(9), 1556 doi: 10.1063/1.1787945
[42]
Yu K M, Walukiewicz W, Wojtowicz T, et al. Effect of film thickness on the incorporation of Mn interstitials in Ga1− xMn xAs. Appl Phys Lett, 2005, 86(4), 042102 doi: 10.1063/1.1855430
[43]
Lee H, Bac S K, Lee S, et al. Experimental determination of next-nearest-neighbor interlayer exchange coupling in ferromagnetic (Ga,Mn)As/GaAs: Be multilayers. Appl Phys Lett, 2015, 107(19), 192403 doi: 10.1063/1.4935597
[44]
Han J H, Lee H W. Interlayer exchange coupling between next nearest neighbor layers. Phys Rev B, 2012, 86(17), 174426 doi: 10.1103/PhysRevB.86.174426
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    Received: 22 May 2019 Revised: 03 June 2019 Online: Accepted Manuscript: 02 July 2019Uncorrected proof: 04 July 2019Published: 09 August 2019

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      Sanghoon Lee, Sunjae Chung, Hakjoon Lee, Xinyu Liu, M. Dobrowolska, J. K. Furdyna. Interlayer exchange coupling in (Ga,Mn)As ferromagnetic semiconductor multilayer systems[J]. Journal of Semiconductors, 2019, 40(8): 081503. doi: 10.1088/1674-4926/40/8/081503 S Lee, S Chung, H Lee, X Y Liu, M Dobrowolska, J K Furdyna, Interlayer exchange coupling in (Ga,Mn)As ferromagnetic semiconductor multilayer systems[J]. J. Semicond., 2019, 40(8): 081503. doi: 10.1088/1674-4926/40/8/081503.Export: BibTex EndNote
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      Sanghoon Lee, Sunjae Chung, Hakjoon Lee, Xinyu Liu, M. Dobrowolska, J. K. Furdyna. Interlayer exchange coupling in (Ga,Mn)As ferromagnetic semiconductor multilayer systems[J]. Journal of Semiconductors, 2019, 40(8): 081503. doi: 10.1088/1674-4926/40/8/081503

      S Lee, S Chung, H Lee, X Y Liu, M Dobrowolska, J K Furdyna, Interlayer exchange coupling in (Ga,Mn)As ferromagnetic semiconductor multilayer systems[J]. J. Semicond., 2019, 40(8): 081503. doi: 10.1088/1674-4926/40/8/081503.
      Export: BibTex EndNote

      Interlayer exchange coupling in (Ga,Mn)As ferromagnetic semiconductor multilayer systems

      doi: 10.1088/1674-4926/40/8/081503
      More Information
      • Corresponding author: slee3@korea.ac.kr
      • Received Date: 2019-05-22
      • Revised Date: 2019-06-03
      • Published Date: 2019-08-01

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