Experimental probing of exchange interactions between localized spins in the dilute magnetic insulator (Ga,Mn)N

The sign, magnitude, and range of the exchange couplings between pairs of Mn ions is determined for (Ga,Mn)N and (Ga,Mn)N:Si with $x\lesssim 3$%. The samples have been grown by metalorganic vapor phase epitaxy and characterized by secondary-ion mass spectroscopy; high-resolution transmission electron microscopy with capabilities allowing for chemical analysis, including the annular dark-field mode and electron energy loss spectroscopy; high-resolution and synchrotron x-ray diffraction; synchrotron extended x-ray absorption fine-structure; synchrotron x-ray absorption near-edge structure; infrared optics; and electron spin resonance. The results of high-resolution magnetic measurements and their quantitative interpretation have allowed us to verify a series of ab initio predictions on the possibility of ferromagnetism in dilute magnetic insulators and to demonstrate that the interaction changes from ferromagnetic to antiferromagnetic when the charge state of the Mn ions is reduced from 3+ to 2+.

Figure 1

Exchange energy $J_{\text{nn}}$ for the nearest-neighbor (nn) coupling from ab initio computations by various authors, as listed in Ref. 7. To obtain $J_{\text{nn}}$, the calculated energy differences for antiferromagnetic and ferromagnetic arrangements of spins within the nn Mn pair of the determined exchange energies have been mapped on the classical Heisenberg Hamiltonian.

Figure 2

Low-magnification TEM (left panel) and HR-TEM (right panel) for (Ga,Mn)N ($x=3.1$%, upper panels) and (Ga,$\delta$Mn)N ($x_{\text{av}}=2.6$%, lower panels) without any evidence of crystallographic phase separation.

Figure 3

XRD radial scans of (Ga,Mn)N and (Ga,$\delta$Mn)N: (a) HR-XRD MRD, (b) SXRD collected at the BM20 of the ESRF.

Figure 4

Magnitude of the Fourier-transformed $k^2$-weighted EXAFS data (inset) in the range $k_{\min }$–$k_{\max }$ with relative fits (described in the text) in the range $R_{\min }$–$R_{\max }$ for representative samples: (Ga,$\delta$Mn)N ($x_{\mathrm{av}}=2.6$%), (Ga,Mn)N ($x=3.1$%), and (Ga,Mn)N:Si ($x=3.3$%)

Figure 5

SIMS depth profiles of Mn and Si in the (Ga,Mn)N:Si film with $x=1.9$%. The residual contamination by H, O, Fe, and Mg is also shown.

Figure 6

(a) HAADF-STEM image of (Ga,Mn)N ($x=3.1$%)–change in intensity (chemical contrast), when going from the substrate into the doped layer (from left to right). (b) EELS spectra for points 0 (GaN buffer layer) and 1 (nominally Mn-doped layer): evidence of the presence of Mn only in the Mn-doped layer (right side of the image). (c)–(f) Determination of the Mn distribution in the digitally Mn-doped sample (Ga,$\delta$Mn)N ($x_{\text{av}}=2.6$%, 160 Mn periods, layer thickness 135 nm). (c,e) HAADF-STEM scans in the Mn-doped region giving modulated chemical contrast. (d,f) EELS spectra of points 0, 1, and 2, as marked in (c) and (e), respectively.

Figure 7

Optical reflectivity spectra for (Ga,Mn)N without and with Si codoping (upper and lower panel, respectively). The Mn concentration is 1.8% in both samples. The absorption feature at 1.41 eV is clearly resolved. The fitting results by the transfer-matrix multilayer model are given by the dashed lines.

Figure 8

Optical transmission spectra for samples with a Mn concentration $x\approx 0.5$%. Upper and lower graphs: data for samples without and with Si codoping, respectively. Next to the main absorption line at 1.41 eV, the phonon replicas of the line are observed. The fitting results by the multilayer model are given by the dashed lines.

Figure 9

Results of ESR studies at 2 K for (Ga,Mn)N without and with Si codoping (lower and upper curve, respectively) showing the emergence of Mn${}^{2+}$ signal on Si doping. The Mn concentration is $x\approx 0.5$%.

Figure 10

Partial fluorescence yield XANES spectra (integrated $K_{\alpha 1,2}$ fluorescence lines) for (Ga,Mn)N and (Ga,Mn)N:Si samples with the polarization vector parallel to the wurtzite $c$ axis. Inset: focus on the shift of the main absorption edge between the two spectra. The position of the pre-edge peaks is constant.

Figure 11

Magnetization at 1.85 K (normalized to its in-plane value at 50 kOe) as a function of the magnetic field applied perpendicular (circles) and parallel (triangles) to the wz $c$ axis of (Ga,Mn)N (a,b) and (Ga,Mn)N:Si (c,d) films where Mn is introduced either uniformly (a,c,d) or digitally (b). Solid and dashed lines are calculated according to the group-theoretical model for noninteracting Mn${}^{3+}$ ions in wz-GaN for $H$ perpendicular and parallel to the $c$ axis, respectively.[17] Insets: low-field magnetization loops.

Figure 12

Comparison of magnetization saturation as a function of the magnetic field between (a) (Ga,Mn)N—no antiferromagnetic interactions and (b) (Ga,Mn)N:Si—with antiferromagnetic interactions. The relative experimental error is about one-half of the point size. Solid lines and the dashed line in (b) are calculated for noninteracting Mn${}^{3+}$ and Mn${}^{2+}$ ions, respectively.

Figure 13

Magnetic susceptibility $M/H$ for $c\perp H$ as a function of the inverse temperature for uniformly (solid symbols) and digitally (open symbols) doped (Ga,Mn)N (circles) and (Ga,Mn)N:Si (triangles) as well as GaN/sapphire control sample (light gray circles). Solid lines serve to determine the Curie constants at high temperatures. Deviations of their values from zero at $1/T=0$ show the accuracy of the substrate subtraction.

Figure 14

Normalized Curie constant $C_{\text{norm}}$ as a function of the Mn content for uniformly (solid symbols) and digitally (open symbols) doped (Ga,Mn)N (circles) and (Ga,Mn)N:Si (triangles). The solid lines are computed assuming a random distribution of Mn${}^{3+}$ ions, and either ferromagnetic or antiferromagnetic strong coupling between the nearest-neighbor (nn) Mn spins, $|J_{\text{nn}}|S^2\gg k_{B}T$. Dashed and dotted lines are calculated assuming that $4\times {10}^{20}$ cm${}^{-3}$ Mn ions are in the $2+$ charge state, and nn interactions are ferromagnetic except for nn Mn${}^{2+}$ pairs, for which $J_{\text{nn}}=0$ or $-J_{\text{nn}}{S}^2\gg k_{B}T$, respectively.