Origin of low-temperature magnetic ordering in Ga${}_{1-x}$Mn${}_x$N

By using highly sensitive millikelvin superconducting quantum interference device magnetometry, the magnitude of the Curie temperature as a function of the Mn concentration $x$ is determined for thoroughly characterized Ga${}_{1-x}$Mn${}_x$N. The interpretation of the results in the frame of tight-binding theory and of Monte Carlo simulations allows us to assign the spin interaction to ferromagnetic superexchange and to point out the limited accuracy of state-of-the-art ab initio methods in predicting the magnetic characteristics of dilute magnetic insulators.

Figure 1

(a) Sketch of the millikelvin magnetometer employed for this work. For maximum linearity of the setup the superconducting pickup coils are made of pure niobium wire and the magnetic field is generated by a copper-wound electromagnet immersed in a helium Dewar. An additional copper-made flux-balancing coil (c.c.) is placed asymmetrically with respect to the main coil and is connected to the same power supply through a resistive current divider (R1 and R2) adjusted to obtain an adequately flat magnetic field (reference) response when a reference undoped GaN layer is placed inside the pickup. The whole setup has been calibrated against the known magnetic moment of a signal coil located at the sample position. (b)–(d) Magnetic hysteresis loops at various temperatures for Ga${}_{1-x}$Mn${}_x$N measured in the dilution refrigerator setup (lines) and in a commercial SQUID magnetometer (bullets), respectively. The reported values of the magnetization are normalized to their magnitudes at 70 kOe and at 1.85 K.

Figure 2

Magnitude of the coercive field as a function of temperature for the considered Ga${}_{1-x}$Mn${}_x$N samples (full points), employed to determine the Curie temperatures. Inset: Experimental Curie temperatures as a function of Mn content $x$, together with the experimental result of Ref. 11 (solid squares and circles, respectively). The dotted line shows the scaling dependence $T_{\text{C}}\propto x^m$ with $m=2.2$. The results of ab initio (Ref. 4, open diamonds) and tight-binding (this work, open squares) approaches are also shown.

Figure 3

Exchange energies provided by the tight-binding model for Mn pairs in zinc blende GaN as a function of the distance between Mn spins in units of the lattice parameter $a$. The numbers of equivalent cation sites at the particular distances $R_{ij}$ are also given.