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^{1}, Daisuke Sasaki

^{1}, Le Duc Anh

^{1}and Masaaki Tanaka

^{1}

### Abstract

We have investigated the anisotropic magnetoresistance(AMR) of (In,Fe)As ferromagneticsemiconductor layers grown on semi-insulating GaAs substrates. In a 10 nm-thick (In,Fe)As layer which is insulating at low temperature, we observed crystalline AMR with two-fold and eight-fold symmetries. In a metallic 100 nm-thick (In,Fe)As layer with higher electron concentration, only two-fold symmetric crystalline AMR was observed. Our results demonstrate the macroscopic ferromagnetism in (In,Fe)As with magnetic anisotropy that depends on the electron concentration. Very small (∼10^{−5}) non-crystallineAMR is also observed in the 100 nm-thick layer, suggesting that there is no *s-d*scattering near the Fermi level of (In,Fe)As.

This work was partly supported by Grant-in-Aids for Scientific Research, particularly the Grant-in-Aid for Specially Promoted Research, the Special Coordination Programs for Promoting Science and Technology, the FIRST Program of JSPS, and the Global COE program (C04).

### Key Topics

- Magnetoresistance
- 20.0
- Nuclear acoustic resonance
- 18.0
- Amorphous solids
- 17.0
- Electron scattering
- 11.0
- Magnetic anisotropy
- 11.0

## Figures

Temperature dependence of resistivity of sample A (solid curve) and sample B (dashed curve). Inset shows relationships between the current ** i **, the magnetic field

**, the magnetization**

*H***, and angles**

*M**α*,

*ϕ*, and

*φ*in our measurements.

**is parallel to**

*M***because of the high field (8.7 kOe).**

*H**α*is the angle between

**and the [100] crystal axis,**

*M**ϕ*is the angle between

**and the [110] crystal axis, and**

*M**φ*is the angle between

**and**

*M***.**

*i*Temperature dependence of resistivity of sample A (solid curve) and sample B (dashed curve). Inset shows relationships between the current ** i **, the magnetic field

**, the magnetization**

*H***, and angles**

*M**α*,

*ϕ*, and

*φ*in our measurements.

**is parallel to**

*M***because of the high field (8.7 kOe).**

*H**α*is the angle between

**and the [100] crystal axis,**

*M**ϕ*is the angle between

**and the [110] crystal axis, and**

*M**φ*is the angle between

**and**

*M***.**

*i*Longitudinal anisotropic magnetoresistance data (squares) for (a) the [110] Hall bar (*i =* 10 *μ*A//[110]) and (b) the [] Hall bar (*i =* 10 *μ*A//[]) of sample A as a function of *α*, measured at 20 K under a magnetic field of 8.7 kG. Solid curves are fitting curves using *C* _{2} = −0.038%, *C* _{4} = 0%, *C* _{8} = 0.025% for the [110] Hall bar, and *C* _{2} = −0.052%, *C* _{4} = 0%, *C* _{8} = 0.03% for the [] Hall bar in Eq. (2), respectively.

Longitudinal anisotropic magnetoresistance data (squares) for (a) the [110] Hall bar (*i =* 10 *μ*A//[110]) and (b) the [] Hall bar (*i =* 10 *μ*A//[]) of sample A as a function of *α*, measured at 20 K under a magnetic field of 8.7 kG. Solid curves are fitting curves using *C* _{2} = −0.038%, *C* _{4} = 0%, *C* _{8} = 0.025% for the [110] Hall bar, and *C* _{2} = −0.052%, *C* _{4} = 0%, *C* _{8} = 0.03% for the [] Hall bar in Eq. (2), respectively.

Longitudinal anisotropic magnetoresistance data (squares) for (a) the [110] Hall bar (*i =* 1 mA//[110]), and (b) the [] Hall bar (*i =* 1 mA//[]) of sample B as a function of *α*, measured at 20 K under a magnetic field of 8.7 kG.Solid curves are fitting curves using *C* _{2} = 0.0034%, *C* _{4} = 0%, *C* _{8} = 0% for the [110] Hall bar, and *C* _{2} = 0.012%, *C* _{4} = 0%, *C* _{8} = 0% for the [] Hall bar in Eq. (2), respectively.

Longitudinal anisotropic magnetoresistance data (squares) for (a) the [110] Hall bar (*i =* 1 mA//[110]), and (b) the [] Hall bar (*i =* 1 mA//[]) of sample B as a function of *α*, measured at 20 K under a magnetic field of 8.7 kG.Solid curves are fitting curves using *C* _{2} = 0.0034%, *C* _{4} = 0%, *C* _{8} = 0% for the [110] Hall bar, and *C* _{2} = 0.012%, *C* _{4} = 0%, *C* _{8} = 0% for the [] Hall bar in Eq. (2), respectively.

Planar Hall resistance data (squares) for (a) the [110] Hall bar (*i =* 5 mA//[110]) and (b) the [] Hall bar (*i =* 1 mA//[]) of sample B as a function of *φ*, measured at 20 K under a magnetic field of 8.7 kG. Solid curves are fitting curves using *C* _{1} = −1.8 × 10^{−5}, *C* _{1,c} = 0 for the [110] Hall bar, and *C* _{1} = −2.8 × 10 ^{− 5}, *C* _{1,c} = 0 for the [] Hall bar in Eq. (1b), respectively.

Planar Hall resistance data (squares) for (a) the [110] Hall bar (*i =* 5 mA//[110]) and (b) the [] Hall bar (*i =* 1 mA//[]) of sample B as a function of *φ*, measured at 20 K under a magnetic field of 8.7 kG. Solid curves are fitting curves using *C* _{1} = −1.8 × 10^{−5}, *C* _{1,c} = 0 for the [110] Hall bar, and *C* _{1} = −2.8 × 10 ^{− 5}, *C* _{1,c} = 0 for the [] Hall bar in Eq. (1b), respectively.

Plan view of nearest (a) In atoms and (b) As atoms around an Fe atom. In atoms have an effective charge of +*ɛe*, while As atoms have an effective charge of −*γe*, seen from a *d*-electron. A *d*-electron with the *d* _{ xy } wave function will be closer to its nearest In/As atoms when its wave function is aligned along the 〈110〉 direction (dashed curve) rather than the 〈100〉 direction (solid curve).

Plan view of nearest (a) In atoms and (b) As atoms around an Fe atom. In atoms have an effective charge of +*ɛe*, while As atoms have an effective charge of −*γe*, seen from a *d*-electron. A *d*-electron with the *d* _{ xy } wave function will be closer to its nearest In/As atoms when its wave function is aligned along the 〈110〉 direction (dashed curve) rather than the 〈100〉 direction (solid curve).

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