Anomalous low-field magnetoresistance in Fe$_3$Ga$_4$ single crystals

Abstract

Fe$_3$Ga$_4$ possesses a helical spin spiral with a complex competition between ferromagnetic and antiferromagnetic ground states. This competition generates multiple metamagnetic transitions that are governed by both applied magnetic field and temperature. At intermediate temperatures between T$_1$ (68 K) and T$_2$ (360 K), the ferromagnetically aligned spins transition to an antiferromagnetic spin spiral. In this study, magnetoresistance (MR) measurements are performed on an aligned single crystal and compared to magnetization properties in order to gain insight on the unique alignment of the spins. The high-field MR is positive at low temperatures indicating cyclotronic behavior and negative at high temperature from electron-magnon scattering. Of particular significance is a large anomalous positive MR at low fields, possibly due to emergent spin fluctuations thus prompting further exploration of this multifaceted material.

Figures (3)

• Figure 1: (a) The magnetic phase diagram with applied field ($\mu_0$H) and temperature. The antiferromagnetic state is shown in red, where the red region is given by the change in the magnetic transitions T$_1$ and T$_2$. The values noted in the diagram are from the $b$-axis as noted in the supplemental information.SM The helical spiral (HS) in the diagram in blue is the magnetic step along the $b$-axis, where the low-field behavior is a two dimensional spin spiral,. The HS is also observed along the $a$-axis in the antiferromagnetic region as noted in the supplemental information.SM (b) The magnetoresistance (MR) along the $b$-axis at T = 140 K, where the crystal is in the antiferromagnetic state. The down sweep is in red and the up sweep is in blue. There is a hysteresis oberved at $\mu_0$H $\approx$$\pm$ 1.0 T, which relates to saturation at T = 140 K. There is a smaller change close to $\approx$ 0.75 T, which is the field that the HS transitions to the TCS. (c) The MR at each temperature along the $b$-axis starting from 2.2 K to 300 K. (d) The MR at each temperature along the $b$-axis from 350 K to 65 K.
• Figure 2: (Left) The data for the magnetoresistance (MR) when $\mu_0 H$ is applied along the $a$, $b$, and $c$ crystallographic axes. (Right) The same data as the (left), but focused on the region when $\mu_0 H = 0 - 1.5$ T. The data shows that the MR along the $b-$ axis has a persistant positive contribution below 0.75 T for all temperatures with the exception of the 300 K data. The $a$-axis has a slight positive magnetoresistance for temperatures when the crystal is in its Helical Spin Spiral (HSS) state after T$_1$. The legend for temperatures correspond to all curves in this figure.
• Figure 3: (a) An example of the fits for the $a$, $b$, and $c$-axes at 2.6 K as noted by solid lines, and the regions for designated field ranges are noted by different colors ($\rho_{low}$ is light yellow and $rho_{high}$ is light grey). (inset) The field where saturation occurs and the magnetic step indicating a change from the HS state to the transverse conical spiral (TCS) state along the $b$-axis. Magnetic data describes the data extrapolated from SQUID magnetometry in reference WilfongSC and MR data is the field where the MR decreases in the intermediate field and temperature range. (b) and (c) The fitting values from modeling the low-field positive magnetoresistance where $MR = (\mu \mu_0 H)^q$, where $1<q<2$. The positive magnetoresistance is only found along the $b$-axis.(d) and (e) The values from modeling the high-field data that was fit to the electron-magnon model where MR = $-b_1 \ln(1 + b_2^2 (\mu_0H)^2)$ for the $a$, $b$ and $c$ axes.