Evolution of incommensurate spin order with magnetic field and temperature in the itinerant antiferromagnet GdSi

GdSi exhibits spin-density-wave (SDW) order arising from the cooperative interplay of sizeable local moments and a partially nested Fermi sea of itinerant electrons. Using magnetotransport, magnetization, and nonresonant magnetic x-ray diffraction techniques, we determine the H-T phase diagrams of GdSi for magnetic fields up to 21 T, where antiferromagnetic order is no longer stable, and field directions along each of the three major crystal axes. While the incommensurate magnetic ordering vector that characterizes the SDW is robust under magnetic field, the multiple spin structures of this compound are highly flexible and rotate relative to the applied field via either canting or spin-flop processes. The antiferromagnetic spin densities always arrange themselves transverse to the applied magnetic field direction. The phase diagrams are delineated by two types of phase boundaries: one separates a collinear from a planar spin structure associated with a lattice structural transition, and the other defines a spin flop transition that is only weakly temperature dependent. The major features of the phase diagrams along each of the crystal axes can be explained by the combination of local moment and global Fermi surface physics at play.

Figure 1

(a) Orthorhombic lattice structure of GdSi, with four chemical units inside one unit cell. (b) Lattice (gray) and magnetic (orange and green) diffraction patterns of GdSi in the $KL$ plane. In the collinear phase between the Néel temperature $T_N$ and the spin-flip temperature $T_{\mathrm{SF}}$, the magnetic peaks are found surrounding all nonforbidden lattice peaks such as (0, 2, 0) and (0, 1, 1) with a spin-ordering wave vector Q = (0, $q_b$, $q_c$) ∼ (0, 0.483, 0.093). Below $T_{\mathrm{SF}}$, magnetic diffraction is also observed surrounding forbidden lattice orders such as (010), with much lower intensities. There are two degenerate magnetic domains with Q = (0, ±$q_b$, $q_c$) (orange and green) between $T_N$ and $T_{\mathrm{SF}}$. The magnetic structure is a single-$q$ type that is similar to the SDW state in Cr (Refs. 1, 25, and 26) but different from the double-$q$ state in HoNi${}_2$B${}_2$C (Ref. 28) and GdNi${}_2$B${}_2$C (Ref. 31). Below $T_{\mathrm{SF}}$, the orthorhombic lattice structure transforms into monoclinic and the magnetic degeneracy is lifted as each magnetic domain becomes associated with the lattice structure.

Figure 2

Collinear spin structure in magnetic field. Between $T_{\mathrm{SF}}$ and $T_N$, spins in GdSi are transverse to the magnetic wave vector Q and at $H=$0 lie within the $bc$ plane. When $H$ is applied along either $a$ or $b$, the spins continuously cant towards $H$. For $H$∥$c$, spins initially experience a first order spin-flop transition before canting further toward $H$.

Figure 3

Planar spin structure in a magnetic field. Below $T_{\mathrm{SF}}$, the planar spin structure is transverse to the magnetic wave vector Q at zero field. For $H$∥$b$, all spins continuously cant towards $H$. For both $H$∥$a$ and $H$∥$c$, about half of the spins experience a spin-flop transition. Eventually the spin component along $H$ is totally ferromagnetic, while the spin component transverse to $H$ is antiferromagnetic.

Figure 4

Phase diagrams of GdSi with H parallel to $b$, $a$, and $c$ (top to bottom). The insets show detailed regions around the high-field triple point between the collinear, planar antiferromagnetic, and PM phases. The four antiferromagnetic (I to IV) and paramagnetic (PM) phases are marked in blowup views of regions at low field and high temperature for each field configuration.

Figure 5

Magnetic field dependence of transverse magnetoresistivity under various field-current configurations of (a) $H$∥$a$ and $I$∥$c$; (b) $H$∥$c$ and $I$∥$a$; and (c) $H$∥$b$ and $I$∥$c$. (d) A set of magnetoresistivity curves with $H$∥$b$ and $I$∥$a$ at various temperatures across the triple point at ∼($H=$17.6 T, $T=$27 K). At high temperature, two well-separated transitions are clearly seen. The transition fields converge with lowering temperature, and eventually become one below $T=$28 K.

Figure 6

Resistivity of GdSi as a function of temperature measured at 1 T magnetic field intervals from 0 to 9 T for (a) $H$∥$b$ and $I$∥$a$ and (b) $H$∥$c$ and $I$∥$b$. Susceptibility $M$($T$)/$H$ of GdSi as a function of temperature at various fields for (c) $H$∥$a$ and (d) $H$∥$c$.

Figure 7

Magnetization versus field in GdSi. (a) The ferromagnetic component of the magnetization along the field direction, measured in a SQUID magnetometer at $T=$5 K for $H$ along each of the three crystal axes. (b) The antiferromagnetic spin density along the applied field direction, measured by x-ray magnetic diffraction for two magnetic orders (0, 2 ± $q_b$, ±$q_c$), for $H$∥$a$ at $T=$46 K and $H$∥$c$ at $T=$4.5 K, respectively.

Figure 8

Magnetic field dependence of (a) lattice orders (0, 4, 2) and (0, 2, 0); (b) magnetic vectors (0, 2 ± $q_b$, ±$q_c$) for $H$∥$a$ at $T=$46 K, and (c) magnetic vectors (0, 2 ± $q_b$, ±$q_c$) for $H$∥$c$ at $T=$4.5 K.

Figure 9

Evolution of the spin-ordering wave vector as a function of field and temperature. (a) Temperature dependence of magnetic orders (0, 2 ± $q_b$, ±$q_c$), for $H$∥$c$ at $T=$4.5 K compared to those at $H=$0 (Ref. 10). (b) Evolution of ($q_b$, $q_c$) in the $KL$ plane of reciprocal space for $H=$0 (black), $H$∥$c$ at $T=$4.5 K (solid blue) and from 4.5 to 51.8 K (open blue) and $H$∥$a$ at $T=$46 K (green).