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High-energy magnetic excitations and anomalous spin-wave damping in FeGe 2
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2000 J. Phys.: Condens. Matter 12 8487
(http://iopscience.iop.org/0953-8984/12/39/311)
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J. Phys.: Condens. Matter 12 (2000) 8487–8493. Printed in the UK PII: S0953-8984(00)15871-0
High-energy magnetic excitations and anomalous spin-wave
damping in FeGe2
1. Introduction
C P Adams†, T E Mason† + , E Fawcett† ∗ , A Z Menshikov‡ ∗ , C D Frost§,
J B Forsyth§, T G Perring§ and T M Holden #
† Department of Physics, University of Toronto, Toronto, ON, Canada M5S 1A7
‡ Institute for Metal Physics, Ekaterinburg, Russian Federation
§ ISIS Facility, Rutherford-Appleton Laboratory, Chilton, Didcot OX11 0QX, UK
National Research Council, Chalk River, ON, Canada K0J 1J0
E-mail: carl.adams@nist.gov.
Received 27 July 2000
Abstract. Inelastic neutron scattering has been used to measure the high-energy, low-temperature
magnetic excitations of the itinerant antiferromagnet FeGe2. The spin-wave excitations follow a
Heisenberg dispersion with exchange constant along the c-axis SJFM = 68 ± 1 meV an order
of magnitude higher than the basal-plane antiferromagnetic constant SJAF M =−4.4 ± 0.6 meV.
The c-axis spin waves are highly damped, even at temperatures small compared to SJFM. The
damping is roughly quadratic in energy (as in the hydrodynamic model) up to ∼250 meV, beyond
which a continuum of excitations emerges.
Over the last 10 years there has been growing evidence that a nearby spin-density-wave (SDW)
instability is responsible for the anomalous normal-state transport properties of the high-Tc
oxides [1] and possibly for the superconductivity itself [2–5]. Similar instabilities precede the
SDW transitions in certain other Mott–Hubbard systems [6], such as V2−yO3 [7]. In both cases,
strong electron–electron correlations exist and lead to a breakdown of conventional band theory
and, as in the high-Tc cuprates, a metal–insulator transition. Despite some obvious differences
these novel SDW systems have much in common with non-correlated, fully metallic, SDW
systems, of which chromium [8] is the prototypical example. Notably in all SDW systems the
periodic modulation of the conduction-electron spin density [9] develops as a result of Fermi
surface nesting, i.e., electron exchange between two parallel pieces of Fermi surface [10].
In the light of this commonality the recent interest in the high-Tc oxides has led to renewed
studies of non-correlated SDW systems, where conventional band theory should be able to
answer outstanding questions regarding transport and magnetic properties.
One intriguing feature, common to both correlated and non-correlated SDW systems,
is a complex spectrum of magnetic excitations in both ordered and non-ordered phases;
Present address: NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg,
MD 20899-8562, USA.
+ Present address: Spallation Neutron Source, 701 Scarboro Road, Oak Ridge National Laboratory, Oak Ridge,
TN 37830, USA.
∗ Deceased.
# Retired.
0953-8984/00/398487+07$30.00 © 2000 IOP Publishing Ltd 8487

8488 C P Adams et al
conventional oscillatory, propagating spin waves do not exist in these materials [7, 8, 11, 12].
This has greatly hindered a complete description of SDW systems since it is the spin-wave
dispersion that yields values for the microscopic interaction strengths. From this viewpoint
FeGe2, the non-correlated SDW system that is the subject of this study, is an important
exception, since the first inelastic neutron scattering measurements showed that its lowtemperature
magnetic excitations are propagating spin waves or magnons [13, 14]. A simple
Heisenberg model successfully describes the low-energy magnetic dispersion. However, there
appears to be an intrinsic damping of the spin waves even at low temperatures. Damping of this
magnitude is impossible in a purely localized system where magnon–magnon and magnon–
phonon scattering processes dominate, but in metallic systems, such as FeGe2, scattering
can simply arise from the itinerant electrons even at low T . This dual behaviour (spin-wave
dispersion of local moments, significant damping from itinerant electrons) is also found in
the ferromagnetic (FM) metals iron [15] and nickel [16] and La0.85Sr0.15MnO3 [17], a FM
transition metal oxide near the Mott transition.
A further novel feature of FeGe2 is that the dispersion is so anisotropic that it is well
described as quasi-one-dimensional (quasi-1D), unique among metallic magnetic systems [14].
While the entire a-axis magnon dispersion was measured using thermal neutron scattering at
the Chalk River reactor, the much larger energy scale associated with the c-axis magnons
prevented the observation of resolved spin-wave modes in constant-Q scans. A quantitative
determination of the damping (seen as the intrinsic linewidth) and the high-Q dispersion was
not possible. This prompted a continuation of these measurements up to higher energies at the
ISIS spallation source.
FeGe2 has a body-centred tetragonal crystal structure, as in CuAl2, with space group
I4/mcm and two zero-field magnetic phase transitions [18, 19]. One is a second-order Néel
transition from a paramagnetic phase to an incommensurate (IC) SDW state at TN = 289 K
and the other at TC−IC = 263 K is a typical first-order transition from an IC to a commensurate
phase [19]. The ordering wavevector of the commensurate phase, (2π/a)(1, 0, 0), changes to
(2π/a)(1+δ, 0, 0) in the IC phase where δ varies from 0 to ∼0.05. Nearest-neighbour (NN)
iron atoms are 2.478 Å apart along the c-axis and their magnetic moments have FM alignment
in both phases. The next-NN iron atoms are separated by 4.178 Å along the [110] direction with
antiferromagnetic (AFM) alignment of the moments below TC−IC. The higher-temperature IC
phase appears as a long-wavelength modulation of this structure in the basal plane. AFM IC
structures in metals are a strong indication of an interaction that is mediated by the conduction
electrons (indirect exchange). Superexchange through the germanium ions probably also plays
a role in the net AFM basal-plane interaction. In contrast, the NN spacing along the c-axis is so
close to that of elemental iron (2.50 Å) that the primary magnetic interaction in this direction
is probably a direct FM interaction.
2. Experimental results and discussion
To measure the high-energy magnetic excitations and the damping of spin waves in FeGe2, a
new single crystal sample was prepared. It is roughly semi-cylindrical, 15 mm in radius and
40 mm in length, with a mass of 270 g. The measurements were performed at 11 K in the
low-T AFM phase (effectively at T = 0 compared to TN) using HET, a direct-geometry chopper
spectrometer at the ISIS spallation source. The sample was oriented with [010] vertical so the
horizontal banks of detectors were sensitive to momentum transfers Q with (h0l) components,
designated by Qa and Qc. Since HET is a time-of-flight instrument, energy transfer E is
coupled to Q in a way that in general prevents extraction of constant-E and constant-Q scans
(conventionally employed when using a triple-axis spectrometer). Despite this complication,

High-energy magnetic excitations in FeGe2
8489
a substantial part of the magnetic dispersion can often be measured at one time provided that
a suitable orientation of the sample is chosen.
An example of an HET scan is shown in figure 1. The curved surface in (Q,E) space
scanned by the instrument is projected onto the (Qa,Qc) plane. The contours of constant-E
reflect this curvature and approach the incident energy Ei = 120 meV at the apex. Absolute
scattering intensity, resulting from vanadium normalization, is indicated by spectral colour.
In terms of actual neutron counts, 1 mb meV −1 sr −1 is equal to 20 counts over a 12-hour
scan. No correction was made for sample shape or absorption, which could lead to an error of
15% in the absolute cross-section values. Several features are evident in figure 1: incoherent
elastic scattering along the E = 0 contour, complicated phonon and magnon scattering for
E

8490 C P Adams et al
for various values of Ei are shown in figures 2(a) and 2(b) and resemble the more familiar
constant-E and constant-Q triple-axis scans. Peaks are resolved to high energies (>200 meV)
in both types of cut. The dispersion, which is quite steep in comparison to the Qc-resolution, is
measured with a resolution corrected fit to the peaks in constant-E cuts as shown in figure 2(a).
The constant-Qc cuts show damped magnons with a significant linewidth that increases with
energy. Along the a-axis, similar spin-wave behaviour and damping have been observed with
triple-axis measurements [13] but the zone boundary energy is only 30 meV, much less than
the c-axis spin-wave energies in figures 2(a) and 2(b).
Intensity (mb meV −1 sr −1
)
(a)
0.4
0.2
0.0
x10
x 3
h¯ ω=250 meV
h¯ ω=155 meV
h¯ ω=
77.5 meV
1.2 1.6 2.0 2.4 2.8
Q c (c*)
(b)
0.6
0.4
0.2
0.0
Q c =1.6 c*
Q c =1.74 c*
Q c =1.87 c*
50 100 150 200
Energy (meV)
Figure 2. (a) Constant-E and (b) constant-Qc cuts showing the c-axis magnons. Cuts are taken
from data reduced to the (Qc,E) plane and have been offset vertically (the thick dashed lines
represent zero intensity above the background). Two sets have been rescaled as indicated. The
data in (b) have had the background removed by subtraction of a nearby non-magnetic cut. The
solid lines are the resolution-corrected scattering cross-sections (described in more detail in a later
section).
The c-axis spin-wave dispersion, as measured by Gaussian fits to constant-E cuts, is shown
in figure 3.
The 3D classical, NN Heisenberg model has a Hamiltonian of the form
H =− Jij Si · Sj .
Combining this with the known low-T AFM structure of FeGe2 gives the spin-wave dispersion
[20]:
¯hωQ = 4S({JFM[1 − cos(πl)] − 2JAF M[1 − cos(πh) cos(πk)]}
×{JFM[1 − cos(πl)] − 2JAF M[1 + cos(πh) cos(πk)]}) 1/2
(1)
where the spin-wave energy is ¯hωQ, S is the on-site spin, JFM is the c-axis exchange constant,
JAF M is the [110] exchange constant, and h, k, and l express Q in terms of reciprocal-lattice
coordinates. Triple-axis measurements [13] have shown a gapless (

High-energy magnetic excitations in FeGe2
Energy (meV)
300
200
100
SJ =−4.4 meV
AFM
SJFM =68 meV
0
0.0 0.1 0.2 0.3
Qc (c*)
0.4 0.5 0.6
8491
Figure 3. The c-axis magnon dispersion and the prediction of a NN Heisenberg model. The data
have been corrected for the Qa-energy contribution. Excitations beyond the plotted E-range are
highly damped and not well defined.
gap in the 1D planar model). However, using equation (1) with SJAF M =−4.4 meV (from
the data of [13]) significantly improves the fit to the low-energy dispersion and the overall
scattered intensity (see the next section). The 3D behaviour can be seen in figure 2(b) where
the variation in Qa along a ‘constant-Q’ cut leads to peaks at 45 meV and at 75 meV for
Qc = 1.87 c∗ ; an effect that is correctly predicted by the simulation. The small Qa-dependent
energy contribution arising from equation (1) has been subtracted from the data in figure 3
to leave only the Qc-dependence. The system becomes more 1D at higher energies as this
correction decreases in comparison to ¯hωQ. The fit shown in figure 3 has SJFM = 68±1 meV,
roughly a factor of 15 larger in strength than SJAF M, a uniquely large anisotropy among
3D metals.
Although the Gaussian fits give the dispersion of well defined magnons, they provide no
clear information about the damping since the intrinsic linewidth remains convoluted with the
experimental resolution. This linewidth is determined by using a simulation of the resolution
and a full model for the scattering cross-section per iron atom [20]:
d2σ kf
∝ |F (Q)|
d dE ′
ki
2
1/2 JFM[1 − cos(πl)] − 2JAF M[1 − cos(πh) cos(πk)]
JFM[1 − cos(πl)] − 2JAF M[1 + cos(πh) cos(πk)]
× 1 − exp − E
−1 4 ¯hωQEƔ
kBT π [E2 − (¯hωQ) 2 ] 2 +4(EƔ) 2
. (2)
ki and kf are the lengths of the incident and final neutron wavevectors. F (Q) is a magnetic
form factor appropriate for Fe3+ [22]. The next term, the dynamical structure factor, predicts
that the intensity of pure FM spin waves is uniform throughout the magnetic Brillouin zone
and AFM spin waves have a diverging intensity at magnetic zone centres and zero intensity at
nuclear zone centres. The principle of detailed balance is satisfied by inclusion of the thermal

8492 C P Adams et al
population of magnons. The final term is the appropriate susceptibility for a damped simple
harmonic oscillator (DSHO) with linewidth Ɣ and free-mode energy ¯hωQ. This cross-section
correctly approaches δ-functions in the Ɣ ≪ ¯hωQ limit.
The simulation, using equation (2) and the previously mentioned SJ-values, successfully
describes the spin-wave intensity and dispersion through several magnetic Brillouin zones.
Subsequent fixing of the proportionality in equation (2) gives the results for Ɣ shown in
figure 4. This confirms that the peak broadening in figure 2 is due to increasing Ɣ rather than the
coarsening resolution at higher Ei. The damping increases rapidly beyond ¯hωQ = 220 meV,
wiping out the well defined magnon peaks; uncertainties in peak position and linewidth increase
accordingly. Such large values of Ɣ for T ≪ TN are not expected on the basis of local
models where magnon–magnon scattering dominates. Hence, this damping is anomalous and
must be due to itinerant electrons, a conclusion previously reached in studies of several FM
systems [15–17]. In fact, the itinerant effects eventually predominate over the local behaviour
and the spin waves merge into a continuum of excitations (Ɣ ∼ E). Calculation of Ɣ in
itinerant systems often requires detailed knowledge of the electronic band structure [23] but
in FeGe2 the reduced dimensionality and the lack of electron correlations may simplify such
a prediction, providing important insight into several classes of itinerant magnetic systems.
One result that appears to be preserved from a local-moment model is the quadratic
variation of Ɣ with E predicted by the hydrodynamic model [24]. A range of appropriate
quadratic parametrizations is shown in figure 4 with the best description being given for
Ɣ = 2.7 × 10 −3 E 2 (meV units). The reciprocal of the prefactor is 370 ± 80 meV, comparable
to 4SJFM = 272 meV, half of the zone boundary energy. The hydrodynamic model includes
SJ in a similar way but also includes a T -dependent term, (T /TN) 3 , which would eliminate
low-T damping. This is clearly in disagreement with figure 4.
Figure 4. The magnon linewidth Ɣ versus E. The solid and dashed lines represent the function and
the uncertainty given in the figure. Note the rapid increase of Ɣ beyond 220 meV and the gradual
merging into a continuum of excitations.

High-energy magnetic excitations in FeGe2
8493
The observation of well defined spin-wave modes in an itinerant system such as FeGe2
is particularly noteworthy given the fact that this sort of response has not been seen in Cr,
the prototypical SDW system. In Cr, complex behaviour at low frequencies is observed with
a suggestion of spin-wave modes with a high velocity [8, 25]. However, measurements to
higher frequencies carried out using the same time-of-flight techniques as are employed in the
present study have failed to reveal resolved spin-wave modes such as those shown in figure 2.
The behaviour of FeGe2 is similar to that seen in itinerant FM materials where the magnon
modes have non-zero damping, even in the low-T ground state. The reduced dimensionality
of FeGe2 may hasten a theoretical description of the transition from local to fully itinerant
magnetism.
Acknowledgments
We wish to thank V G Guk from the Ural Technical University for growing the FeGe2 single
crystal and S M Hayden who provided the computer code for the resolution-corrected fits.
Work at Toronto was supported by the Natural Sciences and Engineering Research Council of
Canada and the Canadian Institute for Advanced Research. TEM acknowledges the support
of the A P Sloan Foundation. AZM recognizes the support of the programme ‘Neutron Study
of Matter’ and RFFI Grant No 98-02-16165.
References
[1] Takagi H, Ido T, Ishibashi S, Uota M, Uchida S and Tokura Y 1989 Phys. Rev. B 40 2254
[2] Scalapino D J, Loh E Jr and Hirsch J E 1987 Phys. Rev. B 35 6694
[3] Monthoux P, Balatsky A V and Pines D 1992 Phys. Rev. B 46 14 803
[4] Levin K, Zha Y, Radtke R J, Si Q, Norman M R and Schüttler H-B 1994 J. Supercond. 7 563
[5] Ruvalds J, Rieck C T, Tewari S, Thoma J and Virosztek A 1995 Phys. Rev. B 51 3797
[6] Mott N F 1990 Metal–Insulator Transitions 2nd edn (New York: Taylor and Francis) pp 123–44, 171–97
[7] Bao W, Broholm C, Carter S A, Rosenbaum T F and Aeppli G 1993 Phys. Rev. Lett. 71 766
[8] Fawcett E 1988 Rev. Mod. Phys. 60 209
[9] Herring C 1966 Magnetism vol 4, ed G T Rado and H Suhl (New York: Academic) pp 85–119
[10] Overhauser A W 1962 Phys. Rev. 128 1437
[11] Noakes D R, Holden T M, Fawcett E and deCamargo P C 1990 Phys. Rev. Lett. 65 369
[12] Hayden S M, Doubble R, Aeppli G, Perring T G, Fawcett E, Lowden J and Mitchell P W 1997 Physica B
237+238 421
[13] Holden T M, Menshikov A Z and Fawcett E 1996 J. Phys.: Condens. Matter 8 L291
[14] Mason T E, Adams C P, Mentink SAM,Fawcett E, Menshikov A Z, Frost C D, Forsyth J B, Perring TGand
Holden T M 1997 Physica B 237+238 449
[15] Paul D M c K, Mitchell P W, Mook H A and Steigenberger U 1988 Phys. Rev. B 38 580
[16] Mook HAandPaulDM c K 1985 Phys. Rev. Lett. 54 227
[17] Vasiliu-Doloc L, Lynn J W, Moudden A H, de Leon-Guevara A M and Revcolevschi A 1998 Phys. Rev. B 58
14 913
[18] Corliss L M, Hastings J M, Kunnmann W, Thomas R, Zhuang J, Butera R and Mukamel D 1985 Phys. Rev. B
31 4337
[19] Menshikov A Z, Dorofeev Yu A, Budrina G L and Syromyatnikov V M 1988 J. Magn. Magn. Mater. 73 211
[20] Lovesey S M 1984 Theory of Inelastic Neutron Scattering vol 2 (New York: Oxford University Press) pp 109–19
[21] Villain J 1973 J. Phys. C: Solid State Phys. 6 L97
[22] Brown P J 1995 International Tables for Crystallography volC,edAJCWilson (Boston, MA: Kluwer Academic)
p 392
[23] Cooke J F, Lynn J W and Davis H L 1980 Phys. Rev. B 21 4118
[24] Halperin B I and Hohenberg P C 1969 Phys. Rev. 177 952
[25] Fukuda T and Endoh Y 1998 Physica B 241–243 619

arXiv:cond-mat/9610009v1 [cond-mat.str-el] 1 Oct 1996
Itinerant Antiferromagnetism in FeGe2
T.E. Mason, C.P. Adams, S.A.M. Mentink, E. Fawcett
Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada
A.Z. Menshikov
Institute for Metal Physics, Ekaterinburg, Russia
C.D. Frost, J.B. Forsyth, T.G. Perring
ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX,
United Kingdom
Abstract
T.M. Holden
AECL, Chalk River Laboratories, Chalk River, ON K0J 1J0, Canada
FeGe2, and lightly doped compounds based on it, have a Fermi surface driven instability
which drive them into an incommensurate spin density wave state. Studies
of the temperature and magnetic field dependence of the resistivity have been used
to determine the magnetic phase diagram of the pure material which displays an
incommensurate phase at high temperatures and a commensurate structure below
263 K in zero field. Application of a magnetic field in the tetragonal basal plane
decreases the range of temperatures over which the incommensurate phase is stable.
We have used inelastic neutron scattering to measure the spin dynamics of FeGe2.
Despite the relatively isotropic transport the magnetic dynamics is quasi-one dimensional
in nature. Measurements carried out on HET at ISIS have been used to
map out the spin wave dispersion along the c-axis up the 400 meV, more than an
order of magnitude higher than the zone boundary magnon for wavevectors in the
basal plane.
Preprint submitted to Elsevier Preprint 1 February 2008

Studies of the spin dynamics of the high Tc superconductor, La2−xSrxCuO4,
have shown that this material has incommensurate magnetic fluctuations characteristic
of a metal close to a spin density wave instability[1]. This has led to
a renewed interest in systems which exhibit similar instabilities since there are
many unanswered questions regarding the transport and magnetic properties
of spin density wave systems. The prototypical SDW system is the itinerant
antiferromagnet Cr and dilute alloys of Cr with other transition metals[2].
SDW ordering also occurs in Mott-Hubbard systems where strong correlations
lead to a break down of conventional band theory and, as in the high Tc
cuprates, a metal insulator transition[3]. FeGe2 and lightly doped compounds
based on it have a similar (Fermi surface) spin density wave instability which
drives the system to order and, in its undoped form, exhibits both commensurate
and incommensurate magnetic ordering as temperature is varied. We are
studying the transport and spin dynamics of this system in order to obtain a
better microscopic understanding of how this instability is manifested in the
spin fluctuations.
The properties of FeGe2, a tetragonal material with the CuAl2 structure, have
been studied since 1943[4] and many of the details of the crystal and magnetic
structure have been determined [5–8]. FeGe2 is characterised by two magnetic
phase transitions, the first of which is the Néel transition from a paramagnetic
phase to an incommensurate spin density wave state at TN = 289 K in zero
field. The second one is a commensurate-incommensurate (C-IC) transition
into a collinear antiferromagnetic structure. This transition occurs at Tc =
263 K in zero field. The propagation vector Q of the SDW is parallel to [100]
and varies from 1 to roughly 1.05 a ∗ between the two transitions which are
seen in resistivity[9,10], ultrasonic attenuation[11], heat capacity[5,12], and
AC susceptibility[13] studies. The spins lie in the basal plane and are ferromagnetically
aligned along the c-axis. Although this compound has been
well characterised in zero field there has been very little work done in magnetic
fields and not much is known about the details of the magnetic phase
diagram. The magnon and phonon dispersion were measured (primarily at
low temperatures) and revealed a significant anisotropy of the magnetic interactions
with the spin wave velocity along the c-axis much higher than that
observed for modes propagating in the basal plane [14]. For those thermal
neutron triple-axis measurements it was not possible to fully characterise the
spin wave dispersion along c due to the unsuitability of that technique for
energy transfers beyond about 50 meV.
Incommensurate ordering of the type seen in FeGe2 gives rise to four magnetic
satellites around (100) and related positions occurring at (1±q, 0, 0) and
(1,±q, 0). Elastic neutron scattering can be used to determine the wavevector
of this magnetic ordering, a scan through the incommensurate peaks at 275 K
is shown in the upper panel of Figure 1 compared to that of Fe(Ge0.96Ga0.04)2
at the same temperature. Doping has the effect of increasing the magnitude
2

Intensity (arb. units)
4000
3000
2000
1000
0
600
400
200
(ζ,0,2)
(ζ,0,0)
FeGe 2
T=275 K
Fe(Ge 0.96 Ga 0.04 ) 2
0
0.7 0.8 0.9 1.0
ζ
1.1 1.2 1.3
Fig. 1. Scans through the incommensurate magnetic Bragg peaks for pure (upper
panel) and Ga doped (lower panel) FeGe2 at 275 K obtained on the E3 and C5
triple axis spectrometers at Chalk River. The peak in the centre arises from the two
peaks displaced from the commensurate position along the b-axis, seen due to the
coarse vertical collimation employed in these measurements.
Resistivity (µΩ-cm)
Resistivity (µΩ-cm) Resistivity (µΩ-cm)
100
50
Resistivity (µΩ-cm)
0
70
60
50
40
82
77
250 300
Temperature Tc = 263 K (K)
H=0, i||[110]
T c = 182 K
T N = 289 K
undoped
T N = 285 K
Ga doped
0 50 100 150 200 250 300
Temperature (K)
Fig. 2. Temperature dependence of the resistivity for pure and Ga doped FeGe2
(measured on pieces of the same samples used for Figure 1).
of the incommensurate wavevector (similar to what is seen in lightly doped
alloys of Cr[2]). In the 4 at% Ga doped sample the ordering wavevector varies
between q = 0.12 just below TN = 285K and q = 0.1 below a first order lockin
transition at Tc = 182K. In the pure material the transition to the low
temperature commensurate state (with q = 0) is continuous. The zero field
resistivity for these two compounds is shown in Figure 2. In the doped sample
(bottom panel) the two phase transitions are clearly visible and are denoted by
arrows. In the pure material the anomalies are more subtle but the transitions
3

Magnetic Field (T)
30
25
20
15
10
5
H // [110]
commensurate SDW
incommensurate
SDW
FeGe 2
paramagnetic
0
250 260 270
theory
280 290 300
Temperature (K)
Fig. 3. Magnetic phase diagram for FeGe2 for a magnetic field applied along the [110]
direction determined by resistivity measurements and (for H=0) neutron diffraction.
The line denoted theory corresponds to the approximate phase boundary expected
based on the Ginzburg-Landau theory of Reference [13]
Intensity (mb meV -1 sr -1 )
0.25
0.20
0.15
0.10
0.05
E i =120 meV
∆E=77.5 meV
0.00
1.5 2.0
Q (c*) c
2.5
Fig. 4. Constant energy cut at 77.5 meV through the two counter-propagating spin
wave modes obtained on HET for FeGe2 at 11 K using an incident neutron energy
of 120 meV.
are seen in the inset. The transition temperatures deduced from the resistive
anomalies agree well with those determined by neutron scattering. We have
used similar measurements, together with constant temperature, field scans
which clearly show the lower phase transition, with a magnetic field applied
in the basal plane to determine the magnetic phase diagram for FeGe2, shown
in Figure 3, the behaviour is similar for a field applied along [100].[15]
In order to fully characterise the ground state of FeGe2 we have measured the
spin dynamics at low temperatures (11 K) using the direct geometry timeof-flight
spectrometer HET at ISIS. This instrument allows access to much
higher incident neutron energies than the thermal triple-axis measurements of
Holden et. al.[14] making it possible to fully map out the c-axis dispersion.
Figure 4 shows a constant energy cut through the time-of-flight trajectories of
the 2.5 m detector bank on HET for an energy transfer of 77.5 meV. This was
obtained for an integrated current of 2200 µA-hrs using an incident energy of
120 meV. The two spin wave modes emanating from Qc = 2 are clearly visible,
4

Energy Transfer (meV)
400
300
200
100
0
0.00 0.20 0.40 0.60 0.80 1.00
Momentum Transfer (c*)
Fig. 5. Spin wave dispersion relation obtained from the triple axis data (lowest
energies) and incident energies of 80, 120, 300, 500, and 700 meV on HET. The line
is a fit to a model for a planar one-dimensional ferromagnet with a zone boundary
magnon energy of 400 meV.
for energies higher than 25 meV FeGe2 behaves as a quasi-one-dimensional
ferromagnet so it is permissible to ignore the variation of Qa with energy
transfer, a fact confirmed by more detailed analysis of these results[16]. By
carrying out measurements with incident energies of 80, 120, 300, 500, and
700 meV we have fully mapped out the c-axis dispersion relation which is
shown in Figure 5. The line is the result of a fit to a planar one-dimensional
ferromagnet model in appropriate in the zero temperature classical limit. The
zone boundary magnon energy is 400 meV, more an order of magnitude larger
than the 25 meV found for the a-axis[14]. This substantial anisotropy reflects
the structure of FeGe2, the Fe-Fe distance in the c-axis chains of Fe spins is
similar to that in pure Fe, whereas in the ab-plane the distance between the
Fe ions is 4.2 ˚A. Along the c-axis the interaction is ferromagnetic and mainly
due to d-orbital overlap while in the basal plane the weaker antiferromagnetic
coupling has its origins in the conduction electrons.
FeGe2 is a unique example of quasi-one-dimensional ferromagnetism in an
itinerant electron system. Studies of the magnetic dynamics at higher temperatures[16]
reveal the presence of well resolved magnon-like excitations even
in the paramagnetic state. The much weaker basal plane coupling drives the
three dimensional ordering, the doping dependence of the ordering wavevector
suggests that this is Fermi surface driven, hole doping by substituting Ga for
Ge increases the incommensurate wavevector similar to the effect of increased
Sr doping in La2−xSrxCuO4 [1] or V doping in CrxV1−x[2]. which are quasi-twodimensional
and three-dimensional realizations of systems which exhibit Fermi
surface driven spin density wave instability. The Fe(Ge1−xGax)2 alloy system
represents another such system which is predominantly one-dimensional magnetically
although the relatively small anisotropy in the resistivity (a factor
of two with higher resistivity along c) indicates the charge carriers are not
restricted to the c-axis.
5

We would like to thank the technical staff of ISIS and Chalk River Laboratories
for expert assistance with the neutron scattering measurements described in
this paper. This work was financially supported by NSERC and the CIAR.
References
[1] T.E. Mason, G. Aeppli, S.M. Hayden, A.P. Ramirez, and H.A. Mook, Physica B
199&200 (1994) 284 and references therein.
[2] E. Fawcett, H.L. Alberts, V. Yu. Galkin, D.R. Noakes, and J.V. Yakhmi, Rev.
Mod. Phys. 66 (1994) 25.
[3] W. Bao, C. Broholm, S.A. Carter, T.F. Rosenbaum, and G. Aeppli, Phys. Rev.
Lett. 71 (1993) 766.
[4] H.J. Walbaum, Z. Metallknd. 35 (1943) 218.
[5] L.M. Corliss, J.M. Hastings, W. Kunnmann, R. Thomas, J. Zhuang, R. Butera,
and D. Mukamel, Phys. Rev. B 31 (1985) 4337.
[6] Yu.A. Dorofeyev, A.Z. Menshikov, G.L. Budrina, and V.N. Syromyatnikov, Phys.
Met. Metall. 63 (1987) 62.
[7] A.Z. Menshikov, Yu.A. Dorofeyev, G.L. Budrina, and V.N. Syromyatnikov, J.
Magn. Magn. Mat. 73 (1988) 211.
[8] J.B. Forsyth, C.E. Jonson, and P.J. Brown, Phil. Mag. 10 (1964) 713.
[9] R.P. Krentsis, A.V. Mikhel’son, and P.V. Gel’d, Sov. Phys. Sol. Stat. 12 (1970)
727.
[10] R.P. Krentsis, K.I. Meizer, and P.V. Gel’d, Sov. Phys. Sol. Stat. 14 (1973) 2601.
[11] V. Pluznikov, D. Feder, and E. Fawcett, J. Magn. Magn. Mat. 27 (1982) 343.
[12] A.V. Mikhel’son, R.P. Krentsis, and P.V. Gel’d, Sov. Phys. Sol. Stat. 12 (1971)
1979.
[13] V.V. Tarasenko, V. Pluzhnikov, and E. Fawcett, Phys. Rev. B 40 (1989) 471.
[14] T.M. Holden, A.Z. Menshikov, and E. Fawcett, J. Phys.: Condens. Matter 8
(1996) L291–L294.
[15] C.P. Adams, T.E. Mason, S.A.M. Mentink, and E. Fawcett, J. Phys.: Condens.
Matter, submitted (1996).
[16] C.P. Adams, T.E. Mason, E. Fawcett, A.Z. Menshikov, C.D. Frost, J.B. Forsyth,
T.G. Perring, and T.M. Holden, in preparation (1996).
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