Fragile balance of the exchange interactions in Mn$_{1-x}$Co$_{x}$Ge compounds

2.7 MB·

by  E. Altynbaev

Fragile balance of the exchange interactions in Mn Co Ge compounds
1−x x
E. Altynbaev,1,2 S.-A. Siegfried,3 P. Strauß,4 D. Menzel,4 A.
Heinemann,3 L. Fomicheva,5 A. Tsvyashchenko,5 and S. Grigoriev1,2
1Petersburg Nuclear Physics Institute, Gatchina, 188300 St-Petersburg, Russia
2Faculty of Physics, Saint-Petersburg State University, 198504 Saint Petersburg, Russia
3German Engineering Materials Science Centre (GEMS) at Heinz Maier-Leibnitz Zentrum (MLZ),
Helmholtz-Zentrum Geesthacht GmbH, Lichtenbergstr. 1, 85747 Garching bei Mu¨nchen, Germany
4Institut fu¨r Physik der Kondensierten Materie, Technische Universita¨t Braunschweig, 38106 Braunschweig, Germany
5Institute for High Pressure Physics, 142190, Troitsk, Moscow Region, Russia
ThemagneticsystemofthepseudobinarycompoundMn Co Gehasbeenstudiedusingsmall-
1−x x
angle neutron scattering and SQUID-measurements. It is found that Mn Co Ge orders mag-
1−x x
7
netically at low temperatures in the whole concentration range of x ∈ [0÷0.9]. Three different
1
statesofthemagneticstructurehavebeenfound: ashort-periodichelicalstateatx≤0.45,along-
0
periodic helical state at 0.45<x≤0.8, and a ferromagnetic state at x∼0.9. Taking into account
2 that the relatively large helical wavevector k (cid:29) 1 nm−1 is characteristic for systems with mainly

n Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction, we suggest that the short-periodic helical
a structureatx≤0.45isbasedonaneffectiveRKKYinteraction. Alsothedecayofkwithincreasing
J x is ascribed to a reduction of the interaction between second nearest neighbors and, therefore, to

7 anincreaseoftheinfluenceoftheDzyaloshinskiy-Moriyainteraction(DMI).Asaresultofthecom-
1 petition between these two interactions the quantum phase transition from a long-range ordered
(LRO) to a short-range ordered (SRO) helical structure has been observed upon increase of the

] Co-concentration at x ∼0.25. Further increase of x leads to the appearance of a double peak in
l c1
e the scattering profile at 0.45<x<0.7. The transition from a helical structure to a ferromagnetic
- state found at x=0.9 is caused by the weakening of DMI as compared to the cubic anisotropy. In
r
t summary, the evolution of the magnetic structure of Mn1−xCoxGe with increasing x is an example
s of a continuous transition from a helical structure based on the effective RKKY interaction to a
.
t ferromagnetic structure passing through a helical structure based on DMI.
a
m
PACSnumbers: 61.12.Ex,75.30.Kz,75.40.-s
-
d
n
I. INTRODUCTION Itisalreadywellknownthatthechiralmagneticstruc-
o
ture of MnSi and FeGe compounds caused by the pres-
c
[ The cubic B20-type compounds (MnSi, FeGe, etc) are ence of DMI in the system [4, 15, 16]. However, mea-

2 well known for their incommensurate magnetic struc- surements of the Hall effect in Mn1−xFexSi revealed the
v tures with a very long period. The helical spin struc- presence of effective RKKY interaction in formation of
2 ture in these compounds is caused by the antisym- the magnetic structure [17–20]. The differences of the
2 metric Dzyaloshinskii-Moriya interaction (DMI) due to magneticpropertiesoftheMnGe-basedcompoundsfrom
0 a non-centrosymmetric arrangement of magnetic atoms MnSiandFeGetogetherwiththetheoreticalpredictions
4 [1–4]. The Ge-based B20 compounds (Mn Fe Ge, ofthevalueofDMIconstantmadein[21–23]imply,that
0 Mn Co Ge, Fe Co Ge, etc.) enhance the1−vaxriexty of themaininteractiongeneratingthemagneticstructurein
. 1−x x 1−x x
1 magneticpropertiescomparedtothesilicidesintermsof MnGe is an effective RKKY exchange [24]. Inversely to
0 relatively high phase transition temperatures TC (up to the scenario proposed for Mn1−xFexSi, the substitution
7 278 K for FeGe [4–6]) and a large value of the magnetic of Mn by Fe atoms in MnGe leads to an increase of the
1 wavevector k (up to 2.2 nm−1 for MnGe [5–12]). The DMI constant reducing the coupling between the second
:
v compoundMnGealsoexhibitsamagneticorder-disorder nearest neighbors [14, 24]. This approach also explains
Xi phase transition which is smeared over a wide tempera- the decrease of the wavevector k upon Fe-substitution in
turerangestartingwiththeappearanceofhelicalfluctu- Mn1−xFexGe [5, 6].
r
a ationsbelow100Kandendingwithferromagneticnano- Another intriguing feature observed during the study
regions at temperatures above TSR ∼ 175 K [12, 13]. of the mixed compounds Mn1−xFexGe and Fe1−xCoxGe
The temperature evolution of the magnetic structure of is the change of magnetic chirality upon mixing the two
Mn Fe Ge with x < 0.45 is found to be similar to different magnetic atoms (Mn and Fe, or Fe and Co)
1−x x
pure MnGe [11, 14]. A comprehensive small-angle neu- [5, 6, 25]. Theoretical investigations suggest to ascribe
tron scattering study of Mn Fe Ge with x < 0.45 re- the flip of the helix chirality as function of x to a change
1−x x
vealed that the intrinsic instability, which has been ob- of sign of the DMI constant [21–23].
servedearlierforpureMnGe,isintensifiedbyFe-doping. Despite intensive research of the Ge-based B20 com-
The increase of the Fe content x leads to a quantum pounds, the Mn Co Ge solid solutions have not been
1−x x
phase transition from a LRO to a SRO helical structure studied yet. Similarly to the Mn Fe Ge compounds
1−x x
at x ≈0.35 [14]. [14], a quantum phase transition from the LRO to the
c1
2
1.2x10-5 MnGe Mn Co Ge
mol) 81..00xx1100--65 MMMMnnnn0000....9876CCCCoooo0000....1234GGGGeeee mol) 34xx1100--55 MMMMnnnn00000.....554325CCCCoooo0000....05678.4GGGG5eeee
m³/ Mn0.55Co0.45Ge m³/ Mn0.1Co0.9Ge
( 6.0x10-6 ( 2x10-5
ol ol
m m
c 4.0x10-6 c
1x10-5
2.0x10-6
0.0 0
0 50 100 150 200 250 300 0 50 100 150
(a) Temperature (K) (b) Temperature (K)
FIG. 1: (color online) Temperature dependence of the magnetic susceptibility χ(T) of Mn Co Ge at H = 10 mT for (a)
1−x x
x=0.0, 0.1, 0.2, 0.3, 0.4, 0.45 and (b) x=0.45, 0.5, 0.6, 0.7, 0.8 and 0.9.
SRO of the helical structure upon increase of Co con- up in a ferromagnetic structure has been revealed.
centration is expected. In accordance with the results
of X-ray diffraction in combination with neutron diffrac-
tion [6, 25] as well as Lorentz transmission electron mi- II. SAMPLE PREPARATION AND
croscopy and electron diffraction [5], the Mn-based and MAGNETIZATION
Co-based transition metal monogermanides exhibit the
same chiral connection between the crystalline hand-
Polycrystalline samples of Mn Co Ge have been
1−x x
edness and the chirality of magnetic helix. Therefore,
synthesized by the high pressure method at the Insti-
one possibility of the evolution of magnetic structure of
tuteforHighPressurePhysics,Troitsk,Moscow,Russia.
Mn Co Ge compounds is the double flip of the chi-
1−x x Astheycanbeonlysynthesizedunderhighpressure,the
rality upon increase of x in Mn Co Ge as long as
1−x x sampleshaveapolycrystallineformwithacrystallitesize
such phenomena was observed in both series of the com-
not less than 10−100 microns (see [27] for details). X-
pounds: Mn Fe Ge and Fe Co Ge [5, 6, 25]. An-
1−x x 1−x x raypowderdiffractionconfirmedtheB20structureofthe
other option is the absence of the flip of the chiral link
samples used in experiments with an amount of impuri-
between structure and magnetism if the amount of 3d-
ties less than 2% of volume fraction [28, 29].
electronsisnottheonlydrivingforceforthiseffect. Nev-
Magnetic susceptibility measurements have been per-
ertheless, a transition from a helimagnetic DMI-based
formed in order to obtain the magnetic order temper-
structuretoaferromagneticstateduetothedomination
atures for all the compounds using a Quantum Design
of the cubic anisotropy over the DMI in the compound
MPMS-5S SQUID magnetometer. The temperature de-
[26] cannot be excluded.
pendent susceptibility has been measured upon heat-
In this work we present a comprehensive study of the ing in a magnetic field of 10 mT after zero-field-cooling
changes of the magnetic properties of Mn Co Ge as down to T = 5 K. The susceptibility data obtained
1−x x
function of the Co-substitution x within the range 0.0≤ arepresentedinFig.1forMn Co Gecompoundswith
1−x x
x≤0.9 using small-angle neutron scattering (SANS) to- x=0.0, 0.1, 0.2, 0.3, 0.4, 0.45 (a) and x=0.45, 0.5, 0.6,
gether with SQUID measurements. We show that the 0.7, 0.8, 0.9 (b).
quantum phase transition from the helical LRO to the The magnetization as function of the applied field has
SRO indeed takes place in Mn Co Ge at x ≈ 0.25. been measured at low temperature T =0.2·T far away
1−x x c1 C
The critical Co content at which the DMI as main inter- from the magnetic order transition (Fig. 2a). In the low
actiondominatescompletelytheeffectiveRKKYinterac- range of Co concentration x < 0.5 the curves show a
tionandcausesthemagneticstructurehasbeenfoundas hard magnetic behavior which changes to a more mag-
x ≈ 0.45. With further increase of x, a ferromagnetic netically anisotropic regime for 0.5 ≤ x ≤ 0.8 where
c2
statehasbeenfoundforx≥0.9,whichisascribedtothe the compounds start to saturate at the highest avail-
weakening of DMI as compared to the cubic anisotropy. able field (B = 5 T). For x > 0.8 the slope of the
max
In summary, the evolution of the magnetic structure of magnetization curves restarts to decrease upon Co sub-
the Mn Co Ge with increase of the Co content has stitution. For x ≤ 0.5 and x ≥ 0.8 the magnetization is
1−x x
been investigated and a continuous transition from a he- stillnotsaturatedat5TwhichisforthelowCocontent
lical structure based on the effective RKKY interaction in accordance to the behavior of pure MnGe [7]. The
changing to a DMI-dominated helix which finally ends slope of the magnetization curves reflects the magnetic
3
90
1.0
Mn0.9Co0.1Ge 80 2.5 nits)
Mn Co Ge u
M / M5 T00..05 MMMnnn0000....87655CCCooo000...0234.4GG5Geee on Energy (J/kg) 45670000 12..50 ation Energy (arb.
-0.5 MMnn00..54CCoo00..56GGee netizati 30 1.0 agnetiz
Mn Co Ge g 20 M
Mn0.3Co0.7Ge Ma 0.5 m.
Mn0.2Co0.8Ge 10 or
-1.0 0.1 0.9 N
0 0.0
-4 -2 0 2 4 0.0 0.2 0.4 0.6 0.8 1.0
(a) Magnetic Field (T) (b) Co Concentration x
FIG. 2: (color online) (a) Magnetization curves of Mn Co Ge at T =0.2·T normalized to the magnetization at B =5 T.
1−x x C
(b) Magnetization energy of Mn Co Ge derived from the data in (a) in absolute units (red squares) and taken from the
1−x x
normalized magnetization (blue circles).
anisotropy energy which is connected to the magnetiza- ingexperimentsareneededtoinvestigatecompletelythe
(cid:82)
tionenergyW = H ·dM. InFig. 2bthemagnetization microscopic nature of the magnetic states as function of
energy derived from the magnetizaton curves is plotted. the temperature for the different mixed compounds.
The absolute energy values are directly calculated from
the individual magnetization curve of each mixed com-
pound. The normalized magnetization energy denotes III. SANS EXPERIMENT
the energy from the normalized magnetization M/M
5T
as shown in Fig. 2a. From this curve three different
Inordertoidentifythemagneticstructureofthecom-
regimes can be distinguished: (i) For x ≤ 0.5 the mag-
pounds, SANS measurements were carried out using the
netization energy is relatively high and decreases with
SANS-1instrument[31]attheFRM-IIreactorinGarch-
increasing Co concentration. (ii) For 0.5 ≤ x ≤ 0.8 the
ing, Germany). Neutrons with a mean wavelength of
magnetization energy is low, which is correlated with a
λ=0.6 nm and 1.2 nm were used. The sample–detector
high magnetic anisotropy, and is nearly independent of
distanceof2,7,and20meterswassettocovertherange
the Co concentration. (iii) For x > 0.8 the normalized
of momentum transfer Q from 0.02 nm−1 to 2.7 nm−1
magnetization energy starts to increase again, whereas
with the resolution equal to 20 %. The scattering in-
the absolute values become smaller due to the reduction
tensity was measured upon zero-field cooling from the
of the magnetic moment at high Co concentration. This
paramagnetic phase at T = 300 K to the ordered phase
result already suggests that the exchange mechanism in
at T =5 K.
the Mn Co Ge system changes upon Co substitution
1−x x Figure 4(a-h) shows examples of the small-angle neu-
at x ∼ 0.5 and x ∼ 0.8 as indicated by the two dashed
tron scattering maps for Mn Co Ge with x from 0.0
lines in Fig. 2b. 1−x x
to 0.8 at T = 5 K. The typical powder-like images were
From isothermal magnetization curves Arrott plots detected for the samples with x = 0.0 and 0.1 (Fig. 4a,
have been obtained in order to determine the ordering b). From high resolution X-ray data we conclude that
temperature T . Only in the regime between x = 0.5 all samples have the same size of powder grains in the
C
and x = 0.7 a linear behavior of M1/β vs. (H/M) order of 10 microns [28, 29]. With further increase of
with β = 0.31 can be observed which allows for the x up to 0.4, the intensity of the ring smears over the
identification of T [Fig. 3a for Mn Co Ge]. In the large Q-area (Fig. 4c, d). This implies that the cor-
C 0.3 0.7
range x < 0.5 the field dependence of the magnetiza- relation length of the structure decreases dramatically.
tion changes in a way that the Arrott plots cannot be Oneshouldnotethattheevolutionofthemagneticstruc-
extrapolated to the origin of the diagram [Fig. 3b for ture of Mn Co Ge with x shows a surprising similar-
1−x x
Mn Co Ge]. Thereasonforthedeviationfromlinear- ity to the evolution of the magnetic structure of pure
0.7 0.3
ity of the Arrott plots is most likely related to fluctua- MnGe with the temperature [12]. For Co concentrations
tions close to the magnetic order transition which might x > 0.4 the k-value decreases drastically (Fig. 4e-g).
also be of first order as known from MnSi [30]. Also For the compound with x = 0.9 the value of k is not
for x ≥ 0.8 the Arrott plots do not yield the ordering detected within the resolution of the SANS instrument
temperature [Fig. 3c for Mn Co Ge]. That brings (Fig. 4g). Therefore this compound exhibits ferromag-
0.1 0.9
to the conclusion that the small-angle neutron scatter- netic order rather than a helical spin structure.
4
twoconcentrationrangeshavetobediscussedwithintwo
(a) 2.5x103 different approaches.
47 K
Mn Co Ge
2.0x103 0.3 0.7
1/g) IV. RKKY-BASED HELICAL STRUCTURE
m²/k1.5x103 57 K
A Relativelylargevalueofthehelicalwavevector,ka∼1,
(
1/M1.0x103 whereaisthelatticeconstantofthecompound,[7,9,12]
together with the small predicted value of DMI constant
5.0x102 [21–23] allow us to consider the effective RKKY as the
main driving force that built the magnetic structure of
MnGe [24]. The scattering function consists of two dif-
0.0
0 1x105 2x105 3x105 4x105 ferent parts: the inelastic contribution to the scattering
H/M (kg/m³) functionandthescatteringfromthehelicalmagneticor-
(b) 5.0x104 der. The abnormal scattering at Q < k, well discussed
in [12] and considered as inelastic part of the scatter-
Mn Co Ge
4.0x104 0.7 0.3 50 K ing intensity can only be described by the step function
1/g) cthonisvsotleupte-ldikewistchatLteorrienngtzriiasensfwuintchtixona.t vTehryelionwtetnesmitypeor-f
m²/k3.0x104 59 K atures to its maximal value for x = 0.4 and then starts
A
( to decrease (Fig. 5a). The Bragg reflection coming from
1/M2.0x104 themagneticstructureofMn Co Gecompoundswith
1−x x
x<0.45 and can purely be described by a pseudo-Voigt
1.0x104 function with four different parameters: the scaling fac-
torI ,theLorentzfractionα,thepeakpositionk and
Max
0.0 the width of both, Gaussian and Lorentzian functions κ
0.0 5.0x104 1.0x105 1.5x105 (Fig. 5a). The Lorentzian and Gaussian contribution to
H/M (kg/m³) the Bragg reflection corresponds to the scattering from
(c) the SRO and LRO helix structure, respectively. Thus,

1.5x102 Mn Co Ge as soon as the Bragg reflection is well described by the
0.1 0.9 4 K sumofLorentzianandGaussianfunctionswiththesame
1/g) widthandpeakpositiononecanseparatethefractionsof
k helical fluctuations and stable helical phase in the com-
m²/ 1.0x102 pound. The helical fluctuations have to exhibit a finite
A 12 K
1/M( cmourrcehlastmioanllleerngththan2πth/eκ cahnadralcifteetriimsteicτp,awrahmichetebrosthforarae
5.0x101 LRO helical structure [16].
As was found in [12], pure MnGe undergoes a series
of transitions between different states of the magnetic
0.0 structure. A stable helical structure was observed at low
0.0 2.0x105 4.0x105 6.0x105 8.0x105 1.0x106
temperatures. Withtemperatureincreasetheintensityof
H/M (kg/m³)
theGaussiandecreasesdowntozerowhiletheintensityof
the scattering coming from helical fluctuations increases
FIG.3: Arrottplotswithβ =0.31for(a)Mn0.3Co0.7Ge,(b) and reaches its maximum value at TN = 130 K. Peak
Mn Co Ge, and (c) Mn Co Ge.
0.7 0.3 0.1 0.9 corresponding to a helical structure can be observed be-
lowT =150K.Acomplexmixtureoffluctuatingspins,
h
whichcannotbeidentifiedasacertaintypeofstructure,
The scattering intensity I(Q) was azimuthally aver- isobservedaboveT anduptoT =180K,wherethis
h SRF
aged and plotted for compounds with 0.0 < x < 0.5 mixture transforms into ferromagnetic fluctuations (de-
in Fig. 5a and for compounds with 0.5 < x < 0.9 in fined as short-range ferromagnetic (SRF) state) with a
Fig. 5b. The position of the Bragg reflection decreases characteristic size of not more than 2 nm.
to one-tenth of Q from x = 0.0 towards x = 0.5. In The analysis of the magnetic scattering profile of
addition, the shape of the scattering profile changes dra- Mn Co Ge with x < 0.45 shows that the phase tran-
1−x x
maticallyinthesameconcentrationrangewithincreasing sition of the mixed compounds could be described in the
x (Fig. 5a). With further increase of Co concentration same terms as for MnGe. As a result of the scattering
the value of the wave-vector k tends to zero at x = 0.9. profileevaluation,the(T−x)phasediagramofthemag-
We present the detailed analysis of the SANS data sepa- netic structure of Mn Co Ge with x < 0.5 is plotted
1−x x
ratelyfor0.0<x<0.45and0.5<x<0.9becausethese in Fig. 6. It suggests that the 100% fluctuating spiral
5
Q (nm-1) a Q (nm-1) b Q (nm-1) c Q (nm-1) d
y y y y
1 1 1
1
0 0 0 0
-2 0 1 Qx(nm-1) -2 0 1 Q (nm-1) -2 0 1 Qx(nm-1) -2 0 1 Qx(nm-1)
x
Q (nm-1) e Q (nm-1) f Q (nm-1) g Q (nm-1) h
y y y y
0.3 0.1 0.05 0.05
0 0 0 0
-0.6 0 0.3 Qx(nm-1) -0.2 0 0.1 Qx(nm-1) -0.1 0 0.05 Qx(nm-1) -0.1 0 0.05 Qx(nm-1)
FIG.4: (coloronline)ExamplesoftheneutronscatteringmapsforMn Co Gecompoundswithx=0.0(a),0.1(b),0.3(c),
1−x x
0.4 (d), 0.5 (e), 0.6 (f), 0.7 (g) and 0.8 (h) at T =5 K taken at zero field.
state occurs in a large range of the (T −x) phase dia- neticstructurehassofarnotbeenfoundneitherforpure
gram from T down to the lower border marked as a line MnGe nor for Fe-doped compounds and should appear
h
with α = 1.0 (defining the temperature T ). The tem- at temperatures above 300 K [11, 12, 14].
N
perature T decreases smoothly with increasing x, while
h
the temperature T tends to zero with x → x ≈ 0.25.
N c1
For compounds with x > 0.25 the 100% fluctuating spi- V. DMI-BASED HELICAL STRUCTURE
ralstate(α=1)spreadsoutoverthewholetemperature
range from the lowest measured temperatures up to T
h The temperature evolution of the magnetic structure
(Fig. 6).
of Mn Co Ge with 0.45 < x < 0.9 shows even more
1−x x
ThecoexistenceoftheLROandSROofthespinhelix intriguing properties. As shown in Fig. 4e, the Bragg
structureatlowtemperaturesisreflectedinthenon-zero reflection for Mn Co Ge is strongly asymmetric. The
0.5 0.5
value of α. For pure MnGe α smoothly increases with border of the ring on the inner side (Q < k) is sharper
temperature and is equal to 0.1 at T ≈35 K. As it could than at higher Q. The momentum transfer dependence
be seen in Fig. 6 the fraction of SRO increases with of the scattering intensity was extracted from the SANS
x and dominates completely at xc1 ≈ 0.25. Together maps, and its evolution with temperature has been in-
with the fact that the value of the helical wavevector vestigated. The examples of the I vs. Q plots at tem-
decreases by one order of magnitude with x within the peratures T = 10 and 40 K and the data evaluation are
range x ∈ [0.25 ÷ 0.45] (Fig. 5) the instability found presentedinFig. 7aandbforMn Co Gewithx=0.5
1−x x
at low temperatures should be related to the interplay and 0.6, respectively. At temperatures T < 70 K and
between effective RKKY and DM interactions. Firstly, 20 K < T < 60 K for Mn Co Ge compounds with
1−x x
withincreaseofCoconcentrationinthecompoundupto x = 0.5 and 0.6, respectively, the profile consist of two
xc1 ≈ 0.25 the stable helical structure is completely dis- differentLorentzpeakslocatedatdifferentQ-values. The
appearedmeaningthereductionofthecouplingbetween presence of the second Lorentzian with a center position
thesecondnearestneighbors. Andsecondly,furtherxin- with higher value could be connected to the competition
crease up to xc2 ≈0.45 the k-value drops from 2.0 nm−1 betweenDMinteractionandeffectiveRKKY-interaction
downto0.2nm−1,thatpointsoutanincreaseoftheDMI that still plays an important role as it destabilizes the
constant and change the main interaction that built the magnetic structure. The temperature evolution of the
helical order from effective RKKY to DMI. six fit parameters obtained from the data evaluation for
TheCosubstitutionalsoleadstoadecreaseofthecrit- Mn Co Ge with x = 0.5 and 0.6 is presented in Figs.
1−x x
ical temperature T and to the appearance of a phase 8 and 9, respectively.
SRF
where only paramagnetic scattering can be observed at AsitisshowninFig. 8forMn Co Ge,theincrease
0.5 0.5
temperatures above T (Fig. 6). This paramagnetic of the temperature leads, firstly, to a loss of intensity of
C
scattering is well-fitted with a single Lorentzian function thepeakwithhigherk valuetogetherwithanincreaseof
centered at Q=0. This paramagnetic state of the mag- intensity of the low-k reflection (Fig. 8a), and, secondly,
6
a
x = 0.00
1.0 x = 0.10 200 TC
x = 0.20 T
SRF
x = 0.30
x = 0.40 )K 150 Th
x = 0.45 ( e TN
)stin x = 0.50 ruta 100  = 1.0
u.b 0.5 rep
ra m
( I eT 50
 = 0.1
0
0.0 0.1 0.2 0.3 0.4
0.0 x
0 1 2 3
Q (nm-1)
FIG. 6: (color online). T −x phase diagram of the magnetic
b structureofMn Co Gecompounds. αrepresentsthefrac-
x = 0.50 1−x x
1.0 x = 0.60 tion of the fluctuating spiral phase. The stable spiral phase
(LRO) with α<0.1 is the the ground state of pure MnGe in
x = 0.70
the left-down corner of the graph. The line α = 1.0 defines
x = 0.80
the (x−T) point of the transition to the 100 % fluctuating
x = 0.90
spiralstate. ThistemperatureisdefinedasT . Thetemper-
N
)s atureThdeterminestheupperborderofthefluctuatingspiral
tin phase. The temperature TSRF and TC defines the lower and
u 0.5 upper border of the short-range ferromagnetic fluctuations
.br respectively.
a
(
I
1 T = 10 K a T = 10 K b
0.00.0 0.1 Q (nm-1) 0.2 0.3 )stinu .bra( ytisnetnI0.00.11 T = 40 K )stinu .bra( ytisnetnI 0.11 T = 40 K
0.01
FIG.5: (coloronline)Momentumtransferdependenceofthe 0.2 0.4 0.6 0.8 0.0 0.1 0.2 0.3
Q (nm-1) Q (nm-1)
scatteringintensityatT =10KforMn Co Gecompounds
1−x x
with (a) 0.0<x<0.5 and (b) 0.5<x<0.9.
FIG. 7: The momentum transfer dependence of the
azimutally-averaged scattering intensity extracted from the
SANS maps for x = 0.5 (a) and x = 0.6 (b) at T = 10 and
to a shift of both peak positions towards lower Q values 40 K. Solid lines correspond to thee best fit of data using
(Fig. 8b). It should be noted that the instrument reso- twoLorentzianfunctionswhicharepresentedseparatelywith
lutionofSANS-1waschosenas20%andismuchsmaller dashed lines. The scattering profile for x=0.6 at T =10 K
than the width of the reflections obtained from the data is well fitted with the single Lorentzian.
evaluation. The changes of the peak widths are strongly
connected with the k-value (Fig. 8b). This means that
the higher the temperature and the period of the fluctu-
ating helix are, the more coherent is the magnetic struc-
ture. Thus, the increase of the correlation length of the
magneticstructurewithtemperatureisunexpectedlyas-
sociated with a fragile balance between two coexisting
interactions that generate the magnetic structure.
The analysis of the scattering profile of Mn Co Ge
0.4 0.6
exhibits two remarkable features compared to the pro-
file for x = 0.5 (Fig. 9). First of all, the position of
FIG. 8: Temperature dependence of the integrated (a) in-
the main reflection, which has more intensity and lower
tensity and (b) position and width of two different Bragg re-
k value, is independent of the temperature. Its intensity
flections observed with small angle neutron scattering from
decreases smoothly upon increasing temperature. This
Mn Co Ge compound, at zero field.
fact implies that the influence of the effective RKKY 0.5 0.5
7
tureforthiscompound. Thetruenatureoftheferromag-
netic order can be revealed taking the cubic anisotropy
into account [26]. If the energy of the cubic anisotropy
ishighenoughincomparetotheenergyofDMI,thefer-
romagneticorderismorepreferablethanthehelicalspin
state.
VI. CONCLUSION
FIG. 9: Temperature dependence of the integrated (a) in-
tensity and (b) position and width of two different Bragg re- Combining the experimental facts observed with
flections observed with small angle neutron scattering from SANS,thecompetitionbetweentheeffectiveRKKYand
Mn0.4Co0.6Ge compound, at zero field. the DM interaction, which is present in a large x range
up to x < 0.8 and generates the helical magnetic order,
could be investigated. The DMI destabilizes the mag-
RKKY DM FM
200 netic structure of Mn Co Ge with x increase. The
1−x x
stable helical order disappears completely at x ≈0.25.
c1
K 2 Further increase of Co concentration leads to a dramatic
5 = 150 Te dmeecaanysotfhathtethweaDveMvIeicstothrekdaotmxinc2an≈ti0n.t4e5ra(cFtiigo.n5fo)r. cTohmis-
T m
@ 100 pe pounds with x>xc2.
1-m) 1 Th rature tioInt oisf FimepaotrotmanstintoMnno1t−exFthexaGt ethceomcrpitoiucnaldcnoenecdeendtrtao-
kn( 50 (K) cxoc1m≈ple0t.e3ly5 wdehsitleabtihliezedetchaeyhoeflitchael swtaruvecvtuecretoirsveaqluuealobto-
k (helix) servedatthethesamevalueofxequaltox ≈0.45[14].
c2
0 0 SuchacoincidenceofcriticalvaluesforMn Fe Geand
1−x x
0.0 0.2 0.4 0.6 0.8 1.0
Mn Co Ge compounds could not be connected to the
1−x x
x changes of the electronic structure of MnGe system with
Fe or Co replacement only because Co doping results in
FIG.10: (coloronline)x-dependenceofthehelixwavevector the increase of charge carrier density two times faster in
value k at temperature T = 5 K and of the temperature of
comparetoFereplacementofMnatoms. Thisfactcould
themagneticphasetransition,T ,extractedfromtheanalysis
h be assumed as another reason to consider the interac-
of the temperature evolution of magnetic scattering profile.
tionsbetweensecondnearestneighborsasafundamental
Linesaretheguidefortheeyes. Regionswith0.0<x<0.45,
mechanism that creates the magnetic structure of pure
0.45<x<0.8 and 0.8<x<1.0 correspond to the RKKY-
MnGe.
like helical, DMI-like helical and ferromagnetic-like structure
of the Mn Co Ge system at T =5 K. SANS measurements of the magnetic structure of
1−x x
Mn Co Gecompoundsalsorevealedthattheeffective
1−x x
RKKY interaction still remains notable and destabilizes
interaction, which is dominant in the compounds with the magnetic structure of Mn Co Ge with 0.45<x<
1−x x
lower Co concentration x, is already almost neglectable 0.6. The DMI fully dominates over RKKY at low tem-
for x=0.6. Nevertheless, the second feature of the mag- peratures only for compounds with x>0.6.
netic structure is the appearance of a second reflection The resulting x-dependencies of wave vector k and
with temperature increase, which is connected to a non- the critical temperature of the helices phase T for com-
h
vanishing influence of the still present RKKY interac- pounds with x < 0.8 and T for Mn Co Ge are pre-
C 0.1 0.9
tion. Itspositiondecreasesrapidly,andtheintensityhas sentedinFig. 10. Therelativelyhighvalueofthehelical
a maximum value at T =45 K. wavevector k corresponds to a RKKY-like helical struc-
The experimental results for Mn Co Ge and ture and is observed for 0.0 < x < 0.45. The magnetic
0.3 0.7
Mn Co Ge do not show any scattering additional to structure with k (cid:28)1 nm−1 is ascribed to a DMI-like he-
0.2 0.8
themainreflections,theintensityofwhichdecreasewith lical order at x < x < 0.8. The critical temperatures
c2
risingtemperature,whereastheirpositionstaysconstant obtained with Arrott plots for Mn Co Ge compounds
1−x x
at k =0.03 nm−1 and 0.02 nm−1 respectively. with x within the DMI region coincide with T , which
h
The analysis of the scattering profile of the is estimated from the treatment of the SANS data. The
Mn Co Ge reveals a diffuse magnetic scattering cen- region in Fig. 10 with 0.8 < x < 1.0 corresponds to
0.1 0.9
tered at k <0.02 nm−1 meaning a ferromagnetic-like or- compounds with non-zero critical temperature and un-
der of the compound at low temperatures. The intensity detectable helical wavevector, i.e. the ferromagnetic-like
of this scattering decreases to zero with increasing tem- state of the magnetic structure of these compounds at
peratureuptoT =45Kdefiningtheorderingtempera- T =5 K.
C
8
In summary, a comprehensive small-angle neutron two interactions generating the magnetic structure com-
scattering study of the temperature evolution of petewitheachotherinthesensethattheRKKYinterac-
Mn Co Ge allows one to consider the RKKY as tion destabilizes the DMI-based helical order until x ex-
1−x x
the fundamental interaction for the helical structure in ceedsthevalueof0.6. AfterthattheeffectiveRKKYcan
MnGe. Itcanbe concludedthatanorder-disorder phase beneglected,andonlytheDMIandthecubicanisotropy
transition takes place with increasing x at x ≈ 0.25 determine the magnetic order in Mn Co Ge as being
c1 1−x x
caused by the modification of the effective Ruderman- ferromagnetic or helical depending on the ratio between
Kittel-Kasuya-Yosida exchange interaction within the them.
Heisenbergmodelofmagnetism. TheDMIcanbeconsid-
ered as an instrument for destabilization of the ordered The work was supported by the Russian Foundation
helical structure with x or T, despite the fact that all of Basic Research (Grant No 14-22-01073, 14-02-00001)
Mn Co Ge compounds crystallize in the B20 struc- and the special program of the Department of Physical
1−x x
ture. With further increase of x (x > x ≈ 0.45) these Science, Russian Academy of Sciences.
c2
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