N = 47,459), adoptees (N = 6407), and parent-offspring trios (N = 2534) in three UK and Dutch cohorts. We find that parental cognitive and non-cognitive skills affect offspring education through their environment: on average across cohorts and designs, indirect genetic effects explain 36–40% of population polygenic score associations. However, indirect genetic effects are lower for achievement in the Dutch cohort, and for the adoption design. We identify potential causes of higher sibling- and trio-based estimates: prenatal indirect genetic effects, population stratification, and assortative mating. Our phenotype-agnostic, genetically sensitive approach has established overall environmental effects of parents’ skills, facilitating future mechanistic work.Understanding how parents’ cognitive and non-cognitive skills influence offspring education is essential for educational, family and economic policy. We use genetics (GWAS-by-subtraction) to assess a latent, broad non-cognitive skills dimension. To index parental effects controlling for genetic transmission, we estimate indirect parental genetic effects of polygenic scores on childhood and adulthood educational outcomes, using siblings ( Understanding how parents’ cognitive and non-cognitive skills influence their children’s educational trajectories is important for educational, family and economic policy. Here, the authors investigate parental influence on children’s education using genetic approaches. Since education is highly predictive of social mobility and health across the lifespan3, understanding the mechanisms underlying the intergenerational transmission of education could inform efforts to alleviate inequalities. Many studies have investigated how much certain parental characteristics influence offspring education, but relatively few have considered non-cognitive skills. The term ‘non-cognitive’ describes skills that differ from what has traditionally been education’s primary focus: academic and cognitive performance. The umbrella of non-cognitive skills encompasses a wide range of competencies, including academic motivation, perseverance, mindsets, learning strategies, and social skills5. Cognitive skills like executive functioning, working memory, and verbal IQ are more precisely integral to cognitive functioning, but both cognitive and non-cognitive skills are critical for educational success4. Research in developmental psychology6, economics7, and sociology8 has suggested that parents socially influence their children’s non-cognitive skills including emotion regulation, social capacities, attitudes and motivations10. Given that non-cognitive skills (particularly self-control and emotion regulation12) support education, it follows that parents’ non-cognitive skills may also affect children’s educational outcomes.Parents and children tend to have similar educational outcomesp < 0.05; β = ~0.01 for maternal self-concept and self-esteem, both non-significant)13. Mothers’ cognitive skills, measured by the U.S. Armed Forces Qualifying Test, were a stronger predictor . Another study found that fathers’ non-cognitive skills were associated with sons’ standardised test scores at age 16 (β = 0.09)14. Here, non-cognitive skills were measured by a single composite of extraversion, neuroticism, persistence, and perseverance from a standardised Swedish military-oriented psychological evaluation. Additionally, parents’ attitudes towards education and social skills have been found to account for 8% of the socioeconomic gap in children’s achievement15. The contributions of specific measured parental traits that were included were also not stated.Prior research has detected small associations between measured parental non-cognitive skills and offspring educational outcomes. In one study, mothers’ locus of control was the only significant non-cognitive predictor of offspring college attendance . In the present study, we use this GWAS-by-subtraction measure of non-cognitive skills to capture the overall effect of all non-cognitive parent phenotypes on offspring education. This phenotype-agnostic approach is somewhat loose: it could include parental phenotypes not traditionally classed as ‘non-cognitive’ or ‘skills’. However, it provides a useful first step towards characterizing pathways from specific parental skills to offspring educational outcomes. After establishing overall effects, complementary research designs using measured parental non-cognitive skills can subsequently be used to identify specific mediating mechanisms.Genetic methods offer an alternative approach to defining parents’ non-cognitive skills. Both cognitive and typically-studied non-cognitive skills are substantially genetically influenced, with twin study heritability estimates of 40–70%22. To establish the extent that parents’ (non-)cognitive skills influence child educational outcomes socially, it is vital to control for inherited genetic effects.A second challenge is to distinguish social  from genetic transmission. None of the associations between parental skills and offspring education cited above were estimated using genetically sensitive designs. This is problematic, because from just parent-offspring correlations one cannot conclude that parents’ skills shape offspring education, for instance by providing resources, experiences, and support. Ignoring any shared genetic influences on parents’ skills and child educational outcomes confounds estimation of the effects of parental phenotypes on offspring outcome24. Polygenic scores  for educational attainment based on parents’ non-transmitted variants, are associated with offspring attainment27. Complementary evidence of indirect effects of parents’ education-linked genetics on offspring education has also accumulated from sibling and adoption PGS designs29. To obtain estimates of indirect genetic effects using sibling data, within-sibling genetic associations (first developed to estimate direct genetic effects independent of population biases31) are compared to population-based associations. To obtain estimates of indirect genetic effects using adoption data, genetic associations estimated for adoptees and non-adopted individuals are compared29. Notably, variance decomposition as well as PGS methods can be applied to disentangle direct and indirect genetic effects, but the former requires much larger sample sizes35. It is not known whether parental indirect genetic effects on offspring education occur through cognitive or non-cognitive pathways (or both), because studies have not parsed out the contributions of sub-components of the educational attainment PGS.Genetic study designs can isolate environmental effects of parental skills on offspring education, controlling for genetic transmission. Several designs estimate a genetic effect of the child’s genotype on the child phenotype (direct genetic effect), and an environmentally mediated effect of the parental genotype on the child’s phenotype . For example, non-transmitted genetic variants affect offspring phenotypes indirectly via the environment shaped by parental phenotypes38. Sibling, adoption, and non-transmitted allele designs have different assumptions and subtle differences in biases and components affecting the estimated indirect genetic effect. As shown by our data simulations indirect genetic effect estimates from the adoption design may be less biased by population stratification and assortative mating than the sibling and non-transmitted allele designs (see Supplementary Note 39). However, estimates obtained from the adoption design do not capture prenatal parental environmental effects on child education and may be less generalisable to the population. The sibling design may estimate parental indirect genetic effects with more bias from sibling genetic effects. Triangulation across designs and sensitivity analyses can help detect possible biases and quantify parental indirect genetic effects and other environmental effects40.Here, we directly compare estimates of parental indirect genetic effects obtained from different designs. Estimation of genetic associations may involve numerous biaseshttps://osf.io/mk938/), we use a novel approach to estimate the social effects of parents’ cognitive and non-cognitive skills on offspring education. We deploy GWAS-by-subtraction to estimate individuals’ genetic endowments (PGS) for cognitive and non-cognitive skills, and test how much these operate environmentally via parental influences on offspring educational outcomes. We provide a comparison of parental indirect genetic effects in three cohorts of genotyped families in two countries . Each cohort includes multiple achievement outcome measures  and attainment . We triangulate across three complementary study designs for estimating parental indirect genetic effects and assess the presence of components and biases.In the current study  were regressed on two independent latent variables, Cog and NonCog , up to 3163 twins and siblings in the Netherlands Twin Register (NTR), and up to 2534 NTR individuals with both parents genotyped. Full phenotypic descriptive statistics are available in Supplementary Data To estimate direct offspring-led and indirect parent-led effects of PGS for cognitive and non-cognitive skills on educational outcomes, we considered three family-based genomic designs. The designs are illustrated in Fig. 28. The direct effect of a polygenic score is estimated based on genetic differences between siblings, which are due to random segregations of parental genetic material, independent of shared family effects . Specifically, the direct effect is estimated using a variable representing individuals’ polygenic scores minus the average polygenic score for their family: the within-family beta (βWithin in Eq. (Cog and NonCog PGSNonCog). 0 refers to the intercept, Z are covariates for the individual i: sex, age, sex*age, the first 10 principal components, and genotyping platform. See Supplementary Note First, the sibling design estimates indirect genetic effects by comparing population-level and within-family  PGS associations (Eq. )28. The n in Eq. ). The po29. Therefore, we estimate the regression model shown in Eq. . Transmitted genetic variants are present in an offspring and in at least one of their parents, and so may influence offspring education via both direct and indirect mechanisms. The parental indirect genetic effect is estimated as the effect of a polygenic score based on parental variants that were not transmitted to offspring (βNT). Non-transmitted variants can only take effect on offspring education through the environment. The direct genetic effect is estimated by partialling out the effect of the non-transmitted polygenic score from that of the transmitted polygenic score (βT − βNT). Maternal and paternal scores are averaged to create overall parental non-transmitted polygenic scores. We did not distinguish between maternal and paternal PGS, due to the replicated evidence that mothers’ and fathers’ PGS for educational attainment have equal effects on offspring education42, and to enable closer comparison with the adoption and sibling designs, which yield estimates of the overall parental genetic effect. Notably, regressing offspring phenotype on offspring PGS and parental PGS would allow equivalent estimation of the parental indirect genetic effect without haplotype estimation43.Third, indirect genetic effects can be estimated, and disentangled from direct genetic effects, using information on parental genetic variation that was not transmitted to offspring26 (Eq. ).3\documNonCog = 0.08, SE = 0.03; indirect βCog = 0.10, SE = 0.01), in addition to direct genetic effects . Averaged across all designs, outcomes and cohorts, indirect environmentally mediated effects explained 36% of the population effect of the NonCog PGS, and 40% of the population effect of the Cog PGS. However, results varied depending on the methods used and outcomes investigated. Results per cohort, outcome and design, as well as population genetic effects and the ratio of indirect to population effects are reported in Supplementary Data Z-tests results comparing direct and indirect effects are reported in Supplementary Data We investigated environmental effects of parents’ non-cognitive and cognitive skills on offspring education by estimating parental indirect genetic effects of NonCog and Cog PGS. Figure NonCog = 0.11, SE = 0.03; indirect βCog = 0.06, SE = 0.03) and UK  cohorts. See Supplementary Data Figure NonCog = 0.02, SE = 0.02; indirect βCog = 0.08, SE = 0.02).Figure 39). We consider prenatal and postnatal parental indirect genetic effects as components of the total parental indirect genetic effect, and other simulated contributors as biases. First, unlike the sibling and non-transmitted allele designs, the adoption design does not capture indirect genetic effects occurring in the prenatal period. Second, the adoption design estimates indirect genetic effects with less bias from population stratification. Third, the adoption design estimates indirect genetic effects with less bias from assortative mating than the sibling design, and, most likely, than the non-transmitted alleles design. How the bias in the adoption design estimates compares to the non-transmitted design depends on the precision of the polygenic score, see Supplementary Note Figure With the adoption design, the indirect genetic effect of the NonCog PGS on educational attainment in UK Biobank is 83% lower than with the sibling design, while it is only 33% lower for Cog. This suggests that estimates for NonCog are affected more strongly than Cog by population stratification, assortative mating and/or prenatal indirect genetic effects.Although triangulating designs suggested that prenatal indirect genetic effects, population stratification, and assortative mating may contribute to the higher estimated parental indirect genetic effects from non-transmitted alleles/sibling designs relative to the adoption design, this approach cannot disentangle the relative importance of these individual biases. To this end, we conducted additional sensitivity analyses to assess the magnitudes of these biases (not pre-registered).First, we analysed the GWAS summary data on which the polygenic scores were based, using LD score regression to detect population stratification. The LD score regression ratio statistics of uncorrected educational attainment and cognitive performance GWAS were 0.11 (SE = 0.01) and 0.06 (SE = 0.01), respectively . Sibling PGS intraclass correlations ranged between 0.49 and 0.52 in NTR, and between 0.53 and 0.56 in TEDS and UK Biobank. This supports the presence of assortative mating on NonCog and Cog PGS potentially biasing our estimates of indirect genetic effects in UK cohorts, but less in our Dutch cohort. See Supplementary Data Second, we detected slight evidence of assortative mating, which appeared stronger in the UK than Dutch cohorts. In NTR, parental PGS correlations are non-significant . This result was consistent across countries, generations, outcomes, and analytic designs, with two notable exceptions. First, estimated parental indirect genetic effects were null for childhood achievement in our Dutch cohort (NTR), but not for comparable outcomes in our UK cohort (TEDS). Second, parental indirect genetic effects estimated with the adoption design were lower than for the sibling and non-transmitted allele designs, particularly for the NonCog PGS. Given our evidence from data simulations that the adoption-based estimates of indirect genetic effects do not account for prenatal effects and may be more robust to population stratification and assortative mating, these factors may contribute substantially to estimates from the other two designs, especially for the NonCog PGS. This was supported by results from sensitivity analyses.We used genetic methods to study environmental effects of parents’ skills on child education. We found evidence that characteristics tagged by NonCog and Cog polygenic scores (PGS) are both involved in how parents provide environments conducive to offspring education. Indeed, indirect genetic mechanisms explained 36% of the population effect of the NonCog PGS, and 40% of the population effect of the Cog PGS  and/or more distal environmental effects . The environmental effects of parents’ non-cognitive and cognitive skills are likely to be larger than we estimate, because our approach only captures effects of parent skills tagged by current GWAS. Polygenic scores index a subset of the common genetic component of parent skills, which is in turn a fraction of the total genetic component (missing heritability45), and cannot account for the non-heritable component of parent skills.This study demonstrates the utility of genetic methods for assessing elusive phenomena: non-cognitive skills, and genuine environmental influences from parents, unconfounded by offspring-led effects of inherited genes. Compared to analysing a set of measured parental non-cognitive skills, our GWAS-by-subtraction approach captures a wider array of traits linked genetically to attainment, and therefore broadly quantifies the overall salience of parents’ non-cognitive skills. Our evidence that parents’ non-cognitive and cognitive skills are both important for children’s education complements the growing literature that has considered effects of specific measured skills within both of these domains46). For adult attainment, results were more similar across UK and Dutch cohorts, corresponding with recent evidence for consistent shared-environment influence on educational attainment across social models47. This consistency also suggests that the difference in childhood is not due to a cohort or population difference. The higher indirect genetic effects in adult attainment in the Netherlands might reflect an increase in environmental variance following tracking taking place in secondary schools27. Indeed, socioeconomic disparities in achievement seem to increase more between ages 10 and 15 in the Netherlands than in the UK48 and children whose parents have a higher education are more likely to enrol in a higher educational track independently of their achievement at age 1249, suggestive of greater parental effects on secondary and later education, which should be tested in further studies.The lower importance of parental indirect genetic effects for child achievement in the Netherlands compared to the UK indicates that our UK achievement outcomes more strongly capture variation in family background. This difference could result from the design of these achievement measures: Dutch test results are standardized based on a representative population, but UK teacher reports might still be affected by student social background. Societal differences between the two countries might offer another explanation, as indirect genetic effects might be seen as indicator of social inequality  particularly in the UK cohorts. This country difference in assortment is supported by the lower estimated spouse PGS correlations in NTR  than for the EA PGS in the UK Biobank (0.06)52. There was no statistically significant difference in assortative mating between Cog and NonCog, suggesting that population stratification explains the particularly large design-based discrepancy between estimates of indirect genetic effects for NonCog . Population stratification should be carefully considered in studies using NonCog PGS. Structural equation models, leveraging within-family polygenic scores and phenotypes, are being developed to parse the contributions of indirect and direct genetic effects to complex traits from assortative mating (both disequilibrium and equilibrium forms) and population stratification54. Another consideration for future research is that indirect genetic effects on education might span across more than a single generation, for example the influence of grandparents. Since cumulative indirect genetic effects are all removed when a child is adopted, their presence would contribute to the observed difference in indirect effect between the adoption and other designs.We found that the design used to estimate indirect genetic effects matters, with the adoption design giving systematically lower estimates. Direct comparison of results across designs suggested that 33% (for Cog) and 83% (for NonCog) of the indirect genetic effects on adult educational attainment, estimated using the sibling design, are at least in part due to population stratification, assortative mating, and prenatal indirect genetic effects. The importance of population stratification for genetic associations with educational attainment was suggested by recent UK Biobank studies51. However, other UK Biobank studies have detected indirect effects of older siblings’ EA PGS on younger siblings’ educational attainment55, and parental compensation for sibling EA PGS differences56, suggesting that more subtle analyses are required to understand sibling effects. There is also some evidence for sibling effects on educational attainment in other populations, based on the EA PGS26 and on extended twin family data57. It is possible that our PGS analyses were not sufficiently powered to detect indirect genetic effects of siblings, since they were based on lower sample size than our main analyses. However, our results suggest that indirect genetic effects of siblings on education are small. Therefore, our methods provide good proxies for parental indirect genetic effects, with minimal inflation from sibling effects.Regarding siblings, we did not find evidence that indirect effects of siblings’ NonCog and Cog PGS affect individual differences in educational outcomes, using three different approaches. This corresponds with null findings regarding indirect effects of siblings’ educational attainment genetics in the UK Biobankd = 0.3). These differences likely make adoption-based estimates of indirect genetic effects, which rely on a comparison of the two groups, less reliable. Moreover, three additional factors may make the adoption-based estimates of indirect genetic effects too conservative. First, adoption based indirect effect estimates exclude prenatal indirect genetic effects (and indirect genetic effects taking place between the birth and moment of adoption), which might influence educational outcomes59. While we are unable to test for prenatal indirect effects, these could be investigated in cohorts with pregnancy information, adjusting for postnatal indirect genetic effects. Second, adoptees may have been exposed to a narrower range of environments  compared to non-adopted individuals60. This form of selection bias is likely to increase the genetic variance at the expense of the indirect genetic effect. Third, selective placement of children in adoptive families matching characteristics of their biological families, or adoption of children by close relatives61, could result in correlation between child and (adoptive) parent genotypes, leading to an underestimation of the indirect genetic effect. There is modest evidence for selective placement of adoptees based on education in the US62. We cannot control for selection and relatedness , since there is no information on the adoptive parents in the UK Biobank resource.Our data suggest that the adoption design may provide a useful lower-bound estimate of indirect genetic effects of parents. Given that there was no evidence for sibling effects of the Cog or NonCog PGS, our adoption-based estimates, which appear to be less biased by population stratification and assortative mating, should give a closer measure of  parental indirect genetic effects in the absence of other issues. However, adoptees and non-adopted individuals differ in unobserved and observed ways, including birthweight  phenotypes of the biological parents, and many adoptive parents are also selected based on their  behavioural phenotypes. Additionally, only participants of European descent were included in the analysis.Second, the generalisability of our results is limited. Highly educated individuals are over-represented in all cohorts. Participation bias also affects GWAS resultsThird, replication efforts are needed. Special effort should be targeted to include diverse ancestry participants. While our overall estimates are well powered due to the aggregation of cohorts, some analyses rely on a single sample. As such, results from these analyses might reflect specifics of these samples and not design-specific biases and should be replicated.64, but remains to be investigated for non-transmitted PGS and adoption designs. Population GWAS effects could be differentially affected  for NonCog versus Cog, which would make their respective PGS effects less comparable. Increasingly large within-family GWAS65 of Cog and EA will allow this to be resolved.Fourth, although our within-family methods allowed us to evaluate biases in polygenic score effects within the target samples, the same biases are likely to influence the effect size estimates from the original population-based GWAS used to construct polygenic scores. This problem has been explored in relation to the sibling design in a recent preprint66 but for other classic non-cognitive skills such as motivation and self-control.Finally, while we conceptualize our NonCog PGS as a non-cognitive measure, it could also be considered a ‘not-cognitive PGS’, since it is a residual construct that results from removing heritable variance associated with cognitive skills from the heritable variance in educational attainment. In the future, it may be useful to develop a more precise non-cognitive skills GWAS, by creating the latent Cog and NonCog factors using additional measured phenotypes. To this end, large GWA meta-analyses should be completed not only for personality13), but also ‘not-cognitive’ characteristics that do not appear in non-cognitive skill batteries yet are genetically correlated with the NonCog PGS and phenotypically correlated with offspring achievement. For instance, parental depression is a feasible partial mediator, given that Major Depressive Disorder is significantly genetically correlated with NonCog 20, and maternal depression is associated with offspring mathematics performance, possibly via offspring executive function67. Researchers could also examine mediating child characteristics on the pathway between their parents’ characteristics and their own educational outcomes. Children’s skills themselves might not be involved in these pathways. Indeed, educated parents do not appear to affect offspring education by fostering non-cognitive skill development11, and twin research shows no influence of shared environmental factors on individual differences in children’s measured non-cognitive skills such as grit and self-control70.Several additional future research directions emerge. First, given that we have quantified the overall environmental effects of parents on offspring education tagged by NonCog and Cog PGS, the next step is to identify specific mediating parent characteristics, whether proximal or distal. It will be informative to test not only typical non-cognitive skills measures such as parental locus of control  that mother and father skills show unique associations with offspring education14. Indirect effects of parents’ genetic endowment for non-cognitive skills on child education might be mediated or moderated by parents’ income and cultural capital (including school-related skills and habits). While some evidence suggests that home learning environments may be more cognitively stimulating in families of higher socioeconomic72, there is also evidence suggesting that mothers who have lower reported incomes also report more frequent activities that facilitate cognitive stimulation73.A second future direction is to incorporate gender and socioeconomic status into research on indirect genetic effects on education. Twin data show that shared environmental contributions to educational attainment are larger for women than for menIn sum, this study provides evidence for environmental effects of parents’ non-cognitive and cognitive skills on offspring educational outcomes, indexed by indirect genetic effects of polygenic scores. Combining three cohorts and three designs for estimating indirect genetic effects allowed us to obtain robust findings. These results have significance for human health, as the role parents play in successful cognitive development and  health development go hand in hand.Our research complies with all relevant ethical regulations. Project approval for the Twins Early Development Study (TEDS) was granted by King’s College London’s ethics committee for the Institute of Psychiatry, Psychology and Neuroscience PNM/09/10–104. Ethical approval for the Netherlands Twin Register (NTR) was provided by the Central Ethics Committee on Research Involving Human Subjects of the VU University Medical Center, Amsterdam, and Institutional Review Board certified by the U.S. Office of Human Research Protections  and participants provided informed consent. The UK Biobank has received ethical approval from the National Health Service North West Centre for Research Ethics Committee (reference: 11/NW/0382). Informed consent was obtained from all human participants.https://osf.io/mk938/) on the 24/02/2020. Additional non-preregistered analyses are indicated as such below and should be considered exploratory. Additional deviations from the pre-registration are detailed in Supplementary Note The study methods were pre-registered on the Open Science Framework , we first identified 6407 unrelated adopted individuals who said yes to the question “Were you adopted as a child?” (Data-Field 1767). We restricted the sample to unrelated participants (kinship coefficient <1/(2^9/2))76. Second, our comparison sample (N = 6500) was drawn at random from non-adopted participants who were unrelated to each other and to the adopted participants. Third, we identified 39,500 full siblings, excluding adopted individuals. We defined full-siblings as participants with a kinship coefficient between 1/(2^(3/2)) and 1/(2^(5/2)) and a probability of zero IBS sharing >0.0012, as suggested by75 and76.We defined three subsamples of the UK Biobank to be used for polygenic score analyses: adopted participants, a control group of non-adopted participants, and siblings. Starting with UK Biobank participants with QC genotype data and educational attainment data  data, and 202,815 individuals with cognitive performance (CP) data. We used these remaining individuals for the GWAS of EA and CP, and later meta-analysis with external GWASs78. The demographic characteristics of TEDS participants and their families closely match those of families in the UK. Analyses were conducted on a sub-sample of dizygotic (DZ) twin pairs with genome-wide genotyping and phenotypic data on school achievement at age 12 (1431 DZ pairs) and age 16 (2398 pairs).The Twins Early Development Study (TEDS) is a multivariate, longitudinal study of >10,000 twin pairs representative of England and Wales, recruited 1994–199679 is established by the Department of Biological Psychology at the Vrije Universiteit Amsterdam and recruits children and adults twins for longitudinal research. Data on health, personality, lifestyle and others, as well as genotyping data have been collected on participants and their families.The Netherlands Twin Register (NTR)We included in our analyses genotyped European-ancestry participants. We created a subsample of full-siblings. NTR contains information on numerous monozygotic multiples (twins or triplets). Because MZ multiples share the same genes, we randomly excluded all individuals but one per MZ multiple. Only siblings with complete genetic and outcome data were subsequently included in the analyses: 1631 siblings with CITO (achievement test taken during the last year of primary school) data (from 757 families) and 3163 siblings with EA data available (from 1309 families).We created a subsample with complete offspring, maternal and paternal genotypic data . Among individuals with available parental genotypes, respectively 1526 (from 765 families) and 2534 (from 1337 families) had reported CITO and EA information.The sibling and trio subsets are not independent: for CITO, 823 participants are present in both subsets, 1374 for EA.77. From data-field 6238, educational attainment was defined according to ISCED categories and coded as the number of Years of Education. The response categories are: none of the above  = 7 years of education; Certificate of Secondary Education (CSEs) or equivalent = 10 years; O levels/GCSEs or equivalent = 10 years; A levels/AS levels or equivalent = 13 years; other professional qualification = 15 years; National Vocational Qualification (NVQ) or Higher National Diploma (HNC) or equivalent = 19 years; college or university degree = 20 years of education. For cognitive performance, we used the (standardized) mean of the standardized scores of the fluid intelligence measure (data-field 20016 for in-person and 20191 for an online assessment).Educational attainment and cognitive performance phenotypes were defined following Lee et al. 2018Educational achievement at age 12 was assessed by teacher reports, aggregated across the three core subjects .Educational achievement at age 16 was assessed by self-reported results for standardized tests taken at the end of compulsory education in England, Wales and Northern Ireland: General Certificate of Secondary Education; GCSE). GCSE grades were coded from 4  to 11 . As with the age 12 measure, we analysed a variable representing mean score for the compulsory core subjects.80. This measure was re-coded as the number of years in education, following Okbay et al. 201681.Educational attainment was measured by self-report of the highest obtained degreeAcademic achievement is assessed in the Netherlands by a nation-wide standardized educational performance test (CITO) around the age of 12 during the last year of primary education. CITO is used to determine tracking placement in secondary school in the Netherlands, in combination with teacher advice. The total score ranges from 500 to 550, reflecting the child’s position relative to the other children taking the test this particular year.N = 312,927), excluding SNPs with MAF < 0.01, missingness > 0.05 and HWE p < 10−10, leaving 1,246,531 SNPs. The HWE p-value threshold of 10−10 was based on: http://www.nealelab.is/blog/2019/9/17/genotyped-snps-in-uk-biobank-failing-hardy-weinberg-equilibrium-test. We then created a dataset of 1,246,531 QC-ed SNPs for 456,064 UKB subjects of European ancestry. Principal components were derived from a subset of 131,426 genotyped SNPs, pruned for LD (r2 > 0.2) and long-range LD regions removed82. PCA was conducted on unrelated individuals using flashPCA v283.SNPs from HapMap3 CEU  were filtered out of the imputed UK Biobank dataset. We then did a pre-PCA QC on unrelated individuals, and filtered out SNPs with MAF < 0.01 and missingness > 0.05, leaving 1,252,123 SNPs. After removing individuals with non-European ancestry, we repeated the SNP QC on unrelated Europeans  were genotyped on Illumina HumanOmniExpressExome-8v1.2 arrays. After quality control, 635,269 SNPs remained for AffymetrixGeneChip 6.0 genotypes, and 559,772 SNPs for HumanOmniExpressExome genotypes.84).Genotypes from the two platforms were separately phased and imputed into the Haplotype Reference Consortium (release 1.1) through the Sanger Imputation Service before merging. Genotypes from a total of 10,346 samples  passed quality control, including 3057 individuals genotyped on Affymetrix and 7289 individuals genotyped on Illumina. The identity-by-descent (IBD) between individuals was <0.05 for 99.5% in the merged sample excluding the DZ co-twins (range = 0.00–0.12) and ranged between 0.36 and 0.62 for the DZ twin pairs (mean = 0.49). There were 7,363,646 genotyped or well-imputed SNPs  and excluding high linkage disequilibrium genomic regions to ensure that only genome-wide effects were detected.Principal components were derived from a subset of 39,353 common (MAF > 5%), perfectly imputed (info = 1) autosomal SNPs, after stringent pruning to remove markers in linkage disequilibrium  using Metal software release 2011-03-05. More information on these methods and intermediate GWAS are found in Supplementary Note We ran a GWAS of Educational Attainment and Cognitive Performance in UK Biobank (polygenic score sample left-out). We meta-analysed them with the EA GWAS by Lee et al. excluding 23andMe, UK Biobank and NTR cohorts, and with the CP GWAS by Trampush et al. respectively Each model included cognitive and non-cognitive polygenic scores simultaneously and controlled for: 10 ancestry principal components (PCs), sex and age, interaction between sex and age, and cohort-specific platform covariate . Age was estimated by year of birth, age at recruitment or age at testing depending on the cohorts, see Supplementary Data 26. Note that the variances of the non-transmitted and transmitted PGS were not significantly different prior to scaling . For the adoption design, we scaled the PGS in adopted and non-adopted groups separately. There were no significant differences in variances of adopted and non-adopted PGS prior to scaling . The adoption design was only applied to EA in UKB, hence no meta-analysis was necessary.Meta-analyses were conducted using the command rma.mv in the R package metafor. Design was specified as a random intercept factor, except when results were meta-analysed within-design.87. As a rule of thumb, an LDSC intercept higher than 1 (inflated) indicates presence of population stratification. Because we corrected the standard errors of the EA GWAS for inflation and GenomicSEM corrects for inflation as well, the ratio statistics of the Cog and NonCog GWAS are not a valid indication of population stratification (ratio < 0 following GC correction). We therefore use the ratio statistics of uncorrected EA and CP GWAS as proxies. Ratio and LDscore intercept was assessed with the ldsc software87.Population stratification refers to the presence of systematic difference in allele frequencies across subpopulations, arising from ancestry difference due to non-random mating and genetic drift. This leads to confounding in genetic association studies. In a PGS analysis, bias due to population stratification can arise from both the GWAS used to create the scores and the target sample. We corrected for population stratification in the target sample by adjusting analyses for PCs . For the GWAS summary statistics, the ratio statistics LDSC output is a standard measure of population stratification52. Assortative mating can therefore be inferred from elevated correlations between polygenic scores in siblings (correlations would be 0.5 without assortative mating) and between parents (correlations would be 0 without assortative mating). We estimated sibling intraclass correlations of Cog and NonCog PGS in UKB, TEDS and NTR, and Pearson’s correlations of paternal and maternal Cog and NonCog PGS in NTR. Notably, these observed correlations cannot distinguish assortative mating from population stratification.Assortative mating refers to the non-random mate choice, with a preference for spouses with similar phenotypes. If these preferred phenotypes have a genetic component, assortative mating leads to an increased genetic correlation between spouses, as well as between relativesWe performed three additional analyses to investigate indirect genetic effects of siblings on educational outcomes.NMZ = 818 & NDZ = 865 for CITO and NMZ = 1600 & NDZ = 1369 for EA) and TEDS (NMZ = 546 & NDZ = 2709).First, we ran a linear mixed model extending our main non-transmitted alleles design to include polygenic scores of siblings (Eq. ). To thientclass1pt{minima88 which could result in confounding). By also looking at changes in the effect of the Cog and NonCog PGS on the educational outcome in adopted (unrelated) sibships, we break the correlation between PGS and any sibling effects. If there is a change in PGS effect on the educational outcome in adopted children dependent on the number of  siblings, we can assume this effect to be caused by mechanisms other than a sibling effect. We finally contrast the change in PGS depending on family size in biological and adopted siblings to get an idea of the sibling effect minus any other confounding effects of family size. We use the total number of reported siblings .Third, the presence of sibling genetic effects can be assessed using data on the number of siblings participants have. If an individual has more siblings, we expect their polygenic scores to be more correlated to sibling effects. As the number of siblings increases (if we assume linear increase) so does the degree to which a PGS captures sibling effects. If the sibling genetic effect is positive, the effect of the Cog and NonCog PGS on the educational outcome should increase with the number of siblings. However, family characteristics and environment might differ across families depending on the number of children. Therefore, changes in the effect of the PGS on our outcome with the number of siblings could be due to factors other than sibling genetic effects (for example, there is a known negative genetic association between number of children and EAFurther information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1-11Reporting Summary


BRCA germline pathogenic variants. Unfortunately, not all affected women are tested. We evaluated the acceptability and feasibility for non-genetic healthcare professionals to incorporate germline genetic testing into their daily practice. We developed and implemented a mainstreaming pathway, including a training module, in collaboration with various healthcare professionals and patient organizations. Healthcare professionals from 4 different hospitals were invited to participate. After completing the training module, gynecologic oncologists, gynecologists with a subspecialty training in oncology, and nurse specialists discussed and ordered genetic testing themselves. They received a questionnaire before completing the training module and 6 months after working according to the new pathway. We assessed healthcare professionals’ attitudes, perceived knowledge, and self-efficacy, along with the feasibility of this new mainstream workflow in clinical practice, and evaluated the use and content of the training module. The participation rate for completing the training module was 90% (N = 19/21). At baseline and after 6 months, healthcare professionals had a positive attitude, high perceived knowledge and high self-efficacy toward discussing and ordering genetic testing. Knowledge had increased significantly after 6 months. The training module was rated with an average of 8.1 out of 10 and was considered useful. The majority of healthcare professionals (9/15) was able to discuss a genetic test in five to 10 min. After completion of a training module, non-genetic healthcare professionals feel motivated and competent to discuss and order genetic testing themselves.According to current guidelines, all women with epithelial ovarian cancer are eligible for genetic testing for The online version contains supplementary material available at 10.1007/s10689-021-00277-7. BRCA germline variants, irrespective of age of diagnosis or family history [BRCA gene [Epithelial ovarian cancer (EOC) is the most lethal type of gynecological cancer; around 185,000 women die of the disease every year –4 becaus history . FurtherRCA gene , 7.BRCA1 or BRCA2, family members also become eligible for a genetic test. Family members who carry the same pathogenic variant can take measures to prevent cancer, or diagnose it at an early stage [If a genetic test reveals a germline pathogenic variant in a cancer predisposition gene such as ly stage , 8.Despite the importance of genetic testing for affected women and their family members, studies have shown that substantial numbers of eligible cancer patients are currently not tested , 10. ThiMainstream genetic testing initiatives for women with EOC have been successfully implemented in several countries, with positive experiences among patients and HCPs –19. AlthIn the current study, we aimed to develop and implement a mainstreaming pathway for germline genetic testing in women with EOC, including an online training module for gynecologic oncologists, gynecologists with a subspecialty training in oncology, and nurse specialists. Our specific research objectives were: (1) to assess HCPs’ attitudes toward and knowledge of mainstream genetic testing, and their self-efficacy to discuss genetic testing before and 6 months after completion of a training module, (2) to have our training module evaluated by the users, and (3) to gain insight into the feasibility for HCPs to incorporate mainstream genetic testing into the routine care of women with EOC.We developed a concise online training module for all participating HCPs. The content of this training module was determined by our project team, which consisted of HCPs from the departments of genetics, gynecology, medical oncology and pathology involved in the care of women with EOC, and patient advocates. This resulted in four short (7 min each) educational films (see Supplementary file 1).Our pathway for mainstream genetic testing was adapted from the workflow developed in the Mainstreaming Cancer Genetics Programme . FlowchaWe organized a kick-off meeting in four hospitals in the Utrecht region to introduce the new workflow. These four hospitals are involved in the care of patients with ovarian cancer in this region. Gynecologic oncologists, gynecologists with a subspecialty training in oncology, and nurse specialists working in these hospitals were subsequently invited to complete the online training module in a personal electronic learning environment. After completion, HCPs received a manual with instructions and all necessary forms, including a patient information letter.BRCA1/2, RAD51C/D and BRIP1) and the implications for family members with all newly diagnosed women with EOC  and women who had a personal history of EOC and had not been tested previously. In addition, HCPs completed a checklist (see Supplementary file 2) for every woman indicating whether she required additional counseling at the department of genetics after receiving their test result . If indicated by this checklist based on our national guidelines [In our pathway, trained HCPs discussed the possibility of germline genetic testing .We used a prospective follow-up design. The participating HCPs received two questionnaires. A first questionnaire (T0) had to be completed before starting the online training module and a second questionnaire (T1) was sent 6 months after implementing the new mainstreaming pathway for genetic testing. These questionnaires consisted of self-developed questions based on previous research by George et al. .The T0 and T1 questionnaires consisted of 13 statements to assess HCPs’ attitudes (five statements), perceived knowledge (three statements), and self-efficacy (five statements) toward mainstream genetic testing [Both questionnaires contained the same five knowledge questions, including two statements, and three multiple choice questions. Every statement had three response-categories: true, false and ’I do not know’.After each film, HCPs completed a self-developed questionnaire about the relevance of the discussed topics  and their opinions regarding the duration of the films . Appreciation for each film was evaluated on a scale of one to 10.At the end of the training module, we asked participants to assess the module as a whole, with appreciation on a scale of one to 10, and the usefulness, level of difficulty, duration, and their appreciation of the online format, using a 5-point Likert scale. In addition, they were asked whether they thought that important content was missing or whether they had ideas or advice on improving the training module.After working according to this new workflow for 6 months, we asked the HCPs whether, in retrospect, they felt any information was missing from the training module.We measured the feasibility of HCPs incorporating genetic testing into their routine work in relation to three outcomes: time investment, reasons for not discussing genetic testing, and how often additional appointments were needed to discuss and order genetic testing.After 6 months, the HCPs estimated how much time they needed to discuss and order genetic testing . In addition, they were asked to rate whether this time investment was ‘as expected’ on a 5-point Likert rating scale (much worse than expected to much better than expected).Both at baseline and after 6 months, the HCPs were asked to provide the two most important reasons for not discussing the possibility of genetic testing with all eligible patients.After 6 months they estimated how often their patients needed an additional appointment to discuss genetic testing, and reported the most important reasons for such an appointment.We used descriptive statistics to detail the characteristics of the HCPs, time investment, reasons for not discussing the possibility of genetic testing, and whether additional appointments were needed. We compared the characteristics of the HCPs in the T0 and T1 groups using the independent t-test for continuous variables and the chi-square test for categorical variables to determine whether the HCPs who filled in both questionnaires were representative of the entire group.With paired analysis using the Wilcoxon signed-rank test we compared the total number of correct answers to the knowledge questions between T0 and T1, and all statements regarding attitude, perceived knowledge and self-efficacy between T0 and T1. A p-value < 0.05 was considered as statistically significant. Statistical analyses were performed using IBM SPSS statistics 25.0.0.2.Twenty-one HCPs received login codes to the online training module. Nineteen (90%) HCPs completed the entire training module. One HCP completed part of the online training module.The first questionnaire was completed by 20 out of 21 HCPs (95%) from four hospitals. The second questionnaire was completed by 15 out of 17 HCPs. Two HCPs were not sent a second questionnaire because they had completed the online training module less than 6 months before the end of our study period.The total group consisted of 20 HCPs. Their characteristics are presented in Table Table One HCP had a neutral attitude toward discussing and ordering genetic testing at baseline and thought that discussing and ordering genetic testing would be too time-consuming. The same HCP did have a positive attitude after 6 months. Another HCP had a positive attitude at baseline but a neutral attitude after 6 months; the new workflow was too time-consuming, this HCP felt insecure about their knowledge regarding genetic testing, and felt that clinical geneticists and genetic counselors had more experience and tools to discuss genetic testing.Table The four individual films were ranked, with an average rating of between 7.9 and 8.1 out of 10. The majority (> 75%) of HCPs considered the duration of each individual film to be ‘exactly right’ and all discussed topics to be relevant.The evaluation of the overall online training module is shown in Table HCPs were able to discuss a genetic test in five to 10 min (9/15) or 10 to 20 min (6/15). For 14 out of 15 HCPs this time investment was as expected or better than expected. Most HCPs were able to order the genetic test in less than 5 min (8/14), the remainder needed 5 to 10 min (n = 5) or 10 to 20 min (n = 1). For 13 out of 14 HCPs this time investment was as expected or better than expected.The main reasons for not discussing genetic testing differed between ‘forgotten’ (T0) and ‘no appropriate moment’ (T1) and are illustrated in Fig. Less than half (7/15) of the HCPs reported that they had scheduled an additional appointment to discuss genetic testing for at least one patient. Reasons for this were that patients needed reflection time to consider genetic testing (n = 6), that there was not enough time during the consultation (n = 4), and that discussing genetic testing would be too much information for the patient in one consultation (n = 4).This study shows that gynecologic oncologists, gynecologists with a subspecialty training in oncology and nurse specialists feel motivated and competent to discuss and order germline genetic testing in women with EOC themselves. HCPs had a positive attitude, high self-efficacy, and high perceived knowledge both before and 6 months after working according to the new workflow. This high acceptability among HCPs is comparable to the results of other mainstreaming studies , 17, 19.We considered training an essential part of the implementation of our mainstream genetic testing pathway. Pre-test genetic counseling and informed consent are important, because the results of a genetic test can have serious implications for patients and family members , 4. TraiThe majority of HCPs take around 10 min to discuss and order genetic testing, which was ‘as expected’ or ‘better than expected’ for almost all of them. This time investment is comparable to the results from previous studies , 17 and After 6 months, the participants reported they no longer forgot to discuss genetic testing and their main reason for not discussing genetic testing was because they thought there was no appropriate moment during the consultation. In addition, about half of the HCPs felt confident discussing genetic testing with patients directly after diagnosing ovarian cancer. A standard moment to discuss and order genetic testing can further reduce the risk of HCPs forgetting to discuss it. However, it is important to take into consideration the timing of the different consultations and the amount of information that patients already receive after diagnosis. There are differences between hospitals, and adaptation of pathways or division of tasks in accordance with local workflows is often necessary. Our findings show that it is feasible for HCPs to incorporate germline genetic testing, including asking for patients’ written informed consent, into their daily work. Gleeson et al. showed that the most important barrier for non-genetic HCPs to continue with mainstream genetic testing was that they did not feel confident that there was a structured workflow, including collaboration with a department of genetics . During BRCA1, BRCA2, BRIP1, RAD51C and RAD51D), and it is likely that the gene panel will be expanded with other cancer genes, such as PALB2, in the near future. Tumor testing can also be incorporated into our workflow. Tumor testing has the advantage that it can be used as a pre-test for germline genetic testing [An advantage of the workflow that we implemented is that it can easily be adapted if gene panels change. In the course of our study, the ovarian cancer gene panel consisted of the five core genes Supplementary file2 (DOCX 23 kb)Below is the link to the electronic supplementary material.


The swapping to the vicinity ofTe atoms is facilitated by the spontaneous occurrence of Fe vacancyand its low diffusion barrier. Our calculated magnetic exchange parametersshow the simultaneous presence of ferromagnetic and antiferromagneticexchange among a particular type of Fe atom. The Fe sublattice projectedmagnetization obtained from Monte Carlo simulations clearly demonstratesan exotic temperature-dependent behavior of this Fe type along witha large canting angle at T = 0 K, indicating thepresence of a complex noncollinear magnetic order. We propose thatthe low-temperature crystal structure results from the swapping betweentwo sublattices of Fe, giving rise to peculiar magnetization obtainedin experiments.Recent experimentson Fe In the presence of magnetic anisotropy, however,this restriction is no longer valid, which opens the path for therealization of 2D magnets. Prior to 2016, defect engineering was themain root to induce magnetism in 2D materials.2 However, successful exfoliation of 2D Cr2Ge2Te63 and CrI34 from their bulk van der Waals (vdW) crystalshas opened new doors to the fabrication of stand-alone 2D magnetsand their exploitation in next-generation devices. However, the lowmagnetic ordering temperature in Cr2Ge2Te6 and CrI3 with TC ≈60 K can restrict their functionality. With the advent of metallicvdW magnets, an enormous playground has evolved to study the natureof itinerant magnetic order in 2D materials. Among this family, FenGeTe2 compounds possess the highestmagnetic ordering temperatures. Moreover, they offer exotic propertiessuitable for topology-based spintronic applications, such as an extremelylarge anomalous Hall effect5 and the formationof Neel-type skyrmions at room temperature.6 However, because of the complexity of structure, the physics behindthe exotic magnetic behavior of these materials is not well-understood.7 In these crystals, a metallic film of FenGe is sandwiched between two layers of Te,separating them by a vdW gap. Ferromagnetically ordered Fex3–GeTe28 shows TC at ∼230 and 130 K, in bulk and monolayerforms, respectively. It was shown that, in few-layer flakes of Fex3–GeTe2, TC can increase over 300 K by electrochemical gating.9 Importantly, as the thickness of the metallicfilm increases by adding extra layers of Fe, the magnetic orderingtemperature escalates. In bulk Fex5–GeTe2,12TC varies over a rangeof 270–310 K, depending on the structural properties and thermalhistory of grown crystals. Moreover, this temperature can be furtherenhanced, and a ferromagnetic (FM) to antiferromagnetic (AFM) transitioncan be induced via transition-metal doping.14 Furthermore, the magnetic anisotropy energy (MAE) is sensitive tocrystal preparation methods, evident in various experiments whereout-of-plane and in-plane easy-axis anisotropy has been reported.15 Because of these complications, a unified picture to describe thetemperature dependence of magnetization remains a big missing pieceof this puzzle. A detailed theoretical study on Fe5GeTe2 using an ab initio approach is still less unexplored as comparedto other members in the FenGeTe2  family19 and other vdW magnets like CrX3,26 Cr2GeTe6,28 etc.On the basis of the Mermin-Wagnertheorem,5GeTe2 due to its vdW nature is apiece of evidence that indicates a better understanding of the behavior of free-standing monolayershould be the starting point of unraveling the exotic behavior foundin the bulk form of Fe5GeTe2.From the above discussion, it is clear that an intricate relationshipbetween structural, chemical, and magnetic order exists, which shouldbe thoroughly understood. In this paper, using first-principle approaches,we aim to put forward a model that can link between the controversialexperimental results and create a unified model to justify the magneticbehavior of this compound in the 2D regime. The weak interlayer couplingfound in Fe29 Unlike some other studies,30 we refrained from using the DFT+Hubbard U method, becauseit produces incorrect ground-state properties, for example, latticeparameter and magnetic moments, whereas with GGA, we reproduce theseproperties correctly. Moreover, the d-band widths are larger comparedto U values, and hence, the use of DFT+U may not be appropriate tocapture accurate electronic description and magnetic behavior. Theinteratomic isotropic symmetric exchange parameters Jij of the Heisenberg model were calculatedusing full-potential linear muffin-tin orbital (FP-LMTO) code RSPt.31 Monte Carlo simulations using the parametrizedHeisenberg model with isotropic and anisotropic terms were performedby UppASD code32 to calculate magneticordering temperature TC. Details of thecomputations are provided in the Supporting Information.Densityfunctional theory (DFT)-based calculations were performedusing Vienna Ab Initio Simulation Package (VASP), treating the generalizedgradient approximation (GGA) as the exchange-correlation functional.5GeTe2 monolayer has five atomiclayerscontaining Fe. The Te atoms are situated in two outermost layers,while the Ge layer is placed midway between the Fe layers. Recentexperimental studies have reported, among these five Fe atoms, Fe1situated in the outermost plane of an Fe5Ge subunit canbe located either directly above or below Ge giving rise to two possiblesites for Fe1. This partial occupancy of Fe1 species is revealed inX-ray diffraction data.33 Swapping of Fe1 between thesetwo equally probable sites causes splitting of the Ge site as well;that is, when Fe1 is situated above Ge then it pushes down the Geatom along the c-axis and vice versa. Therefore,the splitting of the Ge site is a consequence of Fe1 split sites,confirmed by scanning tunneling electron microscopy (STEM) experiments.34 More interestingly, the scanningtunneling microscopy (STM) topography obtained at the surface of Fe5GeTe2 has revealed the existence of 31/2 × 31/2 superstructures, which are attributed tothe ordering of the Fe1 layer.35 The intensity of √3× √3R30° reflections is more prominentif a crystal is rapidly quenched.10Fec-plane. c-axis to maintain the proper bond distance.Motivated by the experimental scenario, we thoroughly investigatedthe swapped configuration of Fe1 in a √3 × √3 superstructurein which a maximum of three Fe atoms can be placed at a given 5GeTe2 in the UDU configuration when two of the Fe1 atoms are aboveGe, and one Fe1 is situated below Ge in a √3 × √3cell of the monolayer; filled and empty circles show the presenceand absence of any atom, respectively. Fe1–Ge split sites makethe crystal structure of Fe5GeTe2 more symmetricin nature, which contains three inequivalent Fe sites per unit cell:(1) Fe1U and Fe1D, (2) Fe2 and Fe5, and (3) Fe3 and Fe4. Fe5GeTe2 monolayer can form a lower-symmetry structure wheresplit sites of Fe1 and Ge are absent. According to the recent experimentalstudy by May et al., the higher-symmetry structure is generated fromcrystals that are vapor grown and quenched from a growth temperatureof 1023 K into an ice–water bath, while the lower-symmetrystructure comes from crystals that are cooled naturally in the furnace.12The Fe1–Ge subunit canoccupy one of the two possible splitsites, that is, either above or below Ge giving rise to two Fe1 sublattices.In one scenario, the Fe1 atoms would be arranged in Fe1 (up)-Fe1 (down)-Fe1(up) or UDU order; the other energetically degenerate pattern wouldbe Fe1 (down)-Fe1 (up)- Fe1 (down) or DUD. In nGeTe2 systems, experiments on Fex5–GeTe2 have revealed the presence of Fedeficiency, where x varies from 0.0415 to 0.28,where Fe1 has the maximum tendency to host a vacancy.35 We propose a vacancy diffusion model where the swapping of Fe1 canoccur via diffusion through different Fe-vacancy sites, as shown in Ef. Our results verify the factthat the creation of Fe vacancy is most favored at the Fe1 site, asreported by recent experimental studies.13 Especially, in the case of the UUU configuration, the creation ofan Fe1 vacancy is spontaneous with Ef =−151.0 meV. This again supports that the swapping of Fe1 stabilizesthe Fe5GeTe2 system rather than the scenariowhen all the Fe1 atoms stay in the same z plane (UUUconfiguration). To have an estimate of the concentration of vacanciesin the Fe1 site, we used a (2√3 × 2√3)R30° supercell for both UUU and UDU structures to further calculatethe evolution of formation energy as a function of the number of Fe1vacancies. We found that, in both structures, formation of the firstFe1 vacancy in a unit cell is spontaneous, with Ef = −91.4 and −5.3 meV for UUU and UDU structures,respectively, and therefore, the formation of Fe1 vacancies is possibleeven at T = 0 K. Accordingly, our estimation of theFe1 vacancy concentration amounts to 1.0 × 1014 cm–2  in both structures. On the otherhand, we found that the formation of more than one vacancy per cell,in Fe1 sites, comes with an energy cost, where positive formationenergies of Ef = 19.1 and 177.5 meV werecomputed for the formation of the second Fe1 vacancy in UUU and UDUstructures, respectively. Using the Arrhenius formula, it was foundthat, at room temperature, these formation energies correspond toFe1 vacancy concentrations of 6.5 × 1014 cm–2  and 1.0 × 1014 cm–2  for UUU and UDU structures, respectively. Itcan be noted that the smaller Ef foundin the UUU structure makes it more prone to form vacancies in Fe1sites at high temperatures, which is another sign that the UUU structuretends to transform to the UDU via rearranging its Fe1 atoms. Moreover,our nudged elastic band (NEB) calculations show that the energy barrierfor Fe1 to diffuse to a neighboring vacancy site of Fe2 is only 0.036eV. Therefore, the diffusion of an Fe atom is possible via differentvacancy sites through the unit cell, which can cause the swappingof Fe1 from directly above to below Ge or vice versa.Similar to other Fe1/2 × 31/2 periodic pattern of Fe5GeTe2 and simulated STM images for UDU and UUUconfigurations; see Vbias = −0.05 eV show a dominant contribution from Tep-states appearing as bright ovals (UDU) or circles (UUU). In thecase of UDU, the swapping of one of the Fe1 atoms from above to belowGe is reflected in the corresponding STM image showing one dark centerwith two neighboring bright centers in a given unit cell. On the contrary,the UUU center of each Y appears bright, indicating the presence ofall the three Fe1U atoms above Ge for a given unit cell. The shapeof Te p-orbitals is asymmetric in UDU and different depending on thepresence or absence of Fe1U. This happens because the swapping ofone Fe1U causes a trimerization of surface Te atoms and their electronicstates, which increases the separation between the surrounding Y-shapedpatterns, as observed in the dI/dV conductance map.35 In contrast, the chemicaland crystal environments are highly symmetric for UUU . Our simulated STM imagesare in agreement with the features observed in STM images by Ly etal.33 These results re-establish the factthat the formation of a √3 × √3 pattern in Fe5GeTe2 happens due to the presence of Fe1 splitsites.To confirmthat, we reproduced the experimental scenario with a35GeTe2 is quite complex and different from otherFenGeTe2  or 2D vdW magnets. To investigate the ground-state magnetic configuration,we considered different magnetic arrangements, for example, ferromagnetic(FM) and ferrimagnetic (FiM) for both UUU and UDU configurations.The lowest energy configuration for UUU is FM, as reported by previousstudies.36 In the case of UDU, the FiM configurationnever gets stabilized, and all the moments spontaneously achieve theFM configuration.Similar to the structural properties, magnetism in FenGeTe2  systems have arange of spinmoments, as already reported in previous studies, where the positionof Fe atoms has a mirror reflection along the c-axis,and this symmetry is preserved in the magnitude of their magneticmoments as well.37 We find that the spin momentsof five Fe atoms range from 0.11 to 2.59 μB in theUUU configuration, which are not symmetrically distributed. Also,it is important to note that the moment of an Fe1 species gets highlyquenched in UUU, which agrees well with a recent DFT study on Fe5GeTe2 monolayer.30 Thedistribution of electron occupancy in Fe d-orbitals is responsiblefor such quenching of magnetic moment for Fe1U; see Table S2 in the Supporting Information.Fe atoms present in other Fec-axis, and this fact is reflected in the values the of spin momentfor Fe5, Fe4, Fe3, Fe2, Fe1U, and Fe1D, which is 2.57, 1.98, 2.08,2.51, 1.10, and 1.71 μB, respectively, at T = 0 K. Our results agree well with neutron powder diffractiondata on Fe5GeTe2 reporting spin moments rangingfrom 0.8 to 2.6 μB at 1.5 K.10 The magnetic moments in the UDU configuration clearly signify thefact that Fe atoms belong to four different categories, namely, (i)Fe5, Fe2, (ii) Fe4, Fe3, (iii) Fe1D, and (iv) Fe1U. Fe atoms in Fe5GeTe2 are grouped into three different sites dependingon their relative positions as already identified by recent experimentalstudies,37 but based on their magnetic properties,Fe atoms are classified into four types. For Fe1 species (both Fe1Uand Fe1D), the distribution of electron occupancy between up and downspin channels is different in UDU configuration from UUU; this isthe reason why an Fe1 species regains its moment. Densities of statesprojected on Fe d-orbitals for each Fe species are shown in FigureS2 in the Supporting Information. Differentmoments on Fe1U and Fe1D are due to their different periodicity in√3 × √3 cell and also different coordination withtheir neighbors. For example, the cell parameter for Fe1D sublatticeis 6.99 Å, which is larger than Fe1U (4.00 Å). Also, Fe1Dand Fe1U species have one and three first nearest neighbors at a distanceof 2.46 and 2.44 Å, respectively. Therefore, Fe1U has a largereffective coordination number than Fe1D (see Table S3). It is known that the magnetic moment of Fe always increaseswith cell dimension and decreases with increasing coordination number.39 Note, in the case of DUD, which is the energetically degenerate partnerof UDU, moments of Fe1U and Fe1D just get interchanged and become1.72 and 1.12 μB, respectively, since their crystalenvironment becomes the exact opposite of a UDU configuration.However, for theUDU configuration, the positions of Fe atoms arepartly semisymmetric with respect to Ge along the Jij between the ith and jth atoms. ith and jth Fe atoms, considering the ith atom as Fe1U and Fe5, respectively. The first neighborexchange interaction of Fe1U with both Fe2 and Fe3 is strongly ferromagnetic(FM), while Fe1U–Fe4 and Fe1U–Fe5 interactions are weaklyFM. When the ith site is Fe5, the dominating (firstneighbor) exchange interactions with Fe4 and Fe3 species are stronglyFM. It is important to note that all in-plane Jij couplings between the same species areAFM, while for Fe1U, this AFM interaction is quite significant. Theoverall nature of Jij couplings for the other Fe species, for example, i = Fe4, Fe3, Fe2, and Fe1D, are quite similar. The first neighborinteractions are strongly FM for i ≠ j, while the interaction between the same species is AFM.The Jij values for eachFe species in both UDU and UUU configurations are plotted in FigureS4 in the Supporting Information, whichshows an enhancement of FM exchange couplings in the UDU configuration.To investigate the magnetic interactions among different typesof Fe atoms in a √3 × √3 UDU configuration, wecalculated the isotropic symmetric exchange coupling parameters Jij couplings are AFM in nature. From our calculations,it is found that the Fe5GeTe2 monolayer hasweak MAE along the out-of-plane direction in a UDU configuration,with a magnitude of 0.021 meV/Fe. A weak out-of-plane anisotropy inbulk Fe5GeTe2 has also been reported in recentexperiments.34 For the UUU configuration,the in-plane anisotropy is calculated to be 0.112 meV/Fe, agreeingwell with the previously reported result.36 It is important to note that the MAE for Fe5GeTe2 is quite small compared to other 2D vdW magnets, for example,Fe3GeTe2,36 Fe4GeTe2,36 and CrI3.40 Compared to UDU, Jij interactions for a given i–j pair is weaker in UUU, but the overall trend remains almost similar,except for Fe1U. A significant difference in Jij is observed for Fe1U due to its quenchedmoment. Figure S4 in the Supporting Information shows the comparison in Jij couplings between UDU and UUU configurations.Although from collineartotal energy calculations, the UDU configurationis found to be spontaneously FM, some TC, wemodeled the Heisenberg Hamiltonian with isotropic exchangeinteractions and single-site anisotropy, details of which are givenin the Methods section in the Supporting Information. TC for Fe5GeTe2 monolayer in the UDU configuration obtained from Monte Carlo simulationis 492 K, shown in TC calculated in thisstudy is overestimated compared to the experimental value.33 This difference might arise due to the mixtureof UDU and UUU configurations in experimental samples or some othercomplex arrangements of different domains of these two configurationsin the presence of a vacancy or some impurities.33 Apart from the consideration of these complex structures, propertreatment of electron correlation effects within dynamical mean-fieldtheory can also play an important role. We are pursuing this studyand will report on it in future communication.In orderto obtain the Curie temperature M) versustemperature (T) behavior for the UDU configurationalso supports the classification of five Fe atoms into four differentcategories. The M versus T behavioris strikingly different for an Fe1U sublattice than for others. Thisparticular Fe species primarily governs the magnetic properties andis responsible for anomalous magnetic behavior in a low-temperatureregime.33 Though the easy axis of magnetization for a UDU monolayeris along the out-of-plane direction, the z-componentof magnetization vector (mz) for Fe1U is significantly deviated wrt easy axis of magnetization, that is, z-directioneven at T = 0 K and its close vicinity. Such behaviorof Fe1U can be related to canted moments or spin fluctuations observedin recent experiments for bulk Fe5GeTe2.33 The Fe1 species is special from others because not only TC but also physical properties like Hall andSeebeck coefficients are impacted by the magnetic ordering of Fe1according to experimental data.12Similar to thespin moment values, the magnetization . mz wrt z for each Fe sublattice. In addition, to seethe orientation of spin moments at finite temperatures, the angulardistribution between mz and z at T = 100 and 50 K forFe1U and Fe5 is plotted in Figure S6 in the Supporting Information. Deviation of mz wrt the easy axis is larger for Fe1U than for Fe5 at a finitetemperature supporting the large fluctuation of Fe1 moments reportedby May et al.12 The deviation of mz for other Fe species  wrt z remains the same as that for Fe5,that is, 12°; see Figure S5 in the Supporting Information.On the contrary, in the case of Fe5, the fluctuation of M versus T resultshown in Figure S8 in the Supporting Information. Also, because of a stronger in-plane MAE, the deviation of thein-plane component mx (or my) of the magneticmoment vector for each Fe species is ∼7° from the easyaxis of magnetization, which is smaller than the same for the UDUconfiguration. As already discussed, the moment of Fe1 gets hugelyquenched to 0.11 μB for the UUU configuration. Thisquenching of magnetic moment of Fe1 affects the TC of the monolayer. As a result, we find TC to be 390 K for the UUU configuration. The spin momentsof Fe2, Fe3, and Fe4 sublattices in the UUU configuration differ fromthe same in the UDU configuration, while the moment of Fe5 remainsalmost unchanged. Spin and orbital moments for each Fe species inboth UDU and UUU configurations are reported in Table S1 in the Supporting Information. It is important to notethat Fe1D has the largest orbital moment. The importance of the Dzyaloshinskii-Moriya(DM) interaction for this system has been mentioned in literature.It would be interesting to study the strength of this interactionin various scenarios.In the case of the UUU configuration, whichhas a lower symmetrycompared to the UDU configuration, each Fe species behaves differently,as seen from the Jij interactions  andhence the value of TC. For example, becauseof the absence of one Fe1U outof three in the √3 × √3 unit cell, the remainingFe1 atoms regain their moment to 1.68 μB. The presenceof an Fe1 vacancy increases the moments of Fe2, Fe3, and Fe4 sublatticeswrt pristine UUU, whereas the Fe5 moment remains unchanged provingits robustness. As a result, TC increasesto 435 K. A similar trend has been observed in experiments,15 where TC is observed to be higher fora higher Fe vacancy concentration. However, TC with an Fe1 vacancy concentration of 6.67% falls betweenUDU and UUU configurations; see Figure S7 in the Supporting Information. We also find that the M versus T behavior follows the same trend as thatfor the spin moments; for example, Fe5 and Fe2 sublattices are equivalent,while other Fe sublattices behave differently. The presence of anFe1 vacancy yields a very weak MAE along the out-of-plane direction.There is an ∼12° deviation of the mz component from the z-axisfor Fe1U and Fe5 at 0 K .We also find that the presence of an Fevacancy (6.67%) influences B, respectively. The bottom panel showsDOS for Fe1 situated above (Fe1U) and below (Fe1D) Ge. The main differencebetween the atom-projected DOS of Fe1U (black curve) and Fe1D (redcurve) in UDU is the presence of a large peak in the spin-down channelof Fe1D close to the Fermi level (EF),which comes from the dz2 orbital  and is also evident from the magnetization density plotat E – EF = −0.24eV. Spin-polarized DOS for Ge in UUU and UDU configurations are plottedin (c) and (d). In (d), Ge–U and Ge–D correspond totwo split sites of Ge. A sharp feature appearing in the PDOS of Ge–Ucomes from the pz orbital . A comparison between the total DOSsof UUU and UDU configurations shows that the UUU configuration hasmore fragmented features.We studied the electronic properties ofUDU and UUU configurationsto understand the consequence of swapping as shown in 5GeTe2. Even thoughthe T-dependent M behavior observedin experiments is not properly visible in our present work, this studyis important to understand the structural and magnetic propertiesof Fe5GeTe2, a promising candidate for topology-basedspintronic devices. In our future study, we will use dynamical mean-fieldtheory for treating electron correlation in these metallic systems.In conclusion, using DFT calculations, we show that the swappingof an Fe1 atom occurs via an Fe vacancy-mediated diffusion causingFe1 split sites, which gives rise to a √3 × √3pattern, as observed in experiments. We find that the magnetic behaviorof Fe1 is very different from other Fe atoms, which primarily governsthe magnetic properties of Fe